%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL784-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 10:30:31 AM UTC 2026
% Result : Unsatisfiable 38.81s 8.04s
% Output : CNFRefutation 38.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 318
% Syntax : Number of formulae : 2602 (1801 unt; 0 typ; 0 def)
% Number of atoms : 12252 (5250 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 40779 (2519 ~;3276 |; 0 &;34984 @)
% ( 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 : 94 ( 91 usr; 24 con; 0-5 aty)
% Number of variables : 9112 ( 0 ^;9112 !; 0 ?;9112 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_COMBC,type,
c_COMBC: $i > $i > $i > $i > $i > $i ).
thf(tp_c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(tp_c_HOL_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_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_Omap,type,
c_List_Omap: $i > $i > $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_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__Xlist__app__typeD__1__1,type,
c_Type_Osko__Type__Xlist__app__typeD__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xlist__app__typeE__1__1,type,
c_Type_Osko__Type__Xlist__app__typeE__1__1: $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_Otype_OFun,type,
c_Type_Otype_OFun: $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_fequal,type,
c_fequal: $i > $i > $i > $o ).
thf(tp_class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $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_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_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_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_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_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_T_H____,type,
v_T_H____: $i ).
thf(tp_v_T_Ha______,type,
v_T_Ha______: $i ).
thf(tp_v_T____,type,
v_T____: $i ).
thf(tp_v_e____,type,
v_e____: $i ).
thf(tp_v_ea______,type,
v_ea______: $i ).
thf(tp_v_i____,type,
v_i____: $i ).
thf(tp_v_ia______,type,
v_ia______: $i ).
thf(tp_v_n____,type,
v_n____: $i ).
thf(tp_v_rs____,type,
v_rs____: $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_u____,type,
v_u____: $i ).
thf(tp_v_ua______,type,
v_ua______: $i ).
thf(1,axiom,
! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( c_fequal @ V_X @ V_Y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(2,axiom,
! [V_x: $i,T_a: $i] : ( c_fequal @ V_x @ V_x @ T_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(3,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(4,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(5,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(6,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(7,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(8,axiom,
class_OrderedGroup_Omonoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(9,axiom,
class_OrderedGroup_Osemigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).
thf(10,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(11,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(12,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(13,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(14,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(15,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(16,axiom,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(17,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(18,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(19,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Oorder @ T_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(20,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Opreorder @ T_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(21,axiom,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_u____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).
thf(22,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
thf(23,axiom,
( v_rs____
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(24,axiom,
! [V_dB1_H: $i,V_dB2_H: $i,V_nat: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
thf(25,axiom,
! [V_f: $i,V_a: $i,V_xs: $i,V_ys: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ T_a @ T_b )
= ( c_List_Ofoldl @ V_f @ ( c_List_Ofoldl @ V_f @ V_a @ V_xs @ T_a @ T_b ) @ V_ys @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__append_0) ).
thf(26,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/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I2_J_0) ).
thf(27,axiom,
! [V_s: $i,V_t: $i,V_n: $i,V_ss: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_t )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
thf(28,axiom,
! [V_rs: $i,V_n: $i,V_v: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ V_rs @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_v ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_head__Var__reduction_0) ).
thf(29,axiom,
! [V_t: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ ( c_Lambda_OdB_OVar @ V_i ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).
thf(30,axiom,
! [V_m: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OVar @ V_m )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_1) ).
thf(31,axiom,
! [V_r: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ V_r ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_2) ).
thf(32,axiom,
! [V_t: $i,V_k: $i,V_s: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_k ) ) @ V_s ) @ V_k )
= V_t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lift_0) ).
thf(33,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/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I2_J_0) ).
thf(34,axiom,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_u____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uIT_0) ).
thf(35,axiom,
! [V_s: $i,V_u: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_u ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appL_0) ).
thf(36,axiom,
! [V_u: $i,V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_s ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appR_0) ).
thf(37,axiom,
! [V_r: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ V_r ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lambda_0) ).
thf(38,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/sandbox2/benchmark/theBenchmark.p',cls_var__app__types_1) ).
thf(39,axiom,
! [V_r: $i,V_ts: $i,V_s: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).
thf(40,axiom,
! [V_s: $i,V_ss: $i,V_r: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ V_r ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_1) ).
thf(41,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/sandbox2/benchmark/theBenchmark.p',cls_ex__head__tail_0) ).
thf(42,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/sandbox2/benchmark/theBenchmark.p',cls_dB_Orecs_I2_J_0) ).
thf(43,axiom,
( v_rs____
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil_0) ).
thf(44,axiom,
! [V_r: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_r )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ V_r )
= V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).
thf(45,axiom,
! [V_env: $i,V_x: $i] : ( c_Type_Otyping @ V_env @ ( c_Lambda_OdB_OVar @ V_x ) @ ( hAPP @ V_env @ V_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
thf(46,axiom,
! [V_r: $i,V_s: $i,V_t: $i,V_ts: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ V_r @ V_s @ V_t @ V_ts ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_2) ).
thf(47,axiom,
! [V_r: $i] :
( ( c_Lambda_OdB_OAbs @ V_r )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_2) ).
thf(48,axiom,
! [V_f: $i,V_a: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_a @ T_b )
= ( c_List_Ofoldl @ V_f @ ( hAPP @ ( hAPP @ V_f @ V_a ) @ V_x ) @ V_xs @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).
thf(49,axiom,
! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_x ) ) @ V_s ) @ V_x )
= V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_1) ).
thf(50,axiom,
! [V_f1: $i,V_f2: $i,V_f3: $i,V_nat: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OVar @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I10_J_0) ).
thf(51,axiom,
! [V_m: $i] :
( ( c_Lambda_OdB_OVar @ V_m )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_2) ).
thf(52,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/sandbox2/benchmark/theBenchmark.p',cls_IT_Ocases_5) ).
thf(53,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/sandbox2/benchmark/theBenchmark.p',cls_monoid__add_Ofoldl__absorb0_0) ).
thf(54,axiom,
! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB1: $i,V_dB2: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) @ T_a )
= ( hAPP @ ( hAPP @ V_f2 @ V_dB1 ) @ V_dB2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I11_J_0) ).
thf(55,axiom,
! [V_v: $i,V_n: $i,V_rs: $i] :
( ( V_v
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_v ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_head__Var__reduction_1) ).
thf(56,axiom,
c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_T_H____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nT_0) ).
thf(57,axiom,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_ua______ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var_I3_J_0) ).
thf(58,axiom,
! [V_e: $i,V_i: $i,V_T: $i,V_ts: $i] :
( ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OVar @ V_i ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ V_T @ V_e @ V_i @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_var__app__typesE_0) ).
thf(59,axiom,
! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_s ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ( V_i = V_k )
| ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_2) ).
thf(60,axiom,
! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_r ) @ V_t ) @ V_i ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_s ) @ V_t ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
thf(61,axiom,
c_Type_Otyping @ ( c_Type_Oshift @ v_ea______ @ v_ia______ @ v_T____ @ tc_Type_Otype ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_T_Ha______,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var_I2_J_0) ).
thf(62,axiom,
! [V_t: $i,V_ts: $i,V_u: $i,V_i: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_u ) @ V_i )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_u ) @ V_i ) @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ V_u @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ V_i @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__map_0) ).
thf(63,axiom,
! [V_s: $i,V_t: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ V_k ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_k ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
thf(64,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/sandbox2/benchmark/theBenchmark.p',cls_IT_Ocases_2) ).
thf(65,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_zs: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ T_a )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) @ V_zs @ T_a @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y @ V_zs @ T_a @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__assoc_0) ).
thf(66,axiom,
! [V_e: $i,V_i: $i,V_T: $i] :
( ( ( hAPP @ V_e @ V_i )
= V_T )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OVar @ V_i ) @ V_T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
thf(67,axiom,
! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__IT_0) ).
thf(68,axiom,
! [V_nat: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
thf(69,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_True_0) ).
thf(70,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/sandbox2/benchmark/theBenchmark.p',cls_IT_Ocases_4) ).
thf(71,axiom,
! [V_r: $i,V_s: $i,V_ss: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) ) @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_s ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_r ) @ V_s ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Beta_0) ).
thf(72,axiom,
! [V_f: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Olist_ONil @ T_b ) @ T_a @ T_b )
= V_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
thf(73,axiom,
! [V_t: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__IT_0) ).
thf(74,axiom,
! [V_n: $i,V_ts: $i,V_r: $i,V_ss: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).
thf(75,axiom,
! [V_nat: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
thf(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/sandbox2/benchmark/theBenchmark.p',cls_dB_Orecs_I1_J_0) ).
thf(77,axiom,
! [V_r: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_r )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_1) ).
thf(78,axiom,
! [V_m: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OVar @ V_m )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ V_m )
= V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).
thf(79,axiom,
! [V_r: $i,V_ss: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).
thf(80,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/sandbox2/benchmark/theBenchmark.p',cls_Apps__dB__induct_3) ).
thf(81,axiom,
! [V_r: $i,V_rs: $i,V_ss: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ V_rs @ V_ss @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__betas_0) ).
thf(82,axiom,
! [V_T: $i,V_U: $i,V_e: $i,V_i: $i,V_ts: $i] :
( ( V_T = V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).
thf(83,axiom,
! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) )
| ( V_dB2 = V_dB2_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
thf(84,axiom,
! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) )
| ( V_dB1 = V_dB1_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
thf(85,axiom,
! [V_n: $i,V_rs: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ V_rs @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT_OVar_0) ).
thf(86,axiom,
! [V_r: $i,V_rs: $i,V_s: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_rs = V_ss ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).
thf(87,axiom,
! [V_r: $i,V_rs: $i,V_s: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).
thf(88,axiom,
! [V_s: $i,V_ss: $i,V_r: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ V_r ) )
| ( V_s
= ( c_Lambda_OdB_OAbs @ V_r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).
thf(89,axiom,
! [V_i: $i,V_t: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
thf(90,axiom,
! [V_r: $i,V_s: $i,V_t: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= V_t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_0) ).
thf(91,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/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__beta2_0) ).
thf(92,axiom,
! [V_j: $i,V_u: $i,V_i: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_j ) ) @ V_u ) @ V_i )
= ( c_Lambda_OdB_OVar @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lt_0) ).
thf(93,axiom,
! [V_r: $i,V_i: $i,V_j: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_r ) @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_j ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).
thf(94,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_dB1: $i,V_dB2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_dB1 ) @ V_dB2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit_1) ).
thf(95,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_xb: $i,V_xc: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_xb ) @ V_xc ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_xb ) @ V_xc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit__asm_1) ).
thf(96,axiom,
! [V_k: $i,V_u: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_k ) ) @ V_u ) @ V_k )
= V_u ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__eq_0) ).
thf(97,axiom,
! [V_m: $i,V_rs: $i,V_n: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_rs = V_ss ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).
thf(98,axiom,
! [V_m: $i,V_rs: $i,V_n: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).
thf(99,axiom,
! [V_dB_H: $i,V_dB1: $i,V_dB2: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
thf(100,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_nat: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OVar @ V_nat ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit_0) ).
thf(101,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_xd: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OVar @ V_xd ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_xd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit__asm_0) ).
thf(102,axiom,
! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OVar @ V_nat_H ) )
| ( V_nat = V_nat_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
thf(103,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/sandbox2/benchmark/theBenchmark.p',cls_var__app__typesE_1) ).
thf(104,axiom,
! [V_dB1: $i,V_dB2: $i,V_dB_H: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
thf(105,axiom,
! [V_dB_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
thf(106,axiom,
! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) ) @ V_s ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_k ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_u ) @ V_s ) @ V_k ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__App_0) ).
thf(107,axiom,
! [V_r: $i,V_s: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_4) ).
thf(108,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/sandbox2/benchmark/theBenchmark.p',cls_semigroup__add_Ofoldl__assoc_0) ).
thf(109,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/sandbox2/benchmark/theBenchmark.p',cls_lem_3) ).
thf(110,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(111,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(112,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(113,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/sandbox2/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__into__rtrancl_0) ).
thf(114,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/sandbox2/benchmark/theBenchmark.p',cls_converse__rtranclp__into__rtranclp_0) ).
thf(115,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(116,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/sandbox2/benchmark/theBenchmark.p',cls_lift__type_0) ).
thf(117,axiom,
! [V_xs: $i,V_x: $i,V_ts: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_x @ V_ts @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_x @ T_a ) @ V_ts @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).
thf(118,axiom,
! [V_zs: $i,V_x: $i,T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ V_zs @ V_x @ T_a ) @ V_ys @ T_a )
= ( c_List_Oappend @ V_zs @ ( c_List_Oappend @ V_x @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).
thf(119,axiom,
! [V_xs: $i,V_xs1: $i,V_us: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_xs1 @ V_us @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_xs1 @ T_a ) @ V_us @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).
thf(120,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i,V_zs: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_zs @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_ys @ V_zs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__assoc_0) ).
thf(121,axiom,
! [V_ts: $i] :
( ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ V_ts @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lifts__IT_0) ).
thf(122,axiom,
! [T_a: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).
thf(123,axiom,
c_Type_Otyping @ v_e____ @ v_u____ @ v_T____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uT_0) ).
thf(124,axiom,
! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
( ( ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
!= ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).
thf(125,axiom,
! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
( ( ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
!= ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_xs = V_ys ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).
thf(126,axiom,
! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__is__Nil__conv_0) ).
thf(127,axiom,
! [V_r: $i,V_x: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_5) ).
thf(128,axiom,
! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_1) ).
thf(129,axiom,
! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_t ) @ V_t_H ) )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
thf(130,axiom,
! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_list = V_list_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
thf(131,axiom,
! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_a = V_a_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(132,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/sandbox2/benchmark/theBenchmark.p',cls_IT_Ocases_9) ).
thf(133,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
thf(134,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
thf(135,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
thf(136,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
thf(137,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
thf(138,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
thf(139,axiom,
! [T_a: $i,V_x: $i,V_xs: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).
thf(140,axiom,
! [V_type1: $i,V_type2: $i,V_type1_H: $i,V_type2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H ) )
| ( V_type1 = V_type1_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_0) ).
thf(141,axiom,
! [V_type1: $i,V_type2: $i,V_type1_H: $i,V_type2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H ) )
| ( V_type2 = V_type2_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_1) ).
thf(142,axiom,
! [V_ys: $i,V_xs: $i,T_a: $i] :
( ( V_ys
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).
thf(143,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= V_ys )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).
thf(144,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( V_xs
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_0) ).
thf(145,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= V_xs )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv_0) ).
thf(146,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_xa: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OAbs @ V_xa ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f3 @ V_xa ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit__asm_2) ).
thf(147,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_dB: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OAbs @ V_dB ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f3 @ V_dB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit_2) ).
thf(148,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/sandbox2/benchmark/theBenchmark.p',cls_foldr_Osimps_I2_J_0) ).
thf(149,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
thf(150,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/sandbox2/benchmark/theBenchmark.p',cls_substn__subst__0_0) ).
thf(151,axiom,
! [V_U: $i,V_T: $i,V_e: $i,V_us: $i,V_i: $i,V_ts: $i,V_Ts: $i] :
( ( V_U
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ V_T @ V_U @ V_e @ V_us ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( 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/sandbox2/benchmark/theBenchmark.p',cls_var__app__types_0) ).
thf(152,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/sandbox2/benchmark/theBenchmark.p',cls_shift__gt_0) ).
thf(153,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/sandbox2/benchmark/theBenchmark.p',cls_semigroup__add__class_Oaxioms_0) ).
thf(154,axiom,
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
thf(155,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/sandbox2/benchmark/theBenchmark.p',cls_liftn__0_0) ).
thf(156,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/sandbox2/benchmark/theBenchmark.p',cls_dB_Orecs_I3_J_0) ).
thf(157,axiom,
! [V_A: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_ys @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_2) ).
thf(158,axiom,
! [V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(159,axiom,
! [V_t: $i,V_ts: $i,V_i: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_i )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_i ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ V_i @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__map_0) ).
thf(160,axiom,
! [V_ys: $i,V_xs: $i,V_y: $i,V_x: $i,V_r: $i,T_a: $i] :
( ( V_ys = V_xs )
| ( V_y = V_x )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_2) ).
thf(161,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/sandbox2/benchmark/theBenchmark.p',cls_IT_Ocases_0) ).
thf(162,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/sandbox2/benchmark/theBenchmark.p',cls_foldl__foldr1_0) ).
thf(163,axiom,
! [V_env: $i,V_s: $i,V_t: $i,V_U: $i,V_T: $i] :
( ( c_Type_Otyping @ V_env @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_U )
| ~ ( c_Type_Otyping @ V_env @ V_t @ V_T )
| ~ ( c_Type_Otyping @ V_env @ V_s @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T ) @ V_U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App_0) ).
thf(164,axiom,
! [T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
thf(165,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
thf(166,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(167,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(168,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(169,axiom,
! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(170,axiom,
! [V_P: $i,V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_n ) @ V_m ) )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).
thf(171,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(172,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(173,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(174,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/sandbox2/benchmark/theBenchmark.p',cls_IT_Ocases_7) ).
thf(175,axiom,
! [V_f: $i,V_xs: $i,V_ys: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ T_b @ T_a )
= ( c_List_Oappend @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ ( c_List_Omap @ V_f @ V_ys @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__append_0) ).
thf(176,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/sandbox2/benchmark/theBenchmark.p',cls_semigroup__add_Oadd__assoc_0) ).
thf(177,axiom,
! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( V_xs = V_ys )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_3) ).
thf(178,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
thf(179,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/sandbox2/benchmark/theBenchmark.p',cls_lift__preserves__beta_H_0) ).
thf(180,axiom,
! [V_s: $i,V_t: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_t ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_s ) @ V_t ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta_0) ).
thf(181,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(182,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(183,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(184,axiom,
! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(185,axiom,
! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(186,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/sandbox2/benchmark/theBenchmark.p',cls_IT_Ocases_11) ).
thf(187,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).
thf(188,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).
thf(189,axiom,
! [V_dB: $i,V_dB_H: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_dB )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) )
| ( V_dB = V_dB_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
thf(190,axiom,
! [T_a: $i,V_xs: $i,V_ys: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).
thf(191,axiom,
! [T_a: $i,V_xs: $i,V_ys: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).
thf(192,axiom,
! [V_T1: $i,V_T2: $i,V_t: $i,V_u: $i,V_i: $i,V_e: $i,V_Ta: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1 ) @ V_T2 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_u ) @ V_i ) ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T2 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_T2 @ tc_Type_Otype ) @ V_t @ V_Ta )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MI2_0) ).
thf(193,axiom,
! [V_T1: $i,V_T2: $i,V_t: $i,V_u: $i,V_i: $i,V_e: $i,V_Ta: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1 ) @ V_T2 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_u ) @ V_i ) ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T1 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_T1 @ tc_Type_Otype ) @ V_t @ V_Ta )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MI1_0) ).
thf(194,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/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_2) ).
thf(195,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/sandbox2/benchmark/theBenchmark.p',cls_shift__eq_0) ).
thf(196,axiom,
! [V_env: $i,V_t: $i,V_T: $i,V_U: $i] :
( ( c_Type_Otyping @ V_env @ ( c_Lambda_OdB_OAbs @ V_t ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T ) @ V_U ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_env @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_T @ tc_Type_Otype ) @ V_t @ V_U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs_0) ).
thf(197,axiom,
! [T_a: $i,V_x: $i,V_zs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_zs @ T_a @ T_a ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x @ V_zs @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__absorb0_0) ).
thf(198,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
thf(199,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
thf(200,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
thf(201,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
thf(202,axiom,
! [V_r: $i,V_xs: $i,T_a: $i] :
~ ( c_ListOrder_Ostep1 @ V_r @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__step1__Nil_0) ).
thf(203,axiom,
! [V_r: $i,T_a: $i,V_xs: $i] :
~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_ONil @ T_a ) @ V_xs @ T_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Nil__step1_0) ).
thf(204,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/sandbox2/benchmark/theBenchmark.p',cls_r__into__rtranclp_0) ).
thf(205,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/sandbox2/benchmark/theBenchmark.p',cls_foldr__conv__foldl_0) ).
thf(206,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
thf(207,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/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta2_H_0) ).
thf(208,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/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta_H_0) ).
thf(209,axiom,
! [T_a: $i,V_f: $i,V_xs: $i,T_b: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__map__conv_0) ).
thf(210,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
thf(211,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
thf(212,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/sandbox2/benchmark/theBenchmark.p',cls_monoid__add_Oadd__0__left_0) ).
thf(213,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/sandbox2/benchmark/theBenchmark.p',cls_monoid__add_Oadd__0__right_0) ).
thf(214,axiom,
! [V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ ( c_Lambda_OdB_OAbs @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs_0) ).
thf(215,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(216,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(217,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(218,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(219,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(220,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
thf(221,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(222,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_x )
= V_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(223,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/sandbox2/benchmark/theBenchmark.p',cls_rtranclp__idemp_0) ).
thf(224,axiom,
! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).
thf(225,axiom,
! [V_ys: $i,V_xs: $i,V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( V_ys = V_xs )
| ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_0) ).
thf(226,axiom,
! [T_a: $i,V_f: $i,T_b: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Olist_ONil @ T_b ) @ T_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__map__conv_1) ).
thf(227,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/sandbox2/benchmark/theBenchmark.p',cls_subst__lemma_0) ).
thf(228,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).
thf(229,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/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_1) ).
thf(230,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/sandbox2/benchmark/theBenchmark.p',cls_IT_Ocases_3) ).
thf(231,axiom,
! [V_xs: $i,V_x: $i,T_a: $i] :
( V_xs
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(232,axiom,
! [V_x: $i,V_t: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_t @ T_a )
!= V_t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(233,axiom,
! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_r ) @ V_i ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
thf(234,axiom,
! [V_i: $i,V_k: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
thf(235,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/sandbox2/benchmark/theBenchmark.p',cls_lift__types_0) ).
thf(236,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/sandbox2/benchmark/theBenchmark.p',cls_subject__reduction_H_0) ).
thf(237,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/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_0) ).
thf(238,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/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__beta__App_0) ).
thf(239,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(240,axiom,
! [V_x: $i,V_y: $i,V_r: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( V_x = V_y )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_0) ).
thf(241,axiom,
! [V_a_H: $i,V_list_H: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
thf(242,axiom,
! [V_x: $i,V_xa: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xa @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
thf(243,axiom,
! [V_x: $i,V_xs1: $i,V_zs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xs1 @ V_zs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xs1 @ T_a ) @ V_zs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).
thf(244,axiom,
! [V_x: $i,V_xa: $i,V_zs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xa @ V_zs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ V_zs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).
thf(245,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_a )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) )
| ( V_b = V_c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
thf(246,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) )
| ( V_b = V_c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
thf(247,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) )
| ( V_b = V_c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(248,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) )
| ( V_y = V_z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
thf(249,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/sandbox2/benchmark/theBenchmark.p',cls_IT_Ocases_6) ).
thf(250,axiom,
! [V_f: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_x ) @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map_Osimps_I2_J_0) ).
thf(251,axiom,
! [V_f: $i,V_xa: $i,V_xb: $i,T_b: $i,T_a: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_xa ) @ ( c_List_Omap @ V_f @ V_xb @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_xa @ V_xb @ T_b ) @ T_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__map__conv_3) ).
thf(252,axiom,
! [V_f: $i,V_x: $i,V_xa: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_x ) @ ( c_List_Omap @ V_f @ V_xa @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__eq__Cons__conv_3) ).
thf(253,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/sandbox2/benchmark/theBenchmark.p',cls_foldl__foldr1__lemma_0) ).
thf(254,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/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__beta__AppL_0) ).
thf(255,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/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__beta__AppR_0) ).
thf(256,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ V_ys @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Cons_0) ).
thf(257,axiom,
! [V_x: $i,V_xa: $i,T_a: $i,V_zs: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ V_zs @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xa @ V_zs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).
thf(258,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
thf(259,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/sandbox2/benchmark/theBenchmark.p',cls_substs__lemma_0) ).
thf(260,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/sandbox2/benchmark/theBenchmark.p',cls_IT_Ocases_1) ).
thf(261,axiom,
! [V_r: $i,V_y: $i,V_x: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_1) ).
thf(262,axiom,
! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_ONil @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__is__Nil__conv_1) ).
thf(263,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/sandbox2/benchmark/theBenchmark.p',cls_foldr_Osimps_I1_J_0) ).
thf(264,axiom,
! [V_P: $i,V_Q: $i,T_b: $i,T_c: $i,T_a: $i,V_R: $i] :
( ( hAPP @ ( c_COMBC @ V_P @ V_Q @ T_b @ T_c @ T_a ) @ V_R )
= ( hAPP @ ( hAPP @ V_P @ V_R ) @ V_Q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(265,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i,V_u: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_u ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z )
= V_u ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(266,axiom,
! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).
thf(267,axiom,
! [V_m: $i] :
~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
thf(268,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(269,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_d ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(270,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ V_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(271,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ V_d ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(272,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(273,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(274,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(275,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(276,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) ) @ V_z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(277,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(278,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(279,axiom,
! [V_e: $i,V_t: $i,V_ts: $i,V_T: $i,V_Ts: $i] :
( ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T )
| ~ ( c_Type_Otypings @ V_e @ V_ts @ V_Ts )
| ~ ( c_Type_Otyping @ V_e @ V_t @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ V_Ts @ V_T @ tc_Type_Otype @ tc_Type_Otype ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeI_0) ).
thf(280,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
thf(281,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/sandbox2/benchmark/theBenchmark.p',cls_substn__subst__n_0) ).
thf(282,axiom,
! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_x: $i] :
( ~ ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ V_x @ T_a ) @ ( c_List_Oappend @ V_xs @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__step1I_0) ).
thf(283,axiom,
! [V_r: $i,V_x: $i,V_vs: $i,T_a: $i,V_us: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_x @ V_vs @ T_a ) @ ( c_List_Oappend @ V_x @ V_us @ T_a ) @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ V_vs @ V_us @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__step1I_1) ).
thf(284,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/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__beta__Abs_0) ).
thf(285,axiom,
! [V_A: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Olistsp @ V_A @ V_xs @ T_a )
| ~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_0) ).
thf(286,axiom,
! [V_A: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_List_Olistsp @ V_A @ V_ys @ T_a )
| ~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_1) ).
thf(287,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/sandbox2/benchmark/theBenchmark.p',cls_IT_Ocases_10) ).
thf(288,axiom,
! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OAbs @ V_dB ) @ T_a )
= ( hAPP @ V_f3 @ V_dB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I12_J_0) ).
thf(289,axiom,
! [V_x: $i,V_y: $i,V_xs: $i,V_ys: $i,V_r: $i,T_a: $i] :
( ( V_x = V_y )
| ( V_xs = V_ys )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_2) ).
thf(290,axiom,
! [V_r: $i,V_y: $i,V_xa: $i,V_x: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_xa ) )
| ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_xa @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_4) ).
thf(291,axiom,
! [V_A: $i,T_a: $i] : ( c_List_Olistsp @ V_A @ ( c_List_Olist_ONil @ T_a ) @ T_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).
thf(292,axiom,
! [V_ys: $i,V_xs: $i,T_a: $i,V_zs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_xs @ T_a )
!= ( c_List_Oappend @ V_zs @ V_xs @ T_a ) )
| ( V_ys = V_zs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
thf(293,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i,V_zs: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Oappend @ V_xs @ V_zs @ T_a ) )
| ( V_ys = V_zs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
thf(294,axiom,
c_Type_Otyping @ v_ea______ @ v_ua______ @ v_T____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var_I4_J_0) ).
thf(295,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/sandbox2/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__refl_0) ).
thf(296,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/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Ortranclp__def_1) ).
thf(297,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/sandbox2/benchmark/theBenchmark.p',cls_rtranclp__trans_0) ).
thf(298,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/sandbox2/benchmark/theBenchmark.p',cls_IT_Ocases_8) ).
thf(299,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil2_0) ).
thf(300,axiom,
! [V_x: $i,T_a: $i] :
( V_x
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).
thf(301,axiom,
! [V_xs: $i,T_a: $i] :
( V_xs
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_1) ).
thf(302,axiom,
! [T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a )
= V_ys ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil_0) ).
thf(303,axiom,
! [V_ys: $i,T_a: $i] :
( V_ys
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).
thf(304,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/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta2_0) ).
thf(305,axiom,
! [T_a: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(306,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(307,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(308,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/sandbox2/benchmark/theBenchmark.p',cls_foldr__append_0) ).
thf(309,axiom,
! [V_r: $i,V_y: $i,V_x: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ( V_y = V_x )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_3) ).
thf(310,axiom,
! [V_e: $i,V_ts: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ V_T @ V_e @ V_t @ V_ts ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeD_1) ).
thf(311,axiom,
! [V_e: $i,V_ts: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ V_T @ V_e @ V_t @ V_ts ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeE_1) ).
thf(312,axiom,
! [V_e: $i,V_t: $i,V_T: $i,V_ts: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ V_T @ V_e @ V_t @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeE_0) ).
thf(313,axiom,
! [V_e: $i,V_t: $i,V_T: $i,V_ts: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ V_T @ V_e @ V_t @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeD_0) ).
thf(314,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/sandbox2/benchmark/theBenchmark.p',cls_lem_5) ).
thf(315,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/sandbox2/benchmark/theBenchmark.p',cls_Apps__dB__induct_5) ).
thf(316,axiom,
! [T_a: $i,V_x: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
thf(317,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(318,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[317]) ).
thf(319,negated_conjecture,
~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ v_u____ ) @ v_i____ ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(320,plain,
$false = $false,
inference(unfold_def,[status(thm)],[318]) ).
thf(321,plain,
( ( ! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( c_fequal @ V_X @ V_Y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(322,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_fequal @ V_x @ V_x @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(323,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(324,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(325,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(326,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(327,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(328,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(329,plain,
( ( class_OrderedGroup_Osemigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(330,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(331,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(332,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(333,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(334,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(335,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(336,plain,
( ( class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(337,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(338,plain,
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(339,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)],[19]) ).
thf(340,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)],[20]) ).
thf(341,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_u____ ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(342,plain,
( ( v_n____ = v_i____ )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(343,plain,
( ( v_rs____
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(344,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)],[24]) ).
thf(345,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)],[25]) ).
thf(346,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)],[26]) ).
thf(347,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)],[27]) ).
thf(348,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)],[28]) ).
thf(349,plain,
( ( ! [V_t: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ ( c_Lambda_OdB_OVar @ V_i ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(350,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)],[30]) ).
thf(351,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)],[31]) ).
thf(352,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)],[32]) ).
thf(353,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)],[33]) ).
thf(354,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_u____ ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(355,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)],[35]) ).
thf(356,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)],[36]) ).
thf(357,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)],[37]) ).
thf(358,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)],[38]) ).
thf(359,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)],[39]) ).
thf(360,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)],[40]) ).
thf(361,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)],[41]) ).
thf(362,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)],[42]) ).
thf(363,plain,
( ( v_rs____
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(364,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)],[44]) ).
thf(365,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)],[45]) ).
thf(366,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)],[46]) ).
thf(367,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)],[47]) ).
thf(368,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)],[48]) ).
thf(369,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)],[49]) ).
thf(370,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)],[50]) ).
thf(371,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)],[51]) ).
thf(372,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)],[52]) ).
thf(373,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)],[53]) ).
thf(374,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)],[54]) ).
thf(375,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)],[55]) ).
thf(376,plain,
( ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_T_H____ )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(377,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_ua______ ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(378,plain,
( ( ! [V_e: $i,V_i: $i,V_T: $i,V_ts: $i] :
( ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OVar @ V_i ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ V_T @ V_e @ V_i @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( 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)],[58]) ).
thf(379,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)],[59]) ).
thf(380,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)],[60]) ).
thf(381,plain,
( ( c_Type_Otyping @ ( c_Type_Oshift @ v_ea______ @ v_ia______ @ v_T____ @ tc_Type_Otype ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_T_Ha______ )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(382,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)],[62]) ).
thf(383,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)],[63]) ).
thf(384,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)],[64]) ).
thf(385,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)],[65]) ).
thf(386,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)],[66]) ).
thf(387,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(388,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)],[68]) ).
thf(389,plain,
( ( v_n____ = v_i____ )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(390,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)],[70]) ).
thf(391,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)],[71]) ).
thf(392,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)],[72]) ).
thf(393,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)],[73]) ).
thf(394,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)],[74]) ).
thf(395,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)],[75]) ).
thf(396,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(397,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)],[77]) ).
thf(398,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)],[78]) ).
thf(399,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)],[79]) ).
thf(400,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)],[80]) ).
thf(401,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)],[81]) ).
thf(402,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)],[82]) ).
thf(403,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) )
| ( V_dB2 = V_dB2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(404,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) )
| ( V_dB1 = V_dB1_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(405,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)],[85]) ).
thf(406,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)],[86]) ).
thf(407,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)],[87]) ).
thf(408,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)],[88]) ).
thf(409,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)],[89]) ).
thf(410,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)],[90]) ).
thf(411,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)],[91]) ).
thf(412,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)],[92]) ).
thf(413,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)],[93]) ).
thf(414,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)],[94]) ).
thf(415,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)],[95]) ).
thf(416,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)],[96]) ).
thf(417,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)],[97]) ).
thf(418,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)],[98]) ).
thf(419,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)],[99]) ).
thf(420,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)],[100]) ).
thf(421,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)],[101]) ).
thf(422,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)],[102]) ).
thf(423,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)],[103]) ).
thf(424,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)],[104]) ).
thf(425,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)],[105]) ).
thf(426,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)],[106]) ).
thf(427,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)],[107]) ).
thf(428,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)],[108]) ).
thf(429,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)],[109]) ).
thf(430,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)],[110]) ).
thf(431,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)],[111]) ).
thf(432,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)],[112]) ).
thf(433,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)],[113]) ).
thf(434,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)],[114]) ).
thf(435,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)],[115]) ).
thf(436,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)],[116]) ).
thf(437,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)],[117]) ).
thf(438,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)],[118]) ).
thf(439,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)],[119]) ).
thf(440,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)],[120]) ).
thf(441,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)],[121]) ).
thf(442,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)],[122]) ).
thf(443,plain,
( ( c_Type_Otyping @ v_e____ @ v_u____ @ v_T____ )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(444,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)],[124]) ).
thf(445,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)],[125]) ).
thf(446,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)],[126]) ).
thf(447,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)],[127]) ).
thf(448,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)],[128]) ).
thf(449,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)],[129]) ).
thf(450,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)],[130]) ).
thf(451,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)],[131]) ).
thf(452,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)],[132]) ).
thf(453,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)],[133]) ).
thf(454,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)],[134]) ).
thf(455,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)],[135]) ).
thf(456,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)],[136]) ).
thf(457,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)],[137]) ).
thf(458,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)],[138]) ).
thf(459,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)],[139]) ).
thf(460,plain,
( ( ! [V_type1: $i,V_type2: $i,V_type1_H: $i,V_type2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H ) )
| ( V_type1 = V_type1_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(461,plain,
( ( ! [V_type1: $i,V_type2: $i,V_type1_H: $i,V_type2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H ) )
| ( V_type2 = V_type2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(462,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)],[142]) ).
thf(463,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)],[143]) ).
thf(464,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)],[144]) ).
thf(465,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)],[145]) ).
thf(466,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)],[146]) ).
thf(467,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)],[147]) ).
thf(468,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)],[148]) ).
thf(469,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)],[149]) ).
thf(470,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)],[150]) ).
thf(471,plain,
( ( ! [V_U: $i,V_T: $i,V_e: $i,V_us: $i,V_i: $i,V_ts: $i,V_Ts: $i] :
( ( V_U
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ V_T @ V_U @ V_e @ V_us ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( 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)],[151]) ).
thf(472,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)],[152]) ).
thf(473,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)],[153]) ).
thf(474,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)],[154]) ).
thf(475,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)],[155]) ).
thf(476,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)],[156]) ).
thf(477,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)],[157]) ).
thf(478,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)],[158]) ).
thf(479,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)],[159]) ).
thf(480,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)],[160]) ).
thf(481,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)],[161]) ).
thf(482,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)],[162]) ).
thf(483,plain,
( ( ! [V_env: $i,V_s: $i,V_t: $i,V_U: $i,V_T: $i] :
( ( c_Type_Otyping @ V_env @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_U )
| ~ ( c_Type_Otyping @ V_env @ V_t @ V_T )
| ~ ( c_Type_Otyping @ V_env @ V_s @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T ) @ V_U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(484,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)],[164]) ).
thf(485,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)],[165]) ).
thf(486,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)],[166]) ).
thf(487,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)],[167]) ).
thf(488,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)],[168]) ).
thf(489,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)],[169]) ).
thf(490,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)],[170]) ).
thf(491,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)],[171]) ).
thf(492,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)],[172]) ).
thf(493,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)],[173]) ).
thf(494,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)],[174]) ).
thf(495,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)],[175]) ).
thf(496,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)],[176]) ).
thf(497,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)],[177]) ).
thf(498,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)],[178]) ).
thf(499,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)],[179]) ).
thf(500,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)],[180]) ).
thf(501,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)],[181]) ).
thf(502,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)],[182]) ).
thf(503,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)],[183]) ).
thf(504,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(505,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(506,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)],[186]) ).
thf(507,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)],[187]) ).
thf(508,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)],[188]) ).
thf(509,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)],[189]) ).
thf(510,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)],[190]) ).
thf(511,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)],[191]) ).
thf(512,plain,
( ( ! [V_T1: $i,V_T2: $i,V_t: $i,V_u: $i,V_i: $i,V_e: $i,V_Ta: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1 ) @ V_T2 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_u ) @ V_i ) ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T2 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_T2 @ tc_Type_Otype ) @ V_t @ V_Ta )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(513,plain,
( ( ! [V_T1: $i,V_T2: $i,V_t: $i,V_u: $i,V_i: $i,V_e: $i,V_Ta: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1 ) @ V_T2 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_u ) @ V_i ) ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T1 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_T1 @ tc_Type_Otype ) @ V_t @ V_Ta )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(514,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)],[194]) ).
thf(515,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)],[195]) ).
thf(516,plain,
( ( ! [V_env: $i,V_t: $i,V_T: $i,V_U: $i] :
( ( c_Type_Otyping @ V_env @ ( c_Lambda_OdB_OAbs @ V_t ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T ) @ V_U ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_env @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_T @ tc_Type_Otype ) @ V_t @ V_U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(517,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)],[197]) ).
thf(518,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)],[198]) ).
thf(519,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)],[199]) ).
thf(520,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)],[200]) ).
thf(521,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)],[201]) ).
thf(522,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)],[202]) ).
thf(523,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)],[203]) ).
thf(524,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)],[204]) ).
thf(525,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)],[205]) ).
thf(526,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)],[206]) ).
thf(527,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)],[207]) ).
thf(528,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)],[208]) ).
thf(529,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)],[209]) ).
thf(530,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)],[210]) ).
thf(531,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)],[211]) ).
thf(532,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)],[212]) ).
thf(533,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)],[213]) ).
thf(534,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)],[214]) ).
thf(535,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)],[215]) ).
thf(536,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)],[216]) ).
thf(537,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)],[217]) ).
thf(538,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)],[218]) ).
thf(539,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)],[219]) ).
thf(540,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)],[220]) ).
thf(541,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)],[221]) ).
thf(542,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)],[222]) ).
thf(543,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)],[223]) ).
thf(544,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)],[224]) ).
thf(545,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)],[225]) ).
thf(546,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)],[226]) ).
thf(547,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)],[227]) ).
thf(548,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)],[228]) ).
thf(549,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)],[229]) ).
thf(550,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)],[230]) ).
thf(551,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)],[231]) ).
thf(552,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)],[232]) ).
thf(553,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)],[233]) ).
thf(554,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)],[234]) ).
thf(555,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)],[235]) ).
thf(556,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)],[236]) ).
thf(557,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)],[237]) ).
thf(558,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)],[238]) ).
thf(559,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)],[239]) ).
thf(560,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)],[240]) ).
thf(561,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)],[241]) ).
thf(562,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)],[242]) ).
thf(563,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)],[243]) ).
thf(564,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)],[244]) ).
thf(565,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)],[245]) ).
thf(566,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)],[246]) ).
thf(567,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)],[247]) ).
thf(568,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)],[248]) ).
thf(569,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)],[249]) ).
thf(570,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)],[250]) ).
thf(571,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)],[251]) ).
thf(572,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)],[252]) ).
thf(573,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)],[253]) ).
thf(574,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)],[254]) ).
thf(575,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)],[255]) ).
thf(576,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)],[256]) ).
thf(577,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)],[257]) ).
thf(578,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)],[258]) ).
thf(579,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)],[259]) ).
thf(580,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)],[260]) ).
thf(581,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)],[261]) ).
thf(582,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)],[262]) ).
thf(583,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)],[263]) ).
thf(584,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)],[264]) ).
thf(585,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)],[265]) ).
thf(586,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)],[266]) ).
thf(587,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)],[267]) ).
thf(588,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)],[268]) ).
thf(589,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)],[269]) ).
thf(590,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)],[270]) ).
thf(591,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)],[271]) ).
thf(592,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)],[272]) ).
thf(593,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)],[273]) ).
thf(594,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)],[274]) ).
thf(595,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)],[275]) ).
thf(596,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)],[276]) ).
thf(597,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)],[277]) ).
thf(598,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)],[278]) ).
thf(599,plain,
( ( ! [V_e: $i,V_t: $i,V_ts: $i,V_T: $i,V_Ts: $i] :
( ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T )
| ~ ( c_Type_Otypings @ V_e @ V_ts @ V_Ts )
| ~ ( c_Type_Otyping @ V_e @ V_t @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ V_Ts @ V_T @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(600,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)],[280]) ).
thf(601,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)],[281]) ).
thf(602,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)],[282]) ).
thf(603,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)],[283]) ).
thf(604,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)],[284]) ).
thf(605,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)],[285]) ).
thf(606,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)],[286]) ).
thf(607,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)],[287]) ).
thf(608,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)],[288]) ).
thf(609,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)],[289]) ).
thf(610,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)],[290]) ).
thf(611,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)],[291]) ).
thf(612,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)],[292]) ).
thf(613,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)],[293]) ).
thf(614,plain,
( ( c_Type_Otyping @ v_ea______ @ v_ua______ @ v_T____ )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(615,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)],[295]) ).
thf(616,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)],[296]) ).
thf(617,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)],[297]) ).
thf(618,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)],[298]) ).
thf(619,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)],[299]) ).
thf(620,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)],[300]) ).
thf(621,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)],[301]) ).
thf(622,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)],[302]) ).
thf(623,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)],[303]) ).
thf(624,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)],[304]) ).
thf(625,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)],[305]) ).
thf(626,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)],[306]) ).
thf(627,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)],[307]) ).
thf(628,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)],[308]) ).
thf(629,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)],[309]) ).
thf(630,plain,
( ( ! [V_e: $i,V_ts: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ V_T @ V_e @ V_t @ V_ts ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(631,plain,
( ( ! [V_e: $i,V_ts: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ V_T @ V_e @ V_t @ V_ts ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(632,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i,V_ts: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ V_T @ V_e @ V_t @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(633,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i,V_ts: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ V_T @ V_e @ V_t @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(634,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)],[314]) ).
thf(635,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)],[315]) ).
thf(636,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)],[316]) ).
thf(637,plain,
( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ v_u____ ) @ v_i____ ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(638,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[320]) ).
thf(639,plain,
( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ v_u____ ) @ v_i____ ) ) ) )
= $true ),
inference(copy,[status(thm)],[637]) ).
thf(640,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)],[636]) ).
thf(641,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)],[635]) ).
thf(642,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)],[634]) ).
thf(643,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i,V_ts: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ V_T @ V_e @ V_t @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[633]) ).
thf(644,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i,V_ts: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ V_T @ V_e @ V_t @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[632]) ).
thf(645,plain,
( ( ! [V_e: $i,V_ts: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ V_T @ V_e @ V_t @ V_ts ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[631]) ).
thf(646,plain,
( ( ! [V_e: $i,V_ts: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ V_T @ V_e @ V_t @ V_ts ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[630]) ).
thf(647,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)],[629]) ).
thf(648,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)],[628]) ).
thf(649,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)],[627]) ).
thf(650,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)],[626]) ).
thf(651,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)],[625]) ).
thf(652,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)],[624]) ).
thf(653,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)],[623]) ).
thf(654,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)],[622]) ).
thf(655,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)],[621]) ).
thf(656,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)],[620]) ).
thf(657,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)],[619]) ).
thf(658,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)],[618]) ).
thf(659,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)],[617]) ).
thf(660,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)],[616]) ).
thf(661,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)],[615]) ).
thf(662,plain,
( ( c_Type_Otyping @ v_ea______ @ v_ua______ @ v_T____ )
= $true ),
inference(copy,[status(thm)],[614]) ).
thf(663,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)],[613]) ).
thf(664,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)],[612]) ).
thf(665,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)],[611]) ).
thf(666,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)],[610]) ).
thf(667,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)],[609]) ).
thf(668,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)],[608]) ).
thf(669,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)],[607]) ).
thf(670,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)],[606]) ).
thf(671,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)],[605]) ).
thf(672,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)],[604]) ).
thf(673,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)],[603]) ).
thf(674,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)],[602]) ).
thf(675,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)],[601]) ).
thf(676,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)],[600]) ).
thf(677,plain,
( ( ! [V_e: $i,V_t: $i,V_ts: $i,V_T: $i,V_Ts: $i] :
( ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T )
| ~ ( c_Type_Otypings @ V_e @ V_ts @ V_Ts )
| ~ ( c_Type_Otyping @ V_e @ V_t @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ V_Ts @ V_T @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(copy,[status(thm)],[599]) ).
thf(678,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)],[598]) ).
thf(679,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)],[597]) ).
thf(680,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)],[596]) ).
thf(681,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)],[595]) ).
thf(682,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)],[594]) ).
thf(683,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)],[593]) ).
thf(684,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)],[592]) ).
thf(685,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)],[591]) ).
thf(686,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)],[590]) ).
thf(687,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)],[589]) ).
thf(688,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)],[588]) ).
thf(689,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)],[587]) ).
thf(690,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)],[586]) ).
thf(691,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)],[585]) ).
thf(692,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)],[584]) ).
thf(693,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)],[583]) ).
thf(694,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)],[582]) ).
thf(695,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)],[581]) ).
thf(696,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)],[580]) ).
thf(697,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)],[579]) ).
thf(698,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)],[578]) ).
thf(699,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)],[577]) ).
thf(700,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)],[576]) ).
thf(701,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)],[575]) ).
thf(702,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)],[574]) ).
thf(703,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)],[573]) ).
thf(704,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)],[572]) ).
thf(705,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)],[571]) ).
thf(706,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)],[570]) ).
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 ) )
| ( 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)],[569]) ).
thf(708,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)],[568]) ).
thf(709,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)],[567]) ).
thf(710,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)],[566]) ).
thf(711,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)],[565]) ).
thf(712,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)],[564]) ).
thf(713,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)],[563]) ).
thf(714,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)],[562]) ).
thf(715,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)],[561]) ).
thf(716,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)],[560]) ).
thf(717,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)],[559]) ).
thf(718,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)],[558]) ).
thf(719,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)],[557]) ).
thf(720,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)],[556]) ).
thf(721,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)],[555]) ).
thf(722,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)],[554]) ).
thf(723,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)],[553]) ).
thf(724,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)],[552]) ).
thf(725,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)],[551]) ).
thf(726,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)],[550]) ).
thf(727,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)],[549]) ).
thf(728,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)],[548]) ).
thf(729,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)],[547]) ).
thf(730,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)],[546]) ).
thf(731,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)],[545]) ).
thf(732,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)],[544]) ).
thf(733,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)],[543]) ).
thf(734,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)],[542]) ).
thf(735,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)],[541]) ).
thf(736,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)],[540]) ).
thf(737,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)],[539]) ).
thf(738,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)],[538]) ).
thf(739,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)],[537]) ).
thf(740,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)],[536]) ).
thf(741,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)],[535]) ).
thf(742,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)],[534]) ).
thf(743,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)],[533]) ).
thf(744,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)],[532]) ).
thf(745,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)],[531]) ).
thf(746,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)],[530]) ).
thf(747,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)],[529]) ).
thf(748,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)],[528]) ).
thf(749,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)],[527]) ).
thf(750,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)],[526]) ).
thf(751,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)],[525]) ).
thf(752,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)],[524]) ).
thf(753,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)],[523]) ).
thf(754,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)],[522]) ).
thf(755,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)],[521]) ).
thf(756,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)],[520]) ).
thf(757,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)],[519]) ).
thf(758,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)],[518]) ).
thf(759,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)],[517]) ).
thf(760,plain,
( ( ! [V_env: $i,V_t: $i,V_T: $i,V_U: $i] :
( ( c_Type_Otyping @ V_env @ ( c_Lambda_OdB_OAbs @ V_t ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T ) @ V_U ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_env @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_T @ tc_Type_Otype ) @ V_t @ V_U ) ) )
= $true ),
inference(copy,[status(thm)],[516]) ).
thf(761,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)],[515]) ).
thf(762,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)],[514]) ).
thf(763,plain,
( ( ! [V_T1: $i,V_T2: $i,V_t: $i,V_u: $i,V_i: $i,V_e: $i,V_Ta: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1 ) @ V_T2 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_u ) @ V_i ) ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T1 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_T1 @ tc_Type_Otype ) @ V_t @ V_Ta )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[513]) ).
thf(764,plain,
( ( ! [V_T1: $i,V_T2: $i,V_t: $i,V_u: $i,V_i: $i,V_e: $i,V_Ta: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1 ) @ V_T2 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_u ) @ V_i ) ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T2 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_T2 @ tc_Type_Otype ) @ V_t @ V_Ta )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[512]) ).
thf(765,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)],[511]) ).
thf(766,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)],[510]) ).
thf(767,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)],[509]) ).
thf(768,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)],[508]) ).
thf(769,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)],[507]) ).
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(copy,[status(thm)],[506]) ).
thf(771,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[505]) ).
thf(772,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[504]) ).
thf(773,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)],[503]) ).
thf(774,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)],[502]) ).
thf(775,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)],[501]) ).
thf(776,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)],[500]) ).
thf(777,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)],[499]) ).
thf(778,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)],[498]) ).
thf(779,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)],[497]) ).
thf(780,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)],[496]) ).
thf(781,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)],[495]) ).
thf(782,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)],[494]) ).
thf(783,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)],[493]) ).
thf(784,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)],[492]) ).
thf(785,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)],[491]) ).
thf(786,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)],[490]) ).
thf(787,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)],[489]) ).
thf(788,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)],[488]) ).
thf(789,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)],[487]) ).
thf(790,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)],[486]) ).
thf(791,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)],[485]) ).
thf(792,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)],[484]) ).
thf(793,plain,
( ( ! [V_env: $i,V_s: $i,V_t: $i,V_U: $i,V_T: $i] :
( ( c_Type_Otyping @ V_env @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_U )
| ~ ( c_Type_Otyping @ V_env @ V_t @ V_T )
| ~ ( c_Type_Otyping @ V_env @ V_s @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T ) @ V_U ) ) ) )
= $true ),
inference(copy,[status(thm)],[483]) ).
thf(794,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)],[482]) ).
thf(795,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)],[481]) ).
thf(796,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)],[480]) ).
thf(797,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)],[479]) ).
thf(798,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)],[478]) ).
thf(799,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)],[477]) ).
thf(800,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)],[476]) ).
thf(801,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)],[475]) ).
thf(802,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)],[474]) ).
thf(803,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)],[473]) ).
thf(804,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)],[472]) ).
thf(805,plain,
( ( ! [V_U: $i,V_T: $i,V_e: $i,V_us: $i,V_i: $i,V_ts: $i,V_Ts: $i] :
( ( V_U
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ V_T @ V_U @ V_e @ V_us ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( 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)],[471]) ).
thf(806,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)],[470]) ).
thf(807,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)],[469]) ).
thf(808,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)],[468]) ).
thf(809,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)],[467]) ).
thf(810,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)],[466]) ).
thf(811,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)],[465]) ).
thf(812,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)],[464]) ).
thf(813,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)],[463]) ).
thf(814,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)],[462]) ).
thf(815,plain,
( ( ! [V_type1: $i,V_type2: $i,V_type1_H: $i,V_type2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H ) )
| ( V_type2 = V_type2_H ) ) )
= $true ),
inference(copy,[status(thm)],[461]) ).
thf(816,plain,
( ( ! [V_type1: $i,V_type2: $i,V_type1_H: $i,V_type2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H ) )
| ( V_type1 = V_type1_H ) ) )
= $true ),
inference(copy,[status(thm)],[460]) ).
thf(817,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)],[459]) ).
thf(818,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)],[458]) ).
thf(819,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)],[457]) ).
thf(820,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)],[456]) ).
thf(821,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)],[455]) ).
thf(822,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)],[454]) ).
thf(823,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)],[453]) ).
thf(824,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)],[452]) ).
thf(825,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)],[451]) ).
thf(826,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)],[450]) ).
thf(827,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)],[449]) ).
thf(828,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)],[448]) ).
thf(829,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)],[447]) ).
thf(830,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)],[446]) ).
thf(831,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)],[445]) ).
thf(832,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)],[444]) ).
thf(833,plain,
( ( c_Type_Otyping @ v_e____ @ v_u____ @ v_T____ )
= $true ),
inference(copy,[status(thm)],[443]) ).
thf(834,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)],[442]) ).
thf(835,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)],[441]) ).
thf(836,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)],[440]) ).
thf(837,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)],[439]) ).
thf(838,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)],[438]) ).
thf(839,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)],[437]) ).
thf(840,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)],[436]) ).
thf(841,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)],[435]) ).
thf(842,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)],[434]) ).
thf(843,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)],[433]) ).
thf(844,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(845,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)],[431]) ).
thf(846,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)],[430]) ).
thf(847,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)],[429]) ).
thf(848,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)],[428]) ).
thf(849,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)],[427]) ).
thf(850,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)],[426]) ).
thf(851,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)],[425]) ).
thf(852,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)],[424]) ).
thf(853,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)],[423]) ).
thf(854,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)],[422]) ).
thf(855,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)],[421]) ).
thf(856,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)],[420]) ).
thf(857,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)],[419]) ).
thf(858,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)],[418]) ).
thf(859,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)],[417]) ).
thf(860,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)],[416]) ).
thf(861,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)],[415]) ).
thf(862,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)],[414]) ).
thf(863,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)],[413]) ).
thf(864,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)],[412]) ).
thf(865,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)],[411]) ).
thf(866,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)],[410]) ).
thf(867,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)],[409]) ).
thf(868,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)],[408]) ).
thf(869,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)],[407]) ).
thf(870,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)],[406]) ).
thf(871,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)],[405]) ).
thf(872,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)],[404]) ).
thf(873,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)],[403]) ).
thf(874,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)],[402]) ).
thf(875,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)],[401]) ).
thf(876,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)],[400]) ).
thf(877,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)],[399]) ).
thf(878,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)],[398]) ).
thf(879,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)],[397]) ).
thf(880,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)],[396]) ).
thf(881,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)],[395]) ).
thf(882,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)],[394]) ).
thf(883,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)],[393]) ).
thf(884,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)],[392]) ).
thf(885,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)],[391]) ).
thf(886,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)],[390]) ).
thf(887,plain,
( ( v_n____ = v_i____ )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(888,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)],[388]) ).
thf(889,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[387]) ).
thf(890,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)],[386]) ).
thf(891,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)],[385]) ).
thf(892,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)],[384]) ).
thf(893,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)],[383]) ).
thf(894,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)],[382]) ).
thf(895,plain,
( ( c_Type_Otyping @ ( c_Type_Oshift @ v_ea______ @ v_ia______ @ v_T____ @ tc_Type_Otype ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_T_Ha______ )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(896,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)],[380]) ).
thf(897,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)],[379]) ).
thf(898,plain,
( ( ! [V_e: $i,V_i: $i,V_T: $i,V_ts: $i] :
( ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OVar @ V_i ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ V_T @ V_e @ V_i @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( 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)],[378]) ).
thf(899,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_ua______ ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(900,plain,
( ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_T_H____ )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(901,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)],[375]) ).
thf(902,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)],[374]) ).
thf(903,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)],[373]) ).
thf(904,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)],[372]) ).
thf(905,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)],[371]) ).
thf(906,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)],[370]) ).
thf(907,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)],[369]) ).
thf(908,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)],[368]) ).
thf(909,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)],[367]) ).
thf(910,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)],[366]) ).
thf(911,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)],[365]) ).
thf(912,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)],[364]) ).
thf(913,plain,
( ( v_rs____
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(914,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)],[362]) ).
thf(915,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)],[361]) ).
thf(916,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)],[360]) ).
thf(917,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)],[359]) ).
thf(918,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)],[358]) ).
thf(919,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)],[357]) ).
thf(920,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)],[356]) ).
thf(921,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)],[355]) ).
thf(922,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_u____ ) )
= $true ),
inference(copy,[status(thm)],[354]) ).
thf(923,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)],[353]) ).
thf(924,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)],[352]) ).
thf(925,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)],[351]) ).
thf(926,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)],[350]) ).
thf(927,plain,
( ( ! [V_t: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ ( c_Lambda_OdB_OVar @ V_i ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[349]) ).
thf(928,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)],[348]) ).
thf(929,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)],[347]) ).
thf(930,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)],[346]) ).
thf(931,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)],[345]) ).
thf(932,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)],[344]) ).
thf(933,plain,
( ( v_rs____
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ),
inference(copy,[status(thm)],[343]) ).
thf(934,plain,
( ( v_n____ = v_i____ )
= $true ),
inference(copy,[status(thm)],[342]) ).
thf(935,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_u____ ) )
= $true ),
inference(copy,[status(thm)],[341]) ).
thf(936,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)],[340]) ).
thf(937,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)],[339]) ).
thf(938,plain,
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[338]) ).
thf(939,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat )
= $true ),
inference(copy,[status(thm)],[337]) ).
thf(940,plain,
( ( class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[336]) ).
thf(941,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[335]) ).
thf(942,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[334]) ).
thf(943,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(copy,[status(thm)],[333]) ).
thf(944,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[332]) ).
thf(945,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[331]) ).
thf(946,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[330]) ).
thf(947,plain,
( ( class_OrderedGroup_Osemigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[329]) ).
thf(948,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[328]) ).
thf(949,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[327]) ).
thf(950,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[326]) ).
thf(951,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[325]) ).
thf(952,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[324]) ).
thf(953,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[323]) ).
thf(954,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_fequal @ V_x @ V_x @ T_a ) )
= $true ),
inference(copy,[status(thm)],[322]) ).
thf(955,plain,
( ( ! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( c_fequal @ V_X @ V_Y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[321]) ).
thf(956,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[638]) ).
thf(957,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)],[714]) ).
thf(958,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)],[872]) ).
thf(959,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)],[709]) ).
thf(960,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)],[769]) ).
thf(961,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)],[711]) ).
thf(962,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)],[663]) ).
thf(963,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)],[858]) ).
thf(964,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)],[870]) ).
thf(965,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)],[825]) ).
thf(966,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)],[869]) ).
thf(967,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)],[910]) ).
thf(968,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SX2 ) @ SX3 ) @ SX4 ) ) )
| ~ ( c_Type_Otyping @ SX5 @ SX3 @ SX0 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SX3 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SX5 @ SX4 @ SX0 @ tc_Type_Otype ) @ SX2 @ SX6 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[763]) ).
thf(969,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)],[708]) ).
thf(970,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SX0 ) @ SX1 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SX2 ) @ SX3 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[815]) ).
thf(971,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)],[912]) ).
thf(972,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)],[881]) ).
thf(973,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)],[882]) ).
thf(974,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)],[831]) ).
thf(975,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)],[768]) ).
thf(976,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)],[929]) ).
thf(977,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)],[879]) ).
thf(978,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)],[811]) ).
thf(979,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[724]) ).
thf(980,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( SX0
!= ( c_List_Olist_OCons @ SX1 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[725]) ).
thf(981,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)],[917]) ).
thf(982,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)],[830]) ).
thf(983,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)],[750]) ).
thf(984,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)],[715]) ).
thf(985,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)],[866]) ).
thf(986,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)],[868]) ).
thf(987,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)],[878]) ).
thf(988,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SX0 ) @ SX1 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SX2 ) @ SX3 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[816]) ).
thf(989,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)],[813]) ).
thf(990,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)],[792]) ).
thf(991,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)],[710]) ).
thf(992,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)],[812]) ).
thf(993,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SX2 ) @ SX3 ) @ SX4 ) ) )
| ~ ( c_Type_Otyping @ SX5 @ SX3 @ SX1 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SX3 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SX5 @ SX4 @ SX1 @ tc_Type_Otype ) @ SX2 @ SX6 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[764]) ).
thf(994,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)],[664]) ).
thf(995,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_Lambda_OdB_OVar @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[854]) ).
thf(996,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)],[873]) ).
thf(997,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)],[852]) ).
thf(998,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_Lambda_OdB_OAbs @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[888]) ).
thf(999,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)],[747]) ).
thf(1000,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)],[832]) ).
thf(1001,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)],[814]) ).
thf(1002,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)],[766]) ).
thf(1003,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)],[765]) ).
thf(1004,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_Lambda_OdB_OVar @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[851]) ).
thf(1005,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)],[859]) ).
thf(1006,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)],[932]) ).
thf(1007,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)],[857]) ).
thf(1008,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)],[826]) ).
thf(1009,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)],[916]) ).
thf(1010,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)],[926]) ).
thf(1011,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)],[640]) ).
thf(1012,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_Lambda_OdB_OAbs @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[767]) ).
thf(1013,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)],[691]) ).
thf(1014,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ v_u____ ) @ v_i____ ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[639]) ).
thf(1015,plain,
! [SV1: $i] :
( ( ! [SY970: $i] :
( ( hBOOL @ ( hAPP @ SV1 @ SY970 ) )
| ~ ( hBOOL @ ( hAPP @ SV1 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV1 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4 @ SV1 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ SV1 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV1 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV1 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(1016,plain,
! [SV2: $i] :
( ( ! [SY971: $i] :
( ~ ( hBOOL @ ( hAPP @ SV2 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV2 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__4 @ SV2 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ SV2 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV2 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV2 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ SV2 @ SY971 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(1017,plain,
! [SV3: $i] :
( ( ! [SY972: $i,SY973: $i,SY974: $i] :
( ( c_Type_Otyping @ SV3 @ SY972 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SY973 @ SV3 @ SY972 @ SY974 ) @ SY973 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY972 @ SY974 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY973 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(1018,plain,
! [SV4: $i] :
( ( ! [SY975: $i,SY976: $i,SY977: $i] :
( ( c_Type_Otyping @ SV4 @ SY975 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SY976 @ SV4 @ SY975 @ SY977 ) @ SY976 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV4 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY975 @ SY977 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY976 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(1019,plain,
! [SV5: $i] :
( ( ! [SY978: $i,SY979: $i,SY980: $i] :
( ( c_Type_Otypings @ SV5 @ SY978 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SY979 @ SV5 @ SY980 @ SY978 ) )
| ~ ( c_Type_Otyping @ SV5 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY980 @ SY978 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY979 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(1020,plain,
! [SV6: $i] :
( ( ! [SY981: $i,SY982: $i,SY983: $i] :
( ( c_Type_Otypings @ SV6 @ SY981 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SY982 @ SV6 @ SY983 @ SY981 ) )
| ~ ( c_Type_Otyping @ SV6 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY983 @ SY981 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY982 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(1021,plain,
! [SV7: $i] :
( ( ! [SY984: $i,SY985: $i,SY986: $i,SY987: $i,SY988: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV7 @ SY984 ) @ SY985 ) )
| ( SY984 = SY985 )
| ~ ( c_ListOrder_Ostep1 @ SV7 @ ( c_List_Oappend @ SY986 @ ( c_List_Olist_OCons @ SY984 @ ( c_List_Olist_ONil @ SY987 ) @ SY987 ) @ SY987 ) @ ( c_List_Oappend @ SY988 @ ( c_List_Olist_OCons @ SY985 @ ( c_List_Olist_ONil @ SY987 ) @ SY987 ) @ SY987 ) @ SY987 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(1022,plain,
! [SV8: $i] :
( ( ! [SY989: $i,SY990: $i,SY991: $i,SY992: $i,SY993: $i] :
( ( c_List_Ofoldr @ SV8 @ ( c_List_Oappend @ SY989 @ SY990 @ SY991 ) @ SY992 @ SY991 @ SY993 )
= ( c_List_Ofoldr @ SV8 @ SY989 @ ( c_List_Ofoldr @ SV8 @ SY990 @ SY992 @ SY991 @ SY993 ) @ SY991 @ SY993 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(1023,plain,
! [SV9: $i] :
( ( ! [SY994: $i,SY995: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV9 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV9 ) @ SY994 ) @ SY995 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV9 ) @ SY995 ) @ SY994 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(1024,plain,
! [SV10: $i] :
( ( ! [SY996: $i,SY997: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV10 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV10 ) @ SY996 ) @ SY997 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV10 ) @ SY997 ) @ SY996 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(1025,plain,
! [SV11: $i] :
( ( ! [SY998: $i,SY999: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV11 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV11 ) @ SY998 ) @ SY999 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV11 ) @ SY999 ) @ SY998 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(1026,plain,
! [SV12: $i] :
( ( ! [SY1000: $i,SY1001: $i,SY1002: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV12 ) @ SY1000 ) @ SY1001 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV12 ) @ SY1002 ) @ SY1001 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1000 ) @ SY1002 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(1027,plain,
! [SV13: $i] :
( ( ! [SY1003: $i] :
( SV13
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY1003 ) @ SV13 @ SY1003 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(1028,plain,
! [SV14: $i] :
( ( ! [SY1004: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV14 ) @ SY1004 @ SV14 )
= SY1004 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(1029,plain,
! [SV15: $i] :
( ( ! [SY1005: $i] :
( SV15
= ( c_List_Oappend @ SV15 @ ( c_List_Olist_ONil @ SY1005 ) @ SY1005 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(1030,plain,
! [SV16: $i] :
( ( ! [SY1006: $i] :
( SV16
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY1006 ) @ SV16 @ SY1006 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(1031,plain,
! [SV17: $i] :
( ( ! [SY1007: $i] :
( ( c_List_Oappend @ SV17 @ ( c_List_Olist_ONil @ SY1007 ) @ SY1007 )
= SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(1032,plain,
! [SV18: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV18 ) ) )
| ( SV18
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV18 ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV18 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(1033,plain,
! [SV19: $i] :
( ( ! [SY1008: $i,SY1009: $i,SY1010: $i,SY1011: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV19 @ SY1008 ) @ SY1009 ) @ SY1010 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV19 @ SY1008 ) @ SY1011 ) @ SY1010 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV19 @ SY1008 ) @ SY1009 ) @ SY1011 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(1034,plain,
! [SV20: $i] :
( ( ! [SY1012: $i,SY1013: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV20 @ SY1012 ) @ SY1013 ) @ SY1013 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(1035,plain,
! [SV21: $i] :
( ( ! [SY1014: $i,SY1015: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV21 @ SY1014 ) @ SY1015 ) @ SY1015 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(1036,plain,
! [SV22: $i] :
( ( ! [SY1016: $i] : ( c_List_Olistsp @ SV22 @ ( c_List_Olist_ONil @ SY1016 ) @ SY1016 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(1037,plain,
! [SV23: $i] :
( ( ! [SY1017: $i,SY1018: $i,SY1019: $i,SY1020: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV23 @ SY1017 ) @ SY1018 ) )
| ( c_ListOrder_Ostep1 @ SV23 @ ( c_List_Olist_OCons @ SY1017 @ SY1019 @ SY1020 ) @ ( c_List_Olist_OCons @ SY1018 @ SY1019 @ SY1020 ) @ SY1020 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(1038,plain,
! [SV24: $i] :
( ( ! [SY1021: $i,SY1022: $i,SY1023: $i,SY1024: $i,SY1025: $i] :
( ( SV24 = SY1021 )
| ( SY1022 = SY1023 )
| ~ ( c_ListOrder_Ostep1 @ SY1024 @ ( c_List_Olist_OCons @ SY1021 @ SY1023 @ SY1025 ) @ ( c_List_Olist_OCons @ SV24 @ SY1022 @ SY1025 ) @ SY1025 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(1039,plain,
! [SV25: $i] :
( ( ! [SY1026: $i,SY1027: $i,SY1028: $i,SY1029: $i] :
( ( c_Lambda_OdB_OdB__case @ SV25 @ SY1026 @ SY1027 @ ( c_Lambda_OdB_OAbs @ SY1028 ) @ SY1029 )
= ( hAPP @ SY1027 @ SY1028 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(1040,plain,
! [SV26: $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 @ SV26 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV26 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV26 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV26 ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV26 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(1041,plain,
! [SV27: $i] :
( ( ! [SY1030: $i,SY1031: $i,SY1032: $i] :
( ( c_List_Olistsp @ SV27 @ SY1030 @ SY1031 )
| ~ ( c_List_Olistsp @ SV27 @ ( c_List_Oappend @ SY1032 @ SY1030 @ SY1031 ) @ SY1031 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(1042,plain,
! [SV28: $i] :
( ( ! [SY1033: $i,SY1034: $i,SY1035: $i] :
( ( c_List_Olistsp @ SV28 @ SY1033 @ SY1034 )
| ~ ( c_List_Olistsp @ SV28 @ ( c_List_Oappend @ SY1033 @ SY1035 @ SY1034 ) @ SY1034 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(1043,plain,
! [SV29: $i] :
( ( ! [SY1036: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV29 ) ) @ ( c_Lambda_OdB_OAbs @ SY1036 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV29 ) @ SY1036 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(1044,plain,
! [SV30: $i] :
( ( ! [SY1037: $i,SY1038: $i,SY1039: $i,SY1040: $i] :
( ( c_ListOrder_Ostep1 @ SV30 @ ( c_List_Oappend @ SY1037 @ SY1038 @ SY1039 ) @ ( c_List_Oappend @ SY1037 @ SY1040 @ SY1039 ) @ SY1039 )
| ~ ( c_ListOrder_Ostep1 @ SV30 @ SY1038 @ SY1040 @ SY1039 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(1045,plain,
! [SV31: $i] :
( ( ! [SY1041: $i,SY1042: $i,SY1043: $i,SY1044: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV31 @ SY1041 @ SY1042 @ SY1043 )
| ( c_ListOrder_Ostep1 @ SV31 @ ( c_List_Oappend @ SY1041 @ SY1044 @ SY1043 ) @ ( c_List_Oappend @ SY1042 @ SY1044 @ SY1043 ) @ SY1043 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(1046,plain,
! [SV32: $i] :
( ( ! [SY1045: $i,SY1046: $i] :
( ( c_Lambda_Osubstn @ SV32 @ SY1045 @ SY1046 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV32 ) @ ( c_Lambda_Oliftn @ SY1046 @ SY1045 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ SY1046 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(1047,plain,
! [SV33: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV33 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ ( c_HOL_Ozero__class_Ozero @ SV33 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV33 ) )
= ( c_HOL_Ozero__class_Ozero @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(1048,plain,
! [SV34: $i] :
( ( ! [SY1047: $i,SY1048: $i,SY1049: $i,SY1050: $i] :
( ( c_Type_Otyping @ SV34 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1047 @ SY1048 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1049 )
| ~ ( c_Type_Otypings @ SV34 @ SY1048 @ SY1050 )
| ~ ( c_Type_Otyping @ SV34 @ SY1047 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY1050 @ SY1049 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(1049,plain,
! [SV35: $i] :
( ( ! [SY1051: $i,SY1052: $i,SY1053: $i] :
( ~ ( class_Orderings_Opreorder @ SV35 )
| ( c_HOL_Oord__class_Oless @ SY1051 @ SY1052 @ SV35 )
| ~ ( c_HOL_Oord__class_Oless @ SY1053 @ SY1052 @ SV35 )
| ~ ( c_HOL_Oord__class_Oless @ SY1051 @ SY1053 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(1050,plain,
! [SV36: $i] :
( ( ! [SY1054: $i,SY1055: $i,SY1056: $i] :
( ~ ( class_Orderings_Oorder @ SV36 )
| ( c_HOL_Oord__class_Oless @ SY1054 @ SY1055 @ SV36 )
| ~ ( c_HOL_Oord__class_Oless @ SY1054 @ SY1056 @ SV36 )
| ~ ( c_HOL_Oord__class_Oless @ SY1056 @ SY1055 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(1051,plain,
! [SV37: $i] :
( ( ! [SY1057: $i,SY1058: $i,SY1059: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV37 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SY1057 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SY1058 ) @ SY1059 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SY1057 ) @ SY1058 ) ) @ SY1059 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(1052,plain,
! [SV38: $i] :
( ( ! [SY1060: $i,SY1061: $i,SY1062: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV38 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SY1060 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SY1061 ) @ SY1062 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SY1061 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SY1060 ) @ SY1062 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(1053,plain,
! [SV39: $i] :
( ( ! [SY1063: $i,SY1064: $i,SY1065: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV39 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ SY1063 ) @ SY1064 ) ) @ SY1065 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ SY1063 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ SY1064 ) @ SY1065 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(1054,plain,
! [SV40: $i] :
( ( ! [SY1066: $i,SY1067: $i,SY1068: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV40 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ SY1066 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ SY1067 ) @ SY1068 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ SY1067 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ SY1066 ) @ SY1068 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(1055,plain,
! [SV41: $i] :
( ( ! [SY1069: $i,SY1070: $i,SY1071: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV41 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SY1069 ) @ SY1070 ) ) @ SY1071 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SY1069 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SY1070 ) @ SY1071 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(1056,plain,
! [SV42: $i] :
( ( ! [SY1072: $i,SY1073: $i,SY1074: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV42 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SY1072 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SY1073 ) @ SY1074 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SY1072 ) @ SY1073 ) ) @ SY1074 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(1057,plain,
! [SV43: $i] :
( ( ! [SY1075: $i,SY1076: $i,SY1077: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV43 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ SY1075 ) @ SY1076 ) ) @ SY1077 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ SY1075 ) @ SY1077 ) ) @ SY1076 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(1058,plain,
! [SV44: $i] :
( ( ! [SY1078: $i,SY1079: $i,SY1080: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV44 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SY1078 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SY1079 ) @ SY1080 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SY1079 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SY1078 ) @ SY1080 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(1059,plain,
! [SV45: $i] :
( ( ! [SY1081: $i,SY1082: $i,SY1083: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV45 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV45 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV45 ) @ SY1081 ) @ SY1082 ) ) @ SY1083 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV45 ) @ SY1081 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV45 ) @ SY1082 ) @ SY1083 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(1060,plain,
! [SV46: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV46 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(1061,plain,
! [SV47: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV47 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(1062,plain,
! [SV48: $i] :
( ( ! [SY1084: $i,SY1085: $i,SY1086: $i,SY1087: $i,SY1088: $i] :
( ( hAPP @ ( c_COMBC @ SV48 @ SY1084 @ SY1085 @ SY1086 @ SY1087 ) @ SY1088 )
= ( hAPP @ ( hAPP @ SV48 @ SY1088 ) @ SY1084 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(1063,plain,
! [SV49: $i] :
( ( ! [SY1089: $i,SY1090: $i,SY1091: $i] :
( ( c_List_Ofoldr @ SV49 @ ( c_List_Olist_ONil @ SY1089 ) @ SY1090 @ SY1089 @ SY1091 )
= SY1090 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(1064,plain,
! [SV50: $i] :
( ( ! [SY1092: $i,SY1093: $i] :
( ( c_List_Omap @ SV50 @ ( c_List_Olist_ONil @ SY1092 ) @ SY1092 @ SY1093 )
= ( c_List_Olist_ONil @ SY1093 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(1065,plain,
! [SV51: $i] :
( ( ! [SY1094: $i,SY1095: $i,SY1096: $i,SY1097: $i,SY1098: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV51 @ SY1094 ) @ SY1095 ) )
| ( c_ListOrder_Ostep1 @ SV51 @ SY1096 @ SY1097 @ SY1098 )
| ~ ( c_ListOrder_Ostep1 @ SV51 @ ( c_List_Oappend @ SY1096 @ ( c_List_Olist_OCons @ SY1094 @ ( c_List_Olist_ONil @ SY1098 ) @ SY1098 ) @ SY1098 ) @ ( c_List_Oappend @ SY1097 @ ( c_List_Olist_OCons @ SY1095 @ ( c_List_Olist_ONil @ SY1098 ) @ SY1098 ) @ SY1098 ) @ SY1098 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(1066,plain,
! [SV52: $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 @ SV52 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV52 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV52 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( SV52
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV52 ) ) )
| ( SV52
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV52 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV52 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(1067,plain,
! [SV53: $i] :
( ( ! [SY1099: $i,SY1100: $i,SY1101: $i,SY1102: $i,SY1103: $i] :
( ( c_Type_Otypings @ SV53 @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SY1099 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SY1100 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SY1101 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1102 )
| ~ ( c_Type_Otypings @ ( c_Type_Oshift @ SV53 @ SY1100 @ SY1103 @ tc_Type_Otype ) @ SY1101 @ SY1102 )
| ~ ( c_Type_Otyping @ SV53 @ SY1099 @ SY1103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(1068,plain,
! [SV54: $i] :
( ( ! [SY1104: $i,SY1105: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV54 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SY1104 ) @ SY1105 ) @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV54 )
| ~ ( c_HOL_Oord__class_Oless @ SY1105 @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV54 )
| ~ ( c_HOL_Oord__class_Oless @ SY1104 @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(1069,plain,
! [SV55: $i] :
( ( ! [SY1106: $i,SY1107: $i,SY1108: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV55 @ SY1106 @ SY1107 ) @ SY1108 @ SY1107 )
= ( c_List_Olist_OCons @ SV55 @ ( c_List_Oappend @ SY1106 @ SY1108 @ SY1107 ) @ SY1107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(1070,plain,
! [SV56: $i] :
( ( ! [SY1109: $i,SY1110: $i,SY1111: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV56 @ SY1109 @ SY1110 ) @ SY1111 @ SY1110 )
= ( c_List_Olist_OCons @ SV56 @ ( c_List_Oappend @ SY1109 @ SY1111 @ SY1110 ) @ SY1110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(1071,plain,
! [SV57: $i] :
( ( ! [SY1112: $i,SY1113: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV57 ) @ SY1112 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV57 ) @ SY1113 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1112 ) @ SY1113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(1072,plain,
! [SV58: $i] :
( ( ! [SY1114: $i,SY1115: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV58 ) @ SY1114 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1115 ) @ SY1114 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV58 ) @ SY1115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(1073,plain,
! [SV59: $i] :
( ( ! [SY1116: $i,SY1117: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV59 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SY1116 @ SY1117 @ SV59 @ SV59 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SY1116 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SY1117 @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 @ SV59 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(1074,plain,
! [SV60: $i] :
( ( ! [SY1118: $i,SY1119: $i,SY1120: $i,SY1121: $i] :
( ( c_List_Omap @ SV60 @ ( c_List_Olist_OCons @ SY1118 @ SY1119 @ SY1120 ) @ SY1120 @ SY1121 )
= ( c_List_Olist_OCons @ ( hAPP @ SV60 @ SY1118 ) @ ( c_List_Omap @ SV60 @ SY1119 @ SY1120 @ SY1121 ) @ SY1121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(1075,plain,
! [SV61: $i] :
( ( ! [SY1122: $i,SY1123: $i,SY1124: $i,SY1125: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ SV61 @ SY1122 ) @ ( c_List_Omap @ SV61 @ SY1123 @ SY1124 @ SY1125 ) @ SY1125 )
= ( c_List_Omap @ SV61 @ ( c_List_Olist_OCons @ SY1122 @ SY1123 @ SY1124 ) @ SY1124 @ SY1125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(1076,plain,
! [SV62: $i] :
( ( ! [SY1126: $i,SY1127: $i,SY1128: $i,SY1129: $i] :
( ( c_List_Omap @ SV62 @ ( c_List_Olist_OCons @ SY1126 @ SY1127 @ SY1128 ) @ SY1128 @ SY1129 )
= ( c_List_Olist_OCons @ ( hAPP @ SV62 @ SY1126 ) @ ( c_List_Omap @ SV62 @ SY1127 @ SY1128 @ SY1129 ) @ SY1129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(1077,plain,
! [SV63: $i] :
( ( ( SV63
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV63 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV63 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV63 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV63
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV63 ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV63 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(1078,plain,
! [SV64: $i] :
( ( ! [SY1130: $i,SY1131: $i,SY1132: $i] :
( ( c_List_Olist_OCons @ SV64 @ ( c_List_Oappend @ SY1130 @ SY1131 @ SY1132 ) @ SY1132 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV64 @ SY1130 @ SY1132 ) @ SY1131 @ SY1132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(1079,plain,
! [SV65: $i] :
( ( ! [SY1133: $i,SY1134: $i,SY1135: $i] :
( ( c_List_Olist_OCons @ SV65 @ ( c_List_Oappend @ SY1133 @ SY1134 @ SY1135 ) @ SY1135 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV65 @ SY1133 @ SY1135 ) @ SY1134 @ SY1135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(1080,plain,
! [SV66: $i] :
( ( ! [SY1136: $i,SY1137: $i,SY1138: $i,SY1139: $i,SY1140: $i] :
( ( SV66 = SY1136 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1137 @ SY1136 ) @ SV66 ) )
| ~ ( c_ListOrder_Ostep1 @ SY1137 @ ( c_List_Olist_OCons @ SY1136 @ SY1138 @ SY1139 ) @ ( c_List_Olist_OCons @ SV66 @ SY1140 @ SY1139 ) @ SY1139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(1081,plain,
! [SV67: $i] :
( ( ! [SY1141: $i,SY1142: $i,SY1143: $i,SY1144: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV67 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ SY1141 ) @ SY1142 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ SY1143 ) @ SY1144 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ SY1141 ) @ SY1143 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ SY1142 ) @ SY1144 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(1082,plain,
! [SV68: $i] :
( ( ! [SY1145: $i,SY1146: $i,SY1147: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV68 ) @ SY1145 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1146 ) @ SY1147 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1145 ) @ SY1147 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV68 ) @ SY1146 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(1083,plain,
! [SV69: $i] :
( ( ! [SY1148: $i,SY1149: $i] :
( ( ( c_Lambda_Oliftn @ SV69 @ ( c_Lambda_OdB_OVar @ SY1148 ) @ SY1149 )
= ( c_Lambda_OdB_OVar @ SY1148 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1148 @ SY1149 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(1084,plain,
! [SV70: $i] :
( ( ! [SY1150: $i,SY1151: $i,SY1152: $i] :
( ( c_Type_Otyping @ SV70 @ SY1150 @ SY1151 )
| ~ ( c_Type_Otyping @ SV70 @ SY1152 @ SY1151 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1152 ) @ SY1150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(1085,plain,
! [SV71: $i] :
( ( ! [SY1153: $i,SY1154: $i,SY1155: $i,SY1156: $i] :
( ( c_Type_Otypings @ ( c_Type_Oshift @ SV71 @ SY1153 @ SY1154 @ tc_Type_Otype ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ SY1153 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SY1155 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1156 )
| ~ ( c_Type_Otypings @ SV71 @ SY1155 @ SY1156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(1086,plain,
! [SV72: $i] :
( ( ! [SY1157: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV72 ) ) @ SY1157 )
= ( c_Lambda_OdB_OVar @ SV72 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV72 @ SY1157 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(1087,plain,
! [SV73: $i] :
( ( ! [SY1158: $i,SY1159: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV73 ) @ SY1158 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY1159 ) @ SY1158 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV73 ) @ SY1159 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(1088,plain,
! [SV74: $i] :
( ( ( SV74
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV74 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV74 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV74 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV74 ) ) )
| ( SV74
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV74 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV74 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(1089,plain,
! [SV75: $i] :
( ( ! [SY1160: $i] :
( ( c_HOL_Oord__class_Oless @ SV75 @ SV75 @ tc_nat )
| ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV75 ) @ SY1160 @ SV75 )
= ( c_Lambda_Oliftn @ SV75 @ SY1160 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(1090,plain,
! [SV76: $i] :
( ( ! [SY1161: $i,SY1162: $i] :
( ( c_List_Olist_OCons @ SV76 @ SY1161 @ SY1162 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY1162 ) @ ( c_List_Olist_OCons @ SV76 @ SY1161 @ SY1162 ) @ SY1162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(1091,plain,
! [SV77: $i] :
( ( ! [SY1163: $i,SY1164: $i,SY1165: $i,SY1166: $i,SY1167: $i] :
( ~ ( c_Type_Otyping @ SV77 @ SY1163 @ SY1164 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV77 @ SY1165 @ SY1164 @ tc_Type_Otype ) @ SY1166 @ SY1167 )
| ( c_Type_Otyping @ SV77 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY1166 ) @ SY1163 ) @ SY1165 ) @ SY1167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(1092,plain,
! [SV78: $i] :
( ( ! [SY1168: $i,SY1169: $i] :
( ( c_List_Olist_ONil @ SV78 )
= ( c_List_Omap @ SY1168 @ ( c_List_Olist_ONil @ SY1169 ) @ SY1169 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(1093,plain,
! [SV79: $i] :
( ( ! [SY1170: $i,SY1171: $i,SY1172: $i,SY1173: $i,SY1174: $i] :
( ( SV79 = SY1170 )
| ( c_ListOrder_Ostep1 @ SY1171 @ SV79 @ SY1170 @ SY1172 )
| ~ ( c_ListOrder_Ostep1 @ SY1171 @ ( c_List_Oappend @ SV79 @ ( c_List_Olist_OCons @ SY1173 @ ( c_List_Olist_ONil @ SY1172 ) @ SY1172 ) @ SY1172 ) @ ( c_List_Oappend @ SY1170 @ ( c_List_Olist_OCons @ SY1174 @ ( c_List_Olist_ONil @ SY1172 ) @ SY1172 ) @ SY1172 ) @ SY1172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(1094,plain,
! [SV80: $i] :
( ( ( c_List_Olist_ONil @ SV80 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV80 ) @ ( c_List_Olist_ONil @ SV80 ) @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(1095,plain,
! [SV81: $i] :
( ( ! [SY1175: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ SV81 @ SY1175 ) @ SY1175 )
= ( c_Transitive__Closure_Ortranclp @ SV81 @ SY1175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(1096,plain,
! [SV82: $i] :
( ( ! [SY1176: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV82 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV82 ) @ ( c_HOL_Ozero__class_Ozero @ SV82 ) ) @ SY1176 )
= SY1176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(1097,plain,
! [SV83: $i] :
( ( ! [SY1177: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV83 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV83 ) @ ( c_HOL_Ozero__class_Ozero @ SV83 ) ) @ SY1177 )
= SY1177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(1098,plain,
! [SV84: $i] :
( ( ! [SY1178: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV84 )
| ~ ( class_Int_Onumber__ring @ SV84 )
| ( SY1178
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SY1178 ) @ ( c_HOL_Ozero__class_Ozero @ SV84 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(1099,plain,
! [SV85: $i] :
( ( ! [SY1179: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV85 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV85 ) @ SY1179 ) @ ( c_HOL_Ozero__class_Ozero @ SV85 ) )
= SY1179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(1100,plain,
! [SV86: $i] :
( ( ! [SY1180: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV86 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV86 ) @ ( c_HOL_Ozero__class_Ozero @ SV86 ) ) @ SY1180 )
= SY1180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(1101,plain,
! [SV87: $i] :
( ( ! [SY1181: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV87 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV87 ) @ SY1181 ) @ ( c_HOL_Ozero__class_Ozero @ SV87 ) )
= SY1181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(1102,plain,
! [SV88: $i] :
( ( ! [SY1182: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV88 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV88 ) @ SY1182 ) @ ( c_HOL_Ozero__class_Ozero @ SV88 ) )
= SY1182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(1103,plain,
! [SV89: $i] :
( ( ! [SY1183: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV89 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ ( c_HOL_Ozero__class_Ozero @ SV89 ) ) @ SY1183 )
= SY1183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(1104,plain,
! [SV90: $i] :
( ( ! [SY1184: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV90 ) ) @ ( c_Lambda_OdB_OAbs @ SY1184 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV90 ) @ SY1184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(1105,plain,
! [SV91: $i] :
( ( ! [SY1185: $i,SY1186: $i,SY1187: $i] :
( ( ( hAPP @ ( hAPP @ SV91 @ SY1185 ) @ SY1186 )
= SY1185 )
| ~ ( c_OrderedGroup_Omonoid__add @ SY1186 @ SV91 @ SY1187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(1106,plain,
! [SV92: $i] :
( ( ! [SY1188: $i,SY1189: $i,SY1190: $i] :
( ( ( hAPP @ ( hAPP @ SV92 @ SY1188 ) @ SY1189 )
= SY1189 )
| ~ ( c_OrderedGroup_Omonoid__add @ SY1188 @ SV92 @ SY1190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(1107,plain,
! [SV93: $i] :
( ( ! [SY1191: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV93 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SY1191 @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SY1191 ) @ SY1191 ) @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(1108,plain,
! [SV94: $i] :
( ( ! [SY1192: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV94 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SY1192 ) @ SY1192 ) @ SV94 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SY1192 @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(1109,plain,
! [SV95: $i] :
( ( ! [SY1193: $i,SY1194: $i,SY1195: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV95 ) @ SY1193 ) @ SY1194 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY1195 ) @ SY1193 ) @ SY1194 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV95 ) @ SY1195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(1110,plain,
! [SV96: $i] :
( ( ! [SY1196: $i,SY1197: $i,SY1198: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV96 ) @ SY1196 ) @ SY1197 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV96 ) @ SY1198 ) @ SY1197 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1196 ) @ SY1198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(1111,plain,
! [SV97: $i] :
( ( ! [SY1199: $i,SY1200: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV97 )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SY1199 @ SY1200 @ SV97 @ SV97 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SY1200 @ SY1199 @ SV97 @ SV97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(1112,plain,
! [SV98: $i] :
( ( ! [SY1201: $i,SY1202: $i,SY1203: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV98 @ SY1201 ) @ SY1202 ) @ SY1203 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV98 @ SY1202 ) @ SY1203 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(1113,plain,
! [SV99: $i] :
( ( ! [SY1204: $i,SY1205: $i] :
~ ( c_ListOrder_Ostep1 @ SV99 @ ( c_List_Olist_ONil @ SY1204 ) @ SY1205 @ SY1204 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(1114,plain,
! [SV100: $i] :
( ( ! [SY1206: $i,SY1207: $i] :
~ ( c_ListOrder_Ostep1 @ SV100 @ SY1206 @ ( c_List_Olist_ONil @ SY1207 ) @ SY1207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(1115,plain,
! [SV101: $i] :
( ( ! [SY1208: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV101 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ SY1208 ) @ SY1208 ) @ ( c_HOL_Ozero__class_Ozero @ SV101 ) @ SV101 )
| ~ ( c_HOL_Oord__class_Oless @ SY1208 @ ( c_HOL_Ozero__class_Ozero @ SV101 ) @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(1116,plain,
! [SV102: $i] :
( ( ! [SY1209: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV102 )
| ( c_HOL_Oord__class_Oless @ SY1209 @ ( c_HOL_Ozero__class_Ozero @ SV102 ) @ SV102 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SY1209 ) @ SY1209 ) @ ( c_HOL_Ozero__class_Ozero @ SV102 ) @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(1117,plain,
! [SV103: $i] :
( ( ! [SY1210: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV103 )
| ( c_HOL_Oord__class_Oless @ SY1210 @ ( c_HOL_Ozero__class_Ozero @ SV103 ) @ SV103 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV103 ) @ SY1210 ) @ SY1210 ) @ ( c_HOL_Ozero__class_Ozero @ SV103 ) @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(1118,plain,
! [SV104: $i] :
( ( ! [SY1211: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV104 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV104 ) @ SY1211 ) @ SY1211 ) @ ( c_HOL_Ozero__class_Ozero @ SV104 ) @ SV104 )
| ~ ( c_HOL_Oord__class_Oless @ SY1211 @ ( c_HOL_Ozero__class_Ozero @ SV104 ) @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(1119,plain,
! [SV105: $i] :
( ( ! [SY1212: $i,SY1213: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV105 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SY1212 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ ( c_HOL_Ozero__class_Ozero @ SV105 ) @ SY1213 @ SV105 @ SV105 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SY1212 @ SY1213 @ SV105 @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(1120,plain,
! [SV106: $i] :
( ( ! [SY1214: $i,SY1215: $i,SY1216: $i] :
( ( c_Type_Otyping @ SV106 @ ( c_Lambda_OdB_OAbs @ SY1214 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1215 ) @ SY1216 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV106 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1215 @ tc_Type_Otype ) @ SY1214 @ SY1216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(1121,plain,
! [SV107: $i] :
( ( ! [SY1217: $i,SY1218: $i,SY1219: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV107 @ SY1217 @ SY1218 @ SY1219 ) @ SY1217 )
= SY1218 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(1122,plain,
! [SV108: $i] :
( ( ! [SY1220: $i,SY1221: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV108 ) @ SY1220 @ SY1221 )
= ( c_Lambda_OdB_OVar @ SV108 ) )
| ( SV108 = SY1221 )
| ( c_HOL_Oord__class_Oless @ SY1221 @ SV108 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(1123,plain,
! [SV109: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV109 ) ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV109 ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV109 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(1124,plain,
! [SV110: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV110 @ SV110 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(1125,plain,
! [SV111: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV111 @ SV111 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(1126,plain,
! [SV112: $i] :
( ( ! [SY1222: $i] :
( ~ ( class_Orderings_Oorder @ SV112 )
| ~ ( c_HOL_Oord__class_Oless @ SY1222 @ SY1222 @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(1127,plain,
! [SV113: $i] :
( ( ! [SY1223: $i] :
( ~ ( class_Orderings_Olinorder @ SV113 )
| ~ ( c_HOL_Oord__class_Oless @ SY1223 @ SY1223 @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(1128,plain,
! [SV114: $i] :
( ( ! [SY1224: $i] :
( ~ ( class_Orderings_Opreorder @ SV114 )
| ~ ( c_HOL_Oord__class_Oless @ SY1224 @ SY1224 @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(1129,plain,
! [SV115: $i] :
( ( ! [SY1225: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV115 ) ) @ SY1225 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV115 ) @ SY1225 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(1130,plain,
! [SV116: $i] :
( ( ! [SY1226: $i,SY1227: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV116 ) @ SY1226 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY1227 ) @ SY1226 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV116 ) @ SY1227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(1131,plain,
! [SV117: $i] :
( ( ! [SY1228: $i,SY1229: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV117 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SY1228 ) @ SY1229 ) @ SV117 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SY1229 @ SV117 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SY1228 @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(1132,plain,
! [SV118: $i] :
( ( ! [SY1230: $i,SY1231: $i,SY1232: $i,SY1233: $i,SY1234: $i] :
( ( c_ListOrder_Ostep1 @ SV118 @ SY1230 @ SY1231 @ SY1232 )
| ( SY1231 = SY1230 )
| ~ ( c_ListOrder_Ostep1 @ SV118 @ ( c_List_Olist_OCons @ SY1233 @ SY1230 @ SY1232 ) @ ( c_List_Olist_OCons @ SY1234 @ SY1231 @ SY1232 ) @ SY1232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(1133,plain,
! [SV119: $i] :
( ( ! [SY1235: $i,SY1236: $i,SY1237: $i,SY1238: $i] :
( ( ( hAPP @ ( hAPP @ SV119 @ ( hAPP @ ( hAPP @ SV119 @ SY1235 ) @ SY1236 ) ) @ SY1237 )
= ( hAPP @ ( hAPP @ SV119 @ SY1235 ) @ ( hAPP @ ( hAPP @ SV119 @ SY1236 ) @ SY1237 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV119 @ SY1238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(1134,plain,
! [SV120: $i] :
( ( ! [SY1239: $i,SY1240: $i,SY1241: $i,SY1242: $i] :
( ( c_List_Omap @ SV120 @ ( c_List_Oappend @ SY1239 @ SY1240 @ SY1241 ) @ SY1241 @ SY1242 )
= ( c_List_Oappend @ ( c_List_Omap @ SV120 @ SY1239 @ SY1241 @ SY1242 ) @ ( c_List_Omap @ SV120 @ SY1240 @ SY1241 @ SY1242 ) @ SY1242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(1135,plain,
! [SV121: $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 @ SV121 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV121 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV121 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( SV121
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV121 ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV121 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(1136,plain,
! [SV122: $i] :
( ( ! [SY1243: $i,SY1244: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV122 )
| ( c_HOL_Oord__class_Oless @ SY1243 @ SY1244 @ SV122 )
| ( c_HOL_Oord__class_Oless @ SY1244 @ SY1243 @ SV122 )
| ( SY1244 = SY1243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(1137,plain,
! [SV123: $i] :
( ( ! [SY1245: $i,SY1246: $i] :
( ~ ( class_Orderings_Olinorder @ SV123 )
| ( SY1245 = SY1246 )
| ( c_HOL_Oord__class_Oless @ SY1246 @ SY1245 @ SV123 )
| ( c_HOL_Oord__class_Oless @ SY1245 @ SY1246 @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(1138,plain,
! [SV124: $i] :
( ( ! [SY1247: $i] :
( ( c_HOL_Oord__class_Oless @ SV124 @ SY1247 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY1247 @ SV124 @ tc_nat )
| ( SY1247 = SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(1139,plain,
! [SV125: $i] :
( ( ! [SY1248: $i,SY1249: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV125 @ SY1248 ) @ SY1249 ) )
| ( c_HOL_Oord__class_Oless @ SY1248 @ SY1249 @ tc_nat )
| ( SY1249 = SY1248 )
| ( c_HOL_Oord__class_Oless @ SY1249 @ SY1248 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(1140,plain,
! [SV126: $i] :
( ( ! [SY1250: $i] :
( ( c_HOL_Oord__class_Oless @ SV126 @ SY1250 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY1250 @ SV126 @ tc_nat )
| ( SY1250 = SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(1141,plain,
! [SV127: $i] :
( ( ! [SY1251: $i,SY1252: $i] :
( ~ ( class_Orderings_Olinorder @ SV127 )
| ( c_HOL_Oord__class_Oless @ SY1251 @ SY1252 @ SV127 )
| ( c_HOL_Oord__class_Oless @ SY1252 @ SY1251 @ SV127 )
| ( SY1252 = SY1251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(1142,plain,
! [SV128: $i] :
( ( ! [SY1253: $i,SY1254: $i] :
( ~ ( class_Orderings_Olinorder @ SV128 )
| ( c_HOL_Oord__class_Oless @ SY1253 @ SY1254 @ SV128 )
| ( SY1254 = SY1253 )
| ( c_HOL_Oord__class_Oless @ SY1254 @ SY1253 @ SV128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(1143,plain,
! [SV129: $i] :
( ( ! [SY1255: $i,SY1256: $i] :
( ~ ( class_Orderings_Olinorder @ SV129 )
| ( SY1255 = SY1256 )
| ( c_HOL_Oord__class_Oless @ SY1255 @ SY1256 @ SV129 )
| ( c_HOL_Oord__class_Oless @ SY1256 @ SY1255 @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(1144,plain,
! [SV130: $i] :
( ( ! [SY1257: $i,SY1258: $i,SY1259: $i,SY1260: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV130 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SY1257 ) @ SY1258 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SY1259 ) @ SY1260 ) @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SY1258 @ SY1260 @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SY1257 @ SY1259 @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(1145,plain,
! [SV131: $i] :
( ( ! [SY1261: $i,SY1262: $i,SY1263: $i,SY1264: $i] :
( ( c_Type_Otyping @ SV131 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1261 ) @ SY1262 ) @ SY1263 )
| ~ ( c_Type_Otyping @ SV131 @ SY1262 @ SY1264 )
| ~ ( c_Type_Otyping @ SV131 @ SY1261 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1264 ) @ SY1263 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(1146,plain,
! [SV132: $i] :
( ( ! [SY1265: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV132 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV132 ) @ ( c_HOL_Ozero__class_Ozero @ SV132 ) @ SY1265 @ SV132 @ SV132 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV132 ) @ SY1265 @ ( c_HOL_Ozero__class_Ozero @ SV132 ) @ SV132 @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(1147,plain,
! [SV133: $i] :
( ( ( SV133
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV133 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV133 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV133 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV133
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV133 ) ) )
| ( SV133
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV133 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV133 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(1148,plain,
! [SV134: $i] :
( ( ! [SY1266: $i,SY1267: $i,SY1268: $i,SY1269: $i,SY1270: $i] :
( ( SV134 = SY1266 )
| ( SY1267 = SY1268 )
| ~ ( c_ListOrder_Ostep1 @ SY1269 @ ( c_List_Oappend @ SV134 @ ( c_List_Olist_OCons @ SY1267 @ ( c_List_Olist_ONil @ SY1270 ) @ SY1270 ) @ SY1270 ) @ ( c_List_Oappend @ SY1266 @ ( c_List_Olist_OCons @ SY1268 @ ( c_List_Olist_ONil @ SY1270 ) @ SY1270 ) @ SY1270 ) @ SY1270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(1149,plain,
! [SV135: $i] :
( ( ! [SY1271: $i,SY1272: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV135 @ SY1271 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1272 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV135 ) @ SY1272 ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ SY1272 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SY1271 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(1150,plain,
! [SV136: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV136 @ tc_nat )
| ( SV136
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(1151,plain,
! [SV137: $i] :
( ( ! [SY1273: $i,SY1274: $i,SY1275: $i] :
( ( c_List_Olistsp @ SV137 @ ( c_List_Oappend @ SY1273 @ SY1274 @ SY1275 ) @ SY1275 )
| ~ ( c_List_Olistsp @ SV137 @ SY1274 @ SY1275 )
| ~ ( c_List_Olistsp @ SV137 @ SY1273 @ SY1275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(1152,plain,
! [SV138: $i] :
( ( ! [SY1276: $i,SY1277: $i,SY1278: $i,SY1279: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV138 @ SY1276 @ SY1277 @ ( c_Lambda_OdB_OAbs @ SY1278 ) @ SY1279 )
= ( hAPP @ ( hAPP @ SY1277 @ SY1278 ) @ ( c_Lambda_OdB_OdB__rec @ SV138 @ SY1276 @ SY1277 @ SY1278 @ SY1279 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(1153,plain,
! [SV139: $i] :
( ( ! [SY1280: $i] :
( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV139 @ SY1280 )
= SV139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(1154,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)],[802]) ).
thf(1155,plain,
! [SV140: $i] :
( ( ~ ( class_OrderedGroup_Osemigroup__add @ SV140 )
| ( c_OrderedGroup_Osemigroup__add @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ SV140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(1156,plain,
! [SV141: $i] :
( ( ! [SY1281: $i,SY1282: $i,SY1283: $i,SY1284: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV141 @ SY1281 @ SY1282 @ SY1283 ) @ SY1284 )
= ( hAPP @ SV141 @ SY1284 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1284 @ SY1281 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(1157,plain,
! [SV142: $i] :
( ( ! [SY1285: $i,SY1286: $i,SY1287: $i,SY1288: $i,SY1289: $i,SY1290: $i] :
( ( SV142
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SY1285 @ SV142 @ SY1286 @ SY1287 ) @ SY1285 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SY1286 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1288 ) @ SY1289 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV142 )
| ~ ( c_Type_Otypings @ SY1286 @ SY1289 @ SY1290 )
| ~ ( c_Type_Otyping @ SY1286 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1288 ) @ SY1289 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1287 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(1158,plain,
! [SV143: $i] :
( ( ! [SY1291: $i] :
( ( c_Lambda_Osubstn @ SV143 @ SY1291 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV143 ) @ SY1291 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(1159,plain,
! [SV144: $i] :
( ( ! [SY1292: $i,SY1293: $i,SY1294: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV144 )
| ( c_HOL_Oord__class_Oless @ SY1292 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ SY1293 ) @ SY1294 ) @ SV144 )
| ~ ( c_HOL_Oord__class_Oless @ SY1292 @ SY1294 @ SV144 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV144 ) @ SY1293 @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(1160,plain,
! [SV145: $i] :
( ( ! [SY1295: $i,SY1296: $i,SY1297: $i,SY1298: $i,SY1299: $i] :
( ( c_List_Ofoldr @ SV145 @ ( c_List_Olist_OCons @ SY1295 @ SY1296 @ SY1297 ) @ SY1298 @ SY1297 @ SY1299 )
= ( hAPP @ ( hAPP @ SV145 @ SY1295 ) @ ( c_List_Ofoldr @ SV145 @ SY1296 @ SY1298 @ SY1297 @ SY1299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(1161,plain,
! [SV146: $i] :
( ( ! [SY1300: $i,SY1301: $i,SY1302: $i,SY1303: $i] :
( ~ ( hBOOL @ ( hAPP @ SV146 @ ( c_Lambda_OdB_OdB__case @ SY1300 @ SY1301 @ SY1302 @ ( c_Lambda_OdB_OAbs @ SY1303 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV146 @ ( hAPP @ SY1302 @ SY1303 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(1162,plain,
! [SV147: $i] :
( ( ! [SY1304: $i,SY1305: $i,SY1306: $i,SY1307: $i] :
( ~ ( hBOOL @ ( hAPP @ SV147 @ ( c_Lambda_OdB_OdB__case @ SY1304 @ SY1305 @ SY1306 @ ( c_Lambda_OdB_OAbs @ SY1307 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV147 @ ( hAPP @ SY1306 @ SY1307 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(1163,plain,
! [SV148: $i] :
( ( ! [SY1308: $i,SY1309: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV148 ) @ ( c_List_Olist_OCons @ SY1308 @ SY1309 @ SV148 ) @ SV148 )
= ( c_List_Olist_OCons @ SY1308 @ SY1309 @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(1164,plain,
! [SV149: $i] :
( ( ! [SY1310: $i,SY1311: $i,SY1312: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV149 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SY1310 ) @ SY1311 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SY1312 ) @ SY1311 ) @ SV149 )
| ~ ( c_HOL_Oord__class_Oless @ SY1310 @ SY1312 @ SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(1165,plain,
! [SV150: $i] :
( ( ! [SY1313: $i,SY1314: $i,SY1315: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV150 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV150 ) @ SY1313 ) @ SY1314 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV150 ) @ SY1315 ) @ SY1314 ) @ SV150 )
| ~ ( c_HOL_Oord__class_Oless @ SY1313 @ SY1315 @ SV150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(1166,plain,
! [SV151: $i] :
( ( ! [SY1316: $i,SY1317: $i,SY1318: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV151 )
| ( c_HOL_Oord__class_Oless @ SY1316 @ SY1317 @ SV151 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SY1316 ) @ SY1318 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SY1317 ) @ SY1318 ) @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(1167,plain,
! [SV152: $i] :
( ( ! [SY1319: $i,SY1320: $i,SY1321: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV152 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SY1319 ) @ SY1320 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SY1319 ) @ SY1321 ) @ SV152 )
| ~ ( c_HOL_Oord__class_Oless @ SY1320 @ SY1321 @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(1168,plain,
! [SV153: $i] :
( ( ! [SY1322: $i,SY1323: $i,SY1324: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV153 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SY1322 ) @ SY1323 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SY1322 ) @ SY1324 ) @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SY1323 @ SY1324 @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(1169,plain,
! [SV154: $i] :
( ( ! [SY1325: $i,SY1326: $i,SY1327: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV154 )
| ( c_HOL_Oord__class_Oless @ SY1325 @ SY1326 @ SV154 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SY1327 ) @ SY1325 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SY1327 ) @ SY1326 ) @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(1170,plain,
! [SV155: $i] :
( ( ( SV155
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV155 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV155 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV155 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV155 ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV155 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(1171,plain,
! [SV156: $i] :
( ( ! [SY1328: $i,SY1329: $i,SY1330: $i] :
( ( c_Type_Otyping @ SV156 @ SY1328 @ SY1329 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1330 ) @ SY1328 ) )
| ~ ( c_Type_Otyping @ SV156 @ SY1330 @ SY1329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(1172,plain,
! [SV157: $i] :
( ( ! [SY1331: $i,SY1332: $i,SY1333: $i,SY1334: $i,SY1335: $i] :
( ( c_ListOrder_Ostep1 @ SV157 @ SY1331 @ SY1332 @ SY1333 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV157 @ SY1334 ) @ SY1335 ) )
| ~ ( c_ListOrder_Ostep1 @ SV157 @ ( c_List_Olist_OCons @ SY1334 @ SY1331 @ SY1333 ) @ ( c_List_Olist_OCons @ SY1335 @ SY1332 @ SY1333 ) @ SY1333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(1173,plain,
! [SV158: $i] :
( ( ! [SY1336: $i,SY1337: $i,SY1338: $i,SY1339: $i] :
( ( c_ListOrder_Ostep1 @ SV158 @ ( c_List_Olist_OCons @ SY1336 @ SY1337 @ SY1338 ) @ ( c_List_Olist_OCons @ SY1336 @ SY1339 @ SY1338 ) @ SY1338 )
| ~ ( c_ListOrder_Ostep1 @ SV158 @ SY1337 @ SY1339 @ SY1338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(1174,plain,
! [SV159: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV159 ) @ ( c_List_Olist_ONil @ SV159 ) @ SV159 )
= ( c_List_Olist_ONil @ SV159 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(1175,plain,
! [SV160: $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 ) @ SV160 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV160 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(1176,plain,
! [SV161: $i] :
( ( ! [SY1340: $i,SY1341: $i,SY1342: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV161 @ SY1340 @ SY1341 ) @ SY1342 @ SY1341 )
= ( c_List_Oappend @ SV161 @ ( c_List_Oappend @ SY1340 @ SY1342 @ SY1341 ) @ SY1341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(1177,plain,
! [SV162: $i] :
( ( ! [SY1343: $i,SY1344: $i,SY1345: $i] :
( ( c_List_Oappend @ SV162 @ ( c_List_Oappend @ SY1343 @ SY1344 @ SY1345 ) @ SY1345 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV162 @ SY1343 @ SY1345 ) @ SY1344 @ SY1345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(1178,plain,
! [SV163: $i] :
( ( ! [SY1346: $i,SY1347: $i,SY1348: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV163 @ SY1346 @ SY1347 ) @ SY1348 @ SY1347 )
= ( c_List_Oappend @ SV163 @ ( c_List_Oappend @ SY1346 @ SY1348 @ SY1347 ) @ SY1347 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(1179,plain,
! [SV164: $i] :
( ( ! [SY1349: $i,SY1350: $i,SY1351: $i] :
( ( c_List_Oappend @ SV164 @ ( c_List_Oappend @ SY1349 @ SY1350 @ SY1351 ) @ SY1351 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV164 @ SY1349 @ SY1351 ) @ SY1350 @ SY1351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(1180,plain,
! [SV165: $i] :
( ( ! [SY1352: $i,SY1353: $i,SY1354: $i,SY1355: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV165 @ SY1352 @ SY1353 @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY1354 ) @ SY1352 ) @ SY1355 )
| ~ ( c_Type_Otyping @ SV165 @ SY1354 @ SY1355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(1181,plain,
! [SV166: $i] :
( ( ! [SY1356: $i,SY1357: $i] :
( ~ ( class_Orderings_Oorder @ SV166 )
| ~ ( c_HOL_Oord__class_Oless @ SY1356 @ SY1357 @ SV166 )
| ~ ( c_HOL_Oord__class_Oless @ SY1357 @ SY1356 @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(1182,plain,
! [SV167: $i] :
( ( ! [SY1358: $i,SY1359: $i,SY1360: $i,SY1361: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV167 @ SY1358 ) @ SY1359 ) @ SY1360 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV167 @ SY1358 ) @ SY1361 ) @ SY1360 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV167 @ SY1359 ) @ SY1361 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(1183,plain,
! [SV168: $i] :
( ( ! [SY1362: $i,SY1363: $i,SY1364: $i,SY1365: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV168 @ SY1362 ) @ SY1363 ) @ SY1364 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV168 @ SY1365 ) @ SY1364 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV168 @ SY1362 ) @ SY1363 ) @ SY1365 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(1184,plain,
! [SV169: $i] :
( ( ! [SY1366: $i,SY1367: $i] :
( ~ ( class_Orderings_Olinorder @ SV169 )
| ~ ( c_HOL_Oord__class_Oless @ SY1366 @ SY1367 @ SV169 )
| ~ ( c_HOL_Oord__class_Oless @ SY1367 @ SY1366 @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(1185,plain,
! [SV170: $i] :
( ( ! [SY1368: $i,SY1369: $i] :
( ~ ( class_Orderings_Opreorder @ SV170 )
| ~ ( c_HOL_Oord__class_Oless @ SY1368 @ SY1369 @ SV170 )
| ~ ( c_HOL_Oord__class_Oless @ SY1369 @ SY1368 @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(1186,plain,
! [SV171: $i] :
( ( ! [SY1370: $i,SY1371: $i] :
( ~ ( class_Orderings_Opreorder @ SV171 )
| ~ ( c_HOL_Oord__class_Oless @ SY1370 @ SY1371 @ SV171 )
| ~ ( c_HOL_Oord__class_Oless @ SY1371 @ SY1370 @ SV171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(1187,plain,
! [SV172: $i] :
( ( ! [SY1372: $i] :
( ( hBOOL @ ( hAPP @ SV172 @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV172 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV172 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV172 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV172 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ SV172 @ SY1372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(1188,plain,
! [SV173: $i] :
( ( ! [SY1373: $i,SY1374: $i,SY1375: $i,SY1376: $i] :
( ( ( c_List_Ofoldl @ SV173 @ ( hAPP @ ( hAPP @ SV173 @ SY1373 ) @ SY1374 ) @ SY1375 @ SY1376 @ SY1376 )
= ( hAPP @ ( hAPP @ SV173 @ SY1373 ) @ ( c_List_Ofoldl @ SV173 @ SY1374 @ SY1375 @ SY1376 @ SY1376 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV173 @ SY1376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(1189,plain,
! [SV174: $i] :
( ( ! [SY1377: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV174 ) @ SY1377 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV174 ) @ SY1377 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(1190,plain,
! [SV175: $i] :
( ( ! [SY1378: $i,SY1379: $i,SY1380: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV175 ) @ SY1378 ) ) @ SY1379 ) @ SY1380 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV175 ) @ SY1379 ) @ SY1380 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY1378 ) @ SY1379 ) @ SY1380 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(1191,plain,
! [SV176: $i] :
( ( ! [SY1381: $i,SY1382: $i,SY1383: $i] :
( ( c_Type_Otypings @ SV176 @ SY1381 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SY1382 @ SV176 @ SY1383 @ SY1381 ) )
| ~ ( c_Type_Otyping @ SV176 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1383 ) @ SY1381 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(1192,plain,
! [SV177: $i] :
( ( ! [SY1384: $i,SY1385: $i,SY1386: $i,SY1387: $i] :
( ~ ( hBOOL @ ( hAPP @ SV177 @ ( c_Lambda_OdB_OdB__case @ SY1384 @ SY1385 @ SY1386 @ ( c_Lambda_OdB_OVar @ SY1387 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV177 @ ( hAPP @ SY1384 @ SY1387 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(1193,plain,
! [SV178: $i] :
( ( ! [SY1388: $i,SY1389: $i,SY1390: $i,SY1391: $i] :
( ~ ( hBOOL @ ( hAPP @ SV178 @ ( c_Lambda_OdB_OdB__case @ SY1388 @ SY1389 @ SY1390 @ ( c_Lambda_OdB_OVar @ SY1391 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV178 @ ( hAPP @ SY1388 @ SY1391 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(1194,plain,
! [SV179: $i] :
( ( ! [SY1392: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV179 ) ) @ SY1392 ) @ SV179 )
= SY1392 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(1195,plain,
! [SV180: $i] :
( ( ! [SY1393: $i,SY1394: $i,SY1395: $i,SY1396: $i,SY1397: $i] :
( ~ ( hBOOL @ ( hAPP @ SV180 @ ( c_Lambda_OdB_OdB__case @ SY1393 @ SY1394 @ SY1395 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1396 ) @ SY1397 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV180 @ ( hAPP @ ( hAPP @ SY1394 @ SY1396 ) @ SY1397 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1196,plain,
! [SV181: $i] :
( ( ! [SY1398: $i,SY1399: $i,SY1400: $i,SY1401: $i,SY1402: $i] :
( ~ ( hBOOL @ ( hAPP @ SV181 @ ( c_Lambda_OdB_OdB__case @ SY1398 @ SY1399 @ SY1400 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1401 ) @ SY1402 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV181 @ ( hAPP @ ( hAPP @ SY1399 @ SY1401 ) @ SY1402 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(1197,plain,
! [SV182: $i] :
( ( ! [SY1403: $i,SY1404: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV182 ) @ ( c_Lambda_OdB_OVar @ SY1403 ) ) @ SY1404 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[863]) ).
thf(1198,plain,
! [SV183: $i] :
( ( ! [SY1405: $i,SY1406: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV183 ) ) @ SY1405 ) @ SY1406 )
= ( c_Lambda_OdB_OVar @ SV183 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV183 @ SY1406 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(1199,plain,
! [SV184: $i] :
( ( ! [SY1407: $i,SY1408: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV184 @ SY1407 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1408 @ SY1407 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV184 ) @ SY1408 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(1200,plain,
! [SV185: $i] :
( ( ! [SY1409: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV185 ) ) @ SY1409 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(1201,plain,
! [SV186: $i] :
( ( ! [SY1410: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV186 ) @ SY1410 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SY1410 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(1202,plain,
! [SV187: $i] :
( ( ! [SY1411: $i,SY1412: $i,SY1413: $i,SY1414: $i] :
( ( SV187 = SY1411 )
| ~ ( c_Type_Otyping @ SY1412 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1413 ) @ SY1414 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1411 )
| ~ ( c_Type_Otyping @ SY1412 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1413 ) @ SY1414 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(1203,plain,
! [SV188: $i] :
( ( ! [SY1415: $i,SY1416: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV188 @ SY1415 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV188 @ SY1416 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SY1415 @ SY1416 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(1204,plain,
! [SV189: $i] :
( ( ! [SY1417: $i] :
( ( hBOOL @ ( hAPP @ SV189 @ SY1417 ) )
| ( hBOOL @ ( hAPP @ SV189 @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV189 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV189 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV189 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV189 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(1205,plain,
! [SV190: $i] :
( ( ! [SY1418: $i,SY1419: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV190 @ SY1418 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1419 @ SY1418 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV190 ) @ SY1419 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[877]) ).
thf(1206,plain,
! [SV191: $i] :
( ( ! [SY1420: $i,SY1421: $i,SY1422: $i,SY1423: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV191 @ SY1420 @ SY1421 @ ( c_Lambda_OdB_OVar @ SY1422 ) @ SY1423 )
= ( hAPP @ SV191 @ SY1422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(1207,plain,
! [SV192: $i] :
( ( ! [SY1424: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV192 ) @ SY1424 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV192 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(1208,plain,
! [SV193: $i] :
( ( ! [SY1425: $i,SY1426: $i,SY1427: $i] :
( ( c_List_Ofoldl @ SV193 @ SY1425 @ ( c_List_Olist_ONil @ SY1426 ) @ SY1427 @ SY1426 )
= SY1425 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(1209,plain,
! [SV194: $i] :
( ( ! [SY1428: $i,SY1429: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV194 ) ) @ SY1428 ) @ SY1429 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1428 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV194 ) @ SY1428 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1429 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(1210,plain,
! [SV195: $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 @ SV195 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV195 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV195 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV195 ) ) )
| ( SV195
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV195 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV195 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(1211,plain,
! [SV196: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(1212,plain,
! [SV197: $i] :
( ( ! [SY1430: $i,SY1431: $i] :
( ( ( hAPP @ SV197 @ SY1430 )
= SY1431 )
| ~ ( c_Type_Otyping @ SV197 @ ( c_Lambda_OdB_OVar @ SY1430 ) @ SY1431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(1213,plain,
! [SV198: $i] :
( ( ! [SY1432: $i,SY1433: $i,SY1434: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ SV198 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ SY1432 ) @ SY1433 ) @ SY1434 @ SV198 @ SV198 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ SY1432 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ SY1433 @ SY1434 @ SV198 @ SV198 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(1214,plain,
! [SV199: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV199 ) ) )
| ( SV199
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV199 ) ) )
| ( SV199
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV199 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV199 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(1215,plain,
! [SV200: $i] :
( ( ! [SY1435: $i,SY1436: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV200 ) @ SY1435 ) ) @ SY1436 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV200 ) @ SY1436 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY1435 ) @ SY1436 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(1216,plain,
! [SV201: $i] :
( ( ! [SY1437: $i,SY1438: $i,SY1439: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV201 @ SY1437 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1438 ) @ SY1439 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV201 ) @ SY1438 ) @ SY1439 ) @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SY1438 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SY1439 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SY1437 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1217,plain,
! [SV202: $i] :
( ( ! [SY1440: $i,SY1441: $i,SY1442: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV202 ) @ SY1440 ) @ SY1441 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY1442 ) @ SY1440 ) @ SY1441 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV202 ) @ SY1442 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1218,plain,
! [SV203: $i] :
( ( ! [SY1443: $i,SY1444: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV203 ) ) @ SY1443 ) @ SY1444 )
= ( c_Lambda_OdB_OVar @ SV203 ) )
| ( SV203 = SY1444 )
| ( c_HOL_Oord__class_Oless @ SY1444 @ SV203 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1219,plain,
! [SV204: $i] :
( ( ! [SY1445: $i,SY1446: $i,SY1447: $i] :
( ( c_Type_Otyping @ SV204 @ ( c_Lambda_OdB_OVar @ SY1445 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SY1446 @ SV204 @ SY1445 @ SY1447 ) @ SY1446 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV204 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1445 ) @ SY1447 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(1220,plain,
! [SV205: $i] :
( ( ! [SY1448: $i,SY1449: $i] :
( ( SV205
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1448 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SY1448 @ SY1449 @ SV205 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1448 ) @ SY1449 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV205 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(1221,plain,
! [SV206: $i] :
( ( ! [SY1450: $i,SY1451: $i,SY1452: $i,SY1453: $i,SY1454: $i] :
( ( c_Lambda_OdB_OdB__case @ SV206 @ SY1450 @ SY1451 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1452 ) @ SY1453 ) @ SY1454 )
= ( hAPP @ ( hAPP @ SY1450 @ SY1452 ) @ SY1453 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(1222,plain,
! [SV207: $i] :
( ( ! [SY1455: $i,SY1456: $i,SY1457: $i,SY1458: $i] :
( ( ( hAPP @ ( hAPP @ SV207 @ SY1455 ) @ ( c_List_Ofoldl @ SV207 @ SY1456 @ SY1457 @ SY1458 @ SY1458 ) )
= ( c_List_Ofoldl @ SV207 @ SY1455 @ SY1457 @ SY1458 @ SY1458 ) )
| ~ ( c_OrderedGroup_Omonoid__add @ SY1456 @ SV207 @ SY1458 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(1223,plain,
! [SV208: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV208 ) ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV208 ) ) )
| ( SV208
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV208 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV208 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(1224,plain,
! [SV209: $i] :
( ( ( c_Lambda_OdB_OVar @ SV209 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV209 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(1225,plain,
! [SV210: $i] :
( ( ! [SY1459: $i,SY1460: $i,SY1461: $i,SY1462: $i] :
( ( c_Lambda_OdB_OdB__case @ SV210 @ SY1459 @ SY1460 @ ( c_Lambda_OdB_OVar @ SY1461 ) @ SY1462 )
= ( hAPP @ SV210 @ SY1461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(1226,plain,
! [SV211: $i] :
( ( ! [SY1463: $i] :
( ( c_HOL_Oord__class_Oless @ SV211 @ SV211 @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV211 ) ) @ SY1463 ) @ SV211 )
= SY1463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(1227,plain,
! [SV212: $i] :
( ( ! [SY1464: $i,SY1465: $i,SY1466: $i,SY1467: $i,SY1468: $i] :
( ( c_List_Ofoldl @ SV212 @ SY1464 @ ( c_List_Olist_OCons @ SY1465 @ SY1466 @ SY1467 ) @ SY1468 @ SY1467 )
= ( c_List_Ofoldl @ SV212 @ ( hAPP @ ( hAPP @ SV212 @ SY1464 ) @ SY1465 ) @ SY1466 @ SY1468 @ SY1467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(1228,plain,
! [SV213: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV213 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV213 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1229,plain,
! [SV214: $i] :
( ( ! [SY1469: $i] : ( c_Type_Otyping @ SV214 @ ( c_Lambda_OdB_OVar @ SY1469 ) @ ( hAPP @ SV214 @ SY1469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1230,plain,
! [SV215: $i] :
( ( ! [SY1470: $i,SY1471: $i,SY1472: $i,SY1473: $i,SY1474: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV215 @ SY1470 @ SY1471 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1472 ) @ SY1473 ) @ SY1474 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SY1470 @ SY1472 ) @ SY1473 ) @ ( c_Lambda_OdB_OdB__rec @ SV215 @ SY1470 @ SY1471 @ SY1472 @ SY1474 ) ) @ ( c_Lambda_OdB_OdB__rec @ SV215 @ SY1470 @ SY1471 @ SY1473 @ SY1474 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(1231,plain,
! [SV216: $i] :
( ( SV216
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2 @ SV216 ) @ ( c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1 @ SV216 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1232,plain,
! [SV217: $i] :
( ( ! [SY1475: $i,SY1476: $i,SY1477: $i,SY1478: $i,SY1479: $i,SY1480: $i] :
( ( c_Type_Otypings @ SV217 @ SY1475 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SY1476 @ SY1477 @ SV217 @ SY1475 ) )
| ~ ( c_Type_Otyping @ SV217 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1478 ) @ SY1479 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1477 )
| ~ ( c_Type_Otypings @ SV217 @ SY1479 @ SY1480 )
| ~ ( c_Type_Otyping @ SV217 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1478 ) @ SY1479 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1475 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1233,plain,
! [SV218: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV218 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1234,plain,
! [SV219: $i] :
( ( ! [SY1481: $i,SY1482: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV219 ) @ SY1481 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV219 ) @ SY1482 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1481 ) @ SY1482 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1235,plain,
! [SV220: $i] :
( ( ! [SY1483: $i,SY1484: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV220 ) @ SY1483 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1484 ) @ SY1483 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV220 ) @ SY1484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1236,plain,
! [SV221: $i] :
( ( ! [SY1485: $i,SY1486: $i,SY1487: $i] :
( ( c_Lambda_Oliftn @ SV221 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1485 ) @ SY1486 ) @ SY1487 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ SV221 @ SY1485 @ SY1487 ) ) @ ( c_Lambda_Oliftn @ SV221 @ SY1486 @ SY1487 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1237,plain,
! [SV222: $i] :
( ( ! [SY1488: $i,SY1489: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV222 ) @ SY1488 ) ) @ SY1489 ) @ SY1488 )
= SV222 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1238,plain,
! [SV223: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV223 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV223 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1239,plain,
! [SV224: $i] :
( ( ! [SY1490: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV224 ) @ ( c_Lambda_OdB_OVar @ SY1490 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1240,plain,
! [SV225: $i] :
( ( ! [SY1491: $i,SY1492: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV225 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SY1491 @ SV225 @ SY1492 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1491 ) @ SV225 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1492 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1241,plain,
! [SV226: $i] :
( ( ! [SY1493: $i,SY1494: $i,SY1495: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV226 ) @ SY1493 ) @ SY1494 @ SY1495 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ SV226 @ SY1494 @ SY1495 ) ) @ ( c_Lambda_Osubstn @ SY1493 @ SY1494 @ SY1495 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(1242,plain,
! [SV227: $i] :
( ( ! [SY1496: $i,SY1497: $i,SY1498: $i,SY1499: $i,SY1500: $i] :
( ( c_List_Ofoldl @ SV227 @ SY1496 @ ( c_List_Oappend @ SY1497 @ SY1498 @ SY1499 ) @ SY1500 @ SY1499 )
= ( c_List_Ofoldl @ SV227 @ ( c_List_Ofoldl @ SV227 @ SY1496 @ SY1497 @ SY1500 @ SY1499 ) @ SY1498 @ SY1500 @ SY1499 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1243,plain,
! [SV228: $i] :
( ( ! [SY1501: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ SV228 @ SY1501 ) )
| ~ ( class_Orderings_Opreorder @ SY1501 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1244,plain,
! [SV229: $i] :
( ( ! [SY1502: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ SV229 @ SY1502 ) )
| ~ ( class_Orderings_Oorder @ SY1502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1245,plain,
! [SV230: $i] :
( ( ! [SY1503: $i] : ( c_fequal @ SV230 @ SV230 @ SY1503 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1246,plain,
! [SV231: $i] :
( ( ! [SY1504: $i,SY1505: $i] :
( ( SV231 = SY1504 )
| ~ ( c_fequal @ SV231 @ SY1504 @ SY1505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1247,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[956]) ).
thf(1248,plain,
! [SV232: $i] :
( ( ! [SY1506: $i,SY1507: $i] :
( ( c_List_Olist_OCons @ SV232 @ SY1506 @ SY1507 )
!= ( c_List_Olist_ONil @ SY1507 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1249,plain,
! [SV233: $i] :
( ( ! [SY1508: $i,SY1509: $i,SY1510: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV233 ) @ SY1508 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1509 ) @ SY1510 ) )
| ( SV233 = SY1509 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1250,plain,
! [SV234: $i] :
( ( ! [SY1511: $i,SY1512: $i,SY1513: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV234 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SY1511 ) @ SY1512 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SY1511 ) @ SY1513 ) )
| ( SY1512 = SY1513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1251,plain,
! [SV235: $i] :
( ( ! [SY1514: $i,SY1515: $i] :
( ( ( c_List_Oappend @ SV235 @ SY1514 @ SY1515 )
!= ( c_List_Olist_ONil @ SY1515 ) )
| ( SY1514
= ( c_List_Olist_ONil @ SY1515 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1252,plain,
! [SV236: $i] :
( ( ! [SY1516: $i,SY1517: $i,SY1518: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV236 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV236 ) @ SY1516 ) @ SY1517 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV236 ) @ SY1518 ) @ SY1517 ) )
| ( SY1516 = SY1518 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1253,plain,
! [SV237: $i] :
( ( ! [SY1519: $i,SY1520: $i,SY1521: $i] :
( ( ( c_List_Oappend @ SV237 @ SY1519 @ SY1520 )
!= ( c_List_Oappend @ SV237 @ SY1521 @ SY1520 ) )
| ( SY1519 = SY1521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1254,plain,
! [SV238: $i] :
( ( ! [SY1522: $i,SY1523: $i,SY1524: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV238 ) @ SY1522 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1523 ) @ SY1524 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV238 = SY1523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(1255,plain,
! [SV239: $i] :
( ( ! [SY1525: $i,SY1526: $i,SY1527: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV239 ) @ SY1525 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1526 ) @ SY1527 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1525 = SY1527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1256,plain,
! [SV240: $i] :
( ( ! [SY1528: $i,SY1529: $i,SY1530: $i,SY1531: $i] :
( ( ( c_List_Olist_OCons @ SV240 @ SY1528 @ SY1529 )
!= ( c_List_Olist_OCons @ SY1530 @ SY1531 @ SY1529 ) )
| ( SV240 = SY1530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1257,plain,
! [SV241: $i] :
( ( ! [SY1532: $i,SY1533: $i,SY1534: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV241 ) @ SY1532 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1533 ) @ SY1534 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV241 = SY1533 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1258,plain,
! [SV242: $i] :
( ( ! [SY1535: $i,SY1536: $i,SY1537: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV242 ) @ SY1535 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1536 @ SY1537 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV242
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1536 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV242 @ SY1535 @ SY1536 @ SY1537 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1537
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1259,plain,
! [SV243: $i] :
( ( ! [SY1538: $i,SY1539: $i,SY1540: $i,SY1541: $i,SY1542: $i,SY1543: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV243 ) @ SY1538 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY1539 ) @ SY1540 ) @ SY1541 ) ) )
| ~ ( c_Type_Otyping @ SY1542 @ SY1540 @ SV243 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1540 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY1542 @ SY1541 @ SV243 @ tc_Type_Otype ) @ SY1539 @ SY1543 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1539 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1260,plain,
! [SV244: $i] :
( ( ! [SY1544: $i,SY1545: $i,SY1546: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV244 )
| ~ ( class_Int_Onumber__ring @ SV244 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV244 ) @ SY1544 ) @ SY1545 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV244 ) @ SY1544 ) @ SY1546 ) )
| ( SY1545 = SY1546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1261,plain,
! [SV245: $i] :
( ( ! [SY1547: $i,SY1548: $i,SY1549: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV245 ) @ SY1547 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1548 ) @ SY1549 ) )
| ( SY1547 = SY1549 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1262,plain,
! [SV246: $i] :
( ( ! [SY1550: $i,SY1551: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV246 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1550 @ SY1551 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV246 )
= SY1550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1263,plain,
! [SV247: $i] :
( ( ! [SY1552: $i,SY1553: $i] :
( ( c_Lambda_OdB_OVar @ SV247 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1552 ) @ SY1553 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1264,plain,
! [SV248: $i] :
( ( ! [SY1554: $i,SY1555: $i,SY1556: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV248 ) @ SY1554 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1555 ) @ SY1556 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1265,plain,
! [SV249: $i] :
( ( ! [SY1557: $i,SY1558: $i,SY1559: $i,SY1560: $i] :
( ( ( c_List_Oappend @ SV249 @ ( c_List_Olist_OCons @ SY1557 @ ( c_List_Olist_ONil @ SY1558 ) @ SY1558 ) @ SY1558 )
!= ( c_List_Oappend @ SY1559 @ ( c_List_Olist_OCons @ SY1560 @ ( c_List_Olist_ONil @ SY1558 ) @ SY1558 ) @ SY1558 ) )
| ( SV249 = SY1559 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1266,plain,
! [SV250: $i] :
( ( ! [SY1561: $i,SY1562: $i] :
( ( ( c_List_Oappend @ SV250 @ SY1561 @ SY1562 )
!= ( c_List_Olist_ONil @ SY1562 ) )
| ( SV250
= ( c_List_Olist_ONil @ SY1562 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1267,plain,
! [SV251: $i] :
( ( ! [SY1563: $i,SY1564: $i,SY1565: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV251 ) ) @ SY1563 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1564 ) @ SY1565 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1268,plain,
! [SV252: $i] :
( ( ! [SY1566: $i,SY1567: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV252 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1566 @ SY1567 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1567
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1269,plain,
! [SV253: $i] :
( ( ! [SY1568: $i,SY1569: $i] :
( ( ( c_List_Oappend @ SV253 @ SY1568 @ SY1569 )
!= SV253 )
| ( SY1568
= ( c_List_Olist_ONil @ SY1569 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1270,plain,
! [SV254: $i] :
( ( ! [SY1570: $i,SY1571: $i] :
( ( c_List_Olist_OCons @ SV254 @ SY1570 @ SY1571 )
!= SY1570 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1271,plain,
! [SV255: $i] :
( ( ! [SY1572: $i,SY1573: $i] :
( SV255
!= ( c_List_Olist_OCons @ SY1572 @ SV255 @ SY1573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1272,plain,
! [SV256: $i] :
( ( ! [SY1574: $i,SY1575: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV256 @ SY1574 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1575 @ SY1574 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV256 = SY1575 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1273,plain,
! [SV257: $i] :
( ( ! [SY1576: $i,SY1577: $i,SY1578: $i] :
( ( ( c_List_Omap @ SV257 @ SY1576 @ SY1577 @ SY1578 )
!= ( c_List_Olist_ONil @ SY1578 ) )
| ( SY1576
= ( c_List_Olist_ONil @ SY1577 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1274,plain,
! [SV258: $i] :
( ( ! [SY1579: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV258 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SY1579 ) @ SY1579 )
!= ( c_HOL_Ozero__class_Ozero @ SV258 ) )
| ( SY1579
= ( c_HOL_Ozero__class_Ozero @ SV258 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1275,plain,
! [SV259: $i] :
( ( ! [SY1580: $i,SY1581: $i] :
( ( c_List_Olist_OCons @ SV259 @ SY1580 @ SY1581 )
!= ( c_List_Olist_ONil @ SY1581 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1276,plain,
! [SV260: $i] :
( ( ! [SY1582: $i,SY1583: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV260 ) @ SY1582 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1583 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV260 ) @ SY1582 )
= SY1583 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1277,plain,
! [SV261: $i] :
( ( ! [SY1584: $i,SY1585: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV261 @ SY1584 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY1585 ) )
| ( SV261
= ( c_Lambda_OdB_OAbs @ SY1585 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1278,plain,
! [SV262: $i] :
( ( ! [SY1586: $i,SY1587: $i] :
( ( ( c_Lambda_OdB_OVar @ SV262 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1586 @ SY1587 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV262 )
= SY1586 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1279,plain,
! [SV263: $i] :
( ( ! [SY1588: $i,SY1589: $i,SY1590: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV263 ) @ SY1588 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1589 ) @ SY1590 ) )
| ( SV263 = SY1589 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1280,plain,
! [SV264: $i] :
( ( ! [SY1591: $i,SY1592: $i] :
( ( ( c_List_Oappend @ SV264 @ SY1591 @ SY1592 )
!= SY1591 )
| ( SV264
= ( c_List_Olist_ONil @ SY1592 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1281,plain,
! [SV265: $i] :
( ( ! [SY1593: $i,SY1594: $i] :
( ( c_List_Olist_ONil @ SV265 )
!= ( c_List_Olist_OCons @ SY1593 @ SY1594 @ SV265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1282,plain,
! [SV266: $i] :
( ( ! [SY1595: $i,SY1596: $i,SY1597: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV266 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV266 ) @ SY1595 ) @ SY1596 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV266 ) @ SY1595 ) @ SY1597 ) )
| ( SY1596 = SY1597 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1283,plain,
! [SV267: $i] :
( ( ! [SY1598: $i,SY1599: $i] :
( ( SV267
!= ( c_List_Oappend @ SV267 @ SY1598 @ SY1599 ) )
| ( SY1598
= ( c_List_Olist_ONil @ SY1599 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1284,plain,
! [SV268: $i] :
( ( ! [SY1600: $i,SY1601: $i,SY1602: $i,SY1603: $i,SY1604: $i,SY1605: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV268 ) @ SY1600 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY1601 ) @ SY1602 ) @ SY1603 ) ) )
| ~ ( c_Type_Otyping @ SY1604 @ SY1602 @ SY1600 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1602 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY1604 @ SY1603 @ SY1600 @ tc_Type_Otype ) @ SY1601 @ SY1605 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1601 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1285,plain,
! [SV269: $i] :
( ( ! [SY1606: $i,SY1607: $i,SY1608: $i] :
( ( ( c_List_Oappend @ SV269 @ SY1606 @ SY1607 )
!= ( c_List_Oappend @ SY1608 @ SY1606 @ SY1607 ) )
| ( SV269 = SY1608 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1286,plain,
! [SV270: $i] :
( ( ! [SY1609: $i] :
( ( ( c_Lambda_OdB_OVar @ SV270 )
!= ( c_Lambda_OdB_OVar @ SY1609 ) )
| ( SV270 = SY1609 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1287,plain,
! [SV271: $i] :
( ( ! [SY1610: $i,SY1611: $i,SY1612: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV271 ) @ SY1610 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1611 ) @ SY1612 ) )
| ( SY1610 = SY1612 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1288,plain,
! [SV272: $i] :
( ( ! [SY1613: $i,SY1614: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV272 ) @ SY1613 )
!= ( c_Lambda_OdB_OAbs @ SY1614 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1289,plain,
! [SV273: $i] :
( ( ! [SY1615: $i] :
( ( c_Lambda_OdB_OVar @ SV273 )
!= ( c_Lambda_OdB_OAbs @ SY1615 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1290,plain,
! [SV274: $i] :
( ( ! [SY1616: $i,SY1617: $i,SY1618: $i] :
( ( ( c_List_Olist_ONil @ SV274 )
!= ( c_List_Omap @ SY1616 @ SY1617 @ SY1618 @ SV274 ) )
| ( SY1617
= ( c_List_Olist_ONil @ SY1618 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1291,plain,
! [SV275: $i] :
( ( ! [SY1619: $i,SY1620: $i,SY1621: $i,SY1622: $i] :
( ( ( c_List_Oappend @ SV275 @ ( c_List_Olist_OCons @ SY1619 @ ( c_List_Olist_ONil @ SY1620 ) @ SY1620 ) @ SY1620 )
!= ( c_List_Oappend @ SY1621 @ ( c_List_Olist_OCons @ SY1622 @ ( c_List_Olist_ONil @ SY1620 ) @ SY1620 ) @ SY1620 ) )
| ( SY1619 = SY1622 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1292,plain,
! [SV276: $i] :
( ( ! [SY1623: $i,SY1624: $i] :
( ( SV276
!= ( c_List_Oappend @ SY1623 @ SV276 @ SY1624 ) )
| ( SY1623
= ( c_List_Olist_ONil @ SY1624 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1293,plain,
! [SV277: $i] :
( ( ! [SY1625: $i,SY1626: $i] :
( ( ( c_List_Olist_ONil @ SV277 )
!= ( c_List_Oappend @ SY1625 @ SY1626 @ SV277 ) )
| ( SY1626
= ( c_List_Olist_ONil @ SV277 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1294,plain,
! [SV278: $i] :
( ( ! [SY1627: $i,SY1628: $i] :
( ( ( c_List_Olist_ONil @ SV278 )
!= ( c_List_Oappend @ SY1627 @ SY1628 @ SV278 ) )
| ( SY1627
= ( c_List_Olist_ONil @ SV278 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1295,plain,
! [SV279: $i] :
( ( ! [SY1629: $i] :
( ( c_Lambda_OdB_OAbs @ SV279 )
!= ( c_Lambda_OdB_OVar @ SY1629 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1296,plain,
! [SV280: $i] :
( ( ! [SY1630: $i,SY1631: $i,SY1632: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV280 ) @ SY1630 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1631 ) @ SY1632 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1630 = SY1632 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1297,plain,
! [SV281: $i] :
( ( ! [SY1633: $i,SY1634: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV281 ) @ SY1633 )
!= ( c_Lambda_OdB_OVar @ SY1634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1298,plain,
! [SV282: $i] :
( ( ! [SY1635: $i,SY1636: $i] :
( ( c_Lambda_OdB_OAbs @ SV282 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1635 ) @ SY1636 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1299,plain,
! [SV283: $i] :
( ( ! [SY1637: $i,SY1638: $i,SY1639: $i,SY1640: $i] :
( ( ( c_List_Olist_OCons @ SV283 @ SY1637 @ SY1638 )
!= ( c_List_Olist_OCons @ SY1639 @ SY1640 @ SY1638 ) )
| ( SY1637 = SY1640 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1300,plain,
! [SV284: $i] :
( ( ! [SY1641: $i,SY1642: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV284 @ SY1641 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY1642 ) )
| ( SY1641
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1301,plain,
! [SV285: $i] :
( ( ! [SY1643: $i,SY1644: $i] :
( ( ( c_Lambda_OdB_OVar @ SV285 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1643 @ SY1644 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1644
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1302,plain,
! [SV286: $i] :
( ( ! [SY1645: $i,SY1646: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV286 )
| ~ ( class_Int_Onumber__ring @ SV286 )
| ( SY1645
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV286 ) @ SY1645 ) @ SY1646 ) )
| ( SY1646
= ( c_HOL_Ozero__class_Ozero @ SV286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1303,plain,
! [SV287: $i] :
( ( ! [SY1647: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV287 )
!= ( c_Lambda_OdB_OAbs @ SY1647 ) )
| ( SV287 = SY1647 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1304,plain,
! [SV288: $i] :
( ( ! [SY1648: $i,SY1649: $i,SY1650: $i,SY1651: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV288 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SY1648 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SY1649 ) @ SY1650 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SY1649 ) @ SY1651 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SY1648 ) @ SY1650 )
= SY1651 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1305,plain,
! [SV289: $i,SV1: $i] :
( ( ( hBOOL @ ( hAPP @ SV1 @ SV289 ) )
| ~ ( hBOOL @ ( hAPP @ SV1 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV1 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4 @ SV1 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ SV1 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV1 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV1 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1306,plain,
! [SV290: $i,SV2: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV2 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV2 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__4 @ SV2 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ SV2 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV2 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV2 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ SV2 @ SV290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1307,plain,
! [SV291: $i,SV3: $i] :
( ( ! [SY1652: $i,SY1653: $i] :
( ( c_Type_Otyping @ SV3 @ SV291 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SY1652 @ SV3 @ SV291 @ SY1653 ) @ SY1652 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV291 @ SY1653 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1652 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1308,plain,
! [SV292: $i,SV4: $i] :
( ( ! [SY1654: $i,SY1655: $i] :
( ( c_Type_Otyping @ SV4 @ SV292 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SY1654 @ SV4 @ SV292 @ SY1655 ) @ SY1654 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV4 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV292 @ SY1655 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1654 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1309,plain,
! [SV293: $i,SV5: $i] :
( ( ! [SY1656: $i,SY1657: $i] :
( ( c_Type_Otypings @ SV5 @ SV293 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SY1656 @ SV5 @ SY1657 @ SV293 ) )
| ~ ( c_Type_Otyping @ SV5 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1657 @ SV293 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1656 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1310,plain,
! [SV294: $i,SV6: $i] :
( ( ! [SY1658: $i,SY1659: $i] :
( ( c_Type_Otypings @ SV6 @ SV294 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SY1658 @ SV6 @ SY1659 @ SV294 ) )
| ~ ( c_Type_Otyping @ SV6 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1659 @ SV294 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1658 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1311,plain,
! [SV295: $i,SV7: $i] :
( ( ! [SY1660: $i,SY1661: $i,SY1662: $i,SY1663: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV7 @ SV295 ) @ SY1660 ) )
| ( SV295 = SY1660 )
| ~ ( c_ListOrder_Ostep1 @ SV7 @ ( c_List_Oappend @ SY1661 @ ( c_List_Olist_OCons @ SV295 @ ( c_List_Olist_ONil @ SY1662 ) @ SY1662 ) @ SY1662 ) @ ( c_List_Oappend @ SY1663 @ ( c_List_Olist_OCons @ SY1660 @ ( c_List_Olist_ONil @ SY1662 ) @ SY1662 ) @ SY1662 ) @ SY1662 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1312,plain,
! [SV296: $i,SV8: $i] :
( ( ! [SY1664: $i,SY1665: $i,SY1666: $i,SY1667: $i] :
( ( c_List_Ofoldr @ SV8 @ ( c_List_Oappend @ SV296 @ SY1664 @ SY1665 ) @ SY1666 @ SY1665 @ SY1667 )
= ( c_List_Ofoldr @ SV8 @ SV296 @ ( c_List_Ofoldr @ SV8 @ SY1664 @ SY1666 @ SY1665 @ SY1667 ) @ SY1665 @ SY1667 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1313,plain,
! [SV297: $i,SV9: $i] :
( ( ! [SY1668: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV9 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV9 ) @ SV297 ) @ SY1668 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV9 ) @ SY1668 ) @ SV297 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1314,plain,
! [SV298: $i,SV10: $i] :
( ( ! [SY1669: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV10 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV10 ) @ SV298 ) @ SY1669 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV10 ) @ SY1669 ) @ SV298 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1315,plain,
! [SV299: $i,SV11: $i] :
( ( ! [SY1670: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV11 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV11 ) @ SV299 ) @ SY1670 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV11 ) @ SY1670 ) @ SV299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1316,plain,
! [SV300: $i,SV12: $i] :
( ( ! [SY1671: $i,SY1672: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV12 ) @ SV300 ) @ SY1671 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV12 ) @ SY1672 ) @ SY1671 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV300 ) @ SY1672 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1317,plain,
! [SV301: $i,SV13: $i] :
( ( SV13
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV301 ) @ SV13 @ SV301 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1318,plain,
! [SV302: $i,SV14: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV14 ) @ SV302 @ SV14 )
= SV302 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1319,plain,
! [SV303: $i,SV15: $i] :
( ( SV15
= ( c_List_Oappend @ SV15 @ ( c_List_Olist_ONil @ SV303 ) @ SV303 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1320,plain,
! [SV304: $i,SV16: $i] :
( ( SV16
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV304 ) @ SV16 @ SV304 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1030]) ).
thf(1321,plain,
! [SV305: $i,SV17: $i] :
( ( ( c_List_Oappend @ SV17 @ ( c_List_Olist_ONil @ SV305 ) @ SV305 )
= SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1322,plain,
! [SV18: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV18 ) ) )
= $true )
| ( ( ( SV18
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV18 ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV18 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1032]) ).
thf(1323,plain,
! [SV306: $i,SV19: $i] :
( ( ! [SY1673: $i,SY1674: $i,SY1675: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV19 @ SV306 ) @ SY1673 ) @ SY1674 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV19 @ SV306 ) @ SY1675 ) @ SY1674 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV19 @ SV306 ) @ SY1673 ) @ SY1675 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1324,plain,
! [SV307: $i,SV20: $i] :
( ( ! [SY1676: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV20 @ SV307 ) @ SY1676 ) @ SY1676 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1034]) ).
thf(1325,plain,
! [SV308: $i,SV21: $i] :
( ( ! [SY1677: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV21 @ SV308 ) @ SY1677 ) @ SY1677 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1326,plain,
! [SV309: $i,SV22: $i] :
( ( c_List_Olistsp @ SV22 @ ( c_List_Olist_ONil @ SV309 ) @ SV309 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1036]) ).
thf(1327,plain,
! [SV310: $i,SV23: $i] :
( ( ! [SY1678: $i,SY1679: $i,SY1680: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV23 @ SV310 ) @ SY1678 ) )
| ( c_ListOrder_Ostep1 @ SV23 @ ( c_List_Olist_OCons @ SV310 @ SY1679 @ SY1680 ) @ ( c_List_Olist_OCons @ SY1678 @ SY1679 @ SY1680 ) @ SY1680 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1328,plain,
! [SV311: $i,SV24: $i] :
( ( ! [SY1681: $i,SY1682: $i,SY1683: $i,SY1684: $i] :
( ( SV24 = SV311 )
| ( SY1681 = SY1682 )
| ~ ( c_ListOrder_Ostep1 @ SY1683 @ ( c_List_Olist_OCons @ SV311 @ SY1682 @ SY1684 ) @ ( c_List_Olist_OCons @ SV24 @ SY1681 @ SY1684 ) @ SY1684 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1329,plain,
! [SV312: $i,SV25: $i] :
( ( ! [SY1685: $i,SY1686: $i,SY1687: $i] :
( ( c_Lambda_OdB_OdB__case @ SV25 @ SV312 @ SY1685 @ ( c_Lambda_OdB_OAbs @ SY1686 ) @ SY1687 )
= ( hAPP @ SY1685 @ SY1686 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1330,plain,
! [SV26: $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 @ SV26 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV26 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV26 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV26 ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV26 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1040]) ).
thf(1331,plain,
! [SV313: $i,SV27: $i] :
( ( ! [SY1688: $i,SY1689: $i] :
( ( c_List_Olistsp @ SV27 @ SV313 @ SY1688 )
| ~ ( c_List_Olistsp @ SV27 @ ( c_List_Oappend @ SY1689 @ SV313 @ SY1688 ) @ SY1688 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1332,plain,
! [SV314: $i,SV28: $i] :
( ( ! [SY1690: $i,SY1691: $i] :
( ( c_List_Olistsp @ SV28 @ SV314 @ SY1690 )
| ~ ( c_List_Olistsp @ SV28 @ ( c_List_Oappend @ SV314 @ SY1691 @ SY1690 ) @ SY1690 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1333,plain,
! [SV315: $i,SV29: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV29 ) ) @ ( c_Lambda_OdB_OAbs @ SV315 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV29 ) @ SV315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1334,plain,
! [SV316: $i,SV30: $i] :
( ( ! [SY1692: $i,SY1693: $i,SY1694: $i] :
( ( c_ListOrder_Ostep1 @ SV30 @ ( c_List_Oappend @ SV316 @ SY1692 @ SY1693 ) @ ( c_List_Oappend @ SV316 @ SY1694 @ SY1693 ) @ SY1693 )
| ~ ( c_ListOrder_Ostep1 @ SV30 @ SY1692 @ SY1694 @ SY1693 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1335,plain,
! [SV317: $i,SV31: $i] :
( ( ! [SY1695: $i,SY1696: $i,SY1697: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV31 @ SV317 @ SY1695 @ SY1696 )
| ( c_ListOrder_Ostep1 @ SV31 @ ( c_List_Oappend @ SV317 @ SY1697 @ SY1696 ) @ ( c_List_Oappend @ SY1695 @ SY1697 @ SY1696 ) @ SY1696 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1336,plain,
! [SV318: $i,SV32: $i] :
( ( ! [SY1698: $i] :
( ( c_Lambda_Osubstn @ SV32 @ SV318 @ SY1698 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV32 ) @ ( c_Lambda_Oliftn @ SY1698 @ SV318 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ SY1698 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1337,plain,
! [SV33: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV33 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ ( c_HOL_Ozero__class_Ozero @ SV33 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV33 ) )
= ( c_HOL_Ozero__class_Ozero @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1047]) ).
thf(1338,plain,
! [SV319: $i,SV34: $i] :
( ( ! [SY1699: $i,SY1700: $i,SY1701: $i] :
( ( c_Type_Otyping @ SV34 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV319 @ SY1699 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1700 )
| ~ ( c_Type_Otypings @ SV34 @ SY1699 @ SY1701 )
| ~ ( c_Type_Otyping @ SV34 @ SV319 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY1701 @ SY1700 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1339,plain,
! [SV320: $i,SV35: $i] :
( ( ! [SY1702: $i,SY1703: $i] :
( ~ ( class_Orderings_Opreorder @ SV35 )
| ( c_HOL_Oord__class_Oless @ SV320 @ SY1702 @ SV35 )
| ~ ( c_HOL_Oord__class_Oless @ SY1703 @ SY1702 @ SV35 )
| ~ ( c_HOL_Oord__class_Oless @ SV320 @ SY1703 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1340,plain,
! [SV321: $i,SV36: $i] :
( ( ! [SY1704: $i,SY1705: $i] :
( ~ ( class_Orderings_Oorder @ SV36 )
| ( c_HOL_Oord__class_Oless @ SV321 @ SY1704 @ SV36 )
| ~ ( c_HOL_Oord__class_Oless @ SV321 @ SY1705 @ SV36 )
| ~ ( c_HOL_Oord__class_Oless @ SY1705 @ SY1704 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1341,plain,
! [SV322: $i,SV37: $i] :
( ( ! [SY1706: $i,SY1707: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV37 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV322 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SY1706 ) @ SY1707 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV322 ) @ SY1706 ) ) @ SY1707 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1342,plain,
! [SV323: $i,SV38: $i] :
( ( ! [SY1708: $i,SY1709: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV38 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV323 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SY1708 ) @ SY1709 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SY1708 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV323 ) @ SY1709 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1343,plain,
! [SV324: $i,SV39: $i] :
( ( ! [SY1710: $i,SY1711: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV39 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ SV324 ) @ SY1710 ) ) @ SY1711 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ SV324 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ SY1710 ) @ SY1711 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1344,plain,
! [SV325: $i,SV40: $i] :
( ( ! [SY1712: $i,SY1713: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV40 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ SV325 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ SY1712 ) @ SY1713 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ SY1712 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ SV325 ) @ SY1713 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1345,plain,
! [SV326: $i,SV41: $i] :
( ( ! [SY1714: $i,SY1715: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV41 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV326 ) @ SY1714 ) ) @ SY1715 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV326 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SY1714 ) @ SY1715 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1346,plain,
! [SV327: $i,SV42: $i] :
( ( ! [SY1716: $i,SY1717: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV42 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV327 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SY1716 ) @ SY1717 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV327 ) @ SY1716 ) ) @ SY1717 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1347,plain,
! [SV328: $i,SV43: $i] :
( ( ! [SY1718: $i,SY1719: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV43 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ SV328 ) @ SY1718 ) ) @ SY1719 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ SV328 ) @ SY1719 ) ) @ SY1718 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1348,plain,
! [SV329: $i,SV44: $i] :
( ( ! [SY1720: $i,SY1721: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV44 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SV329 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SY1720 ) @ SY1721 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SY1720 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SV329 ) @ SY1721 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1349,plain,
! [SV330: $i,SV45: $i] :
( ( ! [SY1722: $i,SY1723: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV45 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV45 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV45 ) @ SV330 ) @ SY1722 ) ) @ SY1723 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV45 ) @ SV330 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV45 ) @ SY1722 ) @ SY1723 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1350,plain,
! [SV46: $i] :
( ( c_HOL_Oord__class_Oless @ SV46 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1060]) ).
thf(1351,plain,
! [SV47: $i] :
( ( c_HOL_Oord__class_Oless @ SV47 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1061]) ).
thf(1352,plain,
! [SV331: $i,SV48: $i] :
( ( ! [SY1724: $i,SY1725: $i,SY1726: $i,SY1727: $i] :
( ( hAPP @ ( c_COMBC @ SV48 @ SV331 @ SY1724 @ SY1725 @ SY1726 ) @ SY1727 )
= ( hAPP @ ( hAPP @ SV48 @ SY1727 ) @ SV331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1353,plain,
! [SV332: $i,SV49: $i] :
( ( ! [SY1728: $i,SY1729: $i] :
( ( c_List_Ofoldr @ SV49 @ ( c_List_Olist_ONil @ SV332 ) @ SY1728 @ SV332 @ SY1729 )
= SY1728 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1354,plain,
! [SV333: $i,SV50: $i] :
( ( ! [SY1730: $i] :
( ( c_List_Omap @ SV50 @ ( c_List_Olist_ONil @ SV333 ) @ SV333 @ SY1730 )
= ( c_List_Olist_ONil @ SY1730 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1355,plain,
! [SV334: $i,SV51: $i] :
( ( ! [SY1731: $i,SY1732: $i,SY1733: $i,SY1734: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV51 @ SV334 ) @ SY1731 ) )
| ( c_ListOrder_Ostep1 @ SV51 @ SY1732 @ SY1733 @ SY1734 )
| ~ ( c_ListOrder_Ostep1 @ SV51 @ ( c_List_Oappend @ SY1732 @ ( c_List_Olist_OCons @ SV334 @ ( c_List_Olist_ONil @ SY1734 ) @ SY1734 ) @ SY1734 ) @ ( c_List_Oappend @ SY1733 @ ( c_List_Olist_OCons @ SY1731 @ ( c_List_Olist_ONil @ SY1734 ) @ SY1734 ) @ SY1734 ) @ SY1734 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1065]) ).
thf(1356,plain,
! [SV52: $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 @ SV52 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV52 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV52 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ( SV52
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV52 ) ) )
| ( SV52
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV52 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV52 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1066]) ).
thf(1357,plain,
! [SV335: $i,SV53: $i] :
( ( ! [SY1735: $i,SY1736: $i,SY1737: $i,SY1738: $i] :
( ( c_Type_Otypings @ SV53 @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SV335 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SY1735 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SY1736 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1737 )
| ~ ( c_Type_Otypings @ ( c_Type_Oshift @ SV53 @ SY1735 @ SY1738 @ tc_Type_Otype ) @ SY1736 @ SY1737 )
| ~ ( c_Type_Otyping @ SV53 @ SV335 @ SY1738 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1358,plain,
! [SV336: $i,SV54: $i] :
( ( ! [SY1739: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV54 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV336 ) @ SY1739 ) @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV54 )
| ~ ( c_HOL_Oord__class_Oless @ SY1739 @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV54 )
| ~ ( c_HOL_Oord__class_Oless @ SV336 @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1359,plain,
! [SV337: $i,SV55: $i] :
( ( ! [SY1740: $i,SY1741: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV55 @ SV337 @ SY1740 ) @ SY1741 @ SY1740 )
= ( c_List_Olist_OCons @ SV55 @ ( c_List_Oappend @ SV337 @ SY1741 @ SY1740 ) @ SY1740 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1360,plain,
! [SV338: $i,SV56: $i] :
( ( ! [SY1742: $i,SY1743: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV56 @ SV338 @ SY1742 ) @ SY1743 @ SY1742 )
= ( c_List_Olist_OCons @ SV56 @ ( c_List_Oappend @ SV338 @ SY1743 @ SY1742 ) @ SY1742 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1361,plain,
! [SV339: $i,SV57: $i] :
( ( ! [SY1744: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV57 ) @ SV339 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV57 ) @ SY1744 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV339 ) @ SY1744 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1362,plain,
! [SV340: $i,SV58: $i] :
( ( ! [SY1745: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV58 ) @ SV340 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1745 ) @ SV340 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV58 ) @ SY1745 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1072]) ).
thf(1363,plain,
! [SV341: $i,SV59: $i] :
( ( ! [SY1746: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV59 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV341 @ SY1746 @ SV59 @ SV59 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV341 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SY1746 @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 @ SV59 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1364,plain,
! [SV342: $i,SV60: $i] :
( ( ! [SY1747: $i,SY1748: $i,SY1749: $i] :
( ( c_List_Omap @ SV60 @ ( c_List_Olist_OCons @ SV342 @ SY1747 @ SY1748 ) @ SY1748 @ SY1749 )
= ( c_List_Olist_OCons @ ( hAPP @ SV60 @ SV342 ) @ ( c_List_Omap @ SV60 @ SY1747 @ SY1748 @ SY1749 ) @ SY1749 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1365,plain,
! [SV343: $i,SV61: $i] :
( ( ! [SY1750: $i,SY1751: $i,SY1752: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ SV61 @ SV343 ) @ ( c_List_Omap @ SV61 @ SY1750 @ SY1751 @ SY1752 ) @ SY1752 )
= ( c_List_Omap @ SV61 @ ( c_List_Olist_OCons @ SV343 @ SY1750 @ SY1751 ) @ SY1751 @ SY1752 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1366,plain,
! [SV344: $i,SV62: $i] :
( ( ! [SY1753: $i,SY1754: $i,SY1755: $i] :
( ( c_List_Omap @ SV62 @ ( c_List_Olist_OCons @ SV344 @ SY1753 @ SY1754 ) @ SY1754 @ SY1755 )
= ( c_List_Olist_OCons @ ( hAPP @ SV62 @ SV344 ) @ ( c_List_Omap @ SV62 @ SY1753 @ SY1754 @ SY1755 ) @ SY1755 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1367,plain,
! [SV63: $i] :
( ( ( SV63
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV63 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV63 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV63 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( SV63
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV63 ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV63 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV63 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1077]) ).
thf(1368,plain,
! [SV345: $i,SV64: $i] :
( ( ! [SY1756: $i,SY1757: $i] :
( ( c_List_Olist_OCons @ SV64 @ ( c_List_Oappend @ SV345 @ SY1756 @ SY1757 ) @ SY1757 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV64 @ SV345 @ SY1757 ) @ SY1756 @ SY1757 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1369,plain,
! [SV346: $i,SV65: $i] :
( ( ! [SY1758: $i,SY1759: $i] :
( ( c_List_Olist_OCons @ SV65 @ ( c_List_Oappend @ SV346 @ SY1758 @ SY1759 ) @ SY1759 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV65 @ SV346 @ SY1759 ) @ SY1758 @ SY1759 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1370,plain,
! [SV347: $i,SV66: $i] :
( ( ! [SY1760: $i,SY1761: $i,SY1762: $i,SY1763: $i] :
( ( SV66 = SV347 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1760 @ SV347 ) @ SV66 ) )
| ~ ( c_ListOrder_Ostep1 @ SY1760 @ ( c_List_Olist_OCons @ SV347 @ SY1761 @ SY1762 ) @ ( c_List_Olist_OCons @ SV66 @ SY1763 @ SY1762 ) @ SY1762 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1371,plain,
! [SV348: $i,SV67: $i] :
( ( ! [SY1764: $i,SY1765: $i,SY1766: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV67 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ SV348 ) @ SY1764 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ SY1765 ) @ SY1766 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ SV348 ) @ SY1765 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ SY1764 ) @ SY1766 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1372,plain,
! [SV349: $i,SV68: $i] :
( ( ! [SY1767: $i,SY1768: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV68 ) @ SV349 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1767 ) @ SY1768 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV349 ) @ SY1768 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV68 ) @ SY1767 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1373,plain,
! [SV350: $i,SV69: $i] :
( ( ! [SY1769: $i] :
( ( ( c_Lambda_Oliftn @ SV69 @ ( c_Lambda_OdB_OVar @ SV350 ) @ SY1769 )
= ( c_Lambda_OdB_OVar @ SV350 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV350 @ SY1769 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1374,plain,
! [SV351: $i,SV70: $i] :
( ( ! [SY1770: $i,SY1771: $i] :
( ( c_Type_Otyping @ SV70 @ SV351 @ SY1770 )
| ~ ( c_Type_Otyping @ SV70 @ SY1771 @ SY1770 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1771 ) @ SV351 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1375,plain,
! [SV352: $i,SV71: $i] :
( ( ! [SY1772: $i,SY1773: $i,SY1774: $i] :
( ( c_Type_Otypings @ ( c_Type_Oshift @ SV71 @ SV352 @ SY1772 @ tc_Type_Otype ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ SV352 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SY1773 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1774 )
| ~ ( c_Type_Otypings @ SV71 @ SY1773 @ SY1774 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1376,plain,
! [SV353: $i,SV72: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV72 ) ) @ SV353 )
= ( c_Lambda_OdB_OVar @ SV72 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV72 @ SV353 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1377,plain,
! [SV354: $i,SV73: $i] :
( ( ! [SY1775: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV73 ) @ SV354 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY1775 ) @ SV354 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV73 ) @ SY1775 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1378,plain,
! [SV74: $i] :
( ( ( SV74
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV74 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV74 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV74 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV74 ) ) )
| ( SV74
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV74 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV74 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV74 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1088]) ).
thf(1379,plain,
! [SV355: $i,SV75: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV75 @ SV75 @ tc_nat )
| ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV75 ) @ SV355 @ SV75 )
= ( c_Lambda_Oliftn @ SV75 @ SV355 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1380,plain,
! [SV356: $i,SV76: $i] :
( ( ! [SY1776: $i] :
( ( c_List_Olist_OCons @ SV76 @ SV356 @ SY1776 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY1776 ) @ ( c_List_Olist_OCons @ SV76 @ SV356 @ SY1776 ) @ SY1776 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1381,plain,
! [SV357: $i,SV77: $i] :
( ( ! [SY1777: $i,SY1778: $i,SY1779: $i,SY1780: $i] :
( ~ ( c_Type_Otyping @ SV77 @ SV357 @ SY1777 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV77 @ SY1778 @ SY1777 @ tc_Type_Otype ) @ SY1779 @ SY1780 )
| ( c_Type_Otyping @ SV77 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY1779 ) @ SV357 ) @ SY1778 ) @ SY1780 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1382,plain,
! [SV358: $i,SV78: $i] :
( ( ! [SY1781: $i] :
( ( c_List_Olist_ONil @ SV78 )
= ( c_List_Omap @ SV358 @ ( c_List_Olist_ONil @ SY1781 ) @ SY1781 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1383,plain,
! [SV359: $i,SV79: $i] :
( ( ! [SY1782: $i,SY1783: $i,SY1784: $i,SY1785: $i] :
( ( SV79 = SV359 )
| ( c_ListOrder_Ostep1 @ SY1782 @ SV79 @ SV359 @ SY1783 )
| ~ ( c_ListOrder_Ostep1 @ SY1782 @ ( c_List_Oappend @ SV79 @ ( c_List_Olist_OCons @ SY1784 @ ( c_List_Olist_ONil @ SY1783 ) @ SY1783 ) @ SY1783 ) @ ( c_List_Oappend @ SV359 @ ( c_List_Olist_OCons @ SY1785 @ ( c_List_Olist_ONil @ SY1783 ) @ SY1783 ) @ SY1783 ) @ SY1783 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1093]) ).
thf(1384,plain,
! [SV360: $i,SV81: $i] :
( ( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ SV81 @ SV360 ) @ SV360 )
= ( c_Transitive__Closure_Ortranclp @ SV81 @ SV360 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1385,plain,
! [SV361: $i,SV82: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV82 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV82 ) @ ( c_HOL_Ozero__class_Ozero @ SV82 ) ) @ SV361 )
= SV361 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1386,plain,
! [SV362: $i,SV83: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV83 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV83 ) @ ( c_HOL_Ozero__class_Ozero @ SV83 ) ) @ SV362 )
= SV362 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1387,plain,
! [SV363: $i,SV84: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV84 )
| ~ ( class_Int_Onumber__ring @ SV84 )
| ( SV363
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV363 ) @ ( c_HOL_Ozero__class_Ozero @ SV84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1388,plain,
! [SV364: $i,SV85: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV85 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV85 ) @ SV364 ) @ ( c_HOL_Ozero__class_Ozero @ SV85 ) )
= SV364 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1389,plain,
! [SV365: $i,SV86: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV86 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV86 ) @ ( c_HOL_Ozero__class_Ozero @ SV86 ) ) @ SV365 )
= SV365 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1390,plain,
! [SV366: $i,SV87: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV87 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV87 ) @ SV366 ) @ ( c_HOL_Ozero__class_Ozero @ SV87 ) )
= SV366 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1391,plain,
! [SV367: $i,SV88: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV88 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV88 ) @ SV367 ) @ ( c_HOL_Ozero__class_Ozero @ SV88 ) )
= SV367 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1392,plain,
! [SV368: $i,SV89: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV89 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ ( c_HOL_Ozero__class_Ozero @ SV89 ) ) @ SV368 )
= SV368 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1393,plain,
! [SV369: $i,SV90: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV90 ) ) @ ( c_Lambda_OdB_OAbs @ SV369 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV90 ) @ SV369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1394,plain,
! [SV370: $i,SV91: $i] :
( ( ! [SY1786: $i,SY1787: $i] :
( ( ( hAPP @ ( hAPP @ SV91 @ SV370 ) @ SY1786 )
= SV370 )
| ~ ( c_OrderedGroup_Omonoid__add @ SY1786 @ SV91 @ SY1787 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1395,plain,
! [SV371: $i,SV92: $i] :
( ( ! [SY1788: $i,SY1789: $i] :
( ( ( hAPP @ ( hAPP @ SV92 @ SV371 ) @ SY1788 )
= SY1788 )
| ~ ( c_OrderedGroup_Omonoid__add @ SV371 @ SV92 @ SY1789 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1106]) ).
thf(1396,plain,
! [SV372: $i,SV93: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV93 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV372 @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV372 ) @ SV372 ) @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1397,plain,
! [SV373: $i,SV94: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV94 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV373 ) @ SV373 ) @ SV94 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV373 @ SV94 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1398,plain,
! [SV374: $i,SV95: $i] :
( ( ! [SY1790: $i,SY1791: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV95 ) @ SV374 ) @ SY1790 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY1791 ) @ SV374 ) @ SY1790 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV95 ) @ SY1791 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1399,plain,
! [SV375: $i,SV96: $i] :
( ( ! [SY1792: $i,SY1793: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV96 ) @ SV375 ) @ SY1792 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV96 ) @ SY1793 ) @ SY1792 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV375 ) @ SY1793 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1400,plain,
! [SV376: $i,SV97: $i] :
( ( ! [SY1794: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV97 )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SV376 @ SY1794 @ SV97 @ SV97 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SY1794 @ SV376 @ SV97 @ SV97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1401,plain,
! [SV377: $i,SV98: $i] :
( ( ! [SY1795: $i,SY1796: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV98 @ SV377 ) @ SY1795 ) @ SY1796 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV98 @ SY1795 ) @ SY1796 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1402,plain,
! [SV378: $i,SV99: $i] :
( ( ! [SY1797: $i] :
~ ( c_ListOrder_Ostep1 @ SV99 @ ( c_List_Olist_ONil @ SV378 ) @ SY1797 @ SV378 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1113]) ).
thf(1403,plain,
! [SV379: $i,SV100: $i] :
( ( ! [SY1798: $i] :
~ ( c_ListOrder_Ostep1 @ SV100 @ SV379 @ ( c_List_Olist_ONil @ SY1798 ) @ SY1798 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1404,plain,
! [SV380: $i,SV101: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV101 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ SV380 ) @ SV380 ) @ ( c_HOL_Ozero__class_Ozero @ SV101 ) @ SV101 )
| ~ ( c_HOL_Oord__class_Oless @ SV380 @ ( c_HOL_Ozero__class_Ozero @ SV101 ) @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1405,plain,
! [SV381: $i,SV102: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV102 )
| ( c_HOL_Oord__class_Oless @ SV381 @ ( c_HOL_Ozero__class_Ozero @ SV102 ) @ SV102 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SV381 ) @ SV381 ) @ ( c_HOL_Ozero__class_Ozero @ SV102 ) @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1406,plain,
! [SV382: $i,SV103: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV103 )
| ( c_HOL_Oord__class_Oless @ SV382 @ ( c_HOL_Ozero__class_Ozero @ SV103 ) @ SV103 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV103 ) @ SV382 ) @ SV382 ) @ ( c_HOL_Ozero__class_Ozero @ SV103 ) @ SV103 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1407,plain,
! [SV383: $i,SV104: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV104 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV104 ) @ SV383 ) @ SV383 ) @ ( c_HOL_Ozero__class_Ozero @ SV104 ) @ SV104 )
| ~ ( c_HOL_Oord__class_Oless @ SV383 @ ( c_HOL_Ozero__class_Ozero @ SV104 ) @ SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1408,plain,
! [SV384: $i,SV105: $i] :
( ( ! [SY1799: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV105 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV384 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ ( c_HOL_Ozero__class_Ozero @ SV105 ) @ SY1799 @ SV105 @ SV105 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV384 @ SY1799 @ SV105 @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1409,plain,
! [SV385: $i,SV106: $i] :
( ( ! [SY1800: $i,SY1801: $i] :
( ( c_Type_Otyping @ SV106 @ ( c_Lambda_OdB_OAbs @ SV385 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1800 ) @ SY1801 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV106 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1800 @ tc_Type_Otype ) @ SV385 @ SY1801 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1410,plain,
! [SV386: $i,SV107: $i] :
( ( ! [SY1802: $i,SY1803: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV107 @ SV386 @ SY1802 @ SY1803 ) @ SV386 )
= SY1802 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1411,plain,
! [SV387: $i,SV108: $i] :
( ( ! [SY1804: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV108 ) @ SV387 @ SY1804 )
= ( c_Lambda_OdB_OVar @ SV108 ) )
| ( SV108 = SY1804 )
| ( c_HOL_Oord__class_Oless @ SY1804 @ SV108 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1412,plain,
! [SV109: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV109 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV109 ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV109 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV109 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1123]) ).
thf(1413,plain,
! [SV110: $i] :
( ( c_HOL_Oord__class_Oless @ SV110 @ SV110 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1124]) ).
thf(1414,plain,
! [SV111: $i] :
( ( c_HOL_Oord__class_Oless @ SV111 @ SV111 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1125]) ).
thf(1415,plain,
! [SV388: $i,SV112: $i] :
( ( ~ ( class_Orderings_Oorder @ SV112 )
| ~ ( c_HOL_Oord__class_Oless @ SV388 @ SV388 @ SV112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1416,plain,
! [SV389: $i,SV113: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV113 )
| ~ ( c_HOL_Oord__class_Oless @ SV389 @ SV389 @ SV113 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1417,plain,
! [SV390: $i,SV114: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV114 )
| ~ ( c_HOL_Oord__class_Oless @ SV390 @ SV390 @ SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1418,plain,
! [SV391: $i,SV115: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV115 ) ) @ SV391 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV115 ) @ SV391 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1419,plain,
! [SV392: $i,SV116: $i] :
( ( ! [SY1805: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV116 ) @ SV392 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY1805 ) @ SV392 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV116 ) @ SY1805 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1420,plain,
! [SV393: $i,SV117: $i] :
( ( ! [SY1806: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV117 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV393 ) @ SY1806 ) @ SV117 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SY1806 @ SV117 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV393 @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1421,plain,
! [SV394: $i,SV118: $i] :
( ( ! [SY1807: $i,SY1808: $i,SY1809: $i,SY1810: $i] :
( ( c_ListOrder_Ostep1 @ SV118 @ SV394 @ SY1807 @ SY1808 )
| ( SY1807 = SV394 )
| ~ ( c_ListOrder_Ostep1 @ SV118 @ ( c_List_Olist_OCons @ SY1809 @ SV394 @ SY1808 ) @ ( c_List_Olist_OCons @ SY1810 @ SY1807 @ SY1808 ) @ SY1808 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1422,plain,
! [SV395: $i,SV119: $i] :
( ( ! [SY1811: $i,SY1812: $i,SY1813: $i] :
( ( ( hAPP @ ( hAPP @ SV119 @ ( hAPP @ ( hAPP @ SV119 @ SV395 ) @ SY1811 ) ) @ SY1812 )
= ( hAPP @ ( hAPP @ SV119 @ SV395 ) @ ( hAPP @ ( hAPP @ SV119 @ SY1811 ) @ SY1812 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV119 @ SY1813 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1423,plain,
! [SV396: $i,SV120: $i] :
( ( ! [SY1814: $i,SY1815: $i,SY1816: $i] :
( ( c_List_Omap @ SV120 @ ( c_List_Oappend @ SV396 @ SY1814 @ SY1815 ) @ SY1815 @ SY1816 )
= ( c_List_Oappend @ ( c_List_Omap @ SV120 @ SV396 @ SY1815 @ SY1816 ) @ ( c_List_Omap @ SV120 @ SY1814 @ SY1815 @ SY1816 ) @ SY1816 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1424,plain,
! [SV121: $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 @ SV121 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV121 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV121 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ( SV121
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV121 ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV121 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV121 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1135]) ).
thf(1425,plain,
! [SV397: $i,SV122: $i] :
( ( ! [SY1817: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV122 )
| ( c_HOL_Oord__class_Oless @ SV397 @ SY1817 @ SV122 )
| ( c_HOL_Oord__class_Oless @ SY1817 @ SV397 @ SV122 )
| ( SY1817 = SV397 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1426,plain,
! [SV398: $i,SV123: $i] :
( ( ! [SY1818: $i] :
( ~ ( class_Orderings_Olinorder @ SV123 )
| ( SV398 = SY1818 )
| ( c_HOL_Oord__class_Oless @ SY1818 @ SV398 @ SV123 )
| ( c_HOL_Oord__class_Oless @ SV398 @ SY1818 @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1427,plain,
! [SV399: $i,SV124: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV124 @ SV399 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV399 @ SV124 @ tc_nat )
| ( SV399 = SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1428,plain,
! [SV400: $i,SV125: $i] :
( ( ! [SY1819: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV125 @ SV400 ) @ SY1819 ) )
| ( c_HOL_Oord__class_Oless @ SV400 @ SY1819 @ tc_nat )
| ( SY1819 = SV400 )
| ( c_HOL_Oord__class_Oless @ SY1819 @ SV400 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1429,plain,
! [SV401: $i,SV126: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV126 @ SV401 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV401 @ SV126 @ tc_nat )
| ( SV401 = SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1430,plain,
! [SV402: $i,SV127: $i] :
( ( ! [SY1820: $i] :
( ~ ( class_Orderings_Olinorder @ SV127 )
| ( c_HOL_Oord__class_Oless @ SV402 @ SY1820 @ SV127 )
| ( c_HOL_Oord__class_Oless @ SY1820 @ SV402 @ SV127 )
| ( SY1820 = SV402 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1431,plain,
! [SV403: $i,SV128: $i] :
( ( ! [SY1821: $i] :
( ~ ( class_Orderings_Olinorder @ SV128 )
| ( c_HOL_Oord__class_Oless @ SV403 @ SY1821 @ SV128 )
| ( SY1821 = SV403 )
| ( c_HOL_Oord__class_Oless @ SY1821 @ SV403 @ SV128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1432,plain,
! [SV404: $i,SV129: $i] :
( ( ! [SY1822: $i] :
( ~ ( class_Orderings_Olinorder @ SV129 )
| ( SV404 = SY1822 )
| ( c_HOL_Oord__class_Oless @ SV404 @ SY1822 @ SV129 )
| ( c_HOL_Oord__class_Oless @ SY1822 @ SV404 @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1433,plain,
! [SV405: $i,SV130: $i] :
( ( ! [SY1823: $i,SY1824: $i,SY1825: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV130 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SV405 ) @ SY1823 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SY1824 ) @ SY1825 ) @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SY1823 @ SY1825 @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SV405 @ SY1824 @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1434,plain,
! [SV406: $i,SV131: $i] :
( ( ! [SY1826: $i,SY1827: $i,SY1828: $i] :
( ( c_Type_Otyping @ SV131 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV406 ) @ SY1826 ) @ SY1827 )
| ~ ( c_Type_Otyping @ SV131 @ SY1826 @ SY1828 )
| ~ ( c_Type_Otyping @ SV131 @ SV406 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1828 ) @ SY1827 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1435,plain,
! [SV407: $i,SV132: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV132 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV132 ) @ ( c_HOL_Ozero__class_Ozero @ SV132 ) @ SV407 @ SV132 @ SV132 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV132 ) @ SV407 @ ( c_HOL_Ozero__class_Ozero @ SV132 ) @ SV132 @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1436,plain,
! [SV133: $i] :
( ( ( SV133
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV133 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV133 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV133 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( SV133
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV133 ) ) )
| ( SV133
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV133 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV133 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV133 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1147]) ).
thf(1437,plain,
! [SV408: $i,SV134: $i] :
( ( ! [SY1829: $i,SY1830: $i,SY1831: $i,SY1832: $i] :
( ( SV134 = SV408 )
| ( SY1829 = SY1830 )
| ~ ( c_ListOrder_Ostep1 @ SY1831 @ ( c_List_Oappend @ SV134 @ ( c_List_Olist_OCons @ SY1829 @ ( c_List_Olist_ONil @ SY1832 ) @ SY1832 ) @ SY1832 ) @ ( c_List_Oappend @ SV408 @ ( c_List_Olist_OCons @ SY1830 @ ( c_List_Olist_ONil @ SY1832 ) @ SY1832 ) @ SY1832 ) @ SY1832 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1148]) ).
thf(1438,plain,
! [SV409: $i,SV135: $i] :
( ( ! [SY1833: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV135 @ SV409 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1833 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV135 ) @ SY1833 ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ SY1833 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV409 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1149]) ).
thf(1439,plain,
! [SV136: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV136 @ tc_nat )
= $true )
| ( ( SV136
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1150]) ).
thf(1440,plain,
! [SV410: $i,SV137: $i] :
( ( ! [SY1834: $i,SY1835: $i] :
( ( c_List_Olistsp @ SV137 @ ( c_List_Oappend @ SV410 @ SY1834 @ SY1835 ) @ SY1835 )
| ~ ( c_List_Olistsp @ SV137 @ SY1834 @ SY1835 )
| ~ ( c_List_Olistsp @ SV137 @ SV410 @ SY1835 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1441,plain,
! [SV411: $i,SV138: $i] :
( ( ! [SY1836: $i,SY1837: $i,SY1838: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV138 @ SV411 @ SY1836 @ ( c_Lambda_OdB_OAbs @ SY1837 ) @ SY1838 )
= ( hAPP @ ( hAPP @ SY1836 @ SY1837 ) @ ( c_Lambda_OdB_OdB__rec @ SV138 @ SV411 @ SY1836 @ SY1837 @ SY1838 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1442,plain,
! [SV412: $i,SV139: $i] :
( ( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV139 @ SV412 )
= SV139 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1443,plain,
! [SV140: $i] :
( ( ( ~ ( class_OrderedGroup_Osemigroup__add @ SV140 ) )
= $true )
| ( ( c_OrderedGroup_Osemigroup__add @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ SV140 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1155]) ).
thf(1444,plain,
! [SV413: $i,SV141: $i] :
( ( ! [SY1839: $i,SY1840: $i,SY1841: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV141 @ SV413 @ SY1839 @ SY1840 ) @ SY1841 )
= ( hAPP @ SV141 @ SY1841 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1841 @ SV413 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1445,plain,
! [SV414: $i,SV142: $i] :
( ( ! [SY1842: $i,SY1843: $i,SY1844: $i,SY1845: $i,SY1846: $i] :
( ( SV142
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV414 @ SV142 @ SY1842 @ SY1843 ) @ SV414 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SY1842 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1844 ) @ SY1845 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV142 )
| ~ ( c_Type_Otypings @ SY1842 @ SY1845 @ SY1846 )
| ~ ( c_Type_Otyping @ SY1842 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1844 ) @ SY1845 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1843 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1446,plain,
! [SV415: $i,SV143: $i] :
( ( ( c_Lambda_Osubstn @ SV143 @ SV415 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV143 ) @ SV415 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1158]) ).
thf(1447,plain,
! [SV416: $i,SV144: $i] :
( ( ! [SY1847: $i,SY1848: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV144 )
| ( c_HOL_Oord__class_Oless @ SV416 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ SY1847 ) @ SY1848 ) @ SV144 )
| ~ ( c_HOL_Oord__class_Oless @ SV416 @ SY1848 @ SV144 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV144 ) @ SY1847 @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1448,plain,
! [SV417: $i,SV145: $i] :
( ( ! [SY1849: $i,SY1850: $i,SY1851: $i,SY1852: $i] :
( ( c_List_Ofoldr @ SV145 @ ( c_List_Olist_OCons @ SV417 @ SY1849 @ SY1850 ) @ SY1851 @ SY1850 @ SY1852 )
= ( hAPP @ ( hAPP @ SV145 @ SV417 ) @ ( c_List_Ofoldr @ SV145 @ SY1849 @ SY1851 @ SY1850 @ SY1852 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1160]) ).
thf(1449,plain,
! [SV418: $i,SV146: $i] :
( ( ! [SY1853: $i,SY1854: $i,SY1855: $i] :
( ~ ( hBOOL @ ( hAPP @ SV146 @ ( c_Lambda_OdB_OdB__case @ SV418 @ SY1853 @ SY1854 @ ( c_Lambda_OdB_OAbs @ SY1855 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV146 @ ( hAPP @ SY1854 @ SY1855 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1450,plain,
! [SV419: $i,SV147: $i] :
( ( ! [SY1856: $i,SY1857: $i,SY1858: $i] :
( ~ ( hBOOL @ ( hAPP @ SV147 @ ( c_Lambda_OdB_OdB__case @ SV419 @ SY1856 @ SY1857 @ ( c_Lambda_OdB_OAbs @ SY1858 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV147 @ ( hAPP @ SY1857 @ SY1858 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1451,plain,
! [SV420: $i,SV148: $i] :
( ( ! [SY1859: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV148 ) @ ( c_List_Olist_OCons @ SV420 @ SY1859 @ SV148 ) @ SV148 )
= ( c_List_Olist_OCons @ SV420 @ SY1859 @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1452,plain,
! [SV421: $i,SV149: $i] :
( ( ! [SY1860: $i,SY1861: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV149 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV421 ) @ SY1860 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SY1861 ) @ SY1860 ) @ SV149 )
| ~ ( c_HOL_Oord__class_Oless @ SV421 @ SY1861 @ SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1453,plain,
! [SV422: $i,SV150: $i] :
( ( ! [SY1862: $i,SY1863: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV150 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV150 ) @ SV422 ) @ SY1862 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV150 ) @ SY1863 ) @ SY1862 ) @ SV150 )
| ~ ( c_HOL_Oord__class_Oless @ SV422 @ SY1863 @ SV150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1454,plain,
! [SV423: $i,SV151: $i] :
( ( ! [SY1864: $i,SY1865: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV151 )
| ( c_HOL_Oord__class_Oless @ SV423 @ SY1864 @ SV151 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV423 ) @ SY1865 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SY1864 ) @ SY1865 ) @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1455,plain,
! [SV424: $i,SV152: $i] :
( ( ! [SY1866: $i,SY1867: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV152 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV424 ) @ SY1866 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV424 ) @ SY1867 ) @ SV152 )
| ~ ( c_HOL_Oord__class_Oless @ SY1866 @ SY1867 @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1167]) ).
thf(1456,plain,
! [SV425: $i,SV153: $i] :
( ( ! [SY1868: $i,SY1869: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV153 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV425 ) @ SY1868 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV425 ) @ SY1869 ) @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SY1868 @ SY1869 @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1457,plain,
! [SV426: $i,SV154: $i] :
( ( ! [SY1870: $i,SY1871: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV154 )
| ( c_HOL_Oord__class_Oless @ SV426 @ SY1870 @ SV154 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SY1871 ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SY1871 ) @ SY1870 ) @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1458,plain,
! [SV155: $i] :
( ( ( SV155
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV155 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV155 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV155 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV155 ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV155 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV155 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1170]) ).
thf(1459,plain,
! [SV427: $i,SV156: $i] :
( ( ! [SY1872: $i,SY1873: $i] :
( ( c_Type_Otyping @ SV156 @ SV427 @ SY1872 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1873 ) @ SV427 ) )
| ~ ( c_Type_Otyping @ SV156 @ SY1873 @ SY1872 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1171]) ).
thf(1460,plain,
! [SV428: $i,SV157: $i] :
( ( ! [SY1874: $i,SY1875: $i,SY1876: $i,SY1877: $i] :
( ( c_ListOrder_Ostep1 @ SV157 @ SV428 @ SY1874 @ SY1875 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV157 @ SY1876 ) @ SY1877 ) )
| ~ ( c_ListOrder_Ostep1 @ SV157 @ ( c_List_Olist_OCons @ SY1876 @ SV428 @ SY1875 ) @ ( c_List_Olist_OCons @ SY1877 @ SY1874 @ SY1875 ) @ SY1875 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1461,plain,
! [SV429: $i,SV158: $i] :
( ( ! [SY1878: $i,SY1879: $i,SY1880: $i] :
( ( c_ListOrder_Ostep1 @ SV158 @ ( c_List_Olist_OCons @ SV429 @ SY1878 @ SY1879 ) @ ( c_List_Olist_OCons @ SV429 @ SY1880 @ SY1879 ) @ SY1879 )
| ~ ( c_ListOrder_Ostep1 @ SV158 @ SY1878 @ SY1880 @ SY1879 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1462,plain,
! [SV160: $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 ) @ SV160 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV160 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1175]) ).
thf(1463,plain,
! [SV430: $i,SV161: $i] :
( ( ! [SY1881: $i,SY1882: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV161 @ SV430 @ SY1881 ) @ SY1882 @ SY1881 )
= ( c_List_Oappend @ SV161 @ ( c_List_Oappend @ SV430 @ SY1882 @ SY1881 ) @ SY1881 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1176]) ).
thf(1464,plain,
! [SV431: $i,SV162: $i] :
( ( ! [SY1883: $i,SY1884: $i] :
( ( c_List_Oappend @ SV162 @ ( c_List_Oappend @ SV431 @ SY1883 @ SY1884 ) @ SY1884 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV162 @ SV431 @ SY1884 ) @ SY1883 @ SY1884 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1465,plain,
! [SV432: $i,SV163: $i] :
( ( ! [SY1885: $i,SY1886: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV163 @ SV432 @ SY1885 ) @ SY1886 @ SY1885 )
= ( c_List_Oappend @ SV163 @ ( c_List_Oappend @ SV432 @ SY1886 @ SY1885 ) @ SY1885 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1466,plain,
! [SV433: $i,SV164: $i] :
( ( ! [SY1887: $i,SY1888: $i] :
( ( c_List_Oappend @ SV164 @ ( c_List_Oappend @ SV433 @ SY1887 @ SY1888 ) @ SY1888 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV164 @ SV433 @ SY1888 ) @ SY1887 @ SY1888 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1467,plain,
! [SV434: $i,SV165: $i] :
( ( ! [SY1889: $i,SY1890: $i,SY1891: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV165 @ SV434 @ SY1889 @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY1890 ) @ SV434 ) @ SY1891 )
| ~ ( c_Type_Otyping @ SV165 @ SY1890 @ SY1891 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1180]) ).
thf(1468,plain,
! [SV435: $i,SV166: $i] :
( ( ! [SY1892: $i] :
( ~ ( class_Orderings_Oorder @ SV166 )
| ~ ( c_HOL_Oord__class_Oless @ SV435 @ SY1892 @ SV166 )
| ~ ( c_HOL_Oord__class_Oless @ SY1892 @ SV435 @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1469,plain,
! [SV436: $i,SV167: $i] :
( ( ! [SY1893: $i,SY1894: $i,SY1895: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV167 @ SV436 ) @ SY1893 ) @ SY1894 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV167 @ SV436 ) @ SY1895 ) @ SY1894 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV167 @ SY1893 ) @ SY1895 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1470,plain,
! [SV437: $i,SV168: $i] :
( ( ! [SY1896: $i,SY1897: $i,SY1898: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV168 @ SV437 ) @ SY1896 ) @ SY1897 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV168 @ SY1898 ) @ SY1897 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV168 @ SV437 ) @ SY1896 ) @ SY1898 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1183]) ).
thf(1471,plain,
! [SV438: $i,SV169: $i] :
( ( ! [SY1899: $i] :
( ~ ( class_Orderings_Olinorder @ SV169 )
| ~ ( c_HOL_Oord__class_Oless @ SV438 @ SY1899 @ SV169 )
| ~ ( c_HOL_Oord__class_Oless @ SY1899 @ SV438 @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1472,plain,
! [SV439: $i,SV170: $i] :
( ( ! [SY1900: $i] :
( ~ ( class_Orderings_Opreorder @ SV170 )
| ~ ( c_HOL_Oord__class_Oless @ SV439 @ SY1900 @ SV170 )
| ~ ( c_HOL_Oord__class_Oless @ SY1900 @ SV439 @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1473,plain,
! [SV440: $i,SV171: $i] :
( ( ! [SY1901: $i] :
( ~ ( class_Orderings_Opreorder @ SV171 )
| ~ ( c_HOL_Oord__class_Oless @ SV440 @ SY1901 @ SV171 )
| ~ ( c_HOL_Oord__class_Oless @ SY1901 @ SV440 @ SV171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1186]) ).
thf(1474,plain,
! [SV441: $i,SV172: $i] :
( ( ( hBOOL @ ( hAPP @ SV172 @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV172 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV172 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV172 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV172 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ SV172 @ SV441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1475,plain,
! [SV442: $i,SV173: $i] :
( ( ! [SY1902: $i,SY1903: $i,SY1904: $i] :
( ( ( c_List_Ofoldl @ SV173 @ ( hAPP @ ( hAPP @ SV173 @ SV442 ) @ SY1902 ) @ SY1903 @ SY1904 @ SY1904 )
= ( hAPP @ ( hAPP @ SV173 @ SV442 ) @ ( c_List_Ofoldl @ SV173 @ SY1902 @ SY1903 @ SY1904 @ SY1904 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV173 @ SY1904 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1476,plain,
! [SV443: $i,SV174: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV174 ) @ SV443 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV174 ) @ SV443 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1477,plain,
! [SV444: $i,SV175: $i] :
( ( ! [SY1905: $i,SY1906: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV175 ) @ SV444 ) ) @ SY1905 ) @ SY1906 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV175 ) @ SY1905 ) @ SY1906 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV444 ) @ SY1905 ) @ SY1906 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1190]) ).
thf(1478,plain,
! [SV445: $i,SV176: $i] :
( ( ! [SY1907: $i,SY1908: $i] :
( ( c_Type_Otypings @ SV176 @ SV445 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SY1907 @ SV176 @ SY1908 @ SV445 ) )
| ~ ( c_Type_Otyping @ SV176 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1908 ) @ SV445 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1907 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1191]) ).
thf(1479,plain,
! [SV446: $i,SV177: $i] :
( ( ! [SY1909: $i,SY1910: $i,SY1911: $i] :
( ~ ( hBOOL @ ( hAPP @ SV177 @ ( c_Lambda_OdB_OdB__case @ SV446 @ SY1909 @ SY1910 @ ( c_Lambda_OdB_OVar @ SY1911 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV177 @ ( hAPP @ SV446 @ SY1911 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1192]) ).
thf(1480,plain,
! [SV447: $i,SV178: $i] :
( ( ! [SY1912: $i,SY1913: $i,SY1914: $i] :
( ~ ( hBOOL @ ( hAPP @ SV178 @ ( c_Lambda_OdB_OdB__case @ SV447 @ SY1912 @ SY1913 @ ( c_Lambda_OdB_OVar @ SY1914 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV178 @ ( hAPP @ SV447 @ SY1914 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1193]) ).
thf(1481,plain,
! [SV448: $i,SV179: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV179 ) ) @ SV448 ) @ SV179 )
= SV448 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1482,plain,
! [SV449: $i,SV180: $i] :
( ( ! [SY1915: $i,SY1916: $i,SY1917: $i,SY1918: $i] :
( ~ ( hBOOL @ ( hAPP @ SV180 @ ( c_Lambda_OdB_OdB__case @ SV449 @ SY1915 @ SY1916 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1917 ) @ SY1918 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV180 @ ( hAPP @ ( hAPP @ SY1915 @ SY1917 ) @ SY1918 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1483,plain,
! [SV450: $i,SV181: $i] :
( ( ! [SY1919: $i,SY1920: $i,SY1921: $i,SY1922: $i] :
( ~ ( hBOOL @ ( hAPP @ SV181 @ ( c_Lambda_OdB_OdB__case @ SV450 @ SY1919 @ SY1920 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1921 ) @ SY1922 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV181 @ ( hAPP @ ( hAPP @ SY1919 @ SY1921 ) @ SY1922 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1484,plain,
! [SV451: $i,SV182: $i] :
( ( ! [SY1923: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV182 ) @ ( c_Lambda_OdB_OVar @ SV451 ) ) @ SY1923 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1485,plain,
! [SV452: $i,SV183: $i] :
( ( ! [SY1924: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV183 ) ) @ SV452 ) @ SY1924 )
= ( c_Lambda_OdB_OVar @ SV183 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV183 @ SY1924 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1486,plain,
! [SV453: $i,SV184: $i] :
( ( ! [SY1925: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV184 @ SV453 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1925 @ SV453 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV184 ) @ SY1925 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(1487,plain,
! [SV454: $i,SV185: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV185 ) ) @ SV454 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1488,plain,
! [SV455: $i,SV186: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV186 ) @ SV455 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV455 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1489,plain,
! [SV456: $i,SV187: $i] :
( ( ! [SY1926: $i,SY1927: $i,SY1928: $i] :
( ( SV187 = SV456 )
| ~ ( c_Type_Otyping @ SY1926 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1927 ) @ SY1928 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV456 )
| ~ ( c_Type_Otyping @ SY1926 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1927 ) @ SY1928 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1202]) ).
thf(1490,plain,
! [SV457: $i,SV188: $i] :
( ( ! [SY1929: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV188 @ SV457 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV188 @ SY1929 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV457 @ SY1929 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1491,plain,
! [SV458: $i,SV189: $i] :
( ( ( hBOOL @ ( hAPP @ SV189 @ SV458 ) )
| ( hBOOL @ ( hAPP @ SV189 @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV189 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV189 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV189 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV189 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1492,plain,
! [SV459: $i,SV190: $i] :
( ( ! [SY1930: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV190 @ SV459 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1930 @ SV459 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV190 ) @ SY1930 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1493,plain,
! [SV460: $i,SV191: $i] :
( ( ! [SY1931: $i,SY1932: $i,SY1933: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV191 @ SV460 @ SY1931 @ ( c_Lambda_OdB_OVar @ SY1932 ) @ SY1933 )
= ( hAPP @ SV191 @ SY1932 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1206]) ).
thf(1494,plain,
! [SV461: $i,SV192: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV192 ) @ SV461 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1495,plain,
! [SV462: $i,SV193: $i] :
( ( ! [SY1934: $i,SY1935: $i] :
( ( c_List_Ofoldl @ SV193 @ SV462 @ ( c_List_Olist_ONil @ SY1934 ) @ SY1935 @ SY1934 )
= SV462 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1208]) ).
thf(1496,plain,
! [SV463: $i,SV194: $i] :
( ( ! [SY1936: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV194 ) ) @ SV463 ) @ SY1936 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV463 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV194 ) @ SV463 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1936 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1497,plain,
! [SV195: $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 @ SV195 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV195 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV195 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV195 ) ) )
| ( SV195
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV195 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV195 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV195 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1210]) ).
thf(1498,plain,
! [SV464: $i,SV197: $i] :
( ( ! [SY1937: $i] :
( ( ( hAPP @ SV197 @ SV464 )
= SY1937 )
| ~ ( c_Type_Otyping @ SV197 @ ( c_Lambda_OdB_OVar @ SV464 ) @ SY1937 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1499,plain,
! [SV465: $i,SV198: $i] :
( ( ! [SY1938: $i,SY1939: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ SV198 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ SV465 ) @ SY1938 ) @ SY1939 @ SV198 @ SV198 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ SV465 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ SY1938 @ SY1939 @ SV198 @ SV198 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1500,plain,
! [SV199: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV199 ) ) )
= $true )
| ( ( ( SV199
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV199 ) ) )
| ( SV199
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV199 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV199 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV199 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1214]) ).
thf(1501,plain,
! [SV466: $i,SV200: $i] :
( ( ! [SY1940: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV200 ) @ SV466 ) ) @ SY1940 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV200 ) @ SY1940 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV466 ) @ SY1940 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1502,plain,
! [SV467: $i,SV201: $i] :
( ( ! [SY1941: $i,SY1942: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV201 @ SV467 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1941 ) @ SY1942 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV201 ) @ SY1941 ) @ SY1942 ) @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SY1941 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SY1942 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV467 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1216]) ).
thf(1503,plain,
! [SV468: $i,SV202: $i] :
( ( ! [SY1943: $i,SY1944: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV202 ) @ SV468 ) @ SY1943 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY1944 ) @ SV468 ) @ SY1943 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV202 ) @ SY1944 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1217]) ).
thf(1504,plain,
! [SV469: $i,SV203: $i] :
( ( ! [SY1945: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV203 ) ) @ SV469 ) @ SY1945 )
= ( c_Lambda_OdB_OVar @ SV203 ) )
| ( SV203 = SY1945 )
| ( c_HOL_Oord__class_Oless @ SY1945 @ SV203 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1218]) ).
thf(1505,plain,
! [SV470: $i,SV204: $i] :
( ( ! [SY1946: $i,SY1947: $i] :
( ( c_Type_Otyping @ SV204 @ ( c_Lambda_OdB_OVar @ SV470 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SY1946 @ SV204 @ SV470 @ SY1947 ) @ SY1946 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV204 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV470 ) @ SY1947 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1946 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1219]) ).
thf(1506,plain,
! [SV471: $i,SV205: $i] :
( ( ! [SY1948: $i] :
( ( SV205
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV471 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV471 @ SY1948 @ SV205 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV471 ) @ SY1948 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV205 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1507,plain,
! [SV472: $i,SV206: $i] :
( ( ! [SY1949: $i,SY1950: $i,SY1951: $i,SY1952: $i] :
( ( c_Lambda_OdB_OdB__case @ SV206 @ SV472 @ SY1949 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1950 ) @ SY1951 ) @ SY1952 )
= ( hAPP @ ( hAPP @ SV472 @ SY1950 ) @ SY1951 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1508,plain,
! [SV473: $i,SV207: $i] :
( ( ! [SY1953: $i,SY1954: $i,SY1955: $i] :
( ( ( hAPP @ ( hAPP @ SV207 @ SV473 ) @ ( c_List_Ofoldl @ SV207 @ SY1953 @ SY1954 @ SY1955 @ SY1955 ) )
= ( c_List_Ofoldl @ SV207 @ SV473 @ SY1954 @ SY1955 @ SY1955 ) )
| ~ ( c_OrderedGroup_Omonoid__add @ SY1953 @ SV207 @ SY1955 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1509,plain,
! [SV208: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV208 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV208 ) ) )
| ( SV208
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV208 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV208 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV208 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1223]) ).
thf(1510,plain,
! [SV474: $i,SV210: $i] :
( ( ! [SY1956: $i,SY1957: $i,SY1958: $i] :
( ( c_Lambda_OdB_OdB__case @ SV210 @ SV474 @ SY1956 @ ( c_Lambda_OdB_OVar @ SY1957 ) @ SY1958 )
= ( hAPP @ SV210 @ SY1957 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1511,plain,
! [SV475: $i,SV211: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV211 @ SV211 @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV211 ) ) @ SV475 ) @ SV211 )
= SV475 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1512,plain,
! [SV476: $i,SV212: $i] :
( ( ! [SY1959: $i,SY1960: $i,SY1961: $i,SY1962: $i] :
( ( c_List_Ofoldl @ SV212 @ SV476 @ ( c_List_Olist_OCons @ SY1959 @ SY1960 @ SY1961 ) @ SY1962 @ SY1961 )
= ( c_List_Ofoldl @ SV212 @ ( hAPP @ ( hAPP @ SV212 @ SV476 ) @ SY1959 ) @ SY1960 @ SY1962 @ SY1961 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1513,plain,
! [SV477: $i,SV214: $i] :
( ( c_Type_Otyping @ SV214 @ ( c_Lambda_OdB_OVar @ SV477 ) @ ( hAPP @ SV214 @ SV477 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1514,plain,
! [SV478: $i,SV215: $i] :
( ( ! [SY1963: $i,SY1964: $i,SY1965: $i,SY1966: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV215 @ SV478 @ SY1963 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1964 ) @ SY1965 ) @ SY1966 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV478 @ SY1964 ) @ SY1965 ) @ ( c_Lambda_OdB_OdB__rec @ SV215 @ SV478 @ SY1963 @ SY1964 @ SY1966 ) ) @ ( c_Lambda_OdB_OdB__rec @ SV215 @ SV478 @ SY1963 @ SY1965 @ SY1966 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1230]) ).
thf(1515,plain,
! [SV479: $i,SV217: $i] :
( ( ! [SY1967: $i,SY1968: $i,SY1969: $i,SY1970: $i,SY1971: $i] :
( ( c_Type_Otypings @ SV217 @ SV479 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SY1967 @ SY1968 @ SV217 @ SV479 ) )
| ~ ( c_Type_Otyping @ SV217 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1969 ) @ SY1970 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1968 )
| ~ ( c_Type_Otypings @ SV217 @ SY1970 @ SY1971 )
| ~ ( c_Type_Otyping @ SV217 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1969 ) @ SY1970 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV479 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1967 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1516,plain,
! [SV218: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV218 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV218 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1233]) ).
thf(1517,plain,
! [SV480: $i,SV219: $i] :
( ( ! [SY1972: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV219 ) @ SV480 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV219 ) @ SY1972 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV480 ) @ SY1972 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1234]) ).
thf(1518,plain,
! [SV481: $i,SV220: $i] :
( ( ! [SY1973: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV220 ) @ SV481 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1973 ) @ SV481 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV220 ) @ SY1973 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1519,plain,
! [SV482: $i,SV221: $i] :
( ( ! [SY1974: $i,SY1975: $i] :
( ( c_Lambda_Oliftn @ SV221 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV482 ) @ SY1974 ) @ SY1975 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ SV221 @ SV482 @ SY1975 ) ) @ ( c_Lambda_Oliftn @ SV221 @ SY1974 @ SY1975 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1520,plain,
! [SV483: $i,SV222: $i] :
( ( ! [SY1976: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV222 ) @ SV483 ) ) @ SY1976 ) @ SV483 )
= SV222 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1237]) ).
thf(1521,plain,
! [SV484: $i,SV224: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV224 ) @ ( c_Lambda_OdB_OVar @ SV484 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1239]) ).
thf(1522,plain,
! [SV485: $i,SV225: $i] :
( ( ! [SY1977: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV225 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV485 @ SV225 @ SY1977 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV485 ) @ SV225 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1977 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1240]) ).
thf(1523,plain,
! [SV486: $i,SV226: $i] :
( ( ! [SY1978: $i,SY1979: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV226 ) @ SV486 ) @ SY1978 @ SY1979 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ SV226 @ SY1978 @ SY1979 ) ) @ ( c_Lambda_Osubstn @ SV486 @ SY1978 @ SY1979 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1524,plain,
! [SV487: $i,SV227: $i] :
( ( ! [SY1980: $i,SY1981: $i,SY1982: $i,SY1983: $i] :
( ( c_List_Ofoldl @ SV227 @ SV487 @ ( c_List_Oappend @ SY1980 @ SY1981 @ SY1982 ) @ SY1983 @ SY1982 )
= ( c_List_Ofoldl @ SV227 @ ( c_List_Ofoldl @ SV227 @ SV487 @ SY1980 @ SY1983 @ SY1982 ) @ SY1981 @ SY1983 @ SY1982 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1242]) ).
thf(1525,plain,
! [SV488: $i,SV228: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV228 @ SV488 ) )
| ~ ( class_Orderings_Opreorder @ SV488 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1526,plain,
! [SV489: $i,SV229: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV229 @ SV489 ) )
| ~ ( class_Orderings_Oorder @ SV489 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1527,plain,
! [SV490: $i,SV230: $i] :
( ( c_fequal @ SV230 @ SV230 @ SV490 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1528,plain,
! [SV491: $i,SV231: $i] :
( ( ! [SY1984: $i] :
( ( SV231 = SV491 )
| ~ ( c_fequal @ SV231 @ SV491 @ SY1984 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1529,plain,
! [SV492: $i,SV232: $i] :
( ( ! [SY1985: $i] :
( ( c_List_Olist_OCons @ SV232 @ SV492 @ SY1985 )
!= ( c_List_Olist_ONil @ SY1985 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1530,plain,
! [SV493: $i,SV233: $i] :
( ( ! [SY1986: $i,SY1987: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV233 ) @ SV493 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1986 ) @ SY1987 ) )
| ( SV233 = SY1986 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1531,plain,
! [SV494: $i,SV234: $i] :
( ( ! [SY1988: $i,SY1989: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV234 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV494 ) @ SY1988 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV494 ) @ SY1989 ) )
| ( SY1988 = SY1989 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1532,plain,
! [SV495: $i,SV235: $i] :
( ( ! [SY1990: $i] :
( ( ( c_List_Oappend @ SV235 @ SV495 @ SY1990 )
!= ( c_List_Olist_ONil @ SY1990 ) )
| ( SV495
= ( c_List_Olist_ONil @ SY1990 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1533,plain,
! [SV496: $i,SV236: $i] :
( ( ! [SY1991: $i,SY1992: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV236 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV236 ) @ SV496 ) @ SY1991 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV236 ) @ SY1992 ) @ SY1991 ) )
| ( SV496 = SY1992 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1534,plain,
! [SV497: $i,SV237: $i] :
( ( ! [SY1993: $i,SY1994: $i] :
( ( ( c_List_Oappend @ SV237 @ SV497 @ SY1993 )
!= ( c_List_Oappend @ SV237 @ SY1994 @ SY1993 ) )
| ( SV497 = SY1994 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1535,plain,
! [SV498: $i,SV238: $i] :
( ( ! [SY1995: $i,SY1996: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV238 ) @ SV498 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1995 ) @ SY1996 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV238 = SY1995 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1536,plain,
! [SV499: $i,SV239: $i] :
( ( ! [SY1997: $i,SY1998: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV239 ) @ SV499 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1997 ) @ SY1998 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV499 = SY1998 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1537,plain,
! [SV500: $i,SV240: $i] :
( ( ! [SY1999: $i,SY2000: $i,SY2001: $i] :
( ( ( c_List_Olist_OCons @ SV240 @ SV500 @ SY1999 )
!= ( c_List_Olist_OCons @ SY2000 @ SY2001 @ SY1999 ) )
| ( SV240 = SY2000 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1538,plain,
! [SV501: $i,SV241: $i] :
( ( ! [SY2002: $i,SY2003: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV241 ) @ SV501 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY2002 ) @ SY2003 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV241 = SY2002 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1539,plain,
! [SV502: $i,SV242: $i] :
( ( ! [SY2004: $i,SY2005: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV242 ) @ SV502 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2004 @ SY2005 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV242
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2004 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV242 @ SV502 @ SY2004 @ SY2005 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2005
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1540,plain,
! [SV503: $i,SV243: $i] :
( ( ! [SY2006: $i,SY2007: $i,SY2008: $i,SY2009: $i,SY2010: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV243 ) @ SV503 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY2006 ) @ SY2007 ) @ SY2008 ) ) )
| ~ ( c_Type_Otyping @ SY2009 @ SY2007 @ SV243 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY2007 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY2009 @ SY2008 @ SV243 @ tc_Type_Otype ) @ SY2006 @ SY2010 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY2006 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1541,plain,
! [SV504: $i,SV244: $i] :
( ( ! [SY2011: $i,SY2012: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV244 )
| ~ ( class_Int_Onumber__ring @ SV244 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV244 ) @ SV504 ) @ SY2011 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV244 ) @ SV504 ) @ SY2012 ) )
| ( SY2011 = SY2012 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1542,plain,
! [SV505: $i,SV245: $i] :
( ( ! [SY2013: $i,SY2014: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV245 ) @ SV505 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY2013 ) @ SY2014 ) )
| ( SV505 = SY2014 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1543,plain,
! [SV506: $i,SV246: $i] :
( ( ! [SY2015: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV246 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV506 @ SY2015 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV246 )
= SV506 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1544,plain,
! [SV507: $i,SV247: $i] :
( ( ! [SY2016: $i] :
( ( c_Lambda_OdB_OVar @ SV247 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV507 ) @ SY2016 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1545,plain,
! [SV508: $i,SV248: $i] :
( ( ! [SY2017: $i,SY2018: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV248 ) @ SV508 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY2017 ) @ SY2018 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1264]) ).
thf(1546,plain,
! [SV509: $i,SV249: $i] :
( ( ! [SY2019: $i,SY2020: $i,SY2021: $i] :
( ( ( c_List_Oappend @ SV249 @ ( c_List_Olist_OCons @ SV509 @ ( c_List_Olist_ONil @ SY2019 ) @ SY2019 ) @ SY2019 )
!= ( c_List_Oappend @ SY2020 @ ( c_List_Olist_OCons @ SY2021 @ ( c_List_Olist_ONil @ SY2019 ) @ SY2019 ) @ SY2019 ) )
| ( SV249 = SY2020 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1547,plain,
! [SV510: $i,SV250: $i] :
( ( ! [SY2022: $i] :
( ( ( c_List_Oappend @ SV250 @ SV510 @ SY2022 )
!= ( c_List_Olist_ONil @ SY2022 ) )
| ( SV250
= ( c_List_Olist_ONil @ SY2022 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1548,plain,
! [SV511: $i,SV251: $i] :
( ( ! [SY2023: $i,SY2024: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV251 ) ) @ SV511 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2023 ) @ SY2024 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1549,plain,
! [SV512: $i,SV252: $i] :
( ( ! [SY2025: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV252 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV512 @ SY2025 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2025
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1268]) ).
thf(1550,plain,
! [SV513: $i,SV253: $i] :
( ( ! [SY2026: $i] :
( ( ( c_List_Oappend @ SV253 @ SV513 @ SY2026 )
!= SV253 )
| ( SV513
= ( c_List_Olist_ONil @ SY2026 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1269]) ).
thf(1551,plain,
! [SV514: $i,SV254: $i] :
( ( ! [SY2027: $i] :
( ( c_List_Olist_OCons @ SV254 @ SV514 @ SY2027 )
!= SV514 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1552,plain,
! [SV515: $i,SV255: $i] :
( ( ! [SY2028: $i] :
( SV255
!= ( c_List_Olist_OCons @ SV515 @ SV255 @ SY2028 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1271]) ).
thf(1553,plain,
! [SV516: $i,SV256: $i] :
( ( ! [SY2029: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV256 @ SV516 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2029 @ SV516 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV256 = SY2029 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1554,plain,
! [SV517: $i,SV257: $i] :
( ( ! [SY2030: $i,SY2031: $i] :
( ( ( c_List_Omap @ SV257 @ SV517 @ SY2030 @ SY2031 )
!= ( c_List_Olist_ONil @ SY2031 ) )
| ( SV517
= ( c_List_Olist_ONil @ SY2030 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1555,plain,
! [SV518: $i,SV258: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV258 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SV518 ) @ SV518 )
!= ( c_HOL_Ozero__class_Ozero @ SV258 ) )
| ( SV518
= ( c_HOL_Ozero__class_Ozero @ SV258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1274]) ).
thf(1556,plain,
! [SV519: $i,SV259: $i] :
( ( ! [SY2032: $i] :
( ( c_List_Olist_OCons @ SV259 @ SV519 @ SY2032 )
!= ( c_List_Olist_ONil @ SY2032 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(1557,plain,
! [SV520: $i,SV260: $i] :
( ( ! [SY2033: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV260 ) @ SV520 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2033 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV260 ) @ SV520 )
= SY2033 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1558,plain,
! [SV521: $i,SV261: $i] :
( ( ! [SY2034: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV261 @ SV521 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY2034 ) )
| ( SV261
= ( c_Lambda_OdB_OAbs @ SY2034 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1559,plain,
! [SV522: $i,SV262: $i] :
( ( ! [SY2035: $i] :
( ( ( c_Lambda_OdB_OVar @ SV262 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV522 @ SY2035 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV262 )
= SV522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1278]) ).
thf(1560,plain,
! [SV523: $i,SV263: $i] :
( ( ! [SY2036: $i,SY2037: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV263 ) @ SV523 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY2036 ) @ SY2037 ) )
| ( SV263 = SY2036 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1279]) ).
thf(1561,plain,
! [SV524: $i,SV264: $i] :
( ( ! [SY2038: $i] :
( ( ( c_List_Oappend @ SV264 @ SV524 @ SY2038 )
!= SV524 )
| ( SV264
= ( c_List_Olist_ONil @ SY2038 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1280]) ).
thf(1562,plain,
! [SV525: $i,SV265: $i] :
( ( ! [SY2039: $i] :
( ( c_List_Olist_ONil @ SV265 )
!= ( c_List_Olist_OCons @ SV525 @ SY2039 @ SV265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1281]) ).
thf(1563,plain,
! [SV526: $i,SV266: $i] :
( ( ! [SY2040: $i,SY2041: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV266 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV266 ) @ SV526 ) @ SY2040 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV266 ) @ SV526 ) @ SY2041 ) )
| ( SY2040 = SY2041 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1564,plain,
! [SV527: $i,SV267: $i] :
( ( ! [SY2042: $i] :
( ( SV267
!= ( c_List_Oappend @ SV267 @ SV527 @ SY2042 ) )
| ( SV527
= ( c_List_Olist_ONil @ SY2042 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1565,plain,
! [SV528: $i,SV268: $i] :
( ( ! [SY2043: $i,SY2044: $i,SY2045: $i,SY2046: $i,SY2047: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV268 ) @ SV528 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY2043 ) @ SY2044 ) @ SY2045 ) ) )
| ~ ( c_Type_Otyping @ SY2046 @ SY2044 @ SV528 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY2044 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY2046 @ SY2045 @ SV528 @ tc_Type_Otype ) @ SY2043 @ SY2047 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY2043 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1566,plain,
! [SV529: $i,SV269: $i] :
( ( ! [SY2048: $i,SY2049: $i] :
( ( ( c_List_Oappend @ SV269 @ SV529 @ SY2048 )
!= ( c_List_Oappend @ SY2049 @ SV529 @ SY2048 ) )
| ( SV269 = SY2049 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1285]) ).
thf(1567,plain,
! [SV530: $i,SV270: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV270 )
!= ( c_Lambda_OdB_OVar @ SV530 ) )
| ( SV270 = SV530 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1286]) ).
thf(1568,plain,
! [SV531: $i,SV271: $i] :
( ( ! [SY2050: $i,SY2051: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV271 ) @ SV531 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2050 ) @ SY2051 ) )
| ( SV531 = SY2051 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1569,plain,
! [SV532: $i,SV272: $i] :
( ( ! [SY2052: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV272 ) @ SV532 )
!= ( c_Lambda_OdB_OAbs @ SY2052 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1570,plain,
! [SV533: $i,SV273: $i] :
( ( ( c_Lambda_OdB_OVar @ SV273 )
!= ( c_Lambda_OdB_OAbs @ SV533 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1571,plain,
! [SV534: $i,SV274: $i] :
( ( ! [SY2053: $i,SY2054: $i] :
( ( ( c_List_Olist_ONil @ SV274 )
!= ( c_List_Omap @ SV534 @ SY2053 @ SY2054 @ SV274 ) )
| ( SY2053
= ( c_List_Olist_ONil @ SY2054 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1290]) ).
thf(1572,plain,
! [SV535: $i,SV275: $i] :
( ( ! [SY2055: $i,SY2056: $i,SY2057: $i] :
( ( ( c_List_Oappend @ SV275 @ ( c_List_Olist_OCons @ SV535 @ ( c_List_Olist_ONil @ SY2055 ) @ SY2055 ) @ SY2055 )
!= ( c_List_Oappend @ SY2056 @ ( c_List_Olist_OCons @ SY2057 @ ( c_List_Olist_ONil @ SY2055 ) @ SY2055 ) @ SY2055 ) )
| ( SV535 = SY2057 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1291]) ).
thf(1573,plain,
! [SV536: $i,SV276: $i] :
( ( ! [SY2058: $i] :
( ( SV276
!= ( c_List_Oappend @ SV536 @ SV276 @ SY2058 ) )
| ( SV536
= ( c_List_Olist_ONil @ SY2058 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1574,plain,
! [SV537: $i,SV277: $i] :
( ( ! [SY2059: $i] :
( ( ( c_List_Olist_ONil @ SV277 )
!= ( c_List_Oappend @ SV537 @ SY2059 @ SV277 ) )
| ( SY2059
= ( c_List_Olist_ONil @ SV277 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1575,plain,
! [SV538: $i,SV278: $i] :
( ( ! [SY2060: $i] :
( ( ( c_List_Olist_ONil @ SV278 )
!= ( c_List_Oappend @ SV538 @ SY2060 @ SV278 ) )
| ( SV538
= ( c_List_Olist_ONil @ SV278 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1576,plain,
! [SV539: $i,SV279: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV279 )
!= ( c_Lambda_OdB_OVar @ SV539 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1295]) ).
thf(1577,plain,
! [SV540: $i,SV280: $i] :
( ( ! [SY2061: $i,SY2062: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV280 ) @ SV540 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2061 ) @ SY2062 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV540 = SY2062 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1578,plain,
! [SV541: $i,SV281: $i] :
( ( ! [SY2063: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV281 ) @ SV541 )
!= ( c_Lambda_OdB_OVar @ SY2063 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1297]) ).
thf(1579,plain,
! [SV542: $i,SV282: $i] :
( ( ! [SY2064: $i] :
( ( c_Lambda_OdB_OAbs @ SV282 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV542 ) @ SY2064 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1298]) ).
thf(1580,plain,
! [SV543: $i,SV283: $i] :
( ( ! [SY2065: $i,SY2066: $i,SY2067: $i] :
( ( ( c_List_Olist_OCons @ SV283 @ SV543 @ SY2065 )
!= ( c_List_Olist_OCons @ SY2066 @ SY2067 @ SY2065 ) )
| ( SV543 = SY2067 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1581,plain,
! [SV544: $i,SV284: $i] :
( ( ! [SY2068: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV284 @ SV544 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY2068 ) )
| ( SV544
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1582,plain,
! [SV545: $i,SV285: $i] :
( ( ! [SY2069: $i] :
( ( ( c_Lambda_OdB_OVar @ SV285 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV545 @ SY2069 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2069
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1583,plain,
! [SV546: $i,SV286: $i] :
( ( ! [SY2070: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV286 )
| ~ ( class_Int_Onumber__ring @ SV286 )
| ( SV546
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV286 ) @ SV546 ) @ SY2070 ) )
| ( SY2070
= ( c_HOL_Ozero__class_Ozero @ SV286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1302]) ).
thf(1584,plain,
! [SV547: $i,SV287: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV287 )
!= ( c_Lambda_OdB_OAbs @ SV547 ) )
| ( SV287 = SV547 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1303]) ).
thf(1585,plain,
! [SV548: $i,SV288: $i] :
( ( ! [SY2071: $i,SY2072: $i,SY2073: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV288 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV548 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SY2071 ) @ SY2072 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SY2071 ) @ SY2073 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV548 ) @ SY2072 )
= SY2073 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1304]) ).
thf(1586,plain,
! [SV289: $i,SV1: $i] :
( ( ( hBOOL @ ( hAPP @ SV1 @ SV289 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV1 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4 @ SV1 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ SV1 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV1 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV1 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1305]) ).
thf(1587,plain,
! [SV290: $i,SV2: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV2 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV2 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__4 @ SV2 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV2 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV2 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV2 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ SV2 @ SV290 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1306]) ).
thf(1588,plain,
! [SV549: $i,SV291: $i,SV3: $i] :
( ( ! [SY2074: $i] :
( ( c_Type_Otyping @ SV3 @ SV291 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV549 @ SV3 @ SV291 @ SY2074 ) @ SV549 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV291 @ SY2074 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV549 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1589,plain,
! [SV550: $i,SV292: $i,SV4: $i] :
( ( ! [SY2075: $i] :
( ( c_Type_Otyping @ SV4 @ SV292 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV550 @ SV4 @ SV292 @ SY2075 ) @ SV550 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV4 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV292 @ SY2075 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1308]) ).
thf(1590,plain,
! [SV551: $i,SV293: $i,SV5: $i] :
( ( ! [SY2076: $i] :
( ( c_Type_Otypings @ SV5 @ SV293 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV551 @ SV5 @ SY2076 @ SV293 ) )
| ~ ( c_Type_Otyping @ SV5 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2076 @ SV293 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1309]) ).
thf(1591,plain,
! [SV552: $i,SV294: $i,SV6: $i] :
( ( ! [SY2077: $i] :
( ( c_Type_Otypings @ SV6 @ SV294 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV552 @ SV6 @ SY2077 @ SV294 ) )
| ~ ( c_Type_Otyping @ SV6 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2077 @ SV294 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV552 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1592,plain,
! [SV553: $i,SV295: $i,SV7: $i] :
( ( ! [SY2078: $i,SY2079: $i,SY2080: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV7 @ SV295 ) @ SV553 ) )
| ( SV295 = SV553 )
| ~ ( c_ListOrder_Ostep1 @ SV7 @ ( c_List_Oappend @ SY2078 @ ( c_List_Olist_OCons @ SV295 @ ( c_List_Olist_ONil @ SY2079 ) @ SY2079 ) @ SY2079 ) @ ( c_List_Oappend @ SY2080 @ ( c_List_Olist_OCons @ SV553 @ ( c_List_Olist_ONil @ SY2079 ) @ SY2079 ) @ SY2079 ) @ SY2079 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1593,plain,
! [SV554: $i,SV296: $i,SV8: $i] :
( ( ! [SY2081: $i,SY2082: $i,SY2083: $i] :
( ( c_List_Ofoldr @ SV8 @ ( c_List_Oappend @ SV296 @ SV554 @ SY2081 ) @ SY2082 @ SY2081 @ SY2083 )
= ( c_List_Ofoldr @ SV8 @ SV296 @ ( c_List_Ofoldr @ SV8 @ SV554 @ SY2082 @ SY2081 @ SY2083 ) @ SY2081 @ SY2083 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1312]) ).
thf(1594,plain,
! [SV555: $i,SV297: $i,SV9: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV9 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV9 ) @ SV297 ) @ SV555 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV9 ) @ SV555 ) @ SV297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1313]) ).
thf(1595,plain,
! [SV556: $i,SV298: $i,SV10: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV10 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV10 ) @ SV298 ) @ SV556 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV10 ) @ SV556 ) @ SV298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1596,plain,
! [SV557: $i,SV299: $i,SV11: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV11 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV11 ) @ SV299 ) @ SV557 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV11 ) @ SV557 ) @ SV299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1597,plain,
! [SV558: $i,SV300: $i,SV12: $i] :
( ( ! [SY2084: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV12 ) @ SV300 ) @ SV558 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV12 ) @ SY2084 ) @ SV558 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV300 ) @ SY2084 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1598,plain,
! [SV18: $i] :
( ( ( SV18
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV18 ) ) )
= $true )
| ( ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV18 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV18 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1322]) ).
thf(1599,plain,
! [SV559: $i,SV306: $i,SV19: $i] :
( ( ! [SY2085: $i,SY2086: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV19 @ SV306 ) @ SV559 ) @ SY2085 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV19 @ SV306 ) @ SY2086 ) @ SY2085 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV19 @ SV306 ) @ SV559 ) @ SY2086 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1600,plain,
! [SV560: $i,SV307: $i,SV20: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV20 @ SV307 ) @ SV560 ) @ SV560 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1601,plain,
! [SV561: $i,SV308: $i,SV21: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV21 @ SV308 ) @ SV561 ) @ SV561 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1602,plain,
! [SV562: $i,SV310: $i,SV23: $i] :
( ( ! [SY2087: $i,SY2088: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV23 @ SV310 ) @ SV562 ) )
| ( c_ListOrder_Ostep1 @ SV23 @ ( c_List_Olist_OCons @ SV310 @ SY2087 @ SY2088 ) @ ( c_List_Olist_OCons @ SV562 @ SY2087 @ SY2088 ) @ SY2088 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1327]) ).
thf(1603,plain,
! [SV563: $i,SV311: $i,SV24: $i] :
( ( ! [SY2089: $i,SY2090: $i,SY2091: $i] :
( ( SV24 = SV311 )
| ( SV563 = SY2089 )
| ~ ( c_ListOrder_Ostep1 @ SY2090 @ ( c_List_Olist_OCons @ SV311 @ SY2089 @ SY2091 ) @ ( c_List_Olist_OCons @ SV24 @ SV563 @ SY2091 ) @ SY2091 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1328]) ).
thf(1604,plain,
! [SV564: $i,SV312: $i,SV25: $i] :
( ( ! [SY2092: $i,SY2093: $i] :
( ( c_Lambda_OdB_OdB__case @ SV25 @ SV312 @ SV564 @ ( c_Lambda_OdB_OAbs @ SY2092 ) @ SY2093 )
= ( hAPP @ SV564 @ SY2092 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1329]) ).
thf(1605,plain,
! [SV26: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV26 ) ) )
= $true )
| ( ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV26 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV26 ) ) )
= $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 @ SV26 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV26 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV26 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1330]) ).
thf(1606,plain,
! [SV565: $i,SV313: $i,SV27: $i] :
( ( ! [SY2094: $i] :
( ( c_List_Olistsp @ SV27 @ SV313 @ SV565 )
| ~ ( c_List_Olistsp @ SV27 @ ( c_List_Oappend @ SY2094 @ SV313 @ SV565 ) @ SV565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1331]) ).
thf(1607,plain,
! [SV566: $i,SV314: $i,SV28: $i] :
( ( ! [SY2095: $i] :
( ( c_List_Olistsp @ SV28 @ SV314 @ SV566 )
| ~ ( c_List_Olistsp @ SV28 @ ( c_List_Oappend @ SV314 @ SY2095 @ SV566 ) @ SV566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1332]) ).
thf(1608,plain,
! [SV315: $i,SV29: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV29 ) ) @ ( c_Lambda_OdB_OAbs @ SV315 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV29 ) @ SV315 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1333]) ).
thf(1609,plain,
! [SV567: $i,SV316: $i,SV30: $i] :
( ( ! [SY2096: $i,SY2097: $i] :
( ( c_ListOrder_Ostep1 @ SV30 @ ( c_List_Oappend @ SV316 @ SV567 @ SY2096 ) @ ( c_List_Oappend @ SV316 @ SY2097 @ SY2096 ) @ SY2096 )
| ~ ( c_ListOrder_Ostep1 @ SV30 @ SV567 @ SY2097 @ SY2096 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1334]) ).
thf(1610,plain,
! [SV568: $i,SV317: $i,SV31: $i] :
( ( ! [SY2098: $i,SY2099: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV31 @ SV317 @ SV568 @ SY2098 )
| ( c_ListOrder_Ostep1 @ SV31 @ ( c_List_Oappend @ SV317 @ SY2099 @ SY2098 ) @ ( c_List_Oappend @ SV568 @ SY2099 @ SY2098 ) @ SY2098 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1335]) ).
thf(1611,plain,
! [SV569: $i,SV318: $i,SV32: $i] :
( ( ( c_Lambda_Osubstn @ SV32 @ SV318 @ SV569 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV32 ) @ ( c_Lambda_Oliftn @ SV569 @ SV318 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ SV569 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1612,plain,
! [SV33: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV33 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ ( c_HOL_Ozero__class_Ozero @ SV33 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV33 ) )
= ( c_HOL_Ozero__class_Ozero @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1337]) ).
thf(1613,plain,
! [SV570: $i,SV319: $i,SV34: $i] :
( ( ! [SY2100: $i,SY2101: $i] :
( ( c_Type_Otyping @ SV34 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV319 @ SV570 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2100 )
| ~ ( c_Type_Otypings @ SV34 @ SV570 @ SY2101 )
| ~ ( c_Type_Otyping @ SV34 @ SV319 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY2101 @ SY2100 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(1614,plain,
! [SV571: $i,SV320: $i,SV35: $i] :
( ( ! [SY2102: $i] :
( ~ ( class_Orderings_Opreorder @ SV35 )
| ( c_HOL_Oord__class_Oless @ SV320 @ SV571 @ SV35 )
| ~ ( c_HOL_Oord__class_Oless @ SY2102 @ SV571 @ SV35 )
| ~ ( c_HOL_Oord__class_Oless @ SV320 @ SY2102 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1339]) ).
thf(1615,plain,
! [SV572: $i,SV321: $i,SV36: $i] :
( ( ! [SY2103: $i] :
( ~ ( class_Orderings_Oorder @ SV36 )
| ( c_HOL_Oord__class_Oless @ SV321 @ SV572 @ SV36 )
| ~ ( c_HOL_Oord__class_Oless @ SV321 @ SY2103 @ SV36 )
| ~ ( c_HOL_Oord__class_Oless @ SY2103 @ SV572 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1616,plain,
! [SV573: $i,SV322: $i,SV37: $i] :
( ( ! [SY2104: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV37 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV322 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV573 ) @ SY2104 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV322 ) @ SV573 ) ) @ SY2104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1341]) ).
thf(1617,plain,
! [SV574: $i,SV323: $i,SV38: $i] :
( ( ! [SY2105: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV38 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV323 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV574 ) @ SY2105 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV574 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV323 ) @ SY2105 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(1618,plain,
! [SV575: $i,SV324: $i,SV39: $i] :
( ( ! [SY2106: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV39 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ SV324 ) @ SV575 ) ) @ SY2106 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ SV324 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ SV575 ) @ SY2106 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1343]) ).
thf(1619,plain,
! [SV576: $i,SV325: $i,SV40: $i] :
( ( ! [SY2107: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV40 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ SV325 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ SV576 ) @ SY2107 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ SV576 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ SV325 ) @ SY2107 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1344]) ).
thf(1620,plain,
! [SV577: $i,SV326: $i,SV41: $i] :
( ( ! [SY2108: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV41 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV326 ) @ SV577 ) ) @ SY2108 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV326 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV577 ) @ SY2108 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1345]) ).
thf(1621,plain,
! [SV578: $i,SV327: $i,SV42: $i] :
( ( ! [SY2109: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV42 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV327 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV578 ) @ SY2109 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV327 ) @ SV578 ) ) @ SY2109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1346]) ).
thf(1622,plain,
! [SV579: $i,SV328: $i,SV43: $i] :
( ( ! [SY2110: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV43 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ SV328 ) @ SV579 ) ) @ SY2110 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ SV328 ) @ SY2110 ) ) @ SV579 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1347]) ).
thf(1623,plain,
! [SV580: $i,SV329: $i,SV44: $i] :
( ( ! [SY2111: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV44 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SV329 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SV580 ) @ SY2111 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SV580 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SV329 ) @ SY2111 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1348]) ).
thf(1624,plain,
! [SV581: $i,SV330: $i,SV45: $i] :
( ( ! [SY2112: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV45 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV45 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV45 ) @ SV330 ) @ SV581 ) ) @ SY2112 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV45 ) @ SV330 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV45 ) @ SV581 ) @ SY2112 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1349]) ).
thf(1625,plain,
! [SV582: $i,SV331: $i,SV48: $i] :
( ( ! [SY2113: $i,SY2114: $i,SY2115: $i] :
( ( hAPP @ ( c_COMBC @ SV48 @ SV331 @ SV582 @ SY2113 @ SY2114 ) @ SY2115 )
= ( hAPP @ ( hAPP @ SV48 @ SY2115 ) @ SV331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1352]) ).
thf(1626,plain,
! [SV583: $i,SV332: $i,SV49: $i] :
( ( ! [SY2116: $i] :
( ( c_List_Ofoldr @ SV49 @ ( c_List_Olist_ONil @ SV332 ) @ SV583 @ SV332 @ SY2116 )
= SV583 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1353]) ).
thf(1627,plain,
! [SV584: $i,SV333: $i,SV50: $i] :
( ( ( c_List_Omap @ SV50 @ ( c_List_Olist_ONil @ SV333 ) @ SV333 @ SV584 )
= ( c_List_Olist_ONil @ SV584 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1354]) ).
thf(1628,plain,
! [SV585: $i,SV334: $i,SV51: $i] :
( ( ! [SY2117: $i,SY2118: $i,SY2119: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV51 @ SV334 ) @ SV585 ) )
| ( c_ListOrder_Ostep1 @ SV51 @ SY2117 @ SY2118 @ SY2119 )
| ~ ( c_ListOrder_Ostep1 @ SV51 @ ( c_List_Oappend @ SY2117 @ ( c_List_Olist_OCons @ SV334 @ ( c_List_Olist_ONil @ SY2119 ) @ SY2119 ) @ SY2119 ) @ ( c_List_Oappend @ SY2118 @ ( c_List_Olist_OCons @ SV585 @ ( c_List_Olist_ONil @ SY2119 ) @ SY2119 ) @ SY2119 ) @ SY2119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1355]) ).
thf(1629,plain,
! [SV52: $i] :
( ( ( SV52
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV52 ) ) )
= $true )
| ( ( ( SV52
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV52 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV52 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV52 ) ) )
= $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 @ SV52 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV52 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV52 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1356]) ).
thf(1630,plain,
! [SV586: $i,SV335: $i,SV53: $i] :
( ( ! [SY2120: $i,SY2121: $i,SY2122: $i] :
( ( c_Type_Otypings @ SV53 @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SV335 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV586 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SY2120 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2121 )
| ~ ( c_Type_Otypings @ ( c_Type_Oshift @ SV53 @ SV586 @ SY2122 @ tc_Type_Otype ) @ SY2120 @ SY2121 )
| ~ ( c_Type_Otyping @ SV53 @ SV335 @ SY2122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1357]) ).
thf(1631,plain,
! [SV587: $i,SV336: $i,SV54: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV54 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV336 ) @ SV587 ) @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV54 )
| ~ ( c_HOL_Oord__class_Oless @ SV587 @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV54 )
| ~ ( c_HOL_Oord__class_Oless @ SV336 @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1358]) ).
thf(1632,plain,
! [SV588: $i,SV337: $i,SV55: $i] :
( ( ! [SY2123: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV55 @ SV337 @ SV588 ) @ SY2123 @ SV588 )
= ( c_List_Olist_OCons @ SV55 @ ( c_List_Oappend @ SV337 @ SY2123 @ SV588 ) @ SV588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1359]) ).
thf(1633,plain,
! [SV589: $i,SV338: $i,SV56: $i] :
( ( ! [SY2124: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV56 @ SV338 @ SV589 ) @ SY2124 @ SV589 )
= ( c_List_Olist_OCons @ SV56 @ ( c_List_Oappend @ SV338 @ SY2124 @ SV589 ) @ SV589 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1360]) ).
thf(1634,plain,
! [SV590: $i,SV339: $i,SV57: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV57 ) @ SV339 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV57 ) @ SV590 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV339 ) @ SV590 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1361]) ).
thf(1635,plain,
! [SV591: $i,SV340: $i,SV58: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV58 ) @ SV340 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV591 ) @ SV340 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV58 ) @ SV591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1362]) ).
thf(1636,plain,
! [SV592: $i,SV341: $i,SV59: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV59 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV341 @ SV592 @ SV59 @ SV59 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV341 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV592 @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 @ SV59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1363]) ).
thf(1637,plain,
! [SV593: $i,SV342: $i,SV60: $i] :
( ( ! [SY2125: $i,SY2126: $i] :
( ( c_List_Omap @ SV60 @ ( c_List_Olist_OCons @ SV342 @ SV593 @ SY2125 ) @ SY2125 @ SY2126 )
= ( c_List_Olist_OCons @ ( hAPP @ SV60 @ SV342 ) @ ( c_List_Omap @ SV60 @ SV593 @ SY2125 @ SY2126 ) @ SY2126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1364]) ).
thf(1638,plain,
! [SV594: $i,SV343: $i,SV61: $i] :
( ( ! [SY2127: $i,SY2128: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ SV61 @ SV343 ) @ ( c_List_Omap @ SV61 @ SV594 @ SY2127 @ SY2128 ) @ SY2128 )
= ( c_List_Omap @ SV61 @ ( c_List_Olist_OCons @ SV343 @ SV594 @ SY2127 ) @ SY2127 @ SY2128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1365]) ).
thf(1639,plain,
! [SV595: $i,SV344: $i,SV62: $i] :
( ( ! [SY2129: $i,SY2130: $i] :
( ( c_List_Omap @ SV62 @ ( c_List_Olist_OCons @ SV344 @ SV595 @ SY2129 ) @ SY2129 @ SY2130 )
= ( c_List_Olist_OCons @ ( hAPP @ SV62 @ SV344 ) @ ( c_List_Omap @ SV62 @ SV595 @ SY2129 @ SY2130 ) @ SY2130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1366]) ).
thf(1640,plain,
! [SV63: $i] :
( ( ( SV63
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV63 ) ) )
= $true )
| ( ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV63 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV63 ) ) )
= $true )
| ( ( SV63
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV63 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV63 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV63 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1367]) ).
thf(1641,plain,
! [SV596: $i,SV345: $i,SV64: $i] :
( ( ! [SY2131: $i] :
( ( c_List_Olist_OCons @ SV64 @ ( c_List_Oappend @ SV345 @ SV596 @ SY2131 ) @ SY2131 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV64 @ SV345 @ SY2131 ) @ SV596 @ SY2131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1368]) ).
thf(1642,plain,
! [SV597: $i,SV346: $i,SV65: $i] :
( ( ! [SY2132: $i] :
( ( c_List_Olist_OCons @ SV65 @ ( c_List_Oappend @ SV346 @ SV597 @ SY2132 ) @ SY2132 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV65 @ SV346 @ SY2132 ) @ SV597 @ SY2132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1643,plain,
! [SV598: $i,SV347: $i,SV66: $i] :
( ( ! [SY2133: $i,SY2134: $i,SY2135: $i] :
( ( SV66 = SV347 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV598 @ SV347 ) @ SV66 ) )
| ~ ( c_ListOrder_Ostep1 @ SV598 @ ( c_List_Olist_OCons @ SV347 @ SY2133 @ SY2134 ) @ ( c_List_Olist_OCons @ SV66 @ SY2135 @ SY2134 ) @ SY2134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1644,plain,
! [SV599: $i,SV348: $i,SV67: $i] :
( ( ! [SY2136: $i,SY2137: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV67 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ SV348 ) @ SV599 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ SY2136 ) @ SY2137 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ SV348 ) @ SY2136 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ SV599 ) @ SY2137 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(1645,plain,
! [SV600: $i,SV349: $i,SV68: $i] :
( ( ! [SY2138: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV68 ) @ SV349 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV600 ) @ SY2138 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV349 ) @ SY2138 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV68 ) @ SV600 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1372]) ).
thf(1646,plain,
! [SV601: $i,SV350: $i,SV69: $i] :
( ( ( ( c_Lambda_Oliftn @ SV69 @ ( c_Lambda_OdB_OVar @ SV350 ) @ SV601 )
= ( c_Lambda_OdB_OVar @ SV350 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV350 @ SV601 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1373]) ).
thf(1647,plain,
! [SV602: $i,SV351: $i,SV70: $i] :
( ( ! [SY2139: $i] :
( ( c_Type_Otyping @ SV70 @ SV351 @ SV602 )
| ~ ( c_Type_Otyping @ SV70 @ SY2139 @ SV602 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY2139 ) @ SV351 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1374]) ).
thf(1648,plain,
! [SV603: $i,SV352: $i,SV71: $i] :
( ( ! [SY2140: $i,SY2141: $i] :
( ( c_Type_Otypings @ ( c_Type_Oshift @ SV71 @ SV352 @ SV603 @ tc_Type_Otype ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ SV352 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SY2140 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2141 )
| ~ ( c_Type_Otypings @ SV71 @ SY2140 @ SY2141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1375]) ).
thf(1649,plain,
! [SV353: $i,SV72: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV72 ) ) @ SV353 )
= ( c_Lambda_OdB_OVar @ SV72 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV72 @ SV353 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1376]) ).
thf(1650,plain,
! [SV604: $i,SV354: $i,SV73: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV73 ) @ SV354 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV604 ) @ SV354 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV73 ) @ SV604 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1377]) ).
thf(1651,plain,
! [SV74: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV74 ) ) )
= $true )
| ( ( ( SV74
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV74 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV74 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV74 ) ) )
= $true )
| ( ( SV74
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV74 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV74 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV74 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1378]) ).
thf(1652,plain,
! [SV355: $i,SV75: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV75 @ SV75 @ tc_nat )
= $true )
| ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV75 ) @ SV355 @ SV75 )
= ( c_Lambda_Oliftn @ SV75 @ SV355 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1379]) ).
thf(1653,plain,
! [SV605: $i,SV356: $i,SV76: $i] :
( ( ( c_List_Olist_OCons @ SV76 @ SV356 @ SV605 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV605 ) @ ( c_List_Olist_OCons @ SV76 @ SV356 @ SV605 ) @ SV605 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1380]) ).
thf(1654,plain,
! [SV606: $i,SV357: $i,SV77: $i] :
( ( ! [SY2142: $i,SY2143: $i,SY2144: $i] :
( ~ ( c_Type_Otyping @ SV77 @ SV357 @ SV606 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV77 @ SY2142 @ SV606 @ tc_Type_Otype ) @ SY2143 @ SY2144 )
| ( c_Type_Otyping @ SV77 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY2143 ) @ SV357 ) @ SY2142 ) @ SY2144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1381]) ).
thf(1655,plain,
! [SV607: $i,SV358: $i,SV78: $i] :
( ( ( c_List_Olist_ONil @ SV78 )
= ( c_List_Omap @ SV358 @ ( c_List_Olist_ONil @ SV607 ) @ SV607 @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1382]) ).
thf(1656,plain,
! [SV608: $i,SV359: $i,SV79: $i] :
( ( ! [SY2145: $i,SY2146: $i,SY2147: $i] :
( ( SV79 = SV359 )
| ( c_ListOrder_Ostep1 @ SV608 @ SV79 @ SV359 @ SY2145 )
| ~ ( c_ListOrder_Ostep1 @ SV608 @ ( c_List_Oappend @ SV79 @ ( c_List_Olist_OCons @ SY2146 @ ( c_List_Olist_ONil @ SY2145 ) @ SY2145 ) @ SY2145 ) @ ( c_List_Oappend @ SV359 @ ( c_List_Olist_OCons @ SY2147 @ ( c_List_Olist_ONil @ SY2145 ) @ SY2145 ) @ SY2145 ) @ SY2145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1383]) ).
thf(1657,plain,
! [SV361: $i,SV82: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV82 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV82 ) @ ( c_HOL_Ozero__class_Ozero @ SV82 ) ) @ SV361 )
= SV361 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1385]) ).
thf(1658,plain,
! [SV362: $i,SV83: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV83 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV83 ) @ ( c_HOL_Ozero__class_Ozero @ SV83 ) ) @ SV362 )
= SV362 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1386]) ).
thf(1659,plain,
! [SV363: $i,SV84: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV84 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV84 )
| ( SV363
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV363 ) @ ( c_HOL_Ozero__class_Ozero @ SV84 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1387]) ).
thf(1660,plain,
! [SV364: $i,SV85: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV85 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV85 ) @ SV364 ) @ ( c_HOL_Ozero__class_Ozero @ SV85 ) )
= SV364 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1388]) ).
thf(1661,plain,
! [SV365: $i,SV86: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV86 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV86 ) @ ( c_HOL_Ozero__class_Ozero @ SV86 ) ) @ SV365 )
= SV365 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1389]) ).
thf(1662,plain,
! [SV366: $i,SV87: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV87 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV87 ) @ SV366 ) @ ( c_HOL_Ozero__class_Ozero @ SV87 ) )
= SV366 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1390]) ).
thf(1663,plain,
! [SV367: $i,SV88: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV88 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV88 ) @ SV367 ) @ ( c_HOL_Ozero__class_Ozero @ SV88 ) )
= SV367 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1391]) ).
thf(1664,plain,
! [SV368: $i,SV89: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV89 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ ( c_HOL_Ozero__class_Ozero @ SV89 ) ) @ SV368 )
= SV368 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1392]) ).
thf(1665,plain,
! [SV369: $i,SV90: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV90 ) ) @ ( c_Lambda_OdB_OAbs @ SV369 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV90 ) @ SV369 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1393]) ).
thf(1666,plain,
! [SV609: $i,SV370: $i,SV91: $i] :
( ( ! [SY2148: $i] :
( ( ( hAPP @ ( hAPP @ SV91 @ SV370 ) @ SV609 )
= SV370 )
| ~ ( c_OrderedGroup_Omonoid__add @ SV609 @ SV91 @ SY2148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1667,plain,
! [SV610: $i,SV371: $i,SV92: $i] :
( ( ! [SY2149: $i] :
( ( ( hAPP @ ( hAPP @ SV92 @ SV371 ) @ SV610 )
= SV610 )
| ~ ( c_OrderedGroup_Omonoid__add @ SV371 @ SV92 @ SY2149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1395]) ).
thf(1668,plain,
! [SV372: $i,SV93: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV93 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV372 @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV372 ) @ SV372 ) @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1396]) ).
thf(1669,plain,
! [SV373: $i,SV94: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV94 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV373 ) @ SV373 ) @ SV94 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV373 @ SV94 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1397]) ).
thf(1670,plain,
! [SV611: $i,SV374: $i,SV95: $i] :
( ( ! [SY2150: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV95 ) @ SV374 ) @ SV611 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY2150 ) @ SV374 ) @ SV611 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV95 ) @ SY2150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1398]) ).
thf(1671,plain,
! [SV612: $i,SV375: $i,SV96: $i] :
( ( ! [SY2151: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV96 ) @ SV375 ) @ SV612 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV96 ) @ SY2151 ) @ SV612 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV375 ) @ SY2151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1399]) ).
thf(1672,plain,
! [SV613: $i,SV376: $i,SV97: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV97 )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SV376 @ SV613 @ SV97 @ SV97 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SV613 @ SV376 @ SV97 @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1400]) ).
thf(1673,plain,
! [SV614: $i,SV377: $i,SV98: $i] :
( ( ! [SY2152: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV98 @ SV377 ) @ SV614 ) @ SY2152 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV98 @ SV614 ) @ SY2152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1401]) ).
thf(1674,plain,
! [SV615: $i,SV378: $i,SV99: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV99 @ ( c_List_Olist_ONil @ SV378 ) @ SV615 @ SV378 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1402]) ).
thf(1675,plain,
! [SV616: $i,SV379: $i,SV100: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV100 @ SV379 @ ( c_List_Olist_ONil @ SV616 ) @ SV616 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1403]) ).
thf(1676,plain,
! [SV380: $i,SV101: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV101 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ SV380 ) @ SV380 ) @ ( c_HOL_Ozero__class_Ozero @ SV101 ) @ SV101 )
| ~ ( c_HOL_Oord__class_Oless @ SV380 @ ( c_HOL_Ozero__class_Ozero @ SV101 ) @ SV101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1404]) ).
thf(1677,plain,
! [SV381: $i,SV102: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV102 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV381 @ ( c_HOL_Ozero__class_Ozero @ SV102 ) @ SV102 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SV381 ) @ SV381 ) @ ( c_HOL_Ozero__class_Ozero @ SV102 ) @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1405]) ).
thf(1678,plain,
! [SV382: $i,SV103: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV103 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV382 @ ( c_HOL_Ozero__class_Ozero @ SV103 ) @ SV103 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV103 ) @ SV382 ) @ SV382 ) @ ( c_HOL_Ozero__class_Ozero @ SV103 ) @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1406]) ).
thf(1679,plain,
! [SV383: $i,SV104: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV104 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV104 ) @ SV383 ) @ SV383 ) @ ( c_HOL_Ozero__class_Ozero @ SV104 ) @ SV104 )
| ~ ( c_HOL_Oord__class_Oless @ SV383 @ ( c_HOL_Ozero__class_Ozero @ SV104 ) @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1407]) ).
thf(1680,plain,
! [SV617: $i,SV384: $i,SV105: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV105 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV384 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ ( c_HOL_Ozero__class_Ozero @ SV105 ) @ SV617 @ SV105 @ SV105 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV384 @ SV617 @ SV105 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1408]) ).
thf(1681,plain,
! [SV618: $i,SV385: $i,SV106: $i] :
( ( ! [SY2153: $i] :
( ( c_Type_Otyping @ SV106 @ ( c_Lambda_OdB_OAbs @ SV385 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV618 ) @ SY2153 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV106 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV618 @ tc_Type_Otype ) @ SV385 @ SY2153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1409]) ).
thf(1682,plain,
! [SV619: $i,SV386: $i,SV107: $i] :
( ( ! [SY2154: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV107 @ SV386 @ SV619 @ SY2154 ) @ SV386 )
= SV619 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1410]) ).
thf(1683,plain,
! [SV620: $i,SV387: $i,SV108: $i] :
( ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV108 ) @ SV387 @ SV620 )
= ( c_Lambda_OdB_OVar @ SV108 ) )
| ( SV108 = SV620 )
| ( c_HOL_Oord__class_Oless @ SV620 @ SV108 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1411]) ).
thf(1684,plain,
! [SV109: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV109 ) ) )
= $true )
| ( ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV109 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV109 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV109 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1412]) ).
thf(1685,plain,
! [SV388: $i,SV112: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV112 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV388 @ SV388 @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1415]) ).
thf(1686,plain,
! [SV389: $i,SV113: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV113 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV389 @ SV389 @ SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1416]) ).
thf(1687,plain,
! [SV390: $i,SV114: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV114 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV390 @ SV390 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1417]) ).
thf(1688,plain,
! [SV621: $i,SV392: $i,SV116: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV116 ) @ SV392 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV621 ) @ SV392 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV116 ) @ SV621 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1419]) ).
thf(1689,plain,
! [SV622: $i,SV393: $i,SV117: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV117 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV393 ) @ SV622 ) @ SV117 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV622 @ SV117 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV393 @ SV117 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(1690,plain,
! [SV623: $i,SV394: $i,SV118: $i] :
( ( ! [SY2155: $i,SY2156: $i,SY2157: $i] :
( ( c_ListOrder_Ostep1 @ SV118 @ SV394 @ SV623 @ SY2155 )
| ( SV623 = SV394 )
| ~ ( c_ListOrder_Ostep1 @ SV118 @ ( c_List_Olist_OCons @ SY2156 @ SV394 @ SY2155 ) @ ( c_List_Olist_OCons @ SY2157 @ SV623 @ SY2155 ) @ SY2155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(1691,plain,
! [SV624: $i,SV395: $i,SV119: $i] :
( ( ! [SY2158: $i,SY2159: $i] :
( ( ( hAPP @ ( hAPP @ SV119 @ ( hAPP @ ( hAPP @ SV119 @ SV395 ) @ SV624 ) ) @ SY2158 )
= ( hAPP @ ( hAPP @ SV119 @ SV395 ) @ ( hAPP @ ( hAPP @ SV119 @ SV624 ) @ SY2158 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV119 @ SY2159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1422]) ).
thf(1692,plain,
! [SV625: $i,SV396: $i,SV120: $i] :
( ( ! [SY2160: $i,SY2161: $i] :
( ( c_List_Omap @ SV120 @ ( c_List_Oappend @ SV396 @ SV625 @ SY2160 ) @ SY2160 @ SY2161 )
= ( c_List_Oappend @ ( c_List_Omap @ SV120 @ SV396 @ SY2160 @ SY2161 ) @ ( c_List_Omap @ SV120 @ SV625 @ SY2160 @ SY2161 ) @ SY2161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1423]) ).
thf(1693,plain,
! [SV121: $i] :
( ( ( SV121
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV121 ) ) )
= $true )
| ( ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV121 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV121 ) ) )
= $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 @ SV121 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV121 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV121 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1424]) ).
thf(1694,plain,
! [SV626: $i,SV397: $i,SV122: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV122 )
| ( c_HOL_Oord__class_Oless @ SV397 @ SV626 @ SV122 )
| ( c_HOL_Oord__class_Oless @ SV626 @ SV397 @ SV122 )
| ( SV626 = SV397 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1425]) ).
thf(1695,plain,
! [SV627: $i,SV398: $i,SV123: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV123 )
| ( SV398 = SV627 )
| ( c_HOL_Oord__class_Oless @ SV627 @ SV398 @ SV123 )
| ( c_HOL_Oord__class_Oless @ SV398 @ SV627 @ SV123 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1426]) ).
thf(1696,plain,
! [SV399: $i,SV124: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV124 @ SV399 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV399 @ SV124 @ tc_nat )
| ( SV399 = SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1427]) ).
thf(1697,plain,
! [SV628: $i,SV400: $i,SV125: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV125 @ SV400 ) @ SV628 ) )
| ( c_HOL_Oord__class_Oless @ SV400 @ SV628 @ tc_nat )
| ( SV628 = SV400 )
| ( c_HOL_Oord__class_Oless @ SV628 @ SV400 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1428]) ).
thf(1698,plain,
! [SV401: $i,SV126: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV126 @ SV401 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV401 @ SV126 @ tc_nat )
| ( SV401 = SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1429]) ).
thf(1699,plain,
! [SV629: $i,SV402: $i,SV127: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV127 )
| ( c_HOL_Oord__class_Oless @ SV402 @ SV629 @ SV127 )
| ( c_HOL_Oord__class_Oless @ SV629 @ SV402 @ SV127 )
| ( SV629 = SV402 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1430]) ).
thf(1700,plain,
! [SV630: $i,SV403: $i,SV128: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV128 )
| ( c_HOL_Oord__class_Oless @ SV403 @ SV630 @ SV128 )
| ( SV630 = SV403 )
| ( c_HOL_Oord__class_Oless @ SV630 @ SV403 @ SV128 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1431]) ).
thf(1701,plain,
! [SV631: $i,SV404: $i,SV129: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV129 )
| ( SV404 = SV631 )
| ( c_HOL_Oord__class_Oless @ SV404 @ SV631 @ SV129 )
| ( c_HOL_Oord__class_Oless @ SV631 @ SV404 @ SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1432]) ).
thf(1702,plain,
! [SV632: $i,SV405: $i,SV130: $i] :
( ( ! [SY2162: $i,SY2163: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV130 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SV405 ) @ SV632 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SY2162 ) @ SY2163 ) @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SV632 @ SY2163 @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SV405 @ SY2162 @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1433]) ).
thf(1703,plain,
! [SV633: $i,SV406: $i,SV131: $i] :
( ( ! [SY2164: $i,SY2165: $i] :
( ( c_Type_Otyping @ SV131 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV406 ) @ SV633 ) @ SY2164 )
| ~ ( c_Type_Otyping @ SV131 @ SV633 @ SY2165 )
| ~ ( c_Type_Otyping @ SV131 @ SV406 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY2165 ) @ SY2164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1434]) ).
thf(1704,plain,
! [SV407: $i,SV132: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV132 ) )
= $true )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV132 ) @ ( c_HOL_Ozero__class_Ozero @ SV132 ) @ SV407 @ SV132 @ SV132 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV132 ) @ SV407 @ ( c_HOL_Ozero__class_Ozero @ SV132 ) @ SV132 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1435]) ).
thf(1705,plain,
! [SV133: $i] :
( ( ( SV133
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV133 ) ) )
= $true )
| ( ( ( SV133
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV133 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV133 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV133 ) ) )
= $true )
| ( ( SV133
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV133 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV133 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV133 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1436]) ).
thf(1706,plain,
! [SV634: $i,SV408: $i,SV134: $i] :
( ( ! [SY2166: $i,SY2167: $i,SY2168: $i] :
( ( SV134 = SV408 )
| ( SV634 = SY2166 )
| ~ ( c_ListOrder_Ostep1 @ SY2167 @ ( c_List_Oappend @ SV134 @ ( c_List_Olist_OCons @ SV634 @ ( c_List_Olist_ONil @ SY2168 ) @ SY2168 ) @ SY2168 ) @ ( c_List_Oappend @ SV408 @ ( c_List_Olist_OCons @ SY2166 @ ( c_List_Olist_ONil @ SY2168 ) @ SY2168 ) @ SY2168 ) @ SY2168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(1707,plain,
! [SV635: $i,SV409: $i,SV135: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV135 @ SV409 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV635 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV135 ) @ SV635 ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ SV635 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV409 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1708,plain,
! [SV636: $i,SV410: $i,SV137: $i] :
( ( ! [SY2169: $i] :
( ( c_List_Olistsp @ SV137 @ ( c_List_Oappend @ SV410 @ SV636 @ SY2169 ) @ SY2169 )
| ~ ( c_List_Olistsp @ SV137 @ SV636 @ SY2169 )
| ~ ( c_List_Olistsp @ SV137 @ SV410 @ SY2169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1440]) ).
thf(1709,plain,
! [SV637: $i,SV411: $i,SV138: $i] :
( ( ! [SY2170: $i,SY2171: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV138 @ SV411 @ SV637 @ ( c_Lambda_OdB_OAbs @ SY2170 ) @ SY2171 )
= ( hAPP @ ( hAPP @ SV637 @ SY2170 ) @ ( c_Lambda_OdB_OdB__rec @ SV138 @ SV411 @ SV637 @ SY2170 @ SY2171 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(1710,plain,
! [SV140: $i] :
( ( ( class_OrderedGroup_Osemigroup__add @ SV140 )
= $false )
| ( ( c_OrderedGroup_Osemigroup__add @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ SV140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1443]) ).
thf(1711,plain,
! [SV638: $i,SV413: $i,SV141: $i] :
( ( ! [SY2172: $i,SY2173: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV141 @ SV413 @ SV638 @ SY2172 ) @ SY2173 )
= ( hAPP @ SV141 @ SY2173 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2173 @ SV413 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1444]) ).
thf(1712,plain,
! [SV639: $i,SV414: $i,SV142: $i] :
( ( ! [SY2174: $i,SY2175: $i,SY2176: $i,SY2177: $i] :
( ( SV142
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV414 @ SV142 @ SV639 @ SY2174 ) @ SV414 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV639 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2175 ) @ SY2176 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV142 )
| ~ ( c_Type_Otypings @ SV639 @ SY2176 @ SY2177 )
| ~ ( c_Type_Otyping @ SV639 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2175 ) @ SY2176 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2174 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(1713,plain,
! [SV640: $i,SV416: $i,SV144: $i] :
( ( ! [SY2178: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV144 )
| ( c_HOL_Oord__class_Oless @ SV416 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ SV640 ) @ SY2178 ) @ SV144 )
| ~ ( c_HOL_Oord__class_Oless @ SV416 @ SY2178 @ SV144 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV144 ) @ SV640 @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(1714,plain,
! [SV641: $i,SV417: $i,SV145: $i] :
( ( ! [SY2179: $i,SY2180: $i,SY2181: $i] :
( ( c_List_Ofoldr @ SV145 @ ( c_List_Olist_OCons @ SV417 @ SV641 @ SY2179 ) @ SY2180 @ SY2179 @ SY2181 )
= ( hAPP @ ( hAPP @ SV145 @ SV417 ) @ ( c_List_Ofoldr @ SV145 @ SV641 @ SY2180 @ SY2179 @ SY2181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(1715,plain,
! [SV642: $i,SV418: $i,SV146: $i] :
( ( ! [SY2182: $i,SY2183: $i] :
( ~ ( hBOOL @ ( hAPP @ SV146 @ ( c_Lambda_OdB_OdB__case @ SV418 @ SV642 @ SY2182 @ ( c_Lambda_OdB_OAbs @ SY2183 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV146 @ ( hAPP @ SY2182 @ SY2183 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1449]) ).
thf(1716,plain,
! [SV643: $i,SV419: $i,SV147: $i] :
( ( ! [SY2184: $i,SY2185: $i] :
( ~ ( hBOOL @ ( hAPP @ SV147 @ ( c_Lambda_OdB_OdB__case @ SV419 @ SV643 @ SY2184 @ ( c_Lambda_OdB_OAbs @ SY2185 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV147 @ ( hAPP @ SY2184 @ SY2185 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1450]) ).
thf(1717,plain,
! [SV644: $i,SV420: $i,SV148: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV148 ) @ ( c_List_Olist_OCons @ SV420 @ SV644 @ SV148 ) @ SV148 )
= ( c_List_Olist_OCons @ SV420 @ SV644 @ SV148 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(1718,plain,
! [SV645: $i,SV421: $i,SV149: $i] :
( ( ! [SY2186: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV149 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV421 ) @ SV645 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SY2186 ) @ SV645 ) @ SV149 )
| ~ ( c_HOL_Oord__class_Oless @ SV421 @ SY2186 @ SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(1719,plain,
! [SV646: $i,SV422: $i,SV150: $i] :
( ( ! [SY2187: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV150 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV150 ) @ SV422 ) @ SV646 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV150 ) @ SY2187 ) @ SV646 ) @ SV150 )
| ~ ( c_HOL_Oord__class_Oless @ SV422 @ SY2187 @ SV150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(1720,plain,
! [SV647: $i,SV423: $i,SV151: $i] :
( ( ! [SY2188: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV151 )
| ( c_HOL_Oord__class_Oless @ SV423 @ SV647 @ SV151 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV423 ) @ SY2188 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV647 ) @ SY2188 ) @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(1721,plain,
! [SV648: $i,SV424: $i,SV152: $i] :
( ( ! [SY2189: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV152 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV424 ) @ SV648 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV424 ) @ SY2189 ) @ SV152 )
| ~ ( c_HOL_Oord__class_Oless @ SV648 @ SY2189 @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1455]) ).
thf(1722,plain,
! [SV649: $i,SV425: $i,SV153: $i] :
( ( ! [SY2190: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV153 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV425 ) @ SV649 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV425 ) @ SY2190 ) @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SV649 @ SY2190 @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(1723,plain,
! [SV650: $i,SV426: $i,SV154: $i] :
( ( ! [SY2191: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV154 )
| ( c_HOL_Oord__class_Oless @ SV426 @ SV650 @ SV154 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SY2191 ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SY2191 ) @ SV650 ) @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1457]) ).
thf(1724,plain,
! [SV155: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV155 ) ) )
= $true )
| ( ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV155 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV155 ) ) )
= $true )
| ( ( SV155
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV155 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV155 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV155 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1458]) ).
thf(1725,plain,
! [SV651: $i,SV427: $i,SV156: $i] :
( ( ! [SY2192: $i] :
( ( c_Type_Otyping @ SV156 @ SV427 @ SV651 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY2192 ) @ SV427 ) )
| ~ ( c_Type_Otyping @ SV156 @ SY2192 @ SV651 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(1726,plain,
! [SV652: $i,SV428: $i,SV157: $i] :
( ( ! [SY2193: $i,SY2194: $i,SY2195: $i] :
( ( c_ListOrder_Ostep1 @ SV157 @ SV428 @ SV652 @ SY2193 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV157 @ SY2194 ) @ SY2195 ) )
| ~ ( c_ListOrder_Ostep1 @ SV157 @ ( c_List_Olist_OCons @ SY2194 @ SV428 @ SY2193 ) @ ( c_List_Olist_OCons @ SY2195 @ SV652 @ SY2193 ) @ SY2193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1727,plain,
! [SV653: $i,SV429: $i,SV158: $i] :
( ( ! [SY2196: $i,SY2197: $i] :
( ( c_ListOrder_Ostep1 @ SV158 @ ( c_List_Olist_OCons @ SV429 @ SV653 @ SY2196 ) @ ( c_List_Olist_OCons @ SV429 @ SY2197 @ SY2196 ) @ SY2196 )
| ~ ( c_ListOrder_Ostep1 @ SV158 @ SV653 @ SY2197 @ SY2196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1461]) ).
thf(1728,plain,
! [SV160: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ SV160 @ 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 ) @ SV160 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1462]) ).
thf(1729,plain,
! [SV654: $i,SV430: $i,SV161: $i] :
( ( ! [SY2198: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV161 @ SV430 @ SV654 ) @ SY2198 @ SV654 )
= ( c_List_Oappend @ SV161 @ ( c_List_Oappend @ SV430 @ SY2198 @ SV654 ) @ SV654 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(1730,plain,
! [SV655: $i,SV431: $i,SV162: $i] :
( ( ! [SY2199: $i] :
( ( c_List_Oappend @ SV162 @ ( c_List_Oappend @ SV431 @ SV655 @ SY2199 ) @ SY2199 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV162 @ SV431 @ SY2199 ) @ SV655 @ SY2199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1464]) ).
thf(1731,plain,
! [SV656: $i,SV432: $i,SV163: $i] :
( ( ! [SY2200: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV163 @ SV432 @ SV656 ) @ SY2200 @ SV656 )
= ( c_List_Oappend @ SV163 @ ( c_List_Oappend @ SV432 @ SY2200 @ SV656 ) @ SV656 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(1732,plain,
! [SV657: $i,SV433: $i,SV164: $i] :
( ( ! [SY2201: $i] :
( ( c_List_Oappend @ SV164 @ ( c_List_Oappend @ SV433 @ SV657 @ SY2201 ) @ SY2201 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV164 @ SV433 @ SY2201 ) @ SV657 @ SY2201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1466]) ).
thf(1733,plain,
! [SV658: $i,SV434: $i,SV165: $i] :
( ( ! [SY2202: $i,SY2203: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV165 @ SV434 @ SV658 @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY2202 ) @ SV434 ) @ SY2203 )
| ~ ( c_Type_Otyping @ SV165 @ SY2202 @ SY2203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1467]) ).
thf(1734,plain,
! [SV659: $i,SV435: $i,SV166: $i] :
( ( ~ ( class_Orderings_Oorder @ SV166 )
| ~ ( c_HOL_Oord__class_Oless @ SV435 @ SV659 @ SV166 )
| ~ ( c_HOL_Oord__class_Oless @ SV659 @ SV435 @ SV166 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(1735,plain,
! [SV660: $i,SV436: $i,SV167: $i] :
( ( ! [SY2204: $i,SY2205: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV167 @ SV436 ) @ SV660 ) @ SY2204 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV167 @ SV436 ) @ SY2205 ) @ SY2204 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV167 @ SV660 ) @ SY2205 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1469]) ).
thf(1736,plain,
! [SV661: $i,SV437: $i,SV168: $i] :
( ( ! [SY2206: $i,SY2207: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV168 @ SV437 ) @ SV661 ) @ SY2206 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV168 @ SY2207 ) @ SY2206 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV168 @ SV437 ) @ SV661 ) @ SY2207 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1470]) ).
thf(1737,plain,
! [SV662: $i,SV438: $i,SV169: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV169 )
| ~ ( c_HOL_Oord__class_Oless @ SV438 @ SV662 @ SV169 )
| ~ ( c_HOL_Oord__class_Oless @ SV662 @ SV438 @ SV169 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1471]) ).
thf(1738,plain,
! [SV663: $i,SV439: $i,SV170: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV170 )
| ~ ( c_HOL_Oord__class_Oless @ SV439 @ SV663 @ SV170 )
| ~ ( c_HOL_Oord__class_Oless @ SV663 @ SV439 @ SV170 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1472]) ).
thf(1739,plain,
! [SV664: $i,SV440: $i,SV171: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV171 )
| ~ ( c_HOL_Oord__class_Oless @ SV440 @ SV664 @ SV171 )
| ~ ( c_HOL_Oord__class_Oless @ SV664 @ SV440 @ SV171 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1473]) ).
thf(1740,plain,
! [SV441: $i,SV172: $i] :
( ( ( hBOOL @ ( hAPP @ SV172 @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV172 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV172 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV172 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV172 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ SV172 @ SV441 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1474]) ).
thf(1741,plain,
! [SV665: $i,SV442: $i,SV173: $i] :
( ( ! [SY2208: $i,SY2209: $i] :
( ( ( c_List_Ofoldl @ SV173 @ ( hAPP @ ( hAPP @ SV173 @ SV442 ) @ SV665 ) @ SY2208 @ SY2209 @ SY2209 )
= ( hAPP @ ( hAPP @ SV173 @ SV442 ) @ ( c_List_Ofoldl @ SV173 @ SV665 @ SY2208 @ SY2209 @ SY2209 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV173 @ SY2209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(1742,plain,
! [SV666: $i,SV444: $i,SV175: $i] :
( ( ! [SY2210: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV175 ) @ SV444 ) ) @ SV666 ) @ SY2210 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV175 ) @ SV666 ) @ SY2210 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV444 ) @ SV666 ) @ SY2210 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(1743,plain,
! [SV667: $i,SV445: $i,SV176: $i] :
( ( ! [SY2211: $i] :
( ( c_Type_Otypings @ SV176 @ SV445 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV667 @ SV176 @ SY2211 @ SV445 ) )
| ~ ( c_Type_Otyping @ SV176 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2211 ) @ SV445 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV667 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1478]) ).
thf(1744,plain,
! [SV668: $i,SV446: $i,SV177: $i] :
( ( ! [SY2212: $i,SY2213: $i] :
( ~ ( hBOOL @ ( hAPP @ SV177 @ ( c_Lambda_OdB_OdB__case @ SV446 @ SV668 @ SY2212 @ ( c_Lambda_OdB_OVar @ SY2213 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV177 @ ( hAPP @ SV446 @ SY2213 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(1745,plain,
! [SV669: $i,SV447: $i,SV178: $i] :
( ( ! [SY2214: $i,SY2215: $i] :
( ~ ( hBOOL @ ( hAPP @ SV178 @ ( c_Lambda_OdB_OdB__case @ SV447 @ SV669 @ SY2214 @ ( c_Lambda_OdB_OVar @ SY2215 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV178 @ ( hAPP @ SV447 @ SY2215 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1480]) ).
thf(1746,plain,
! [SV670: $i,SV449: $i,SV180: $i] :
( ( ! [SY2216: $i,SY2217: $i,SY2218: $i] :
( ~ ( hBOOL @ ( hAPP @ SV180 @ ( c_Lambda_OdB_OdB__case @ SV449 @ SV670 @ SY2216 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2217 ) @ SY2218 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV180 @ ( hAPP @ ( hAPP @ SV670 @ SY2217 ) @ SY2218 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1482]) ).
thf(1747,plain,
! [SV671: $i,SV450: $i,SV181: $i] :
( ( ! [SY2219: $i,SY2220: $i,SY2221: $i] :
( ~ ( hBOOL @ ( hAPP @ SV181 @ ( c_Lambda_OdB_OdB__case @ SV450 @ SV671 @ SY2219 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2220 ) @ SY2221 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV181 @ ( hAPP @ ( hAPP @ SV671 @ SY2220 ) @ SY2221 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1483]) ).
thf(1748,plain,
! [SV672: $i,SV451: $i,SV182: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV182 ) @ ( c_Lambda_OdB_OVar @ SV451 ) ) @ SV672 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1484]) ).
thf(1749,plain,
! [SV673: $i,SV452: $i,SV183: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV183 ) ) @ SV452 ) @ SV673 )
= ( c_Lambda_OdB_OVar @ SV183 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV183 @ SV673 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1485]) ).
thf(1750,plain,
! [SV674: $i,SV453: $i,SV184: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV184 @ SV453 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV674 @ SV453 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV184 ) @ SV674 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1486]) ).
thf(1751,plain,
! [SV454: $i,SV185: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV185 ) ) @ SV454 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1487]) ).
thf(1752,plain,
! [SV455: $i,SV186: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV186 ) @ SV455 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV455 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1488]) ).
thf(1753,plain,
! [SV675: $i,SV456: $i,SV187: $i] :
( ( ! [SY2222: $i,SY2223: $i] :
( ( SV187 = SV456 )
| ~ ( c_Type_Otyping @ SV675 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2222 ) @ SY2223 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV456 )
| ~ ( c_Type_Otyping @ SV675 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2222 ) @ SY2223 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1489]) ).
thf(1754,plain,
! [SV676: $i,SV457: $i,SV188: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV188 @ SV457 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV188 @ SV676 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV457 @ SV676 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(1755,plain,
! [SV458: $i,SV189: $i] :
( ( ( hBOOL @ ( hAPP @ SV189 @ SV458 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV189 @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV189 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV189 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV189 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV189 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1491]) ).
thf(1756,plain,
! [SV677: $i,SV459: $i,SV190: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV190 @ SV459 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV677 @ SV459 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV190 ) @ SV677 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1492]) ).
thf(1757,plain,
! [SV678: $i,SV460: $i,SV191: $i] :
( ( ! [SY2224: $i,SY2225: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV191 @ SV460 @ SV678 @ ( c_Lambda_OdB_OVar @ SY2224 ) @ SY2225 )
= ( hAPP @ SV191 @ SY2224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(1758,plain,
! [SV461: $i,SV192: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV192 ) @ SV461 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV192 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1494]) ).
thf(1759,plain,
! [SV679: $i,SV462: $i,SV193: $i] :
( ( ! [SY2226: $i] :
( ( c_List_Ofoldl @ SV193 @ SV462 @ ( c_List_Olist_ONil @ SV679 ) @ SY2226 @ SV679 )
= SV462 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1495]) ).
thf(1760,plain,
! [SV680: $i,SV463: $i,SV194: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV194 ) ) @ SV463 ) @ SV680 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV463 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV194 ) @ SV463 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV680 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1496]) ).
thf(1761,plain,
! [SV195: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV195 ) ) )
= $true )
| ( ( ( SV195
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV195 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV195 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV195 ) ) )
= $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 @ SV195 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV195 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV195 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1497]) ).
thf(1762,plain,
! [SV681: $i,SV464: $i,SV197: $i] :
( ( ( ( hAPP @ SV197 @ SV464 )
= SV681 )
| ~ ( c_Type_Otyping @ SV197 @ ( c_Lambda_OdB_OVar @ SV464 ) @ SV681 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1498]) ).
thf(1763,plain,
! [SV682: $i,SV465: $i,SV198: $i] :
( ( ! [SY2227: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ SV198 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ SV465 ) @ SV682 ) @ SY2227 @ SV198 @ SV198 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ SV465 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ SV682 @ SY2227 @ SV198 @ SV198 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1499]) ).
thf(1764,plain,
! [SV199: $i] :
( ( ( SV199
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV199 ) ) )
= $true )
| ( ( ( SV199
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV199 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV199 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV199 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV199 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1500]) ).
thf(1765,plain,
! [SV683: $i,SV466: $i,SV200: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV200 ) @ SV466 ) ) @ SV683 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV200 ) @ SV683 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV466 ) @ SV683 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1501]) ).
thf(1766,plain,
! [SV684: $i,SV467: $i,SV201: $i] :
( ( ! [SY2228: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV201 @ SV467 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV684 ) @ SY2228 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV201 ) @ SV684 ) @ SY2228 ) @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SV684 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SY2228 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV467 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1502]) ).
thf(1767,plain,
! [SV685: $i,SV468: $i,SV202: $i] :
( ( ! [SY2229: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV202 ) @ SV468 ) @ SV685 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY2229 ) @ SV468 ) @ SV685 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV202 ) @ SY2229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1503]) ).
thf(1768,plain,
! [SV686: $i,SV469: $i,SV203: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV203 ) ) @ SV469 ) @ SV686 )
= ( c_Lambda_OdB_OVar @ SV203 ) )
| ( SV203 = SV686 )
| ( c_HOL_Oord__class_Oless @ SV686 @ SV203 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1504]) ).
thf(1769,plain,
! [SV687: $i,SV470: $i,SV204: $i] :
( ( ! [SY2230: $i] :
( ( c_Type_Otyping @ SV204 @ ( c_Lambda_OdB_OVar @ SV470 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV687 @ SV204 @ SV470 @ SY2230 ) @ SV687 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV204 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV470 ) @ SY2230 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV687 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1505]) ).
thf(1770,plain,
! [SV688: $i,SV471: $i,SV205: $i] :
( ( ( SV205
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV471 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV471 @ SV688 @ SV205 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV471 ) @ SV688 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(1771,plain,
! [SV689: $i,SV472: $i,SV206: $i] :
( ( ! [SY2231: $i,SY2232: $i,SY2233: $i] :
( ( c_Lambda_OdB_OdB__case @ SV206 @ SV472 @ SV689 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2231 ) @ SY2232 ) @ SY2233 )
= ( hAPP @ ( hAPP @ SV472 @ SY2231 ) @ SY2232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1507]) ).
thf(1772,plain,
! [SV690: $i,SV473: $i,SV207: $i] :
( ( ! [SY2234: $i,SY2235: $i] :
( ( ( hAPP @ ( hAPP @ SV207 @ SV473 ) @ ( c_List_Ofoldl @ SV207 @ SV690 @ SY2234 @ SY2235 @ SY2235 ) )
= ( c_List_Ofoldl @ SV207 @ SV473 @ SY2234 @ SY2235 @ SY2235 ) )
| ~ ( c_OrderedGroup_Omonoid__add @ SV690 @ SV207 @ SY2235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(1773,plain,
! [SV208: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV208 ) ) )
= $true )
| ( ( ( SV208
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV208 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV208 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV208 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV208 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1509]) ).
thf(1774,plain,
! [SV691: $i,SV474: $i,SV210: $i] :
( ( ! [SY2236: $i,SY2237: $i] :
( ( c_Lambda_OdB_OdB__case @ SV210 @ SV474 @ SV691 @ ( c_Lambda_OdB_OVar @ SY2236 ) @ SY2237 )
= ( hAPP @ SV210 @ SY2236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(1775,plain,
! [SV475: $i,SV211: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV211 @ SV211 @ tc_nat )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV211 ) ) @ SV475 ) @ SV211 )
= SV475 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1511]) ).
thf(1776,plain,
! [SV692: $i,SV476: $i,SV212: $i] :
( ( ! [SY2238: $i,SY2239: $i,SY2240: $i] :
( ( c_List_Ofoldl @ SV212 @ SV476 @ ( c_List_Olist_OCons @ SV692 @ SY2238 @ SY2239 ) @ SY2240 @ SY2239 )
= ( c_List_Ofoldl @ SV212 @ ( hAPP @ ( hAPP @ SV212 @ SV476 ) @ SV692 ) @ SY2238 @ SY2240 @ SY2239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1512]) ).
thf(1777,plain,
! [SV693: $i,SV478: $i,SV215: $i] :
( ( ! [SY2241: $i,SY2242: $i,SY2243: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV215 @ SV478 @ SV693 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2241 ) @ SY2242 ) @ SY2243 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV478 @ SY2241 ) @ SY2242 ) @ ( c_Lambda_OdB_OdB__rec @ SV215 @ SV478 @ SV693 @ SY2241 @ SY2243 ) ) @ ( c_Lambda_OdB_OdB__rec @ SV215 @ SV478 @ SV693 @ SY2242 @ SY2243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1514]) ).
thf(1778,plain,
! [SV694: $i,SV479: $i,SV217: $i] :
( ( ! [SY2244: $i,SY2245: $i,SY2246: $i,SY2247: $i] :
( ( c_Type_Otypings @ SV217 @ SV479 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV694 @ SY2244 @ SV217 @ SV479 ) )
| ~ ( c_Type_Otyping @ SV217 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2245 ) @ SY2246 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2244 )
| ~ ( c_Type_Otypings @ SV217 @ SY2246 @ SY2247 )
| ~ ( c_Type_Otyping @ SV217 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2245 ) @ SY2246 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV479 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV694 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1515]) ).
thf(1779,plain,
! [SV218: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV218 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV218 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1516]) ).
thf(1780,plain,
! [SV695: $i,SV480: $i,SV219: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV219 ) @ SV480 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV219 ) @ SV695 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV480 ) @ SV695 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1517]) ).
thf(1781,plain,
! [SV696: $i,SV481: $i,SV220: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV220 ) @ SV481 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV696 ) @ SV481 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV220 ) @ SV696 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(1782,plain,
! [SV697: $i,SV482: $i,SV221: $i] :
( ( ! [SY2248: $i] :
( ( c_Lambda_Oliftn @ SV221 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV482 ) @ SV697 ) @ SY2248 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ SV221 @ SV482 @ SY2248 ) ) @ ( c_Lambda_Oliftn @ SV221 @ SV697 @ SY2248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1519]) ).
thf(1783,plain,
! [SV698: $i,SV483: $i,SV222: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV222 ) @ SV483 ) ) @ SV698 ) @ SV483 )
= SV222 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(1784,plain,
! [SV484: $i,SV224: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV224 ) @ ( c_Lambda_OdB_OVar @ SV484 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV224 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1521]) ).
thf(1785,plain,
! [SV699: $i,SV485: $i,SV225: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV225 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV485 @ SV225 @ SV699 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV485 ) @ SV225 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV699 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(1786,plain,
! [SV700: $i,SV486: $i,SV226: $i] :
( ( ! [SY2249: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV226 ) @ SV486 ) @ SV700 @ SY2249 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ SV226 @ SV700 @ SY2249 ) ) @ ( c_Lambda_Osubstn @ SV486 @ SV700 @ SY2249 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(1787,plain,
! [SV701: $i,SV487: $i,SV227: $i] :
( ( ! [SY2250: $i,SY2251: $i,SY2252: $i] :
( ( c_List_Ofoldl @ SV227 @ SV487 @ ( c_List_Oappend @ SV701 @ SY2250 @ SY2251 ) @ SY2252 @ SY2251 )
= ( c_List_Ofoldl @ SV227 @ ( c_List_Ofoldl @ SV227 @ SV487 @ SV701 @ SY2252 @ SY2251 ) @ SY2250 @ SY2252 @ SY2251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1524]) ).
thf(1788,plain,
! [SV488: $i,SV228: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV228 @ SV488 ) )
= $true )
| ( ( ~ ( class_Orderings_Opreorder @ SV488 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1525]) ).
thf(1789,plain,
! [SV489: $i,SV229: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV229 @ SV489 ) )
= $true )
| ( ( ~ ( class_Orderings_Oorder @ SV489 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1526]) ).
thf(1790,plain,
! [SV702: $i,SV491: $i,SV231: $i] :
( ( ( SV231 = SV491 )
| ~ ( c_fequal @ SV231 @ SV491 @ SV702 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(1791,plain,
! [SV703: $i,SV492: $i,SV232: $i] :
( ( ( c_List_Olist_OCons @ SV232 @ SV492 @ SV703 )
!= ( c_List_Olist_ONil @ SV703 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(1792,plain,
! [SV704: $i,SV493: $i,SV233: $i] :
( ( ! [SY2253: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV233 ) @ SV493 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV704 ) @ SY2253 ) )
| ( SV233 = SV704 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1530]) ).
thf(1793,plain,
! [SV705: $i,SV494: $i,SV234: $i] :
( ( ! [SY2254: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV234 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV494 ) @ SV705 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV494 ) @ SY2254 ) )
| ( SV705 = SY2254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(1794,plain,
! [SV706: $i,SV495: $i,SV235: $i] :
( ( ( ( c_List_Oappend @ SV235 @ SV495 @ SV706 )
!= ( c_List_Olist_ONil @ SV706 ) )
| ( SV495
= ( c_List_Olist_ONil @ SV706 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(1795,plain,
! [SV707: $i,SV496: $i,SV236: $i] :
( ( ! [SY2255: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV236 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV236 ) @ SV496 ) @ SV707 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV236 ) @ SY2255 ) @ SV707 ) )
| ( SV496 = SY2255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1533]) ).
thf(1796,plain,
! [SV708: $i,SV497: $i,SV237: $i] :
( ( ! [SY2256: $i] :
( ( ( c_List_Oappend @ SV237 @ SV497 @ SV708 )
!= ( c_List_Oappend @ SV237 @ SY2256 @ SV708 ) )
| ( SV497 = SY2256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(1797,plain,
! [SV709: $i,SV498: $i,SV238: $i] :
( ( ! [SY2257: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV238 ) @ SV498 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV709 ) @ SY2257 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV238 = SV709 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1535]) ).
thf(1798,plain,
! [SV710: $i,SV499: $i,SV239: $i] :
( ( ! [SY2258: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV239 ) @ SV499 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV710 ) @ SY2258 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV499 = SY2258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1536]) ).
thf(1799,plain,
! [SV711: $i,SV500: $i,SV240: $i] :
( ( ! [SY2259: $i,SY2260: $i] :
( ( ( c_List_Olist_OCons @ SV240 @ SV500 @ SV711 )
!= ( c_List_Olist_OCons @ SY2259 @ SY2260 @ SV711 ) )
| ( SV240 = SY2259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(1800,plain,
! [SV712: $i,SV501: $i,SV241: $i] :
( ( ! [SY2261: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV241 ) @ SV501 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV712 ) @ SY2261 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV241 = SV712 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1538]) ).
thf(1801,plain,
! [SV713: $i,SV502: $i,SV242: $i] :
( ( ! [SY2262: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV242 ) @ SV502 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV713 @ SY2262 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV242
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV713 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV242 @ SV502 @ SV713 @ SY2262 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2262
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1539]) ).
thf(1802,plain,
! [SV714: $i,SV503: $i,SV243: $i] :
( ( ! [SY2263: $i,SY2264: $i,SY2265: $i,SY2266: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV243 ) @ SV503 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV714 ) @ SY2263 ) @ SY2264 ) ) )
| ~ ( c_Type_Otyping @ SY2265 @ SY2263 @ SV243 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY2263 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY2265 @ SY2264 @ SV243 @ tc_Type_Otype ) @ SV714 @ SY2266 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV714 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1540]) ).
thf(1803,plain,
! [SV715: $i,SV504: $i,SV244: $i] :
( ( ! [SY2267: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV244 )
| ~ ( class_Int_Onumber__ring @ SV244 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV244 ) @ SV504 ) @ SV715 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV244 ) @ SV504 ) @ SY2267 ) )
| ( SV715 = SY2267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(1804,plain,
! [SV716: $i,SV505: $i,SV245: $i] :
( ( ! [SY2268: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV245 ) @ SV505 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV716 ) @ SY2268 ) )
| ( SV505 = SY2268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1542]) ).
thf(1805,plain,
! [SV717: $i,SV506: $i,SV246: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV246 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV506 @ SV717 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV246 )
= SV506 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1543]) ).
thf(1806,plain,
! [SV718: $i,SV507: $i,SV247: $i] :
( ( ( c_Lambda_OdB_OVar @ SV247 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV507 ) @ SV718 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1544]) ).
thf(1807,plain,
! [SV719: $i,SV508: $i,SV248: $i] :
( ( ! [SY2269: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV248 ) @ SV508 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV719 ) @ SY2269 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(1808,plain,
! [SV720: $i,SV509: $i,SV249: $i] :
( ( ! [SY2270: $i,SY2271: $i] :
( ( ( c_List_Oappend @ SV249 @ ( c_List_Olist_OCons @ SV509 @ ( c_List_Olist_ONil @ SV720 ) @ SV720 ) @ SV720 )
!= ( c_List_Oappend @ SY2270 @ ( c_List_Olist_OCons @ SY2271 @ ( c_List_Olist_ONil @ SV720 ) @ SV720 ) @ SV720 ) )
| ( SV249 = SY2270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(1809,plain,
! [SV721: $i,SV510: $i,SV250: $i] :
( ( ( ( c_List_Oappend @ SV250 @ SV510 @ SV721 )
!= ( c_List_Olist_ONil @ SV721 ) )
| ( SV250
= ( c_List_Olist_ONil @ SV721 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1547]) ).
thf(1810,plain,
! [SV722: $i,SV511: $i,SV251: $i] :
( ( ! [SY2272: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV251 ) ) @ SV511 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV722 ) @ SY2272 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1548]) ).
thf(1811,plain,
! [SV723: $i,SV512: $i,SV252: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV252 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV512 @ SV723 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV723
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(1812,plain,
! [SV724: $i,SV513: $i,SV253: $i] :
( ( ( ( c_List_Oappend @ SV253 @ SV513 @ SV724 )
!= SV253 )
| ( SV513
= ( c_List_Olist_ONil @ SV724 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1550]) ).
thf(1813,plain,
! [SV725: $i,SV514: $i,SV254: $i] :
( ( ( c_List_Olist_OCons @ SV254 @ SV514 @ SV725 )
!= SV514 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(1814,plain,
! [SV726: $i,SV515: $i,SV255: $i] :
( ( SV255
!= ( c_List_Olist_OCons @ SV515 @ SV255 @ SV726 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1552]) ).
thf(1815,plain,
! [SV727: $i,SV516: $i,SV256: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV256 @ SV516 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV727 @ SV516 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV256 = SV727 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1553]) ).
thf(1816,plain,
! [SV728: $i,SV517: $i,SV257: $i] :
( ( ! [SY2273: $i] :
( ( ( c_List_Omap @ SV257 @ SV517 @ SV728 @ SY2273 )
!= ( c_List_Olist_ONil @ SY2273 ) )
| ( SV517
= ( c_List_Olist_ONil @ SV728 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1554]) ).
thf(1817,plain,
! [SV518: $i,SV258: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV258 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SV518 ) @ SV518 )
!= ( c_HOL_Ozero__class_Ozero @ SV258 ) )
| ( SV518
= ( c_HOL_Ozero__class_Ozero @ SV258 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1555]) ).
thf(1818,plain,
! [SV729: $i,SV519: $i,SV259: $i] :
( ( ( c_List_Olist_OCons @ SV259 @ SV519 @ SV729 )
!= ( c_List_Olist_ONil @ SV729 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1556]) ).
thf(1819,plain,
! [SV730: $i,SV520: $i,SV260: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV260 ) @ SV520 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV730 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV260 ) @ SV520 )
= SV730 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(1820,plain,
! [SV731: $i,SV521: $i,SV261: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV261 @ SV521 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV731 ) )
| ( SV261
= ( c_Lambda_OdB_OAbs @ SV731 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(1821,plain,
! [SV732: $i,SV522: $i,SV262: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV262 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV522 @ SV732 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV262 )
= SV522 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1559]) ).
thf(1822,plain,
! [SV733: $i,SV523: $i,SV263: $i] :
( ( ! [SY2274: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV263 ) @ SV523 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV733 ) @ SY2274 ) )
| ( SV263 = SV733 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1560]) ).
thf(1823,plain,
! [SV734: $i,SV524: $i,SV264: $i] :
( ( ( ( c_List_Oappend @ SV264 @ SV524 @ SV734 )
!= SV524 )
| ( SV264
= ( c_List_Olist_ONil @ SV734 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1561]) ).
thf(1824,plain,
! [SV735: $i,SV525: $i,SV265: $i] :
( ( ( c_List_Olist_ONil @ SV265 )
!= ( c_List_Olist_OCons @ SV525 @ SV735 @ SV265 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1562]) ).
thf(1825,plain,
! [SV736: $i,SV526: $i,SV266: $i] :
( ( ! [SY2275: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV266 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV266 ) @ SV526 ) @ SV736 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV266 ) @ SV526 ) @ SY2275 ) )
| ( SV736 = SY2275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1563]) ).
thf(1826,plain,
! [SV737: $i,SV527: $i,SV267: $i] :
( ( ( SV267
!= ( c_List_Oappend @ SV267 @ SV527 @ SV737 ) )
| ( SV527
= ( c_List_Olist_ONil @ SV737 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(1827,plain,
! [SV738: $i,SV528: $i,SV268: $i] :
( ( ! [SY2276: $i,SY2277: $i,SY2278: $i,SY2279: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV268 ) @ SV528 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV738 ) @ SY2276 ) @ SY2277 ) ) )
| ~ ( c_Type_Otyping @ SY2278 @ SY2276 @ SV528 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY2276 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY2278 @ SY2277 @ SV528 @ tc_Type_Otype ) @ SV738 @ SY2279 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV738 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1565]) ).
thf(1828,plain,
! [SV739: $i,SV529: $i,SV269: $i] :
( ( ! [SY2280: $i] :
( ( ( c_List_Oappend @ SV269 @ SV529 @ SV739 )
!= ( c_List_Oappend @ SY2280 @ SV529 @ SV739 ) )
| ( SV269 = SY2280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1566]) ).
thf(1829,plain,
! [SV530: $i,SV270: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV270 )
!= ( c_Lambda_OdB_OVar @ SV530 ) )
= $true )
| ( ( SV270 = SV530 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1567]) ).
thf(1830,plain,
! [SV740: $i,SV531: $i,SV271: $i] :
( ( ! [SY2281: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV271 ) @ SV531 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV740 ) @ SY2281 ) )
| ( SV531 = SY2281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1568]) ).
thf(1831,plain,
! [SV741: $i,SV532: $i,SV272: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV272 ) @ SV532 )
!= ( c_Lambda_OdB_OAbs @ SV741 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1569]) ).
thf(1832,plain,
! [SV533: $i,SV273: $i] :
( ( ( c_Lambda_OdB_OVar @ SV273 )
= ( c_Lambda_OdB_OAbs @ SV533 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1570]) ).
thf(1833,plain,
! [SV742: $i,SV534: $i,SV274: $i] :
( ( ! [SY2282: $i] :
( ( ( c_List_Olist_ONil @ SV274 )
!= ( c_List_Omap @ SV534 @ SV742 @ SY2282 @ SV274 ) )
| ( SV742
= ( c_List_Olist_ONil @ SY2282 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1571]) ).
thf(1834,plain,
! [SV743: $i,SV535: $i,SV275: $i] :
( ( ! [SY2283: $i,SY2284: $i] :
( ( ( c_List_Oappend @ SV275 @ ( c_List_Olist_OCons @ SV535 @ ( c_List_Olist_ONil @ SV743 ) @ SV743 ) @ SV743 )
!= ( c_List_Oappend @ SY2283 @ ( c_List_Olist_OCons @ SY2284 @ ( c_List_Olist_ONil @ SV743 ) @ SV743 ) @ SV743 ) )
| ( SV535 = SY2284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1572]) ).
thf(1835,plain,
! [SV744: $i,SV536: $i,SV276: $i] :
( ( ( SV276
!= ( c_List_Oappend @ SV536 @ SV276 @ SV744 ) )
| ( SV536
= ( c_List_Olist_ONil @ SV744 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1573]) ).
thf(1836,plain,
! [SV745: $i,SV537: $i,SV277: $i] :
( ( ( ( c_List_Olist_ONil @ SV277 )
!= ( c_List_Oappend @ SV537 @ SV745 @ SV277 ) )
| ( SV745
= ( c_List_Olist_ONil @ SV277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1574]) ).
thf(1837,plain,
! [SV746: $i,SV538: $i,SV278: $i] :
( ( ( ( c_List_Olist_ONil @ SV278 )
!= ( c_List_Oappend @ SV538 @ SV746 @ SV278 ) )
| ( SV538
= ( c_List_Olist_ONil @ SV278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(1838,plain,
! [SV539: $i,SV279: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV279 )
= ( c_Lambda_OdB_OVar @ SV539 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1576]) ).
thf(1839,plain,
! [SV747: $i,SV540: $i,SV280: $i] :
( ( ! [SY2285: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV280 ) @ SV540 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV747 ) @ SY2285 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV540 = SY2285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(1840,plain,
! [SV748: $i,SV541: $i,SV281: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV281 ) @ SV541 )
!= ( c_Lambda_OdB_OVar @ SV748 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(1841,plain,
! [SV749: $i,SV542: $i,SV282: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV282 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV542 ) @ SV749 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(1842,plain,
! [SV750: $i,SV543: $i,SV283: $i] :
( ( ! [SY2286: $i,SY2287: $i] :
( ( ( c_List_Olist_OCons @ SV283 @ SV543 @ SV750 )
!= ( c_List_Olist_OCons @ SY2286 @ SY2287 @ SV750 ) )
| ( SV543 = SY2287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1580]) ).
thf(1843,plain,
! [SV751: $i,SV544: $i,SV284: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV284 @ SV544 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV751 ) )
| ( SV544
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1581]) ).
thf(1844,plain,
! [SV752: $i,SV545: $i,SV285: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV285 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV545 @ SV752 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV752
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1582]) ).
thf(1845,plain,
! [SV753: $i,SV546: $i,SV286: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV286 )
| ~ ( class_Int_Onumber__ring @ SV286 )
| ( SV546
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV286 ) @ SV546 ) @ SV753 ) )
| ( SV753
= ( c_HOL_Ozero__class_Ozero @ SV286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1583]) ).
thf(1846,plain,
! [SV547: $i,SV287: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV287 )
!= ( c_Lambda_OdB_OAbs @ SV547 ) )
= $true )
| ( ( SV287 = SV547 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1584]) ).
thf(1847,plain,
! [SV754: $i,SV548: $i,SV288: $i] :
( ( ! [SY2288: $i,SY2289: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV288 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV548 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV754 ) @ SY2288 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV754 ) @ SY2289 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV548 ) @ SY2288 )
= SY2289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1585]) ).
thf(1848,plain,
! [SV289: $i,SV1: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV1 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4 @ SV1 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV1 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV1 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1 @ SV289 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1586]) ).
thf(1849,plain,
! [SV290: $i,SV2: $i] :
( ( ( hBOOL @ ( hAPP @ SV2 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV2 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__4 @ SV2 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV2 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV2 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV2 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ SV2 @ SV290 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1587]) ).
thf(1850,plain,
! [SV755: $i,SV549: $i,SV291: $i,SV3: $i] :
( ( ( c_Type_Otyping @ SV3 @ SV291 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV549 @ SV3 @ SV291 @ SV755 ) @ SV549 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV291 @ SV755 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV549 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1588]) ).
thf(1851,plain,
! [SV756: $i,SV550: $i,SV292: $i,SV4: $i] :
( ( ( c_Type_Otyping @ SV4 @ SV292 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV550 @ SV4 @ SV292 @ SV756 ) @ SV550 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV4 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV292 @ SV756 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV550 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1589]) ).
thf(1852,plain,
! [SV757: $i,SV551: $i,SV293: $i,SV5: $i] :
( ( ( c_Type_Otypings @ SV5 @ SV293 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV551 @ SV5 @ SV757 @ SV293 ) )
| ~ ( c_Type_Otyping @ SV5 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV757 @ SV293 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV551 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(1853,plain,
! [SV758: $i,SV552: $i,SV294: $i,SV6: $i] :
( ( ( c_Type_Otypings @ SV6 @ SV294 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV552 @ SV6 @ SV758 @ SV294 ) )
| ~ ( c_Type_Otyping @ SV6 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV758 @ SV294 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV552 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1591]) ).
thf(1854,plain,
! [SV759: $i,SV553: $i,SV295: $i,SV7: $i] :
( ( ! [SY2290: $i,SY2291: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV7 @ SV295 ) @ SV553 ) )
| ( SV295 = SV553 )
| ~ ( c_ListOrder_Ostep1 @ SV7 @ ( c_List_Oappend @ SV759 @ ( c_List_Olist_OCons @ SV295 @ ( c_List_Olist_ONil @ SY2290 ) @ SY2290 ) @ SY2290 ) @ ( c_List_Oappend @ SY2291 @ ( c_List_Olist_OCons @ SV553 @ ( c_List_Olist_ONil @ SY2290 ) @ SY2290 ) @ SY2290 ) @ SY2290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(1855,plain,
! [SV760: $i,SV554: $i,SV296: $i,SV8: $i] :
( ( ! [SY2292: $i,SY2293: $i] :
( ( c_List_Ofoldr @ SV8 @ ( c_List_Oappend @ SV296 @ SV554 @ SV760 ) @ SY2292 @ SV760 @ SY2293 )
= ( c_List_Ofoldr @ SV8 @ SV296 @ ( c_List_Ofoldr @ SV8 @ SV554 @ SY2292 @ SV760 @ SY2293 ) @ SV760 @ SY2293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(1856,plain,
! [SV555: $i,SV297: $i,SV9: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV9 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV9 ) @ SV297 ) @ SV555 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV9 ) @ SV555 ) @ SV297 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1594]) ).
thf(1857,plain,
! [SV556: $i,SV298: $i,SV10: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV10 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV10 ) @ SV298 ) @ SV556 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV10 ) @ SV556 ) @ SV298 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1595]) ).
thf(1858,plain,
! [SV557: $i,SV299: $i,SV11: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV11 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV11 ) @ SV299 ) @ SV557 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV11 ) @ SV557 ) @ SV299 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1596]) ).
thf(1859,plain,
! [SV761: $i,SV558: $i,SV300: $i,SV12: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV12 ) @ SV300 ) @ SV558 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV12 ) @ SV761 ) @ SV558 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV300 ) @ SV761 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1597]) ).
thf(1860,plain,
! [SV18: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV18 ) @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV18 ) ) )
= $true )
| ( ( SV18
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV18 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1598]) ).
thf(1861,plain,
! [SV762: $i,SV559: $i,SV306: $i,SV19: $i] :
( ( ! [SY2294: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV19 @ SV306 ) @ SV559 ) @ SV762 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV19 @ SV306 ) @ SY2294 ) @ SV762 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV19 @ SV306 ) @ SV559 ) @ SY2294 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1599]) ).
thf(1862,plain,
! [SV763: $i,SV562: $i,SV310: $i,SV23: $i] :
( ( ! [SY2295: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV23 @ SV310 ) @ SV562 ) )
| ( c_ListOrder_Ostep1 @ SV23 @ ( c_List_Olist_OCons @ SV310 @ SV763 @ SY2295 ) @ ( c_List_Olist_OCons @ SV562 @ SV763 @ SY2295 ) @ SY2295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(1863,plain,
! [SV764: $i,SV563: $i,SV311: $i,SV24: $i] :
( ( ! [SY2296: $i,SY2297: $i] :
( ( SV24 = SV311 )
| ( SV563 = SV764 )
| ~ ( c_ListOrder_Ostep1 @ SY2296 @ ( c_List_Olist_OCons @ SV311 @ SV764 @ SY2297 ) @ ( c_List_Olist_OCons @ SV24 @ SV563 @ SY2297 ) @ SY2297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(1864,plain,
! [SV765: $i,SV564: $i,SV312: $i,SV25: $i] :
( ( ! [SY2298: $i] :
( ( c_Lambda_OdB_OdB__case @ SV25 @ SV312 @ SV564 @ ( c_Lambda_OdB_OAbs @ SV765 ) @ SY2298 )
= ( hAPP @ SV564 @ SV765 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1604]) ).
thf(1865,plain,
! [SV26: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV26 ) @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV26 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV26 ) ) )
= $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 @ SV26 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV26 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV26 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1605]) ).
thf(1866,plain,
! [SV766: $i,SV565: $i,SV313: $i,SV27: $i] :
( ( ( c_List_Olistsp @ SV27 @ SV313 @ SV565 )
| ~ ( c_List_Olistsp @ SV27 @ ( c_List_Oappend @ SV766 @ SV313 @ SV565 ) @ SV565 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1606]) ).
thf(1867,plain,
! [SV767: $i,SV566: $i,SV314: $i,SV28: $i] :
( ( ( c_List_Olistsp @ SV28 @ SV314 @ SV566 )
| ~ ( c_List_Olistsp @ SV28 @ ( c_List_Oappend @ SV314 @ SV767 @ SV566 ) @ SV566 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1607]) ).
thf(1868,plain,
! [SV315: $i,SV29: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV29 ) @ SV315 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV29 ) ) @ ( c_Lambda_OdB_OAbs @ SV315 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1608]) ).
thf(1869,plain,
! [SV768: $i,SV567: $i,SV316: $i,SV30: $i] :
( ( ! [SY2299: $i] :
( ( c_ListOrder_Ostep1 @ SV30 @ ( c_List_Oappend @ SV316 @ SV567 @ SV768 ) @ ( c_List_Oappend @ SV316 @ SY2299 @ SV768 ) @ SV768 )
| ~ ( c_ListOrder_Ostep1 @ SV30 @ SV567 @ SY2299 @ SV768 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(1870,plain,
! [SV769: $i,SV568: $i,SV317: $i,SV31: $i] :
( ( ! [SY2300: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV31 @ SV317 @ SV568 @ SV769 )
| ( c_ListOrder_Ostep1 @ SV31 @ ( c_List_Oappend @ SV317 @ SY2300 @ SV769 ) @ ( c_List_Oappend @ SV568 @ SY2300 @ SV769 ) @ SV769 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1610]) ).
thf(1871,plain,
! [SV770: $i,SV570: $i,SV319: $i,SV34: $i] :
( ( ! [SY2301: $i] :
( ( c_Type_Otyping @ SV34 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV319 @ SV570 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV770 )
| ~ ( c_Type_Otypings @ SV34 @ SV570 @ SY2301 )
| ~ ( c_Type_Otyping @ SV34 @ SV319 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY2301 @ SV770 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(1872,plain,
! [SV771: $i,SV571: $i,SV320: $i,SV35: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV35 )
| ( c_HOL_Oord__class_Oless @ SV320 @ SV571 @ SV35 )
| ~ ( c_HOL_Oord__class_Oless @ SV771 @ SV571 @ SV35 )
| ~ ( c_HOL_Oord__class_Oless @ SV320 @ SV771 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1614]) ).
thf(1873,plain,
! [SV772: $i,SV572: $i,SV321: $i,SV36: $i] :
( ( ~ ( class_Orderings_Oorder @ SV36 )
| ( c_HOL_Oord__class_Oless @ SV321 @ SV572 @ SV36 )
| ~ ( c_HOL_Oord__class_Oless @ SV321 @ SV772 @ SV36 )
| ~ ( c_HOL_Oord__class_Oless @ SV772 @ SV572 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1615]) ).
thf(1874,plain,
! [SV773: $i,SV573: $i,SV322: $i,SV37: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV37 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV322 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV573 ) @ SV773 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV322 ) @ SV573 ) ) @ SV773 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1616]) ).
thf(1875,plain,
! [SV774: $i,SV574: $i,SV323: $i,SV38: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV38 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV323 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV574 ) @ SV774 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV574 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV323 ) @ SV774 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1617]) ).
thf(1876,plain,
! [SV775: $i,SV575: $i,SV324: $i,SV39: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV39 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ SV324 ) @ SV575 ) ) @ SV775 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ SV324 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ SV575 ) @ SV775 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1618]) ).
thf(1877,plain,
! [SV776: $i,SV576: $i,SV325: $i,SV40: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV40 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ SV325 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ SV576 ) @ SV776 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ SV576 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ SV325 ) @ SV776 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1619]) ).
thf(1878,plain,
! [SV777: $i,SV577: $i,SV326: $i,SV41: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV41 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV326 ) @ SV577 ) ) @ SV777 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV326 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV577 ) @ SV777 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(1879,plain,
! [SV778: $i,SV578: $i,SV327: $i,SV42: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV42 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV327 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV578 ) @ SV778 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV327 ) @ SV578 ) ) @ SV778 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(1880,plain,
! [SV779: $i,SV579: $i,SV328: $i,SV43: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV43 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ SV328 ) @ SV579 ) ) @ SV779 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ SV328 ) @ SV779 ) ) @ SV579 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1622]) ).
thf(1881,plain,
! [SV780: $i,SV580: $i,SV329: $i,SV44: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV44 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SV329 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SV580 ) @ SV780 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SV580 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SV329 ) @ SV780 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1623]) ).
thf(1882,plain,
! [SV781: $i,SV581: $i,SV330: $i,SV45: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV45 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV45 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV45 ) @ SV330 ) @ SV581 ) ) @ SV781 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV45 ) @ SV330 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV45 ) @ SV581 ) @ SV781 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(1883,plain,
! [SV782: $i,SV582: $i,SV331: $i,SV48: $i] :
( ( ! [SY2302: $i,SY2303: $i] :
( ( hAPP @ ( c_COMBC @ SV48 @ SV331 @ SV582 @ SV782 @ SY2302 ) @ SY2303 )
= ( hAPP @ ( hAPP @ SV48 @ SY2303 ) @ SV331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1625]) ).
thf(1884,plain,
! [SV783: $i,SV583: $i,SV332: $i,SV49: $i] :
( ( ( c_List_Ofoldr @ SV49 @ ( c_List_Olist_ONil @ SV332 ) @ SV583 @ SV332 @ SV783 )
= SV583 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1626]) ).
thf(1885,plain,
! [SV784: $i,SV585: $i,SV334: $i,SV51: $i] :
( ( ! [SY2304: $i,SY2305: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV51 @ SV334 ) @ SV585 ) )
| ( c_ListOrder_Ostep1 @ SV51 @ SV784 @ SY2304 @ SY2305 )
| ~ ( c_ListOrder_Ostep1 @ SV51 @ ( c_List_Oappend @ SV784 @ ( c_List_Olist_OCons @ SV334 @ ( c_List_Olist_ONil @ SY2305 ) @ SY2305 ) @ SY2305 ) @ ( c_List_Oappend @ SY2304 @ ( c_List_Olist_OCons @ SV585 @ ( c_List_Olist_ONil @ SY2305 ) @ SY2305 ) @ SY2305 ) @ SY2305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(1886,plain,
! [SV52: $i] :
( ( ( SV52
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV52 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV52 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV52 ) ) )
= $true )
| ( ( SV52
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV52 ) ) )
= $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 @ SV52 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV52 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV52 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1629]) ).
thf(1887,plain,
! [SV785: $i,SV586: $i,SV335: $i,SV53: $i] :
( ( ! [SY2306: $i,SY2307: $i] :
( ( c_Type_Otypings @ SV53 @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SV335 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV586 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV785 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2306 )
| ~ ( c_Type_Otypings @ ( c_Type_Oshift @ SV53 @ SV586 @ SY2307 @ tc_Type_Otype ) @ SV785 @ SY2306 )
| ~ ( c_Type_Otyping @ SV53 @ SV335 @ SY2307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1630]) ).
thf(1888,plain,
! [SV587: $i,SV336: $i,SV54: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV54 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV336 ) @ SV587 ) @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV54 )
| ~ ( c_HOL_Oord__class_Oless @ SV587 @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV54 )
| ~ ( c_HOL_Oord__class_Oless @ SV336 @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1631]) ).
thf(1889,plain,
! [SV786: $i,SV588: $i,SV337: $i,SV55: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV55 @ SV337 @ SV588 ) @ SV786 @ SV588 )
= ( c_List_Olist_OCons @ SV55 @ ( c_List_Oappend @ SV337 @ SV786 @ SV588 ) @ SV588 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1632]) ).
thf(1890,plain,
! [SV787: $i,SV589: $i,SV338: $i,SV56: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV56 @ SV338 @ SV589 ) @ SV787 @ SV589 )
= ( c_List_Olist_OCons @ SV56 @ ( c_List_Oappend @ SV338 @ SV787 @ SV589 ) @ SV589 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(1891,plain,
! [SV590: $i,SV339: $i,SV57: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV57 ) @ SV339 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV57 ) @ SV590 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV339 ) @ SV590 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1634]) ).
thf(1892,plain,
! [SV591: $i,SV340: $i,SV58: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV58 ) @ SV340 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV591 ) @ SV340 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV58 ) @ SV591 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1635]) ).
thf(1893,plain,
! [SV592: $i,SV341: $i,SV59: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV59 ) )
= $true )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV341 @ SV592 @ SV59 @ SV59 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV341 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV592 @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 @ SV59 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1636]) ).
thf(1894,plain,
! [SV788: $i,SV593: $i,SV342: $i,SV60: $i] :
( ( ! [SY2308: $i] :
( ( c_List_Omap @ SV60 @ ( c_List_Olist_OCons @ SV342 @ SV593 @ SV788 ) @ SV788 @ SY2308 )
= ( c_List_Olist_OCons @ ( hAPP @ SV60 @ SV342 ) @ ( c_List_Omap @ SV60 @ SV593 @ SV788 @ SY2308 ) @ SY2308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(1895,plain,
! [SV789: $i,SV594: $i,SV343: $i,SV61: $i] :
( ( ! [SY2309: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ SV61 @ SV343 ) @ ( c_List_Omap @ SV61 @ SV594 @ SV789 @ SY2309 ) @ SY2309 )
= ( c_List_Omap @ SV61 @ ( c_List_Olist_OCons @ SV343 @ SV594 @ SV789 ) @ SV789 @ SY2309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(1896,plain,
! [SV790: $i,SV595: $i,SV344: $i,SV62: $i] :
( ( ! [SY2310: $i] :
( ( c_List_Omap @ SV62 @ ( c_List_Olist_OCons @ SV344 @ SV595 @ SV790 ) @ SV790 @ SY2310 )
= ( c_List_Olist_OCons @ ( hAPP @ SV62 @ SV344 ) @ ( c_List_Omap @ SV62 @ SV595 @ SV790 @ SY2310 ) @ SY2310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(1897,plain,
! [SV63: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV63 ) @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV63 ) ) )
= $true )
| ( ( SV63
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV63 ) ) )
= $true )
| ( ( SV63
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV63 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV63 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV63 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1640]) ).
thf(1898,plain,
! [SV791: $i,SV596: $i,SV345: $i,SV64: $i] :
( ( ( c_List_Olist_OCons @ SV64 @ ( c_List_Oappend @ SV345 @ SV596 @ SV791 ) @ SV791 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV64 @ SV345 @ SV791 ) @ SV596 @ SV791 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1641]) ).
thf(1899,plain,
! [SV792: $i,SV597: $i,SV346: $i,SV65: $i] :
( ( ( c_List_Olist_OCons @ SV65 @ ( c_List_Oappend @ SV346 @ SV597 @ SV792 ) @ SV792 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV65 @ SV346 @ SV792 ) @ SV597 @ SV792 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1642]) ).
thf(1900,plain,
! [SV793: $i,SV598: $i,SV347: $i,SV66: $i] :
( ( ! [SY2311: $i,SY2312: $i] :
( ( SV66 = SV347 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV598 @ SV347 ) @ SV66 ) )
| ~ ( c_ListOrder_Ostep1 @ SV598 @ ( c_List_Olist_OCons @ SV347 @ SV793 @ SY2311 ) @ ( c_List_Olist_OCons @ SV66 @ SY2312 @ SY2311 ) @ SY2311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1643]) ).
thf(1901,plain,
! [SV794: $i,SV599: $i,SV348: $i,SV67: $i] :
( ( ! [SY2313: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV67 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ SV348 ) @ SV599 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ SV794 ) @ SY2313 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ SV348 ) @ SV794 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ SV599 ) @ SY2313 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1644]) ).
thf(1902,plain,
! [SV795: $i,SV600: $i,SV349: $i,SV68: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV68 ) @ SV349 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV600 ) @ SV795 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV349 ) @ SV795 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV68 ) @ SV600 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1645]) ).
thf(1903,plain,
! [SV601: $i,SV350: $i,SV69: $i] :
( ( ( ( c_Lambda_Oliftn @ SV69 @ ( c_Lambda_OdB_OVar @ SV350 ) @ SV601 )
= ( c_Lambda_OdB_OVar @ SV350 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV350 @ SV601 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1646]) ).
thf(1904,plain,
! [SV796: $i,SV602: $i,SV351: $i,SV70: $i] :
( ( ( c_Type_Otyping @ SV70 @ SV351 @ SV602 )
| ~ ( c_Type_Otyping @ SV70 @ SV796 @ SV602 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV796 ) @ SV351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(1905,plain,
! [SV797: $i,SV603: $i,SV352: $i,SV71: $i] :
( ( ! [SY2314: $i] :
( ( c_Type_Otypings @ ( c_Type_Oshift @ SV71 @ SV352 @ SV603 @ tc_Type_Otype ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ SV352 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV797 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2314 )
| ~ ( c_Type_Otypings @ SV71 @ SV797 @ SY2314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1648]) ).
thf(1906,plain,
! [SV353: $i,SV72: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV72 @ SV353 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV72 ) ) @ SV353 )
= ( c_Lambda_OdB_OVar @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1649]) ).
thf(1907,plain,
! [SV604: $i,SV354: $i,SV73: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV73 ) @ SV354 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV604 ) @ SV354 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV73 ) @ SV604 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1650]) ).
thf(1908,plain,
! [SV74: $i] :
( ( ( SV74
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV74 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV74 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV74 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV74 ) ) )
= $true )
| ( ( SV74
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV74 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV74 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV74 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1651]) ).
thf(1909,plain,
! [SV798: $i,SV606: $i,SV357: $i,SV77: $i] :
( ( ! [SY2315: $i,SY2316: $i] :
( ~ ( c_Type_Otyping @ SV77 @ SV357 @ SV606 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV77 @ SV798 @ SV606 @ tc_Type_Otype ) @ SY2315 @ SY2316 )
| ( c_Type_Otyping @ SV77 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY2315 ) @ SV357 ) @ SV798 ) @ SY2316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(1910,plain,
! [SV799: $i,SV608: $i,SV359: $i,SV79: $i] :
( ( ! [SY2317: $i,SY2318: $i] :
( ( SV79 = SV359 )
| ( c_ListOrder_Ostep1 @ SV608 @ SV79 @ SV359 @ SV799 )
| ~ ( c_ListOrder_Ostep1 @ SV608 @ ( c_List_Oappend @ SV79 @ ( c_List_Olist_OCons @ SY2317 @ ( c_List_Olist_ONil @ SV799 ) @ SV799 ) @ SV799 ) @ ( c_List_Oappend @ SV359 @ ( c_List_Olist_OCons @ SY2318 @ ( c_List_Olist_ONil @ SV799 ) @ SV799 ) @ SV799 ) @ SV799 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(1911,plain,
! [SV361: $i,SV82: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV82 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV82 ) @ ( c_HOL_Ozero__class_Ozero @ SV82 ) ) @ SV361 )
= SV361 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1657]) ).
thf(1912,plain,
! [SV362: $i,SV83: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV83 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV83 ) @ ( c_HOL_Ozero__class_Ozero @ SV83 ) ) @ SV362 )
= SV362 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1658]) ).
thf(1913,plain,
! [SV363: $i,SV84: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV84 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV84 )
| ( SV363
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV363 ) @ ( c_HOL_Ozero__class_Ozero @ SV84 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1659]) ).
thf(1914,plain,
! [SV364: $i,SV85: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV85 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV85 ) @ SV364 ) @ ( c_HOL_Ozero__class_Ozero @ SV85 ) )
= SV364 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1660]) ).
thf(1915,plain,
! [SV365: $i,SV86: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV86 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV86 ) @ ( c_HOL_Ozero__class_Ozero @ SV86 ) ) @ SV365 )
= SV365 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1661]) ).
thf(1916,plain,
! [SV366: $i,SV87: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV87 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV87 ) @ SV366 ) @ ( c_HOL_Ozero__class_Ozero @ SV87 ) )
= SV366 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1662]) ).
thf(1917,plain,
! [SV367: $i,SV88: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV88 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV88 ) @ SV367 ) @ ( c_HOL_Ozero__class_Ozero @ SV88 ) )
= SV367 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1663]) ).
thf(1918,plain,
! [SV368: $i,SV89: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV89 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ ( c_HOL_Ozero__class_Ozero @ SV89 ) ) @ SV368 )
= SV368 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1664]) ).
thf(1919,plain,
! [SV369: $i,SV90: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV90 ) @ SV369 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV90 ) ) @ ( c_Lambda_OdB_OAbs @ SV369 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1665]) ).
thf(1920,plain,
! [SV800: $i,SV609: $i,SV370: $i,SV91: $i] :
( ( ( ( hAPP @ ( hAPP @ SV91 @ SV370 ) @ SV609 )
= SV370 )
| ~ ( c_OrderedGroup_Omonoid__add @ SV609 @ SV91 @ SV800 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1666]) ).
thf(1921,plain,
! [SV801: $i,SV610: $i,SV371: $i,SV92: $i] :
( ( ( ( hAPP @ ( hAPP @ SV92 @ SV371 ) @ SV610 )
= SV610 )
| ~ ( c_OrderedGroup_Omonoid__add @ SV371 @ SV92 @ SV801 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1667]) ).
thf(1922,plain,
! [SV372: $i,SV93: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV93 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV372 @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV372 ) @ SV372 ) @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1668]) ).
thf(1923,plain,
! [SV373: $i,SV94: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV94 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV373 ) @ SV373 ) @ SV94 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV373 @ SV94 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1669]) ).
thf(1924,plain,
! [SV802: $i,SV611: $i,SV374: $i,SV95: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV95 ) @ SV374 ) @ SV611 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV802 ) @ SV374 ) @ SV611 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV95 ) @ SV802 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1670]) ).
thf(1925,plain,
! [SV803: $i,SV612: $i,SV375: $i,SV96: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV96 ) @ SV375 ) @ SV612 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV96 ) @ SV803 ) @ SV612 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV375 ) @ SV803 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1671]) ).
thf(1926,plain,
! [SV613: $i,SV376: $i,SV97: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV97 ) )
= $true )
| ( ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SV376 @ SV613 @ SV97 @ SV97 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SV613 @ SV376 @ SV97 @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1672]) ).
thf(1927,plain,
! [SV804: $i,SV614: $i,SV377: $i,SV98: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV98 @ SV377 ) @ SV614 ) @ SV804 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV98 @ SV614 ) @ SV804 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1673]) ).
thf(1928,plain,
! [SV615: $i,SV378: $i,SV99: $i] :
( ( c_ListOrder_Ostep1 @ SV99 @ ( c_List_Olist_ONil @ SV378 ) @ SV615 @ SV378 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1674]) ).
thf(1929,plain,
! [SV616: $i,SV379: $i,SV100: $i] :
( ( c_ListOrder_Ostep1 @ SV100 @ SV379 @ ( c_List_Olist_ONil @ SV616 ) @ SV616 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1675]) ).
thf(1930,plain,
! [SV380: $i,SV101: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV101 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ SV380 ) @ SV380 ) @ ( c_HOL_Ozero__class_Ozero @ SV101 ) @ SV101 )
| ~ ( c_HOL_Oord__class_Oless @ SV380 @ ( c_HOL_Ozero__class_Ozero @ SV101 ) @ SV101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1676]) ).
thf(1931,plain,
! [SV381: $i,SV102: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV102 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV381 @ ( c_HOL_Ozero__class_Ozero @ SV102 ) @ SV102 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SV381 ) @ SV381 ) @ ( c_HOL_Ozero__class_Ozero @ SV102 ) @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1677]) ).
thf(1932,plain,
! [SV382: $i,SV103: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV103 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV382 @ ( c_HOL_Ozero__class_Ozero @ SV103 ) @ SV103 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV103 ) @ SV382 ) @ SV382 ) @ ( c_HOL_Ozero__class_Ozero @ SV103 ) @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1678]) ).
thf(1933,plain,
! [SV383: $i,SV104: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV104 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV104 ) @ SV383 ) @ SV383 ) @ ( c_HOL_Ozero__class_Ozero @ SV104 ) @ SV104 )
| ~ ( c_HOL_Oord__class_Oless @ SV383 @ ( c_HOL_Ozero__class_Ozero @ SV104 ) @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1679]) ).
thf(1934,plain,
! [SV617: $i,SV384: $i,SV105: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV105 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV384 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ ( c_HOL_Ozero__class_Ozero @ SV105 ) @ SV617 @ SV105 @ SV105 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV384 @ SV617 @ SV105 @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1680]) ).
thf(1935,plain,
! [SV805: $i,SV618: $i,SV385: $i,SV106: $i] :
( ( ( c_Type_Otyping @ SV106 @ ( c_Lambda_OdB_OAbs @ SV385 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV618 ) @ SV805 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV106 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV618 @ tc_Type_Otype ) @ SV385 @ SV805 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1681]) ).
thf(1936,plain,
! [SV806: $i,SV619: $i,SV386: $i,SV107: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV107 @ SV386 @ SV619 @ SV806 ) @ SV386 )
= SV619 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(1937,plain,
! [SV620: $i,SV387: $i,SV108: $i] :
( ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV108 ) @ SV387 @ SV620 )
= ( c_Lambda_OdB_OVar @ SV108 ) )
= $true )
| ( ( ( SV108 = SV620 )
| ( c_HOL_Oord__class_Oless @ SV620 @ SV108 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1683]) ).
thf(1938,plain,
! [SV109: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV109 ) @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV109 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV109 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV109 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1684]) ).
thf(1939,plain,
! [SV388: $i,SV112: $i] :
( ( ( class_Orderings_Oorder @ SV112 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV388 @ SV388 @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1685]) ).
thf(1940,plain,
! [SV389: $i,SV113: $i] :
( ( ( class_Orderings_Olinorder @ SV113 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV389 @ SV389 @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1686]) ).
thf(1941,plain,
! [SV390: $i,SV114: $i] :
( ( ( class_Orderings_Opreorder @ SV114 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV390 @ SV390 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1687]) ).
thf(1942,plain,
! [SV621: $i,SV392: $i,SV116: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV116 ) @ SV392 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV621 ) @ SV392 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV116 ) @ SV621 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1688]) ).
thf(1943,plain,
! [SV622: $i,SV393: $i,SV117: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV117 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV393 ) @ SV622 ) @ SV117 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV622 @ SV117 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV393 @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1689]) ).
thf(1944,plain,
! [SV807: $i,SV623: $i,SV394: $i,SV118: $i] :
( ( ! [SY2319: $i,SY2320: $i] :
( ( c_ListOrder_Ostep1 @ SV118 @ SV394 @ SV623 @ SV807 )
| ( SV623 = SV394 )
| ~ ( c_ListOrder_Ostep1 @ SV118 @ ( c_List_Olist_OCons @ SY2319 @ SV394 @ SV807 ) @ ( c_List_Olist_OCons @ SY2320 @ SV623 @ SV807 ) @ SV807 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1690]) ).
thf(1945,plain,
! [SV808: $i,SV624: $i,SV395: $i,SV119: $i] :
( ( ! [SY2321: $i] :
( ( ( hAPP @ ( hAPP @ SV119 @ ( hAPP @ ( hAPP @ SV119 @ SV395 ) @ SV624 ) ) @ SV808 )
= ( hAPP @ ( hAPP @ SV119 @ SV395 ) @ ( hAPP @ ( hAPP @ SV119 @ SV624 ) @ SV808 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV119 @ SY2321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1691]) ).
thf(1946,plain,
! [SV809: $i,SV625: $i,SV396: $i,SV120: $i] :
( ( ! [SY2322: $i] :
( ( c_List_Omap @ SV120 @ ( c_List_Oappend @ SV396 @ SV625 @ SV809 ) @ SV809 @ SY2322 )
= ( c_List_Oappend @ ( c_List_Omap @ SV120 @ SV396 @ SV809 @ SY2322 ) @ ( c_List_Omap @ SV120 @ SV625 @ SV809 @ SY2322 ) @ SY2322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1692]) ).
thf(1947,plain,
! [SV121: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV121 ) @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV121 ) ) )
= $true )
| ( ( SV121
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV121 ) ) )
= $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 @ SV121 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV121 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV121 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1693]) ).
thf(1948,plain,
! [SV626: $i,SV397: $i,SV122: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV122 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV397 @ SV626 @ SV122 )
| ( c_HOL_Oord__class_Oless @ SV626 @ SV397 @ SV122 )
| ( SV626 = SV397 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1694]) ).
thf(1949,plain,
! [SV627: $i,SV398: $i,SV123: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV123 ) )
= $true )
| ( ( ( SV398 = SV627 )
| ( c_HOL_Oord__class_Oless @ SV627 @ SV398 @ SV123 )
| ( c_HOL_Oord__class_Oless @ SV398 @ SV627 @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1695]) ).
thf(1950,plain,
! [SV124: $i,SV399: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV399 @ SV124 @ tc_nat )
= $true )
| ( ( SV399 = SV124 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV124 @ SV399 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1696]) ).
thf(1951,plain,
! [SV628: $i,SV400: $i,SV125: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV125 @ SV400 ) @ SV628 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV400 @ SV628 @ tc_nat )
| ( SV628 = SV400 )
| ( c_HOL_Oord__class_Oless @ SV628 @ SV400 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1697]) ).
thf(1952,plain,
! [SV126: $i,SV401: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV401 @ SV126 @ tc_nat )
= $true )
| ( ( SV401 = SV126 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV126 @ SV401 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1698]) ).
thf(1953,plain,
! [SV629: $i,SV402: $i,SV127: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV127 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV402 @ SV629 @ SV127 )
| ( c_HOL_Oord__class_Oless @ SV629 @ SV402 @ SV127 )
| ( SV629 = SV402 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1699]) ).
thf(1954,plain,
! [SV630: $i,SV403: $i,SV128: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV128 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV403 @ SV630 @ SV128 )
| ( SV630 = SV403 )
| ( c_HOL_Oord__class_Oless @ SV630 @ SV403 @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1700]) ).
thf(1955,plain,
! [SV631: $i,SV404: $i,SV129: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV129 ) )
= $true )
| ( ( ( SV404 = SV631 )
| ( c_HOL_Oord__class_Oless @ SV404 @ SV631 @ SV129 )
| ( c_HOL_Oord__class_Oless @ SV631 @ SV404 @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1701]) ).
thf(1956,plain,
! [SV810: $i,SV632: $i,SV405: $i,SV130: $i] :
( ( ! [SY2323: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV130 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SV405 ) @ SV632 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SV810 ) @ SY2323 ) @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SV632 @ SY2323 @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SV405 @ SV810 @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1702]) ).
thf(1957,plain,
! [SV811: $i,SV633: $i,SV406: $i,SV131: $i] :
( ( ! [SY2324: $i] :
( ( c_Type_Otyping @ SV131 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV406 ) @ SV633 ) @ SV811 )
| ~ ( c_Type_Otyping @ SV131 @ SV633 @ SY2324 )
| ~ ( c_Type_Otyping @ SV131 @ SV406 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY2324 ) @ SV811 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1703]) ).
thf(1958,plain,
! [SV407: $i,SV132: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV132 )
= $false )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV132 ) @ ( c_HOL_Ozero__class_Ozero @ SV132 ) @ SV407 @ SV132 @ SV132 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV132 ) @ SV407 @ ( c_HOL_Ozero__class_Ozero @ SV132 ) @ SV132 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1704]) ).
thf(1959,plain,
! [SV133: $i] :
( ( ( SV133
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV133 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV133 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV133 ) ) )
= $true )
| ( ( SV133
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV133 ) ) )
= $true )
| ( ( SV133
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV133 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV133 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV133 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1705]) ).
thf(1960,plain,
! [SV812: $i,SV634: $i,SV408: $i,SV134: $i] :
( ( ! [SY2325: $i,SY2326: $i] :
( ( SV134 = SV408 )
| ( SV634 = SV812 )
| ~ ( c_ListOrder_Ostep1 @ SY2325 @ ( c_List_Oappend @ SV134 @ ( c_List_Olist_OCons @ SV634 @ ( c_List_Olist_ONil @ SY2326 ) @ SY2326 ) @ SY2326 ) @ ( c_List_Oappend @ SV408 @ ( c_List_Olist_OCons @ SV812 @ ( c_List_Olist_ONil @ SY2326 ) @ SY2326 ) @ SY2326 ) @ SY2326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1706]) ).
thf(1961,plain,
! [SV813: $i,SV636: $i,SV410: $i,SV137: $i] :
( ( ( c_List_Olistsp @ SV137 @ ( c_List_Oappend @ SV410 @ SV636 @ SV813 ) @ SV813 )
| ~ ( c_List_Olistsp @ SV137 @ SV636 @ SV813 )
| ~ ( c_List_Olistsp @ SV137 @ SV410 @ SV813 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1708]) ).
thf(1962,plain,
! [SV814: $i,SV637: $i,SV411: $i,SV138: $i] :
( ( ! [SY2327: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV138 @ SV411 @ SV637 @ ( c_Lambda_OdB_OAbs @ SV814 ) @ SY2327 )
= ( hAPP @ ( hAPP @ SV637 @ SV814 ) @ ( c_Lambda_OdB_OdB__rec @ SV138 @ SV411 @ SV637 @ SV814 @ SY2327 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1709]) ).
thf(1963,plain,
! [SV815: $i,SV638: $i,SV413: $i,SV141: $i] :
( ( ! [SY2328: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV141 @ SV413 @ SV638 @ SV815 ) @ SY2328 )
= ( hAPP @ SV141 @ SY2328 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2328 @ SV413 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1711]) ).
thf(1964,plain,
! [SV816: $i,SV639: $i,SV414: $i,SV142: $i] :
( ( ! [SY2329: $i,SY2330: $i,SY2331: $i] :
( ( SV142
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV414 @ SV142 @ SV639 @ SV816 ) @ SV414 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV639 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2329 ) @ SY2330 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV142 )
| ~ ( c_Type_Otypings @ SV639 @ SY2330 @ SY2331 )
| ~ ( c_Type_Otyping @ SV639 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2329 ) @ SY2330 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV816 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1712]) ).
thf(1965,plain,
! [SV817: $i,SV640: $i,SV416: $i,SV144: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV144 )
| ( c_HOL_Oord__class_Oless @ SV416 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ SV640 ) @ SV817 ) @ SV144 )
| ~ ( c_HOL_Oord__class_Oless @ SV416 @ SV817 @ SV144 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV144 ) @ SV640 @ SV144 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1713]) ).
thf(1966,plain,
! [SV818: $i,SV641: $i,SV417: $i,SV145: $i] :
( ( ! [SY2332: $i,SY2333: $i] :
( ( c_List_Ofoldr @ SV145 @ ( c_List_Olist_OCons @ SV417 @ SV641 @ SV818 ) @ SY2332 @ SV818 @ SY2333 )
= ( hAPP @ ( hAPP @ SV145 @ SV417 ) @ ( c_List_Ofoldr @ SV145 @ SV641 @ SY2332 @ SV818 @ SY2333 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1714]) ).
thf(1967,plain,
! [SV819: $i,SV642: $i,SV418: $i,SV146: $i] :
( ( ! [SY2334: $i] :
( ~ ( hBOOL @ ( hAPP @ SV146 @ ( c_Lambda_OdB_OdB__case @ SV418 @ SV642 @ SV819 @ ( c_Lambda_OdB_OAbs @ SY2334 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV146 @ ( hAPP @ SV819 @ SY2334 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1715]) ).
thf(1968,plain,
! [SV820: $i,SV643: $i,SV419: $i,SV147: $i] :
( ( ! [SY2335: $i] :
( ~ ( hBOOL @ ( hAPP @ SV147 @ ( c_Lambda_OdB_OdB__case @ SV419 @ SV643 @ SV820 @ ( c_Lambda_OdB_OAbs @ SY2335 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV147 @ ( hAPP @ SV820 @ SY2335 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1716]) ).
thf(1969,plain,
! [SV821: $i,SV645: $i,SV421: $i,SV149: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV149 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV421 ) @ SV645 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV821 ) @ SV645 ) @ SV149 )
| ~ ( c_HOL_Oord__class_Oless @ SV421 @ SV821 @ SV149 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1718]) ).
thf(1970,plain,
! [SV822: $i,SV646: $i,SV422: $i,SV150: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV150 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV150 ) @ SV422 ) @ SV646 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV150 ) @ SV822 ) @ SV646 ) @ SV150 )
| ~ ( c_HOL_Oord__class_Oless @ SV422 @ SV822 @ SV150 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1719]) ).
thf(1971,plain,
! [SV823: $i,SV647: $i,SV423: $i,SV151: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV151 )
| ( c_HOL_Oord__class_Oless @ SV423 @ SV647 @ SV151 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV423 ) @ SV823 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV647 ) @ SV823 ) @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1720]) ).
thf(1972,plain,
! [SV824: $i,SV648: $i,SV424: $i,SV152: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV152 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV424 ) @ SV648 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV424 ) @ SV824 ) @ SV152 )
| ~ ( c_HOL_Oord__class_Oless @ SV648 @ SV824 @ SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1721]) ).
thf(1973,plain,
! [SV825: $i,SV649: $i,SV425: $i,SV153: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV153 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV425 ) @ SV649 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV425 ) @ SV825 ) @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SV649 @ SV825 @ SV153 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1722]) ).
thf(1974,plain,
! [SV826: $i,SV650: $i,SV426: $i,SV154: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV154 )
| ( c_HOL_Oord__class_Oless @ SV426 @ SV650 @ SV154 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SV826 ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SV826 ) @ SV650 ) @ SV154 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1723]) ).
thf(1975,plain,
! [SV155: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV155 ) @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV155 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV155 ) ) )
= $true )
| ( ( SV155
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV155 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV155 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV155 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1724]) ).
thf(1976,plain,
! [SV827: $i,SV651: $i,SV427: $i,SV156: $i] :
( ( ( c_Type_Otyping @ SV156 @ SV427 @ SV651 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV827 ) @ SV427 ) )
| ~ ( c_Type_Otyping @ SV156 @ SV827 @ SV651 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1725]) ).
thf(1977,plain,
! [SV828: $i,SV652: $i,SV428: $i,SV157: $i] :
( ( ! [SY2336: $i,SY2337: $i] :
( ( c_ListOrder_Ostep1 @ SV157 @ SV428 @ SV652 @ SV828 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV157 @ SY2336 ) @ SY2337 ) )
| ~ ( c_ListOrder_Ostep1 @ SV157 @ ( c_List_Olist_OCons @ SY2336 @ SV428 @ SV828 ) @ ( c_List_Olist_OCons @ SY2337 @ SV652 @ SV828 ) @ SV828 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1726]) ).
thf(1978,plain,
! [SV829: $i,SV653: $i,SV429: $i,SV158: $i] :
( ( ! [SY2338: $i] :
( ( c_ListOrder_Ostep1 @ SV158 @ ( c_List_Olist_OCons @ SV429 @ SV653 @ SV829 ) @ ( c_List_Olist_OCons @ SV429 @ SY2338 @ SV829 ) @ SV829 )
| ~ ( c_ListOrder_Ostep1 @ SV158 @ SV653 @ SY2338 @ SV829 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1727]) ).
thf(1979,plain,
! [SV830: $i,SV654: $i,SV430: $i,SV161: $i] :
( ( ( c_List_Oappend @ ( c_List_Oappend @ SV161 @ SV430 @ SV654 ) @ SV830 @ SV654 )
= ( c_List_Oappend @ SV161 @ ( c_List_Oappend @ SV430 @ SV830 @ SV654 ) @ SV654 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1729]) ).
thf(1980,plain,
! [SV831: $i,SV655: $i,SV431: $i,SV162: $i] :
( ( ( c_List_Oappend @ SV162 @ ( c_List_Oappend @ SV431 @ SV655 @ SV831 ) @ SV831 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV162 @ SV431 @ SV831 ) @ SV655 @ SV831 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1730]) ).
thf(1981,plain,
! [SV832: $i,SV656: $i,SV432: $i,SV163: $i] :
( ( ( c_List_Oappend @ ( c_List_Oappend @ SV163 @ SV432 @ SV656 ) @ SV832 @ SV656 )
= ( c_List_Oappend @ SV163 @ ( c_List_Oappend @ SV432 @ SV832 @ SV656 ) @ SV656 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1731]) ).
thf(1982,plain,
! [SV833: $i,SV657: $i,SV433: $i,SV164: $i] :
( ( ( c_List_Oappend @ SV164 @ ( c_List_Oappend @ SV433 @ SV657 @ SV833 ) @ SV833 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV164 @ SV433 @ SV833 ) @ SV657 @ SV833 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1732]) ).
thf(1983,plain,
! [SV834: $i,SV658: $i,SV434: $i,SV165: $i] :
( ( ! [SY2339: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV165 @ SV434 @ SV658 @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV834 ) @ SV434 ) @ SY2339 )
| ~ ( c_Type_Otyping @ SV165 @ SV834 @ SY2339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1733]) ).
thf(1984,plain,
! [SV659: $i,SV435: $i,SV166: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV166 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV435 @ SV659 @ SV166 )
| ~ ( c_HOL_Oord__class_Oless @ SV659 @ SV435 @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1734]) ).
thf(1985,plain,
! [SV835: $i,SV660: $i,SV436: $i,SV167: $i] :
( ( ! [SY2340: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV167 @ SV436 ) @ SV660 ) @ SV835 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV167 @ SV436 ) @ SY2340 ) @ SV835 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV167 @ SV660 ) @ SY2340 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1735]) ).
thf(1986,plain,
! [SV836: $i,SV661: $i,SV437: $i,SV168: $i] :
( ( ! [SY2341: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV168 @ SV437 ) @ SV661 ) @ SV836 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV168 @ SY2341 ) @ SV836 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV168 @ SV437 ) @ SV661 ) @ SY2341 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1736]) ).
thf(1987,plain,
! [SV662: $i,SV438: $i,SV169: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV169 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV438 @ SV662 @ SV169 )
| ~ ( c_HOL_Oord__class_Oless @ SV662 @ SV438 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1737]) ).
thf(1988,plain,
! [SV663: $i,SV439: $i,SV170: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV170 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV439 @ SV663 @ SV170 )
| ~ ( c_HOL_Oord__class_Oless @ SV663 @ SV439 @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1738]) ).
thf(1989,plain,
! [SV664: $i,SV440: $i,SV171: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV171 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV440 @ SV664 @ SV171 )
| ~ ( c_HOL_Oord__class_Oless @ SV664 @ SV440 @ SV171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1739]) ).
thf(1990,plain,
! [SV441: $i,SV172: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV172 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV172 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV172 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV172 @ SV441 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV172 @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV172 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1740]) ).
thf(1991,plain,
! [SV837: $i,SV665: $i,SV442: $i,SV173: $i] :
( ( ! [SY2342: $i] :
( ( ( c_List_Ofoldl @ SV173 @ ( hAPP @ ( hAPP @ SV173 @ SV442 ) @ SV665 ) @ SV837 @ SY2342 @ SY2342 )
= ( hAPP @ ( hAPP @ SV173 @ SV442 ) @ ( c_List_Ofoldl @ SV173 @ SV665 @ SV837 @ SY2342 @ SY2342 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV173 @ SY2342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1741]) ).
thf(1992,plain,
! [SV838: $i,SV666: $i,SV444: $i,SV175: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV175 ) @ SV444 ) ) @ SV666 ) @ SV838 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV175 ) @ SV666 ) @ SV838 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV444 ) @ SV666 ) @ SV838 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1742]) ).
thf(1993,plain,
! [SV839: $i,SV667: $i,SV445: $i,SV176: $i] :
( ( ( c_Type_Otypings @ SV176 @ SV445 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV667 @ SV176 @ SV839 @ SV445 ) )
| ~ ( c_Type_Otyping @ SV176 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV839 ) @ SV445 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV667 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1743]) ).
thf(1994,plain,
! [SV840: $i,SV668: $i,SV446: $i,SV177: $i] :
( ( ! [SY2343: $i] :
( ~ ( hBOOL @ ( hAPP @ SV177 @ ( c_Lambda_OdB_OdB__case @ SV446 @ SV668 @ SV840 @ ( c_Lambda_OdB_OVar @ SY2343 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV177 @ ( hAPP @ SV446 @ SY2343 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1744]) ).
thf(1995,plain,
! [SV841: $i,SV669: $i,SV447: $i,SV178: $i] :
( ( ! [SY2344: $i] :
( ~ ( hBOOL @ ( hAPP @ SV178 @ ( c_Lambda_OdB_OdB__case @ SV447 @ SV669 @ SV841 @ ( c_Lambda_OdB_OVar @ SY2344 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV178 @ ( hAPP @ SV447 @ SY2344 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1745]) ).
thf(1996,plain,
! [SV842: $i,SV670: $i,SV449: $i,SV180: $i] :
( ( ! [SY2345: $i,SY2346: $i] :
( ~ ( hBOOL @ ( hAPP @ SV180 @ ( c_Lambda_OdB_OdB__case @ SV449 @ SV670 @ SV842 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2345 ) @ SY2346 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV180 @ ( hAPP @ ( hAPP @ SV670 @ SY2345 ) @ SY2346 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1746]) ).
thf(1997,plain,
! [SV843: $i,SV671: $i,SV450: $i,SV181: $i] :
( ( ! [SY2347: $i,SY2348: $i] :
( ~ ( hBOOL @ ( hAPP @ SV181 @ ( c_Lambda_OdB_OdB__case @ SV450 @ SV671 @ SV843 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2347 ) @ SY2348 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV181 @ ( hAPP @ ( hAPP @ SV671 @ SY2347 ) @ SY2348 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1747]) ).
thf(1998,plain,
! [SV672: $i,SV451: $i,SV182: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV182 ) @ ( c_Lambda_OdB_OVar @ SV451 ) ) @ SV672 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV182 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1748]) ).
thf(1999,plain,
! [SV673: $i,SV452: $i,SV183: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV183 ) ) @ SV452 ) @ SV673 )
= ( c_Lambda_OdB_OVar @ SV183 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV183 @ SV673 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1749]) ).
thf(2000,plain,
! [SV674: $i,SV453: $i,SV184: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV184 @ SV453 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV674 @ SV453 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV184 ) @ SV674 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1750]) ).
thf(2001,plain,
! [SV186: $i,SV455: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ SV455 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV186 ) @ SV455 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1752]) ).
thf(2002,plain,
! [SV844: $i,SV675: $i,SV456: $i,SV187: $i] :
( ( ! [SY2349: $i] :
( ( SV187 = SV456 )
| ~ ( c_Type_Otyping @ SV675 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV844 ) @ SY2349 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV456 )
| ~ ( c_Type_Otyping @ SV675 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV844 ) @ SY2349 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1753]) ).
thf(2003,plain,
! [SV676: $i,SV457: $i,SV188: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV188 @ SV457 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV188 @ SV676 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV457 @ SV676 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1754]) ).
thf(2004,plain,
! [SV458: $i,SV189: $i] :
( ( ( hBOOL @ ( hAPP @ SV189 @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV189 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV189 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV189 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV189 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV189 @ SV458 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1755]) ).
thf(2005,plain,
! [SV677: $i,SV459: $i,SV190: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV190 @ SV459 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV677 @ SV459 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV190 ) @ SV677 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1756]) ).
thf(2006,plain,
! [SV845: $i,SV678: $i,SV460: $i,SV191: $i] :
( ( ! [SY2350: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV191 @ SV460 @ SV678 @ ( c_Lambda_OdB_OVar @ SV845 ) @ SY2350 )
= ( hAPP @ SV191 @ SV845 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1757]) ).
thf(2007,plain,
! [SV461: $i,SV192: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV192 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV192 ) @ SV461 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1758]) ).
thf(2008,plain,
! [SV846: $i,SV679: $i,SV462: $i,SV193: $i] :
( ( ( c_List_Ofoldl @ SV193 @ SV462 @ ( c_List_Olist_ONil @ SV679 ) @ SV846 @ SV679 )
= SV462 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1759]) ).
thf(2009,plain,
! [SV680: $i,SV463: $i,SV194: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV194 ) ) @ SV463 ) @ SV680 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV463 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV194 ) @ SV463 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV680 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1760]) ).
thf(2010,plain,
! [SV195: $i] :
( ( ( SV195
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV195 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV195 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV195 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV195 ) ) )
= $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 @ SV195 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV195 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV195 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1761]) ).
thf(2011,plain,
! [SV681: $i,SV464: $i,SV197: $i] :
( ( ( ( hAPP @ SV197 @ SV464 )
= SV681 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV197 @ ( c_Lambda_OdB_OVar @ SV464 ) @ SV681 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1762]) ).
thf(2012,plain,
! [SV847: $i,SV682: $i,SV465: $i,SV198: $i] :
( ( ~ ( class_OrderedGroup_Osemigroup__add @ SV198 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ SV465 ) @ SV682 ) @ SV847 @ SV198 @ SV198 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ SV465 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ SV682 @ SV847 @ SV198 @ SV198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1763]) ).
thf(2013,plain,
! [SV199: $i] :
( ( ( SV199
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV199 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV199 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV199 ) ) )
= $true )
| ( ( SV199
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV199 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV199 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1764]) ).
thf(2014,plain,
! [SV848: $i,SV684: $i,SV467: $i,SV201: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV201 @ SV467 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV684 ) @ SV848 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV201 ) @ SV684 ) @ SV848 ) @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SV684 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV848 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV467 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1766]) ).
thf(2015,plain,
! [SV849: $i,SV685: $i,SV468: $i,SV202: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV202 ) @ SV468 ) @ SV685 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV849 ) @ SV468 ) @ SV685 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV202 ) @ SV849 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1767]) ).
thf(2016,plain,
! [SV686: $i,SV469: $i,SV203: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV203 ) ) @ SV469 ) @ SV686 )
= ( c_Lambda_OdB_OVar @ SV203 ) )
= $true )
| ( ( ( SV203 = SV686 )
| ( c_HOL_Oord__class_Oless @ SV686 @ SV203 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1768]) ).
thf(2017,plain,
! [SV850: $i,SV687: $i,SV470: $i,SV204: $i] :
( ( ( c_Type_Otyping @ SV204 @ ( c_Lambda_OdB_OVar @ SV470 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV687 @ SV204 @ SV470 @ SV850 ) @ SV687 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV204 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV470 ) @ SV850 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV687 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1769]) ).
thf(2018,plain,
! [SV688: $i,SV471: $i,SV205: $i] :
( ( ( SV205
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV471 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV471 @ SV688 @ SV205 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV471 ) @ SV688 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV205 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1770]) ).
thf(2019,plain,
! [SV851: $i,SV689: $i,SV472: $i,SV206: $i] :
( ( ! [SY2351: $i,SY2352: $i] :
( ( c_Lambda_OdB_OdB__case @ SV206 @ SV472 @ SV689 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV851 ) @ SY2351 ) @ SY2352 )
= ( hAPP @ ( hAPP @ SV472 @ SV851 ) @ SY2351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1771]) ).
thf(2020,plain,
! [SV852: $i,SV690: $i,SV473: $i,SV207: $i] :
( ( ! [SY2353: $i] :
( ( ( hAPP @ ( hAPP @ SV207 @ SV473 ) @ ( c_List_Ofoldl @ SV207 @ SV690 @ SV852 @ SY2353 @ SY2353 ) )
= ( c_List_Ofoldl @ SV207 @ SV473 @ SV852 @ SY2353 @ SY2353 ) )
| ~ ( c_OrderedGroup_Omonoid__add @ SV690 @ SV207 @ SY2353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1772]) ).
thf(2021,plain,
! [SV208: $i] :
( ( ( SV208
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV208 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV208 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV208 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV208 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV208 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1773]) ).
thf(2022,plain,
! [SV853: $i,SV691: $i,SV474: $i,SV210: $i] :
( ( ! [SY2354: $i] :
( ( c_Lambda_OdB_OdB__case @ SV210 @ SV474 @ SV691 @ ( c_Lambda_OdB_OVar @ SV853 ) @ SY2354 )
= ( hAPP @ SV210 @ SV853 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1774]) ).
thf(2023,plain,
! [SV854: $i,SV692: $i,SV476: $i,SV212: $i] :
( ( ! [SY2355: $i,SY2356: $i] :
( ( c_List_Ofoldl @ SV212 @ SV476 @ ( c_List_Olist_OCons @ SV692 @ SV854 @ SY2355 ) @ SY2356 @ SY2355 )
= ( c_List_Ofoldl @ SV212 @ ( hAPP @ ( hAPP @ SV212 @ SV476 ) @ SV692 ) @ SV854 @ SY2356 @ SY2355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1776]) ).
thf(2024,plain,
! [SV855: $i,SV693: $i,SV478: $i,SV215: $i] :
( ( ! [SY2357: $i,SY2358: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV215 @ SV478 @ SV693 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV855 ) @ SY2357 ) @ SY2358 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV478 @ SV855 ) @ SY2357 ) @ ( c_Lambda_OdB_OdB__rec @ SV215 @ SV478 @ SV693 @ SV855 @ SY2358 ) ) @ ( c_Lambda_OdB_OdB__rec @ SV215 @ SV478 @ SV693 @ SY2357 @ SY2358 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1777]) ).
thf(2025,plain,
! [SV856: $i,SV694: $i,SV479: $i,SV217: $i] :
( ( ! [SY2359: $i,SY2360: $i,SY2361: $i] :
( ( c_Type_Otypings @ SV217 @ SV479 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV694 @ SV856 @ SV217 @ SV479 ) )
| ~ ( c_Type_Otyping @ SV217 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2359 ) @ SY2360 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV856 )
| ~ ( c_Type_Otypings @ SV217 @ SY2360 @ SY2361 )
| ~ ( c_Type_Otyping @ SV217 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2359 ) @ SY2360 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV479 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV694 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1778]) ).
thf(2026,plain,
! [SV695: $i,SV480: $i,SV219: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV219 ) @ SV480 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV219 ) @ SV695 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV480 ) @ SV695 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1780]) ).
thf(2027,plain,
! [SV696: $i,SV481: $i,SV220: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV220 ) @ SV481 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV696 ) @ SV481 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV220 ) @ SV696 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1781]) ).
thf(2028,plain,
! [SV857: $i,SV697: $i,SV482: $i,SV221: $i] :
( ( ( c_Lambda_Oliftn @ SV221 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV482 ) @ SV697 ) @ SV857 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ SV221 @ SV482 @ SV857 ) ) @ ( c_Lambda_Oliftn @ SV221 @ SV697 @ SV857 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1782]) ).
thf(2029,plain,
! [SV484: $i,SV224: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV224 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV224 ) @ ( c_Lambda_OdB_OVar @ SV484 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1784]) ).
thf(2030,plain,
! [SV699: $i,SV485: $i,SV225: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV225 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV485 @ SV225 @ SV699 ) @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV485 ) @ SV225 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV699 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1785]) ).
thf(2031,plain,
! [SV858: $i,SV700: $i,SV486: $i,SV226: $i] :
( ( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV226 ) @ SV486 ) @ SV700 @ SV858 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ SV226 @ SV700 @ SV858 ) ) @ ( c_Lambda_Osubstn @ SV486 @ SV700 @ SV858 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1786]) ).
thf(2032,plain,
! [SV859: $i,SV701: $i,SV487: $i,SV227: $i] :
( ( ! [SY2362: $i,SY2363: $i] :
( ( c_List_Ofoldl @ SV227 @ SV487 @ ( c_List_Oappend @ SV701 @ SV859 @ SY2362 ) @ SY2363 @ SY2362 )
= ( c_List_Ofoldl @ SV227 @ ( c_List_Ofoldl @ SV227 @ SV487 @ SV701 @ SY2363 @ SY2362 ) @ SV859 @ SY2363 @ SY2362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1787]) ).
thf(2033,plain,
! [SV228: $i,SV488: $i] :
( ( ( class_Orderings_Opreorder @ SV488 )
= $false )
| ( ( class_Orderings_Opreorder @ ( tc_fun @ SV228 @ SV488 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1788]) ).
thf(2034,plain,
! [SV229: $i,SV489: $i] :
( ( ( class_Orderings_Oorder @ SV489 )
= $false )
| ( ( class_Orderings_Oorder @ ( tc_fun @ SV229 @ SV489 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1789]) ).
thf(2035,plain,
! [SV702: $i,SV491: $i,SV231: $i] :
( ( ( SV231 = SV491 )
= $true )
| ( ( ~ ( c_fequal @ SV231 @ SV491 @ SV702 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1790]) ).
thf(2036,plain,
! [SV703: $i,SV492: $i,SV232: $i] :
( ( ( c_List_Olist_OCons @ SV232 @ SV492 @ SV703 )
= ( c_List_Olist_ONil @ SV703 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1791]) ).
thf(2037,plain,
! [SV860: $i,SV704: $i,SV493: $i,SV233: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV233 ) @ SV493 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV704 ) @ SV860 ) )
| ( SV233 = SV704 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1792]) ).
thf(2038,plain,
! [SV861: $i,SV705: $i,SV494: $i,SV234: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV234 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV494 ) @ SV705 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV494 ) @ SV861 ) )
| ( SV705 = SV861 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1793]) ).
thf(2039,plain,
! [SV706: $i,SV495: $i,SV235: $i] :
( ( ( ( c_List_Oappend @ SV235 @ SV495 @ SV706 )
!= ( c_List_Olist_ONil @ SV706 ) )
= $true )
| ( ( SV495
= ( c_List_Olist_ONil @ SV706 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1794]) ).
thf(2040,plain,
! [SV862: $i,SV707: $i,SV496: $i,SV236: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV236 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV236 ) @ SV496 ) @ SV707 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV236 ) @ SV862 ) @ SV707 ) )
| ( SV496 = SV862 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1795]) ).
thf(2041,plain,
! [SV863: $i,SV708: $i,SV497: $i,SV237: $i] :
( ( ( ( c_List_Oappend @ SV237 @ SV497 @ SV708 )
!= ( c_List_Oappend @ SV237 @ SV863 @ SV708 ) )
| ( SV497 = SV863 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1796]) ).
thf(2042,plain,
! [SV864: $i,SV709: $i,SV498: $i,SV238: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV238 ) @ SV498 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV709 ) @ SV864 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV238 = SV709 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(2043,plain,
! [SV865: $i,SV710: $i,SV499: $i,SV239: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV239 ) @ SV499 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV710 ) @ SV865 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV499 = SV865 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1798]) ).
thf(2044,plain,
! [SV866: $i,SV711: $i,SV500: $i,SV240: $i] :
( ( ! [SY2364: $i] :
( ( ( c_List_Olist_OCons @ SV240 @ SV500 @ SV711 )
!= ( c_List_Olist_OCons @ SV866 @ SY2364 @ SV711 ) )
| ( SV240 = SV866 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1799]) ).
thf(2045,plain,
! [SV867: $i,SV712: $i,SV501: $i,SV241: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV241 ) @ SV501 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV712 ) @ SV867 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV241 = SV712 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1800]) ).
thf(2046,plain,
! [SV868: $i,SV713: $i,SV502: $i,SV242: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV242 ) @ SV502 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV713 @ SV868 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV242
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV713 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV242 @ SV502 @ SV713 @ SV868 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV868
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1801]) ).
thf(2047,plain,
! [SV869: $i,SV714: $i,SV503: $i,SV243: $i] :
( ( ! [SY2365: $i,SY2366: $i,SY2367: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV243 ) @ SV503 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV714 ) @ SV869 ) @ SY2365 ) ) )
| ~ ( c_Type_Otyping @ SY2366 @ SV869 @ SV243 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV869 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY2366 @ SY2365 @ SV243 @ tc_Type_Otype ) @ SV714 @ SY2367 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV714 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1802]) ).
thf(2048,plain,
! [SV870: $i,SV715: $i,SV504: $i,SV244: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV244 )
| ~ ( class_Int_Onumber__ring @ SV244 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV244 ) @ SV504 ) @ SV715 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV244 ) @ SV504 ) @ SV870 ) )
| ( SV715 = SV870 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1803]) ).
thf(2049,plain,
! [SV871: $i,SV716: $i,SV505: $i,SV245: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV245 ) @ SV505 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV716 ) @ SV871 ) )
| ( SV505 = SV871 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(2050,plain,
! [SV717: $i,SV506: $i,SV246: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV246 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV506 @ SV717 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_Lambda_OdB_OAbs @ SV246 )
= SV506 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1805]) ).
thf(2051,plain,
! [SV718: $i,SV507: $i,SV247: $i] :
( ( ( c_Lambda_OdB_OVar @ SV247 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV507 ) @ SV718 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1806]) ).
thf(2052,plain,
! [SV872: $i,SV719: $i,SV508: $i,SV248: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV248 ) @ SV508 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV719 ) @ SV872 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1807]) ).
thf(2053,plain,
! [SV873: $i,SV720: $i,SV509: $i,SV249: $i] :
( ( ! [SY2368: $i] :
( ( ( c_List_Oappend @ SV249 @ ( c_List_Olist_OCons @ SV509 @ ( c_List_Olist_ONil @ SV720 ) @ SV720 ) @ SV720 )
!= ( c_List_Oappend @ SV873 @ ( c_List_Olist_OCons @ SY2368 @ ( c_List_Olist_ONil @ SV720 ) @ SV720 ) @ SV720 ) )
| ( SV249 = SV873 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1808]) ).
thf(2054,plain,
! [SV721: $i,SV510: $i,SV250: $i] :
( ( ( ( c_List_Oappend @ SV250 @ SV510 @ SV721 )
!= ( c_List_Olist_ONil @ SV721 ) )
= $true )
| ( ( SV250
= ( c_List_Olist_ONil @ SV721 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1809]) ).
thf(2055,plain,
! [SV874: $i,SV722: $i,SV511: $i,SV251: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV251 ) ) @ SV511 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV722 ) @ SV874 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(2056,plain,
! [SV723: $i,SV512: $i,SV252: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV252 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV512 @ SV723 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV723
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1811]) ).
thf(2057,plain,
! [SV724: $i,SV513: $i,SV253: $i] :
( ( ( ( c_List_Oappend @ SV253 @ SV513 @ SV724 )
!= SV253 )
= $true )
| ( ( SV513
= ( c_List_Olist_ONil @ SV724 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1812]) ).
thf(2058,plain,
! [SV725: $i,SV514: $i,SV254: $i] :
( ( ( c_List_Olist_OCons @ SV254 @ SV514 @ SV725 )
= SV514 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1813]) ).
thf(2059,plain,
! [SV726: $i,SV515: $i,SV255: $i] :
( ( SV255
= ( c_List_Olist_OCons @ SV515 @ SV255 @ SV726 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1814]) ).
thf(2060,plain,
! [SV727: $i,SV516: $i,SV256: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV256 @ SV516 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV727 @ SV516 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV256 = SV727 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1815]) ).
thf(2061,plain,
! [SV875: $i,SV728: $i,SV517: $i,SV257: $i] :
( ( ( ( c_List_Omap @ SV257 @ SV517 @ SV728 @ SV875 )
!= ( c_List_Olist_ONil @ SV875 ) )
| ( SV517
= ( c_List_Olist_ONil @ SV728 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1816]) ).
thf(2062,plain,
! [SV518: $i,SV258: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV258 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SV518 ) @ SV518 )
!= ( c_HOL_Ozero__class_Ozero @ SV258 ) )
| ( SV518
= ( c_HOL_Ozero__class_Ozero @ SV258 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1817]) ).
thf(2063,plain,
! [SV729: $i,SV519: $i,SV259: $i] :
( ( ( c_List_Olist_OCons @ SV259 @ SV519 @ SV729 )
= ( c_List_Olist_ONil @ SV729 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1818]) ).
thf(2064,plain,
! [SV730: $i,SV520: $i,SV260: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV260 ) @ SV520 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV730 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV260 ) @ SV520 )
= SV730 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1819]) ).
thf(2065,plain,
! [SV731: $i,SV521: $i,SV261: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV261 @ SV521 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV731 ) )
= $true )
| ( ( SV261
= ( c_Lambda_OdB_OAbs @ SV731 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1820]) ).
thf(2066,plain,
! [SV732: $i,SV522: $i,SV262: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV262 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV522 @ SV732 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_Lambda_OdB_OVar @ SV262 )
= SV522 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1821]) ).
thf(2067,plain,
! [SV876: $i,SV733: $i,SV523: $i,SV263: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV263 ) @ SV523 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV733 ) @ SV876 ) )
| ( SV263 = SV733 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1822]) ).
thf(2068,plain,
! [SV734: $i,SV524: $i,SV264: $i] :
( ( ( ( c_List_Oappend @ SV264 @ SV524 @ SV734 )
!= SV524 )
= $true )
| ( ( SV264
= ( c_List_Olist_ONil @ SV734 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1823]) ).
thf(2069,plain,
! [SV735: $i,SV525: $i,SV265: $i] :
( ( ( c_List_Olist_ONil @ SV265 )
= ( c_List_Olist_OCons @ SV525 @ SV735 @ SV265 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1824]) ).
thf(2070,plain,
! [SV877: $i,SV736: $i,SV526: $i,SV266: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV266 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV266 ) @ SV526 ) @ SV736 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV266 ) @ SV526 ) @ SV877 ) )
| ( SV736 = SV877 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1825]) ).
thf(2071,plain,
! [SV737: $i,SV527: $i,SV267: $i] :
( ( ( SV267
!= ( c_List_Oappend @ SV267 @ SV527 @ SV737 ) )
= $true )
| ( ( SV527
= ( c_List_Olist_ONil @ SV737 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1826]) ).
thf(2072,plain,
! [SV878: $i,SV738: $i,SV528: $i,SV268: $i] :
( ( ! [SY2369: $i,SY2370: $i,SY2371: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV268 ) @ SV528 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV738 ) @ SV878 ) @ SY2369 ) ) )
| ~ ( c_Type_Otyping @ SY2370 @ SV878 @ SV528 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV878 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY2370 @ SY2369 @ SV528 @ tc_Type_Otype ) @ SV738 @ SY2371 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV738 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1827]) ).
thf(2073,plain,
! [SV879: $i,SV739: $i,SV529: $i,SV269: $i] :
( ( ( ( c_List_Oappend @ SV269 @ SV529 @ SV739 )
!= ( c_List_Oappend @ SV879 @ SV529 @ SV739 ) )
| ( SV269 = SV879 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1828]) ).
thf(2074,plain,
! [SV530: $i,SV270: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV270 )
= ( c_Lambda_OdB_OVar @ SV530 ) )
= $false )
| ( ( SV270 = SV530 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1829]) ).
thf(2075,plain,
! [SV880: $i,SV740: $i,SV531: $i,SV271: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV271 ) @ SV531 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV740 ) @ SV880 ) )
| ( SV531 = SV880 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1830]) ).
thf(2076,plain,
! [SV741: $i,SV532: $i,SV272: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV272 ) @ SV532 )
= ( c_Lambda_OdB_OAbs @ SV741 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1831]) ).
thf(2077,plain,
! [SV881: $i,SV742: $i,SV534: $i,SV274: $i] :
( ( ( ( c_List_Olist_ONil @ SV274 )
!= ( c_List_Omap @ SV534 @ SV742 @ SV881 @ SV274 ) )
| ( SV742
= ( c_List_Olist_ONil @ SV881 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1833]) ).
thf(2078,plain,
! [SV882: $i,SV743: $i,SV535: $i,SV275: $i] :
( ( ! [SY2372: $i] :
( ( ( c_List_Oappend @ SV275 @ ( c_List_Olist_OCons @ SV535 @ ( c_List_Olist_ONil @ SV743 ) @ SV743 ) @ SV743 )
!= ( c_List_Oappend @ SV882 @ ( c_List_Olist_OCons @ SY2372 @ ( c_List_Olist_ONil @ SV743 ) @ SV743 ) @ SV743 ) )
| ( SV535 = SY2372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1834]) ).
thf(2079,plain,
! [SV744: $i,SV536: $i,SV276: $i] :
( ( ( SV276
!= ( c_List_Oappend @ SV536 @ SV276 @ SV744 ) )
= $true )
| ( ( SV536
= ( c_List_Olist_ONil @ SV744 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1835]) ).
thf(2080,plain,
! [SV745: $i,SV537: $i,SV277: $i] :
( ( ( ( c_List_Olist_ONil @ SV277 )
!= ( c_List_Oappend @ SV537 @ SV745 @ SV277 ) )
= $true )
| ( ( SV745
= ( c_List_Olist_ONil @ SV277 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1836]) ).
thf(2081,plain,
! [SV746: $i,SV538: $i,SV278: $i] :
( ( ( ( c_List_Olist_ONil @ SV278 )
!= ( c_List_Oappend @ SV538 @ SV746 @ SV278 ) )
= $true )
| ( ( SV538
= ( c_List_Olist_ONil @ SV278 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1837]) ).
thf(2082,plain,
! [SV883: $i,SV747: $i,SV540: $i,SV280: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV280 ) @ SV540 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV747 ) @ SV883 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV540 = SV883 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1839]) ).
thf(2083,plain,
! [SV748: $i,SV541: $i,SV281: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV281 ) @ SV541 )
= ( c_Lambda_OdB_OVar @ SV748 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1840]) ).
thf(2084,plain,
! [SV749: $i,SV542: $i,SV282: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV282 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV542 ) @ SV749 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1841]) ).
thf(2085,plain,
! [SV884: $i,SV750: $i,SV543: $i,SV283: $i] :
( ( ! [SY2373: $i] :
( ( ( c_List_Olist_OCons @ SV283 @ SV543 @ SV750 )
!= ( c_List_Olist_OCons @ SV884 @ SY2373 @ SV750 ) )
| ( SV543 = SY2373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1842]) ).
thf(2086,plain,
! [SV751: $i,SV544: $i,SV284: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV284 @ SV544 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV751 ) )
= $true )
| ( ( SV544
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1843]) ).
thf(2087,plain,
! [SV752: $i,SV545: $i,SV285: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV285 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV545 @ SV752 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV752
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1844]) ).
thf(2088,plain,
! [SV753: $i,SV546: $i,SV286: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV286 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV286 )
| ( SV546
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV286 ) @ SV546 ) @ SV753 ) )
| ( SV753
= ( c_HOL_Ozero__class_Ozero @ SV286 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1845]) ).
thf(2089,plain,
! [SV547: $i,SV287: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV287 )
= ( c_Lambda_OdB_OAbs @ SV547 ) )
= $false )
| ( ( SV287 = SV547 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1846]) ).
thf(2090,plain,
! [SV885: $i,SV754: $i,SV548: $i,SV288: $i] :
( ( ! [SY2374: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV288 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV548 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV754 ) @ SV885 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV754 ) @ SY2374 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV548 ) @ SV885 )
= SY2374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1847]) ).
thf(2091,plain,
! [SV289: $i,SV1: $i] :
( ( ( hBOOL @ ( hAPP @ SV1 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV1 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4 @ SV1 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV1 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV1 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1 @ SV289 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1848]) ).
thf(2092,plain,
! [SV290: $i,SV2: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV2 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV2 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV2 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV2 @ SV290 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV2 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV2 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__4 @ SV2 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1849]) ).
thf(2093,plain,
! [SV755: $i,SV549: $i,SV291: $i,SV3: $i] :
( ( ( c_Type_Otyping @ SV3 @ SV291 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV549 @ SV3 @ SV291 @ SV755 ) @ SV549 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV291 @ SV755 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV549 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1850]) ).
thf(2094,plain,
! [SV756: $i,SV550: $i,SV292: $i,SV4: $i] :
( ( ( c_Type_Otyping @ SV4 @ SV292 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV550 @ SV4 @ SV292 @ SV756 ) @ SV550 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV4 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV292 @ SV756 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1851]) ).
thf(2095,plain,
! [SV757: $i,SV551: $i,SV293: $i,SV5: $i] :
( ( ( c_Type_Otypings @ SV5 @ SV293 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV551 @ SV5 @ SV757 @ SV293 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV5 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV757 @ SV293 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV551 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1852]) ).
thf(2096,plain,
! [SV758: $i,SV552: $i,SV294: $i,SV6: $i] :
( ( ( c_Type_Otypings @ SV6 @ SV294 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV552 @ SV6 @ SV758 @ SV294 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV6 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV758 @ SV294 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV552 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1853]) ).
thf(2097,plain,
! [SV886: $i,SV759: $i,SV553: $i,SV295: $i,SV7: $i] :
( ( ! [SY2375: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV7 @ SV295 ) @ SV553 ) )
| ( SV295 = SV553 )
| ~ ( c_ListOrder_Ostep1 @ SV7 @ ( c_List_Oappend @ SV759 @ ( c_List_Olist_OCons @ SV295 @ ( c_List_Olist_ONil @ SV886 ) @ SV886 ) @ SV886 ) @ ( c_List_Oappend @ SY2375 @ ( c_List_Olist_OCons @ SV553 @ ( c_List_Olist_ONil @ SV886 ) @ SV886 ) @ SV886 ) @ SV886 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1854]) ).
thf(2098,plain,
! [SV887: $i,SV760: $i,SV554: $i,SV296: $i,SV8: $i] :
( ( ! [SY2376: $i] :
( ( c_List_Ofoldr @ SV8 @ ( c_List_Oappend @ SV296 @ SV554 @ SV760 ) @ SV887 @ SV760 @ SY2376 )
= ( c_List_Ofoldr @ SV8 @ SV296 @ ( c_List_Ofoldr @ SV8 @ SV554 @ SV887 @ SV760 @ SY2376 ) @ SV760 @ SY2376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1855]) ).
thf(2099,plain,
! [SV555: $i,SV297: $i,SV9: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV9 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV9 ) @ SV297 ) @ SV555 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV9 ) @ SV555 ) @ SV297 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1856]) ).
thf(2100,plain,
! [SV556: $i,SV298: $i,SV10: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV10 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV10 ) @ SV298 ) @ SV556 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV10 ) @ SV556 ) @ SV298 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1857]) ).
thf(2101,plain,
! [SV557: $i,SV299: $i,SV11: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV11 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV11 ) @ SV299 ) @ SV557 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV11 ) @ SV557 ) @ SV299 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1858]) ).
thf(2102,plain,
! [SV761: $i,SV558: $i,SV300: $i,SV12: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV12 ) @ SV300 ) @ SV558 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV12 ) @ SV761 ) @ SV558 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV300 ) @ SV761 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1859]) ).
thf(2103,plain,
! [SV18: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV18 ) )
= $false )
| ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV18 ) @ tc_Lambda_OdB )
= $true )
| ( ( SV18
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV18 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1860]) ).
thf(2104,plain,
! [SV888: $i,SV762: $i,SV559: $i,SV306: $i,SV19: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV19 @ SV306 ) @ SV559 ) @ SV762 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV19 @ SV306 ) @ SV888 ) @ SV762 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV19 @ SV306 ) @ SV559 ) @ SV888 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1861]) ).
thf(2105,plain,
! [SV889: $i,SV763: $i,SV562: $i,SV310: $i,SV23: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV23 @ SV310 ) @ SV562 ) )
| ( c_ListOrder_Ostep1 @ SV23 @ ( c_List_Olist_OCons @ SV310 @ SV763 @ SV889 ) @ ( c_List_Olist_OCons @ SV562 @ SV763 @ SV889 ) @ SV889 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(2106,plain,
! [SV890: $i,SV764: $i,SV563: $i,SV311: $i,SV24: $i] :
( ( ! [SY2377: $i] :
( ( SV24 = SV311 )
| ( SV563 = SV764 )
| ~ ( c_ListOrder_Ostep1 @ SV890 @ ( c_List_Olist_OCons @ SV311 @ SV764 @ SY2377 ) @ ( c_List_Olist_OCons @ SV24 @ SV563 @ SY2377 ) @ SY2377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(2107,plain,
! [SV891: $i,SV765: $i,SV564: $i,SV312: $i,SV25: $i] :
( ( ( c_Lambda_OdB_OdB__case @ SV25 @ SV312 @ SV564 @ ( c_Lambda_OdB_OAbs @ SV765 ) @ SV891 )
= ( hAPP @ SV564 @ SV765 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(2108,plain,
! [SV26: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV26 ) )
= $false )
| ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV26 ) @ tc_Lambda_OdB )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV26 ) ) )
= $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 @ SV26 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV26 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV26 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1865]) ).
thf(2109,plain,
! [SV766: $i,SV565: $i,SV313: $i,SV27: $i] :
( ( ( c_List_Olistsp @ SV27 @ SV313 @ SV565 )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV27 @ ( c_List_Oappend @ SV766 @ SV313 @ SV565 ) @ SV565 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1866]) ).
thf(2110,plain,
! [SV767: $i,SV566: $i,SV314: $i,SV28: $i] :
( ( ( c_List_Olistsp @ SV28 @ SV314 @ SV566 )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV28 @ ( c_List_Oappend @ SV314 @ SV767 @ SV566 ) @ SV566 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1867]) ).
thf(2111,plain,
! [SV892: $i,SV768: $i,SV567: $i,SV316: $i,SV30: $i] :
( ( ( c_ListOrder_Ostep1 @ SV30 @ ( c_List_Oappend @ SV316 @ SV567 @ SV768 ) @ ( c_List_Oappend @ SV316 @ SV892 @ SV768 ) @ SV768 )
| ~ ( c_ListOrder_Ostep1 @ SV30 @ SV567 @ SV892 @ SV768 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1869]) ).
thf(2112,plain,
! [SV893: $i,SV769: $i,SV568: $i,SV317: $i,SV31: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV31 @ SV317 @ SV568 @ SV769 )
| ( c_ListOrder_Ostep1 @ SV31 @ ( c_List_Oappend @ SV317 @ SV893 @ SV769 ) @ ( c_List_Oappend @ SV568 @ SV893 @ SV769 ) @ SV769 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1870]) ).
thf(2113,plain,
! [SV894: $i,SV770: $i,SV570: $i,SV319: $i,SV34: $i] :
( ( ( c_Type_Otyping @ SV34 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV319 @ SV570 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV770 )
| ~ ( c_Type_Otypings @ SV34 @ SV570 @ SV894 )
| ~ ( c_Type_Otyping @ SV34 @ SV319 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV894 @ SV770 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1871]) ).
thf(2114,plain,
! [SV771: $i,SV571: $i,SV320: $i,SV35: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV35 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV320 @ SV571 @ SV35 )
| ~ ( c_HOL_Oord__class_Oless @ SV771 @ SV571 @ SV35 )
| ~ ( c_HOL_Oord__class_Oless @ SV320 @ SV771 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1872]) ).
thf(2115,plain,
! [SV772: $i,SV572: $i,SV321: $i,SV36: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV36 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV321 @ SV572 @ SV36 )
| ~ ( c_HOL_Oord__class_Oless @ SV321 @ SV772 @ SV36 )
| ~ ( c_HOL_Oord__class_Oless @ SV772 @ SV572 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1873]) ).
thf(2116,plain,
! [SV773: $i,SV573: $i,SV322: $i,SV37: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV37 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV322 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV573 ) @ SV773 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV322 ) @ SV573 ) ) @ SV773 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1874]) ).
thf(2117,plain,
! [SV774: $i,SV574: $i,SV323: $i,SV38: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV38 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV323 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV574 ) @ SV774 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV574 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV323 ) @ SV774 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1875]) ).
thf(2118,plain,
! [SV775: $i,SV575: $i,SV324: $i,SV39: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV39 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ SV324 ) @ SV575 ) ) @ SV775 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ SV324 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ SV575 ) @ SV775 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1876]) ).
thf(2119,plain,
! [SV776: $i,SV576: $i,SV325: $i,SV40: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV40 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ SV325 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ SV576 ) @ SV776 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ SV576 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ SV325 ) @ SV776 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1877]) ).
thf(2120,plain,
! [SV777: $i,SV577: $i,SV326: $i,SV41: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV41 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV326 ) @ SV577 ) ) @ SV777 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV326 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV577 ) @ SV777 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1878]) ).
thf(2121,plain,
! [SV778: $i,SV578: $i,SV327: $i,SV42: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV42 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV327 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV578 ) @ SV778 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV327 ) @ SV578 ) ) @ SV778 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1879]) ).
thf(2122,plain,
! [SV779: $i,SV579: $i,SV328: $i,SV43: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV43 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ SV328 ) @ SV579 ) ) @ SV779 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ SV328 ) @ SV779 ) ) @ SV579 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1880]) ).
thf(2123,plain,
! [SV780: $i,SV580: $i,SV329: $i,SV44: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV44 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SV329 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SV580 ) @ SV780 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SV580 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SV329 ) @ SV780 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1881]) ).
thf(2124,plain,
! [SV781: $i,SV581: $i,SV330: $i,SV45: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV45 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV45 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV45 ) @ SV330 ) @ SV581 ) ) @ SV781 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV45 ) @ SV330 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV45 ) @ SV581 ) @ SV781 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1882]) ).
thf(2125,plain,
! [SV895: $i,SV782: $i,SV582: $i,SV331: $i,SV48: $i] :
( ( ! [SY2378: $i] :
( ( hAPP @ ( c_COMBC @ SV48 @ SV331 @ SV582 @ SV782 @ SV895 ) @ SY2378 )
= ( hAPP @ ( hAPP @ SV48 @ SY2378 ) @ SV331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1883]) ).
thf(2126,plain,
! [SV896: $i,SV784: $i,SV585: $i,SV334: $i,SV51: $i] :
( ( ! [SY2379: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV51 @ SV334 ) @ SV585 ) )
| ( c_ListOrder_Ostep1 @ SV51 @ SV784 @ SV896 @ SY2379 )
| ~ ( c_ListOrder_Ostep1 @ SV51 @ ( c_List_Oappend @ SV784 @ ( c_List_Olist_OCons @ SV334 @ ( c_List_Olist_ONil @ SY2379 ) @ SY2379 ) @ SY2379 ) @ ( c_List_Oappend @ SV896 @ ( c_List_Olist_OCons @ SV585 @ ( c_List_Olist_ONil @ SY2379 ) @ SY2379 ) @ SY2379 ) @ SY2379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(2127,plain,
! [SV52: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV52 ) )
= $false )
| ( ( SV52
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV52 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV52 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV52
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV52 ) ) )
= $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 @ SV52 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV52 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV52 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1886]) ).
thf(2128,plain,
! [SV897: $i,SV785: $i,SV586: $i,SV335: $i,SV53: $i] :
( ( ! [SY2380: $i] :
( ( c_Type_Otypings @ SV53 @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SV335 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV586 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV785 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV897 )
| ~ ( c_Type_Otypings @ ( c_Type_Oshift @ SV53 @ SV586 @ SY2380 @ tc_Type_Otype ) @ SV785 @ SV897 )
| ~ ( c_Type_Otyping @ SV53 @ SV335 @ SY2380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1887]) ).
thf(2129,plain,
! [SV587: $i,SV336: $i,SV54: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV54 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV336 ) @ SV587 ) @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV54 )
| ~ ( c_HOL_Oord__class_Oless @ SV587 @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV54 )
| ~ ( c_HOL_Oord__class_Oless @ SV336 @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1888]) ).
thf(2130,plain,
! [SV57: $i,SV590: $i,SV339: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV339 ) @ SV590 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV57 ) @ SV339 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV57 ) @ SV590 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1891]) ).
thf(2131,plain,
! [SV340: $i,SV591: $i,SV58: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV58 ) @ SV591 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV58 ) @ SV340 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV591 ) @ SV340 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1892]) ).
thf(2132,plain,
! [SV592: $i,SV341: $i,SV59: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV59 )
= $false )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV341 @ SV592 @ SV59 @ SV59 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV341 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV592 @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 @ SV59 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1893]) ).
thf(2133,plain,
! [SV898: $i,SV788: $i,SV593: $i,SV342: $i,SV60: $i] :
( ( ( c_List_Omap @ SV60 @ ( c_List_Olist_OCons @ SV342 @ SV593 @ SV788 ) @ SV788 @ SV898 )
= ( c_List_Olist_OCons @ ( hAPP @ SV60 @ SV342 ) @ ( c_List_Omap @ SV60 @ SV593 @ SV788 @ SV898 ) @ SV898 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1894]) ).
thf(2134,plain,
! [SV899: $i,SV789: $i,SV594: $i,SV343: $i,SV61: $i] :
( ( ( c_List_Olist_OCons @ ( hAPP @ SV61 @ SV343 ) @ ( c_List_Omap @ SV61 @ SV594 @ SV789 @ SV899 ) @ SV899 )
= ( c_List_Omap @ SV61 @ ( c_List_Olist_OCons @ SV343 @ SV594 @ SV789 ) @ SV789 @ SV899 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1895]) ).
thf(2135,plain,
! [SV900: $i,SV790: $i,SV595: $i,SV344: $i,SV62: $i] :
( ( ( c_List_Omap @ SV62 @ ( c_List_Olist_OCons @ SV344 @ SV595 @ SV790 ) @ SV790 @ SV900 )
= ( c_List_Olist_OCons @ ( hAPP @ SV62 @ SV344 ) @ ( c_List_Omap @ SV62 @ SV595 @ SV790 @ SV900 ) @ SV900 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(2136,plain,
! [SV63: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV63 ) )
= $false )
| ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV63 ) @ tc_Lambda_OdB )
= $true )
| ( ( SV63
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV63 ) ) )
= $true )
| ( ( SV63
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV63 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV63 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV63 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1897]) ).
thf(2137,plain,
! [SV901: $i,SV793: $i,SV598: $i,SV347: $i,SV66: $i] :
( ( ! [SY2381: $i] :
( ( SV66 = SV347 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV598 @ SV347 ) @ SV66 ) )
| ~ ( c_ListOrder_Ostep1 @ SV598 @ ( c_List_Olist_OCons @ SV347 @ SV793 @ SV901 ) @ ( c_List_Olist_OCons @ SV66 @ SY2381 @ SV901 ) @ SV901 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1900]) ).
thf(2138,plain,
! [SV902: $i,SV794: $i,SV599: $i,SV348: $i,SV67: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV67 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ SV348 ) @ SV599 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ SV794 ) @ SV902 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ SV348 ) @ SV794 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ SV599 ) @ SV902 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1901]) ).
thf(2139,plain,
! [SV795: $i,SV600: $i,SV349: $i,SV68: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV68 ) @ SV349 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV600 ) @ SV795 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV349 ) @ SV795 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV68 ) @ SV600 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1902]) ).
thf(2140,plain,
! [SV69: $i,SV601: $i,SV350: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV350 @ SV601 @ tc_nat )
= $false )
| ( ( ( c_Lambda_Oliftn @ SV69 @ ( c_Lambda_OdB_OVar @ SV350 ) @ SV601 )
= ( c_Lambda_OdB_OVar @ SV350 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1903]) ).
thf(2141,plain,
! [SV796: $i,SV602: $i,SV351: $i,SV70: $i] :
( ( ( c_Type_Otyping @ SV70 @ SV351 @ SV602 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV70 @ SV796 @ SV602 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV796 ) @ SV351 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1904]) ).
thf(2142,plain,
! [SV903: $i,SV797: $i,SV603: $i,SV352: $i,SV71: $i] :
( ( ( c_Type_Otypings @ ( c_Type_Oshift @ SV71 @ SV352 @ SV603 @ tc_Type_Otype ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ SV352 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV797 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV903 )
| ~ ( c_Type_Otypings @ SV71 @ SV797 @ SV903 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1905]) ).
thf(2143,plain,
! [SV354: $i,SV604: $i,SV73: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV73 ) @ SV604 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV73 ) @ SV354 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV604 ) @ SV354 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1907]) ).
thf(2144,plain,
! [SV74: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV74 ) )
= $false )
| ( ( SV74
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV74 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV74 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV74 ) ) )
= $true )
| ( ( SV74
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV74 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV74 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV74 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1908]) ).
thf(2145,plain,
! [SV904: $i,SV798: $i,SV606: $i,SV357: $i,SV77: $i] :
( ( ! [SY2382: $i] :
( ~ ( c_Type_Otyping @ SV77 @ SV357 @ SV606 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV77 @ SV798 @ SV606 @ tc_Type_Otype ) @ SV904 @ SY2382 )
| ( c_Type_Otyping @ SV77 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV904 ) @ SV357 ) @ SV798 ) @ SY2382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1909]) ).
thf(2146,plain,
! [SV905: $i,SV799: $i,SV608: $i,SV359: $i,SV79: $i] :
( ( ! [SY2383: $i] :
( ( SV79 = SV359 )
| ( c_ListOrder_Ostep1 @ SV608 @ SV79 @ SV359 @ SV799 )
| ~ ( c_ListOrder_Ostep1 @ SV608 @ ( c_List_Oappend @ SV79 @ ( c_List_Olist_OCons @ SV905 @ ( c_List_Olist_ONil @ SV799 ) @ SV799 ) @ SV799 ) @ ( c_List_Oappend @ SV359 @ ( c_List_Olist_OCons @ SY2383 @ ( c_List_Olist_ONil @ SV799 ) @ SV799 ) @ SV799 ) @ SV799 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1910]) ).
thf(2147,plain,
! [SV363: $i,SV84: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV84 ) )
= $true )
| ( ( SV363
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV363 ) @ ( c_HOL_Ozero__class_Ozero @ SV84 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1913]) ).
thf(2148,plain,
! [SV800: $i,SV609: $i,SV370: $i,SV91: $i] :
( ( ( ( hAPP @ ( hAPP @ SV91 @ SV370 ) @ SV609 )
= SV370 )
= $true )
| ( ( ~ ( c_OrderedGroup_Omonoid__add @ SV609 @ SV91 @ SV800 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1920]) ).
thf(2149,plain,
! [SV801: $i,SV610: $i,SV371: $i,SV92: $i] :
( ( ( ( hAPP @ ( hAPP @ SV92 @ SV371 ) @ SV610 )
= SV610 )
= $true )
| ( ( ~ ( c_OrderedGroup_Omonoid__add @ SV371 @ SV92 @ SV801 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1921]) ).
thf(2150,plain,
! [SV372: $i,SV93: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV372 @ SV93 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV372 ) @ SV372 ) @ SV93 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1922]) ).
thf(2151,plain,
! [SV373: $i,SV94: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV373 ) @ SV373 ) @ SV94 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV373 @ SV94 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV94 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1923]) ).
thf(2152,plain,
! [SV802: $i,SV611: $i,SV374: $i,SV95: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV95 ) @ SV374 ) @ SV611 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV802 ) @ SV374 ) @ SV611 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV95 ) @ SV802 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1924]) ).
thf(2153,plain,
! [SV803: $i,SV612: $i,SV375: $i,SV96: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV96 ) @ SV375 ) @ SV612 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV96 ) @ SV803 ) @ SV612 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV375 ) @ SV803 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1925]) ).
thf(2154,plain,
! [SV613: $i,SV376: $i,SV97: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__add @ SV97 )
= $false )
| ( ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SV376 @ SV613 @ SV97 @ SV97 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SV613 @ SV376 @ SV97 @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1926]) ).
thf(2155,plain,
! [SV804: $i,SV614: $i,SV377: $i,SV98: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV98 @ SV377 ) @ SV614 ) @ SV804 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV98 @ SV614 ) @ SV804 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1927]) ).
thf(2156,plain,
! [SV380: $i,SV101: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ SV380 ) @ SV380 ) @ ( c_HOL_Ozero__class_Ozero @ SV101 ) @ SV101 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV380 @ ( c_HOL_Ozero__class_Ozero @ SV101 ) @ SV101 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1930]) ).
thf(2157,plain,
! [SV102: $i,SV381: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV381 @ ( c_HOL_Ozero__class_Ozero @ SV102 ) @ SV102 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SV381 ) @ SV381 ) @ ( c_HOL_Ozero__class_Ozero @ SV102 ) @ SV102 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV102 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1931]) ).
thf(2158,plain,
! [SV103: $i,SV382: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV382 @ ( c_HOL_Ozero__class_Ozero @ SV103 ) @ SV103 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV103 ) @ SV382 ) @ SV382 ) @ ( c_HOL_Ozero__class_Ozero @ SV103 ) @ SV103 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1932]) ).
thf(2159,plain,
! [SV383: $i,SV104: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV104 ) @ SV383 ) @ SV383 ) @ ( c_HOL_Ozero__class_Ozero @ SV104 ) @ SV104 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV383 @ ( c_HOL_Ozero__class_Ozero @ SV104 ) @ SV104 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV104 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1933]) ).
thf(2160,plain,
! [SV617: $i,SV384: $i,SV105: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV105 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV384 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ ( c_HOL_Ozero__class_Ozero @ SV105 ) @ SV617 @ SV105 @ SV105 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV384 @ SV617 @ SV105 @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1934]) ).
thf(2161,plain,
! [SV805: $i,SV618: $i,SV385: $i,SV106: $i] :
( ( ( c_Type_Otyping @ SV106 @ ( c_Lambda_OdB_OAbs @ SV385 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV618 ) @ SV805 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV106 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV618 @ tc_Type_Otype ) @ SV385 @ SV805 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1935]) ).
thf(2162,plain,
! [SV387: $i,SV620: $i,SV108: $i] :
( ( ( SV108 = SV620 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV620 @ SV108 @ tc_nat )
= $true )
| ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV108 ) @ SV387 @ SV620 )
= ( c_Lambda_OdB_OVar @ SV108 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1937]) ).
thf(2163,plain,
! [SV109: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV109 ) )
= $false )
| ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV109 ) @ tc_Lambda_OdB )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV109 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV109 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1938]) ).
thf(2164,plain,
! [SV112: $i,SV388: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV388 @ SV388 @ SV112 )
= $false )
| ( ( class_Orderings_Oorder @ SV112 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1939]) ).
thf(2165,plain,
! [SV113: $i,SV389: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV389 @ SV389 @ SV113 )
= $false )
| ( ( class_Orderings_Olinorder @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1940]) ).
thf(2166,plain,
! [SV114: $i,SV390: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV390 @ SV390 @ SV114 )
= $false )
| ( ( class_Orderings_Opreorder @ SV114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1941]) ).
thf(2167,plain,
! [SV392: $i,SV621: $i,SV116: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV116 ) @ SV621 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV116 ) @ SV392 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV621 ) @ SV392 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1942]) ).
thf(2168,plain,
! [SV622: $i,SV393: $i,SV117: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV117 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV393 ) @ SV622 ) @ SV117 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV622 @ SV117 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV393 @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1943]) ).
thf(2169,plain,
! [SV906: $i,SV807: $i,SV623: $i,SV394: $i,SV118: $i] :
( ( ! [SY2384: $i] :
( ( c_ListOrder_Ostep1 @ SV118 @ SV394 @ SV623 @ SV807 )
| ( SV623 = SV394 )
| ~ ( c_ListOrder_Ostep1 @ SV118 @ ( c_List_Olist_OCons @ SV906 @ SV394 @ SV807 ) @ ( c_List_Olist_OCons @ SY2384 @ SV623 @ SV807 ) @ SV807 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(2170,plain,
! [SV907: $i,SV808: $i,SV624: $i,SV395: $i,SV119: $i] :
( ( ( ( hAPP @ ( hAPP @ SV119 @ ( hAPP @ ( hAPP @ SV119 @ SV395 ) @ SV624 ) ) @ SV808 )
= ( hAPP @ ( hAPP @ SV119 @ SV395 ) @ ( hAPP @ ( hAPP @ SV119 @ SV624 ) @ SV808 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV119 @ SV907 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2171,plain,
! [SV908: $i,SV809: $i,SV625: $i,SV396: $i,SV120: $i] :
( ( ( c_List_Omap @ SV120 @ ( c_List_Oappend @ SV396 @ SV625 @ SV809 ) @ SV809 @ SV908 )
= ( c_List_Oappend @ ( c_List_Omap @ SV120 @ SV396 @ SV809 @ SV908 ) @ ( c_List_Omap @ SV120 @ SV625 @ SV809 @ SV908 ) @ SV908 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(2172,plain,
! [SV121: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV121 ) )
= $false )
| ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV121 ) @ tc_Lambda_OdB )
= $true )
| ( ( SV121
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV121 ) ) )
= $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 @ SV121 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV121 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV121 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1947]) ).
thf(2173,plain,
! [SV626: $i,SV397: $i,SV122: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV122 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV397 @ SV626 @ SV122 )
| ( c_HOL_Oord__class_Oless @ SV626 @ SV397 @ SV122 )
| ( SV626 = SV397 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1948]) ).
thf(2174,plain,
! [SV627: $i,SV398: $i,SV123: $i] :
( ( ( class_Orderings_Olinorder @ SV123 )
= $false )
| ( ( ( SV398 = SV627 )
| ( c_HOL_Oord__class_Oless @ SV627 @ SV398 @ SV123 )
| ( c_HOL_Oord__class_Oless @ SV398 @ SV627 @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1949]) ).
thf(2175,plain,
! [SV125: $i,SV628: $i,SV400: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV400 @ SV628 @ tc_nat )
= $true )
| ( ( ( SV628 = SV400 )
| ( c_HOL_Oord__class_Oless @ SV628 @ SV400 @ tc_nat ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV125 @ SV400 ) @ SV628 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1951]) ).
thf(2176,plain,
! [SV629: $i,SV402: $i,SV127: $i] :
( ( ( class_Orderings_Olinorder @ SV127 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV402 @ SV629 @ SV127 )
| ( c_HOL_Oord__class_Oless @ SV629 @ SV402 @ SV127 )
| ( SV629 = SV402 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1953]) ).
thf(2177,plain,
! [SV630: $i,SV403: $i,SV128: $i] :
( ( ( class_Orderings_Olinorder @ SV128 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV403 @ SV630 @ SV128 )
| ( SV630 = SV403 )
| ( c_HOL_Oord__class_Oless @ SV630 @ SV403 @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1954]) ).
thf(2178,plain,
! [SV631: $i,SV404: $i,SV129: $i] :
( ( ( class_Orderings_Olinorder @ SV129 )
= $false )
| ( ( ( SV404 = SV631 )
| ( c_HOL_Oord__class_Oless @ SV404 @ SV631 @ SV129 )
| ( c_HOL_Oord__class_Oless @ SV631 @ SV404 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1955]) ).
thf(2179,plain,
! [SV909: $i,SV810: $i,SV632: $i,SV405: $i,SV130: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV130 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SV405 ) @ SV632 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SV810 ) @ SV909 ) @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SV632 @ SV909 @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SV405 @ SV810 @ SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(2180,plain,
! [SV910: $i,SV811: $i,SV633: $i,SV406: $i,SV131: $i] :
( ( ( c_Type_Otyping @ SV131 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV406 ) @ SV633 ) @ SV811 )
| ~ ( c_Type_Otyping @ SV131 @ SV633 @ SV910 )
| ~ ( c_Type_Otyping @ SV131 @ SV406 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV910 ) @ SV811 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2181,plain,
! [SV133: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV133 ) )
= $false )
| ( ( SV133
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV133 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV133 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV133
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV133 ) ) )
= $true )
| ( ( SV133
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV133 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV133 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV133 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1959]) ).
thf(2182,plain,
! [SV911: $i,SV812: $i,SV634: $i,SV408: $i,SV134: $i] :
( ( ! [SY2385: $i] :
( ( SV134 = SV408 )
| ( SV634 = SV812 )
| ~ ( c_ListOrder_Ostep1 @ SV911 @ ( c_List_Oappend @ SV134 @ ( c_List_Olist_OCons @ SV634 @ ( c_List_Olist_ONil @ SY2385 ) @ SY2385 ) @ SY2385 ) @ ( c_List_Oappend @ SV408 @ ( c_List_Olist_OCons @ SV812 @ ( c_List_Olist_ONil @ SY2385 ) @ SY2385 ) @ SY2385 ) @ SY2385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1960]) ).
thf(2183,plain,
! [SV813: $i,SV636: $i,SV410: $i,SV137: $i] :
( ( ( c_List_Olistsp @ SV137 @ ( c_List_Oappend @ SV410 @ SV636 @ SV813 ) @ SV813 )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV137 @ SV636 @ SV813 )
| ~ ( c_List_Olistsp @ SV137 @ SV410 @ SV813 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1961]) ).
thf(2184,plain,
! [SV912: $i,SV814: $i,SV637: $i,SV411: $i,SV138: $i] :
( ( ( c_Lambda_OdB_OdB__rec @ SV138 @ SV411 @ SV637 @ ( c_Lambda_OdB_OAbs @ SV814 ) @ SV912 )
= ( hAPP @ ( hAPP @ SV637 @ SV814 ) @ ( c_Lambda_OdB_OdB__rec @ SV138 @ SV411 @ SV637 @ SV814 @ SV912 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(2185,plain,
! [SV913: $i,SV815: $i,SV638: $i,SV413: $i,SV141: $i] :
( ( ( ( hAPP @ ( c_Type_Oshift @ SV141 @ SV413 @ SV638 @ SV815 ) @ SV913 )
= ( hAPP @ SV141 @ SV913 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV913 @ SV413 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1963]) ).
thf(2186,plain,
! [SV914: $i,SV816: $i,SV639: $i,SV414: $i,SV142: $i] :
( ( ! [SY2386: $i,SY2387: $i] :
( ( SV142
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV414 @ SV142 @ SV639 @ SV816 ) @ SV414 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV639 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV914 ) @ SY2386 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV142 )
| ~ ( c_Type_Otypings @ SV639 @ SY2386 @ SY2387 )
| ~ ( c_Type_Otyping @ SV639 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV914 ) @ SY2386 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV816 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1964]) ).
thf(2187,plain,
! [SV817: $i,SV640: $i,SV416: $i,SV144: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV144 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV416 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ SV640 ) @ SV817 ) @ SV144 )
| ~ ( c_HOL_Oord__class_Oless @ SV416 @ SV817 @ SV144 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV144 ) @ SV640 @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1965]) ).
thf(2188,plain,
! [SV915: $i,SV818: $i,SV641: $i,SV417: $i,SV145: $i] :
( ( ! [SY2388: $i] :
( ( c_List_Ofoldr @ SV145 @ ( c_List_Olist_OCons @ SV417 @ SV641 @ SV818 ) @ SV915 @ SV818 @ SY2388 )
= ( hAPP @ ( hAPP @ SV145 @ SV417 ) @ ( c_List_Ofoldr @ SV145 @ SV641 @ SV915 @ SV818 @ SY2388 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1966]) ).
thf(2189,plain,
! [SV916: $i,SV819: $i,SV642: $i,SV418: $i,SV146: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV146 @ ( c_Lambda_OdB_OdB__case @ SV418 @ SV642 @ SV819 @ ( c_Lambda_OdB_OAbs @ SV916 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV146 @ ( hAPP @ SV819 @ SV916 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2190,plain,
! [SV917: $i,SV820: $i,SV643: $i,SV419: $i,SV147: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV147 @ ( c_Lambda_OdB_OdB__case @ SV419 @ SV643 @ SV820 @ ( c_Lambda_OdB_OAbs @ SV917 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV147 @ ( hAPP @ SV820 @ SV917 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(2191,plain,
! [SV821: $i,SV645: $i,SV421: $i,SV149: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV149 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV421 ) @ SV645 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV821 ) @ SV645 ) @ SV149 )
| ~ ( c_HOL_Oord__class_Oless @ SV421 @ SV821 @ SV149 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1969]) ).
thf(2192,plain,
! [SV822: $i,SV646: $i,SV422: $i,SV150: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV150 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV150 ) @ SV422 ) @ SV646 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV150 ) @ SV822 ) @ SV646 ) @ SV150 )
| ~ ( c_HOL_Oord__class_Oless @ SV422 @ SV822 @ SV150 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1970]) ).
thf(2193,plain,
! [SV823: $i,SV647: $i,SV423: $i,SV151: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV151 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV423 @ SV647 @ SV151 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV423 ) @ SV823 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV647 ) @ SV823 ) @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1971]) ).
thf(2194,plain,
! [SV824: $i,SV648: $i,SV424: $i,SV152: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV152 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV424 ) @ SV648 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV424 ) @ SV824 ) @ SV152 )
| ~ ( c_HOL_Oord__class_Oless @ SV648 @ SV824 @ SV152 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1972]) ).
thf(2195,plain,
! [SV825: $i,SV649: $i,SV425: $i,SV153: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV153 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV425 ) @ SV649 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV425 ) @ SV825 ) @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SV649 @ SV825 @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1973]) ).
thf(2196,plain,
! [SV826: $i,SV650: $i,SV426: $i,SV154: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV154 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV426 @ SV650 @ SV154 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SV826 ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SV826 ) @ SV650 ) @ SV154 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1974]) ).
thf(2197,plain,
! [SV155: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV155 ) )
= $false )
| ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV155 ) @ tc_Lambda_OdB )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV155 ) ) )
= $true )
| ( ( SV155
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV155 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV155 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV155 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1975]) ).
thf(2198,plain,
! [SV827: $i,SV651: $i,SV427: $i,SV156: $i] :
( ( ( c_Type_Otyping @ SV156 @ SV427 @ SV651 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV827 ) @ SV427 ) )
| ~ ( c_Type_Otyping @ SV156 @ SV827 @ SV651 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1976]) ).
thf(2199,plain,
! [SV918: $i,SV828: $i,SV652: $i,SV428: $i,SV157: $i] :
( ( ! [SY2389: $i] :
( ( c_ListOrder_Ostep1 @ SV157 @ SV428 @ SV652 @ SV828 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV157 @ SV918 ) @ SY2389 ) )
| ~ ( c_ListOrder_Ostep1 @ SV157 @ ( c_List_Olist_OCons @ SV918 @ SV428 @ SV828 ) @ ( c_List_Olist_OCons @ SY2389 @ SV652 @ SV828 ) @ SV828 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1977]) ).
thf(2200,plain,
! [SV919: $i,SV829: $i,SV653: $i,SV429: $i,SV158: $i] :
( ( ( c_ListOrder_Ostep1 @ SV158 @ ( c_List_Olist_OCons @ SV429 @ SV653 @ SV829 ) @ ( c_List_Olist_OCons @ SV429 @ SV919 @ SV829 ) @ SV829 )
| ~ ( c_ListOrder_Ostep1 @ SV158 @ SV653 @ SV919 @ SV829 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1978]) ).
thf(2201,plain,
! [SV920: $i,SV834: $i,SV658: $i,SV434: $i,SV165: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV165 @ SV434 @ SV658 @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV834 ) @ SV434 ) @ SV920 )
| ~ ( c_Type_Otyping @ SV165 @ SV834 @ SV920 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2202,plain,
! [SV659: $i,SV435: $i,SV166: $i] :
( ( ( class_Orderings_Oorder @ SV166 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV435 @ SV659 @ SV166 )
| ~ ( c_HOL_Oord__class_Oless @ SV659 @ SV435 @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1984]) ).
thf(2203,plain,
! [SV921: $i,SV835: $i,SV660: $i,SV436: $i,SV167: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV167 @ SV436 ) @ SV660 ) @ SV835 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV167 @ SV436 ) @ SV921 ) @ SV835 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV167 @ SV660 ) @ SV921 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1985]) ).
thf(2204,plain,
! [SV922: $i,SV836: $i,SV661: $i,SV437: $i,SV168: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV168 @ SV437 ) @ SV661 ) @ SV836 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV168 @ SV922 ) @ SV836 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV168 @ SV437 ) @ SV661 ) @ SV922 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1986]) ).
thf(2205,plain,
! [SV662: $i,SV438: $i,SV169: $i] :
( ( ( class_Orderings_Olinorder @ SV169 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV438 @ SV662 @ SV169 )
| ~ ( c_HOL_Oord__class_Oless @ SV662 @ SV438 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1987]) ).
thf(2206,plain,
! [SV663: $i,SV439: $i,SV170: $i] :
( ( ( class_Orderings_Opreorder @ SV170 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV439 @ SV663 @ SV170 )
| ~ ( c_HOL_Oord__class_Oless @ SV663 @ SV439 @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1988]) ).
thf(2207,plain,
! [SV664: $i,SV440: $i,SV171: $i] :
( ( ( class_Orderings_Opreorder @ SV171 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV440 @ SV664 @ SV171 )
| ~ ( c_HOL_Oord__class_Oless @ SV664 @ SV440 @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1989]) ).
thf(2208,plain,
! [SV441: $i,SV172: $i] :
( ( ( hBOOL @ ( hAPP @ SV172 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV172 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV172 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV172 @ SV441 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV172 @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV172 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1990]) ).
thf(2209,plain,
! [SV923: $i,SV837: $i,SV665: $i,SV442: $i,SV173: $i] :
( ( ( ( c_List_Ofoldl @ SV173 @ ( hAPP @ ( hAPP @ SV173 @ SV442 ) @ SV665 ) @ SV837 @ SV923 @ SV923 )
= ( hAPP @ ( hAPP @ SV173 @ SV442 ) @ ( c_List_Ofoldl @ SV173 @ SV665 @ SV837 @ SV923 @ SV923 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV173 @ SV923 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1991]) ).
thf(2210,plain,
! [SV839: $i,SV667: $i,SV445: $i,SV176: $i] :
( ( ( c_Type_Otypings @ SV176 @ SV445 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV667 @ SV176 @ SV839 @ SV445 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV176 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV839 ) @ SV445 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV667 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1993]) ).
thf(2211,plain,
! [SV924: $i,SV840: $i,SV668: $i,SV446: $i,SV177: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV177 @ ( c_Lambda_OdB_OdB__case @ SV446 @ SV668 @ SV840 @ ( c_Lambda_OdB_OVar @ SV924 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV177 @ ( hAPP @ SV446 @ SV924 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1994]) ).
thf(2212,plain,
! [SV925: $i,SV841: $i,SV669: $i,SV447: $i,SV178: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV178 @ ( c_Lambda_OdB_OdB__case @ SV447 @ SV669 @ SV841 @ ( c_Lambda_OdB_OVar @ SV925 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV178 @ ( hAPP @ SV447 @ SV925 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1995]) ).
thf(2213,plain,
! [SV926: $i,SV842: $i,SV670: $i,SV449: $i,SV180: $i] :
( ( ! [SY2390: $i] :
( ~ ( hBOOL @ ( hAPP @ SV180 @ ( c_Lambda_OdB_OdB__case @ SV449 @ SV670 @ SV842 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV926 ) @ SY2390 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV180 @ ( hAPP @ ( hAPP @ SV670 @ SV926 ) @ SY2390 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2214,plain,
! [SV927: $i,SV843: $i,SV671: $i,SV450: $i,SV181: $i] :
( ( ! [SY2391: $i] :
( ~ ( hBOOL @ ( hAPP @ SV181 @ ( c_Lambda_OdB_OdB__case @ SV450 @ SV671 @ SV843 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV927 ) @ SY2391 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV181 @ ( hAPP @ ( hAPP @ SV671 @ SV927 ) @ SY2391 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1997]) ).
thf(2215,plain,
! [SV672: $i,SV451: $i,SV182: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV182 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV182 ) @ ( c_Lambda_OdB_OVar @ SV451 ) ) @ SV672 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1998]) ).
thf(2216,plain,
! [SV452: $i,SV673: $i,SV183: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV183 @ SV673 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV183 ) ) @ SV452 ) @ SV673 )
= ( c_Lambda_OdB_OVar @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1999]) ).
thf(2217,plain,
! [SV453: $i,SV674: $i,SV184: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV184 ) @ SV674 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV184 @ SV453 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV674 @ SV453 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2000]) ).
thf(2218,plain,
! [SV928: $i,SV844: $i,SV675: $i,SV456: $i,SV187: $i] :
( ( ( SV187 = SV456 )
| ~ ( c_Type_Otyping @ SV675 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV844 ) @ SV928 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV456 )
| ~ ( c_Type_Otyping @ SV675 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV844 ) @ SV928 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV187 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2002]) ).
thf(2219,plain,
! [SV188: $i,SV676: $i,SV457: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV457 @ SV676 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV188 @ SV457 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV188 @ SV676 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2003]) ).
thf(2220,plain,
! [SV458: $i,SV189: $i] :
( ( ( hBOOL @ ( hAPP @ SV189 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV189 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV189 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV189 @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV189 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV189 @ SV458 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2004]) ).
thf(2221,plain,
! [SV459: $i,SV677: $i,SV190: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV190 ) @ SV677 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV190 @ SV459 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV677 @ SV459 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2005]) ).
thf(2222,plain,
! [SV929: $i,SV845: $i,SV678: $i,SV460: $i,SV191: $i] :
( ( ( c_Lambda_OdB_OdB__rec @ SV191 @ SV460 @ SV678 @ ( c_Lambda_OdB_OVar @ SV845 ) @ SV929 )
= ( hAPP @ SV191 @ SV845 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2006]) ).
thf(2223,plain,
! [SV680: $i,SV194: $i,SV463: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV463 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV194 ) @ SV463 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV680 @ 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 @ SV194 ) ) @ SV463 ) @ SV680 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2009]) ).
thf(2224,plain,
! [SV195: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV195 ) )
= $false )
| ( ( SV195
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV195 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV195 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV195 ) ) )
= $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 @ SV195 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV195 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV195 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2010]) ).
thf(2225,plain,
! [SV681: $i,SV464: $i,SV197: $i] :
( ( ( c_Type_Otyping @ SV197 @ ( c_Lambda_OdB_OVar @ SV464 ) @ SV681 )
= $false )
| ( ( ( hAPP @ SV197 @ SV464 )
= SV681 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2011]) ).
thf(2226,plain,
! [SV847: $i,SV682: $i,SV465: $i,SV198: $i] :
( ( ( ~ ( class_OrderedGroup_Osemigroup__add @ SV198 ) )
= $true )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ SV465 ) @ SV682 ) @ SV847 @ SV198 @ SV198 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ SV465 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ SV682 @ SV847 @ SV198 @ SV198 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2012]) ).
thf(2227,plain,
! [SV199: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV199 ) )
= $false )
| ( ( SV199
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV199 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV199 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV199
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV199 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV199 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2013]) ).
thf(2228,plain,
! [SV849: $i,SV685: $i,SV468: $i,SV202: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV202 ) @ SV468 ) @ SV685 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV849 ) @ SV468 ) @ SV685 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV202 ) @ SV849 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2015]) ).
thf(2229,plain,
! [SV469: $i,SV686: $i,SV203: $i] :
( ( ( SV203 = SV686 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV686 @ SV203 @ tc_nat )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV203 ) ) @ SV469 ) @ SV686 )
= ( c_Lambda_OdB_OVar @ SV203 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2016]) ).
thf(2230,plain,
! [SV850: $i,SV687: $i,SV470: $i,SV204: $i] :
( ( ( c_Type_Otyping @ SV204 @ ( c_Lambda_OdB_OVar @ SV470 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV687 @ SV204 @ SV470 @ SV850 ) @ SV687 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV204 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV470 ) @ SV850 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV687 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2017]) ).
thf(2231,plain,
! [SV205: $i,SV688: $i,SV471: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV471 ) @ SV688 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV205 ) )
= $false )
| ( ( SV205
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV471 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV471 @ SV688 @ SV205 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2018]) ).
thf(2232,plain,
! [SV930: $i,SV851: $i,SV689: $i,SV472: $i,SV206: $i] :
( ( ! [SY2392: $i] :
( ( c_Lambda_OdB_OdB__case @ SV206 @ SV472 @ SV689 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV851 ) @ SV930 ) @ SY2392 )
= ( hAPP @ ( hAPP @ SV472 @ SV851 ) @ SV930 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2019]) ).
thf(2233,plain,
! [SV931: $i,SV852: $i,SV690: $i,SV473: $i,SV207: $i] :
( ( ( ( hAPP @ ( hAPP @ SV207 @ SV473 ) @ ( c_List_Ofoldl @ SV207 @ SV690 @ SV852 @ SV931 @ SV931 ) )
= ( c_List_Ofoldl @ SV207 @ SV473 @ SV852 @ SV931 @ SV931 ) )
| ~ ( c_OrderedGroup_Omonoid__add @ SV690 @ SV207 @ SV931 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2020]) ).
thf(2234,plain,
! [SV208: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV208 ) )
= $false )
| ( ( SV208
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV208 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV208 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV208 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV208 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2021]) ).
thf(2235,plain,
! [SV932: $i,SV853: $i,SV691: $i,SV474: $i,SV210: $i] :
( ( ( c_Lambda_OdB_OdB__case @ SV210 @ SV474 @ SV691 @ ( c_Lambda_OdB_OVar @ SV853 ) @ SV932 )
= ( hAPP @ SV210 @ SV853 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2022]) ).
thf(2236,plain,
! [SV933: $i,SV854: $i,SV692: $i,SV476: $i,SV212: $i] :
( ( ! [SY2393: $i] :
( ( c_List_Ofoldl @ SV212 @ SV476 @ ( c_List_Olist_OCons @ SV692 @ SV854 @ SV933 ) @ SY2393 @ SV933 )
= ( c_List_Ofoldl @ SV212 @ ( hAPP @ ( hAPP @ SV212 @ SV476 ) @ SV692 ) @ SV854 @ SY2393 @ SV933 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2237,plain,
! [SV934: $i,SV855: $i,SV693: $i,SV478: $i,SV215: $i] :
( ( ! [SY2394: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV215 @ SV478 @ SV693 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV855 ) @ SV934 ) @ SY2394 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV478 @ SV855 ) @ SV934 ) @ ( c_Lambda_OdB_OdB__rec @ SV215 @ SV478 @ SV693 @ SV855 @ SY2394 ) ) @ ( c_Lambda_OdB_OdB__rec @ SV215 @ SV478 @ SV693 @ SV934 @ SY2394 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(2238,plain,
! [SV935: $i,SV856: $i,SV694: $i,SV479: $i,SV217: $i] :
( ( ! [SY2395: $i,SY2396: $i] :
( ( c_Type_Otypings @ SV217 @ SV479 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV694 @ SV856 @ SV217 @ SV479 ) )
| ~ ( c_Type_Otyping @ SV217 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV935 ) @ SY2395 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV856 )
| ~ ( c_Type_Otypings @ SV217 @ SY2395 @ SY2396 )
| ~ ( c_Type_Otyping @ SV217 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV935 ) @ SY2395 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV479 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV694 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2025]) ).
thf(2239,plain,
! [SV219: $i,SV695: $i,SV480: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV480 ) @ SV695 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV219 ) @ SV480 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV219 ) @ SV695 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2026]) ).
thf(2240,plain,
! [SV481: $i,SV696: $i,SV220: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV220 ) @ SV696 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV220 ) @ SV481 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV696 ) @ SV481 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2027]) ).
thf(2241,plain,
! [SV699: $i,SV225: $i,SV485: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV485 ) @ SV225 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV699 ) )
= $false )
| ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV225 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV485 @ SV225 @ SV699 ) @ tc_Lambda_OdB )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2030]) ).
thf(2242,plain,
! [SV936: $i,SV859: $i,SV701: $i,SV487: $i,SV227: $i] :
( ( ! [SY2397: $i] :
( ( c_List_Ofoldl @ SV227 @ SV487 @ ( c_List_Oappend @ SV701 @ SV859 @ SV936 ) @ SY2397 @ SV936 )
= ( c_List_Ofoldl @ SV227 @ ( c_List_Ofoldl @ SV227 @ SV487 @ SV701 @ SY2397 @ SV936 ) @ SV859 @ SY2397 @ SV936 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2032]) ).
thf(2243,plain,
! [SV702: $i,SV491: $i,SV231: $i] :
( ( ( c_fequal @ SV231 @ SV491 @ SV702 )
= $false )
| ( ( SV231 = SV491 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2035]) ).
thf(2244,plain,
! [SV860: $i,SV704: $i,SV493: $i,SV233: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV233 ) @ SV493 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV704 ) @ SV860 ) )
= $true )
| ( ( SV233 = SV704 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2037]) ).
thf(2245,plain,
! [SV861: $i,SV705: $i,SV494: $i,SV234: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV234 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV494 ) @ SV705 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV494 ) @ SV861 ) )
| ( SV705 = SV861 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2038]) ).
thf(2246,plain,
! [SV706: $i,SV495: $i,SV235: $i] :
( ( ( ( c_List_Oappend @ SV235 @ SV495 @ SV706 )
= ( c_List_Olist_ONil @ SV706 ) )
= $false )
| ( ( SV495
= ( c_List_Olist_ONil @ SV706 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2039]) ).
thf(2247,plain,
! [SV862: $i,SV707: $i,SV496: $i,SV236: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV236 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV236 ) @ SV496 ) @ SV707 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV236 ) @ SV862 ) @ SV707 ) )
| ( SV496 = SV862 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2040]) ).
thf(2248,plain,
! [SV863: $i,SV708: $i,SV497: $i,SV237: $i] :
( ( ( ( c_List_Oappend @ SV237 @ SV497 @ SV708 )
!= ( c_List_Oappend @ SV237 @ SV863 @ SV708 ) )
= $true )
| ( ( SV497 = SV863 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2041]) ).
thf(2249,plain,
! [SV864: $i,SV709: $i,SV498: $i,SV238: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV238 ) @ SV498 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV709 ) @ SV864 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV238 = SV709 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2042]) ).
thf(2250,plain,
! [SV865: $i,SV710: $i,SV499: $i,SV239: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV239 ) @ SV499 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV710 ) @ SV865 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV499 = SV865 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2043]) ).
thf(2251,plain,
! [SV937: $i,SV866: $i,SV711: $i,SV500: $i,SV240: $i] :
( ( ( ( c_List_Olist_OCons @ SV240 @ SV500 @ SV711 )
!= ( c_List_Olist_OCons @ SV866 @ SV937 @ SV711 ) )
| ( SV240 = SV866 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2252,plain,
! [SV867: $i,SV712: $i,SV501: $i,SV241: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV241 ) @ SV501 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV712 ) @ SV867 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV241 = SV712 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2045]) ).
thf(2253,plain,
! [SV868: $i,SV713: $i,SV502: $i,SV242: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV242 ) @ SV502 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV713 @ SV868 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( SV242
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV713 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV242 @ SV502 @ SV713 @ SV868 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV868
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2046]) ).
thf(2254,plain,
! [SV938: $i,SV869: $i,SV714: $i,SV503: $i,SV243: $i] :
( ( ! [SY2398: $i,SY2399: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV243 ) @ SV503 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV714 ) @ SV869 ) @ SV938 ) ) )
| ~ ( c_Type_Otyping @ SY2398 @ SV869 @ SV243 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV869 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY2398 @ SV938 @ SV243 @ tc_Type_Otype ) @ SV714 @ SY2399 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV714 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2047]) ).
thf(2255,plain,
! [SV870: $i,SV715: $i,SV504: $i,SV244: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV244 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV244 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV244 ) @ SV504 ) @ SV715 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV244 ) @ SV504 ) @ SV870 ) )
| ( SV715 = SV870 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2048]) ).
thf(2256,plain,
! [SV871: $i,SV716: $i,SV505: $i,SV245: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV245 ) @ SV505 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV716 ) @ SV871 ) )
= $true )
| ( ( SV505 = SV871 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2049]) ).
thf(2257,plain,
! [SV717: $i,SV506: $i,SV246: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV246 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV506 @ SV717 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( c_Lambda_OdB_OAbs @ SV246 )
= SV506 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2050]) ).
thf(2258,plain,
! [SV872: $i,SV719: $i,SV508: $i,SV248: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV248 ) @ SV508 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV719 ) @ SV872 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2052]) ).
thf(2259,plain,
! [SV939: $i,SV873: $i,SV720: $i,SV509: $i,SV249: $i] :
( ( ( ( c_List_Oappend @ SV249 @ ( c_List_Olist_OCons @ SV509 @ ( c_List_Olist_ONil @ SV720 ) @ SV720 ) @ SV720 )
!= ( c_List_Oappend @ SV873 @ ( c_List_Olist_OCons @ SV939 @ ( c_List_Olist_ONil @ SV720 ) @ SV720 ) @ SV720 ) )
| ( SV249 = SV873 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2053]) ).
thf(2260,plain,
! [SV721: $i,SV510: $i,SV250: $i] :
( ( ( ( c_List_Oappend @ SV250 @ SV510 @ SV721 )
= ( c_List_Olist_ONil @ SV721 ) )
= $false )
| ( ( SV250
= ( c_List_Olist_ONil @ SV721 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2054]) ).
thf(2261,plain,
! [SV874: $i,SV722: $i,SV511: $i,SV251: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV251 ) ) @ SV511 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV722 ) @ SV874 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2055]) ).
thf(2262,plain,
! [SV723: $i,SV512: $i,SV252: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV252 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV512 @ SV723 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV723
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2056]) ).
thf(2263,plain,
! [SV724: $i,SV513: $i,SV253: $i] :
( ( ( ( c_List_Oappend @ SV253 @ SV513 @ SV724 )
= SV253 )
= $false )
| ( ( SV513
= ( c_List_Olist_ONil @ SV724 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2057]) ).
thf(2264,plain,
! [SV727: $i,SV516: $i,SV256: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV256 @ SV516 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV727 @ SV516 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV256 = SV727 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2060]) ).
thf(2265,plain,
! [SV875: $i,SV728: $i,SV517: $i,SV257: $i] :
( ( ( ( c_List_Omap @ SV257 @ SV517 @ SV728 @ SV875 )
!= ( c_List_Olist_ONil @ SV875 ) )
= $true )
| ( ( SV517
= ( c_List_Olist_ONil @ SV728 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2061]) ).
thf(2266,plain,
! [SV518: $i,SV258: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SV518 ) @ SV518 )
!= ( c_HOL_Ozero__class_Ozero @ SV258 ) )
= $true )
| ( ( SV518
= ( c_HOL_Ozero__class_Ozero @ SV258 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV258 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2062]) ).
thf(2267,plain,
! [SV730: $i,SV520: $i,SV260: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV260 ) @ SV520 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV730 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV260 ) @ SV520 )
= SV730 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2064]) ).
thf(2268,plain,
! [SV731: $i,SV521: $i,SV261: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV261 @ SV521 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV731 ) )
= $false )
| ( ( SV261
= ( c_Lambda_OdB_OAbs @ SV731 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2065]) ).
thf(2269,plain,
! [SV732: $i,SV522: $i,SV262: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV262 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV522 @ SV732 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( c_Lambda_OdB_OVar @ SV262 )
= SV522 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2066]) ).
thf(2270,plain,
! [SV876: $i,SV733: $i,SV523: $i,SV263: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV263 ) @ SV523 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV733 ) @ SV876 ) )
= $true )
| ( ( SV263 = SV733 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2067]) ).
thf(2271,plain,
! [SV734: $i,SV524: $i,SV264: $i] :
( ( ( ( c_List_Oappend @ SV264 @ SV524 @ SV734 )
= SV524 )
= $false )
| ( ( SV264
= ( c_List_Olist_ONil @ SV734 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2068]) ).
thf(2272,plain,
! [SV877: $i,SV736: $i,SV526: $i,SV266: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV266 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV266 ) @ SV526 ) @ SV736 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV266 ) @ SV526 ) @ SV877 ) )
| ( SV736 = SV877 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2070]) ).
thf(2273,plain,
! [SV737: $i,SV527: $i,SV267: $i] :
( ( ( SV267
= ( c_List_Oappend @ SV267 @ SV527 @ SV737 ) )
= $false )
| ( ( SV527
= ( c_List_Olist_ONil @ SV737 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2071]) ).
thf(2274,plain,
! [SV940: $i,SV878: $i,SV738: $i,SV528: $i,SV268: $i] :
( ( ! [SY2400: $i,SY2401: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV268 ) @ SV528 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV738 ) @ SV878 ) @ SV940 ) ) )
| ~ ( c_Type_Otyping @ SY2400 @ SV878 @ SV528 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV878 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY2400 @ SV940 @ SV528 @ tc_Type_Otype ) @ SV738 @ SY2401 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV738 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2072]) ).
thf(2275,plain,
! [SV879: $i,SV739: $i,SV529: $i,SV269: $i] :
( ( ( ( c_List_Oappend @ SV269 @ SV529 @ SV739 )
!= ( c_List_Oappend @ SV879 @ SV529 @ SV739 ) )
= $true )
| ( ( SV269 = SV879 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2073]) ).
thf(2276,plain,
! [SV880: $i,SV740: $i,SV531: $i,SV271: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV271 ) @ SV531 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV740 ) @ SV880 ) )
= $true )
| ( ( SV531 = SV880 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2075]) ).
thf(2277,plain,
! [SV881: $i,SV742: $i,SV534: $i,SV274: $i] :
( ( ( ( c_List_Olist_ONil @ SV274 )
!= ( c_List_Omap @ SV534 @ SV742 @ SV881 @ SV274 ) )
= $true )
| ( ( SV742
= ( c_List_Olist_ONil @ SV881 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2077]) ).
thf(2278,plain,
! [SV941: $i,SV882: $i,SV743: $i,SV535: $i,SV275: $i] :
( ( ( ( c_List_Oappend @ SV275 @ ( c_List_Olist_OCons @ SV535 @ ( c_List_Olist_ONil @ SV743 ) @ SV743 ) @ SV743 )
!= ( c_List_Oappend @ SV882 @ ( c_List_Olist_OCons @ SV941 @ ( c_List_Olist_ONil @ SV743 ) @ SV743 ) @ SV743 ) )
| ( SV535 = SV941 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2078]) ).
thf(2279,plain,
! [SV744: $i,SV536: $i,SV276: $i] :
( ( ( SV276
= ( c_List_Oappend @ SV536 @ SV276 @ SV744 ) )
= $false )
| ( ( SV536
= ( c_List_Olist_ONil @ SV744 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2079]) ).
thf(2280,plain,
! [SV745: $i,SV537: $i,SV277: $i] :
( ( ( ( c_List_Olist_ONil @ SV277 )
= ( c_List_Oappend @ SV537 @ SV745 @ SV277 ) )
= $false )
| ( ( SV745
= ( c_List_Olist_ONil @ SV277 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2080]) ).
thf(2281,plain,
! [SV746: $i,SV538: $i,SV278: $i] :
( ( ( ( c_List_Olist_ONil @ SV278 )
= ( c_List_Oappend @ SV538 @ SV746 @ SV278 ) )
= $false )
| ( ( SV538
= ( c_List_Olist_ONil @ SV278 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2081]) ).
thf(2282,plain,
! [SV883: $i,SV747: $i,SV540: $i,SV280: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV280 ) @ SV540 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV747 ) @ SV883 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV540 = SV883 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2082]) ).
thf(2283,plain,
! [SV942: $i,SV884: $i,SV750: $i,SV543: $i,SV283: $i] :
( ( ( ( c_List_Olist_OCons @ SV283 @ SV543 @ SV750 )
!= ( c_List_Olist_OCons @ SV884 @ SV942 @ SV750 ) )
| ( SV543 = SV942 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2085]) ).
thf(2284,plain,
! [SV751: $i,SV544: $i,SV284: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV284 @ SV544 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV751 ) )
= $false )
| ( ( SV544
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2086]) ).
thf(2285,plain,
! [SV752: $i,SV545: $i,SV285: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV285 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV545 @ SV752 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV752
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2087]) ).
thf(2286,plain,
! [SV753: $i,SV546: $i,SV286: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV286 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV286 )
| ( SV546
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV286 ) @ SV546 ) @ SV753 ) )
| ( SV753
= ( c_HOL_Ozero__class_Ozero @ SV286 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2088]) ).
thf(2287,plain,
! [SV943: $i,SV885: $i,SV754: $i,SV548: $i,SV288: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV288 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV548 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV754 ) @ SV885 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV754 ) @ SV943 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV548 ) @ SV885 )
= SV943 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2090]) ).
thf(2288,plain,
! [SV289: $i,SV1: $i] :
( ( ( hBOOL @ ( hAPP @ SV1 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV1 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV1 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV1 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4 @ SV1 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1 @ SV289 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2091]) ).
thf(2289,plain,
! [SV290: $i,SV2: $i] :
( ( ( hBOOL @ ( hAPP @ SV2 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV2 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV2 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV2 @ SV290 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV2 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV2 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__4 @ SV2 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2092]) ).
thf(2290,plain,
! [SV549: $i,SV755: $i,SV291: $i,SV3: $i] :
( ( ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV291 @ SV755 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV549 )
= $false )
| ( ( c_Type_Otyping @ SV3 @ SV291 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV549 @ SV3 @ SV291 @ SV755 ) @ SV549 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2093]) ).
thf(2291,plain,
! [SV550: $i,SV756: $i,SV292: $i,SV4: $i] :
( ( ( c_Type_Otyping @ SV4 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV292 @ SV756 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV550 )
= $false )
| ( ( c_Type_Otyping @ SV4 @ SV292 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV550 @ SV4 @ SV292 @ SV756 ) @ SV550 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2094]) ).
thf(2292,plain,
! [SV551: $i,SV293: $i,SV757: $i,SV5: $i] :
( ( ( c_Type_Otyping @ SV5 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV757 @ SV293 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV551 )
= $false )
| ( ( c_Type_Otypings @ SV5 @ SV293 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV551 @ SV5 @ SV757 @ SV293 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2095]) ).
thf(2293,plain,
! [SV552: $i,SV294: $i,SV758: $i,SV6: $i] :
( ( ( c_Type_Otyping @ SV6 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV758 @ SV294 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV552 )
= $false )
| ( ( c_Type_Otypings @ SV6 @ SV294 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV552 @ SV6 @ SV758 @ SV294 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2096]) ).
thf(2294,plain,
! [SV944: $i,SV886: $i,SV759: $i,SV553: $i,SV295: $i,SV7: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV7 @ SV295 ) @ SV553 ) )
| ( SV295 = SV553 )
| ~ ( c_ListOrder_Ostep1 @ SV7 @ ( c_List_Oappend @ SV759 @ ( c_List_Olist_OCons @ SV295 @ ( c_List_Olist_ONil @ SV886 ) @ SV886 ) @ SV886 ) @ ( c_List_Oappend @ SV944 @ ( c_List_Olist_OCons @ SV553 @ ( c_List_Olist_ONil @ SV886 ) @ SV886 ) @ SV886 ) @ SV886 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2097]) ).
thf(2295,plain,
! [SV945: $i,SV887: $i,SV760: $i,SV554: $i,SV296: $i,SV8: $i] :
( ( ( c_List_Ofoldr @ SV8 @ ( c_List_Oappend @ SV296 @ SV554 @ SV760 ) @ SV887 @ SV760 @ SV945 )
= ( c_List_Ofoldr @ SV8 @ SV296 @ ( c_List_Ofoldr @ SV8 @ SV554 @ SV887 @ SV760 @ SV945 ) @ SV760 @ SV945 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2098]) ).
thf(2296,plain,
! [SV558: $i,SV12: $i,SV761: $i,SV300: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV300 ) @ SV761 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV12 ) @ SV300 ) @ SV558 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV12 ) @ SV761 ) @ SV558 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2102]) ).
thf(2297,plain,
! [SV888: $i,SV762: $i,SV559: $i,SV306: $i,SV19: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV19 @ SV306 ) @ SV559 ) @ SV762 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV19 @ SV306 ) @ SV888 ) @ SV762 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV19 @ SV306 ) @ SV559 ) @ SV888 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2104]) ).
thf(2298,plain,
! [SV889: $i,SV763: $i,SV562: $i,SV310: $i,SV23: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV23 @ SV310 ) @ SV562 ) ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV23 @ ( c_List_Olist_OCons @ SV310 @ SV763 @ SV889 ) @ ( c_List_Olist_OCons @ SV562 @ SV763 @ SV889 ) @ SV889 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2105]) ).
thf(2299,plain,
! [SV946: $i,SV890: $i,SV764: $i,SV563: $i,SV311: $i,SV24: $i] :
( ( ( SV24 = SV311 )
| ( SV563 = SV764 )
| ~ ( c_ListOrder_Ostep1 @ SV890 @ ( c_List_Olist_OCons @ SV311 @ SV764 @ SV946 ) @ ( c_List_Olist_OCons @ SV24 @ SV563 @ SV946 ) @ SV946 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2106]) ).
thf(2300,plain,
! [SV565: $i,SV313: $i,SV766: $i,SV27: $i] :
( ( ( c_List_Olistsp @ SV27 @ ( c_List_Oappend @ SV766 @ SV313 @ SV565 ) @ SV565 )
= $false )
| ( ( c_List_Olistsp @ SV27 @ SV313 @ SV565 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2109]) ).
thf(2301,plain,
! [SV566: $i,SV767: $i,SV314: $i,SV28: $i] :
( ( ( c_List_Olistsp @ SV28 @ ( c_List_Oappend @ SV314 @ SV767 @ SV566 ) @ SV566 )
= $false )
| ( ( c_List_Olistsp @ SV28 @ SV314 @ SV566 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2110]) ).
thf(2302,plain,
! [SV892: $i,SV768: $i,SV567: $i,SV316: $i,SV30: $i] :
( ( ( c_ListOrder_Ostep1 @ SV30 @ ( c_List_Oappend @ SV316 @ SV567 @ SV768 ) @ ( c_List_Oappend @ SV316 @ SV892 @ SV768 ) @ SV768 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV30 @ SV567 @ SV892 @ SV768 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2111]) ).
thf(2303,plain,
! [SV893: $i,SV769: $i,SV568: $i,SV317: $i,SV31: $i] :
( ( ( ~ ( c_ListOrder_Ostep1 @ SV31 @ SV317 @ SV568 @ SV769 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV31 @ ( c_List_Oappend @ SV317 @ SV893 @ SV769 ) @ ( c_List_Oappend @ SV568 @ SV893 @ SV769 ) @ SV769 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2112]) ).
thf(2304,plain,
! [SV894: $i,SV770: $i,SV570: $i,SV319: $i,SV34: $i] :
( ( ( c_Type_Otyping @ SV34 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV319 @ SV570 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV770 )
= $true )
| ( ( ~ ( c_Type_Otypings @ SV34 @ SV570 @ SV894 )
| ~ ( c_Type_Otyping @ SV34 @ SV319 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV894 @ SV770 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2113]) ).
thf(2305,plain,
! [SV771: $i,SV571: $i,SV320: $i,SV35: $i] :
( ( ( class_Orderings_Opreorder @ SV35 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV320 @ SV571 @ SV35 )
| ~ ( c_HOL_Oord__class_Oless @ SV771 @ SV571 @ SV35 )
| ~ ( c_HOL_Oord__class_Oless @ SV320 @ SV771 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2114]) ).
thf(2306,plain,
! [SV772: $i,SV572: $i,SV321: $i,SV36: $i] :
( ( ( class_Orderings_Oorder @ SV36 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV321 @ SV572 @ SV36 )
| ~ ( c_HOL_Oord__class_Oless @ SV321 @ SV772 @ SV36 )
| ~ ( c_HOL_Oord__class_Oless @ SV772 @ SV572 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2115]) ).
thf(2307,plain,
! [SV773: $i,SV573: $i,SV322: $i,SV37: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV37 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV322 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV573 ) @ SV773 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV322 ) @ SV573 ) ) @ SV773 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2116]) ).
thf(2308,plain,
! [SV774: $i,SV574: $i,SV323: $i,SV38: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV38 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV323 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV574 ) @ SV774 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV574 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV323 ) @ SV774 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2117]) ).
thf(2309,plain,
! [SV775: $i,SV575: $i,SV324: $i,SV39: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV39 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ SV324 ) @ SV575 ) ) @ SV775 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ SV324 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ SV575 ) @ SV775 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2118]) ).
thf(2310,plain,
! [SV776: $i,SV576: $i,SV325: $i,SV40: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV40 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ SV325 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ SV576 ) @ SV776 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ SV576 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ SV325 ) @ SV776 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2119]) ).
thf(2311,plain,
! [SV777: $i,SV577: $i,SV326: $i,SV41: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__add @ SV41 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV326 ) @ SV577 ) ) @ SV777 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV326 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV577 ) @ SV777 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2120]) ).
thf(2312,plain,
! [SV778: $i,SV578: $i,SV327: $i,SV42: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV42 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV327 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV578 ) @ SV778 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV327 ) @ SV578 ) ) @ SV778 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2121]) ).
thf(2313,plain,
! [SV779: $i,SV579: $i,SV328: $i,SV43: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV43 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ SV328 ) @ SV579 ) ) @ SV779 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ SV328 ) @ SV779 ) ) @ SV579 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2122]) ).
thf(2314,plain,
! [SV780: $i,SV580: $i,SV329: $i,SV44: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV44 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SV329 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SV580 ) @ SV780 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SV580 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SV329 ) @ SV780 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2123]) ).
thf(2315,plain,
! [SV781: $i,SV581: $i,SV330: $i,SV45: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV45 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV45 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV45 ) @ SV330 ) @ SV581 ) ) @ SV781 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV45 ) @ SV330 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV45 ) @ SV581 ) @ SV781 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2124]) ).
thf(2316,plain,
! [SV947: $i,SV895: $i,SV782: $i,SV582: $i,SV331: $i,SV48: $i] :
( ( ( hAPP @ ( c_COMBC @ SV48 @ SV331 @ SV582 @ SV782 @ SV895 ) @ SV947 )
= ( hAPP @ ( hAPP @ SV48 @ SV947 ) @ SV331 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2125]) ).
thf(2317,plain,
! [SV948: $i,SV896: $i,SV784: $i,SV585: $i,SV334: $i,SV51: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV51 @ SV334 ) @ SV585 ) )
| ( c_ListOrder_Ostep1 @ SV51 @ SV784 @ SV896 @ SV948 )
| ~ ( c_ListOrder_Ostep1 @ SV51 @ ( c_List_Oappend @ SV784 @ ( c_List_Olist_OCons @ SV334 @ ( c_List_Olist_ONil @ SV948 ) @ SV948 ) @ SV948 ) @ ( c_List_Oappend @ SV896 @ ( c_List_Olist_OCons @ SV585 @ ( c_List_Olist_ONil @ SV948 ) @ SV948 ) @ SV948 ) @ SV948 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2126]) ).
thf(2318,plain,
! [SV949: $i,SV897: $i,SV785: $i,SV586: $i,SV335: $i,SV53: $i] :
( ( ( c_Type_Otypings @ SV53 @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SV335 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV586 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV785 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV897 )
| ~ ( c_Type_Otypings @ ( c_Type_Oshift @ SV53 @ SV586 @ SV949 @ tc_Type_Otype ) @ SV785 @ SV897 )
| ~ ( c_Type_Otyping @ SV53 @ SV335 @ SV949 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2128]) ).
thf(2319,plain,
! [SV587: $i,SV336: $i,SV54: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV336 ) @ SV587 ) @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV54 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV587 @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV54 )
| ~ ( c_HOL_Oord__class_Oless @ SV336 @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV54 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2129]) ).
thf(2320,plain,
! [SV950: $i,SV901: $i,SV793: $i,SV598: $i,SV347: $i,SV66: $i] :
( ( ( SV66 = SV347 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV598 @ SV347 ) @ SV66 ) )
| ~ ( c_ListOrder_Ostep1 @ SV598 @ ( c_List_Olist_OCons @ SV347 @ SV793 @ SV901 ) @ ( c_List_Olist_OCons @ SV66 @ SV950 @ SV901 ) @ SV901 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2137]) ).
thf(2321,plain,
! [SV902: $i,SV794: $i,SV599: $i,SV348: $i,SV67: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV67 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ SV348 ) @ SV599 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ SV794 ) @ SV902 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ SV348 ) @ SV794 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ SV599 ) @ SV902 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2138]) ).
thf(2322,plain,
! [SV600: $i,SV68: $i,SV795: $i,SV349: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV349 ) @ SV795 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV68 ) @ SV600 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV68 ) @ SV349 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV600 ) @ SV795 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2139]) ).
thf(2323,plain,
! [SV351: $i,SV602: $i,SV796: $i,SV70: $i] :
( ( ( ~ ( c_Type_Otyping @ SV70 @ SV796 @ SV602 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV796 ) @ SV351 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV70 @ SV351 @ SV602 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2141]) ).
thf(2324,plain,
! [SV903: $i,SV797: $i,SV603: $i,SV352: $i,SV71: $i] :
( ( ( c_Type_Otypings @ ( c_Type_Oshift @ SV71 @ SV352 @ SV603 @ tc_Type_Otype ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ SV352 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV797 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV903 )
= $true )
| ( ( ~ ( c_Type_Otypings @ SV71 @ SV797 @ SV903 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2142]) ).
thf(2325,plain,
! [SV951: $i,SV904: $i,SV798: $i,SV606: $i,SV357: $i,SV77: $i] :
( ( ~ ( c_Type_Otyping @ SV77 @ SV357 @ SV606 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV77 @ SV798 @ SV606 @ tc_Type_Otype ) @ SV904 @ SV951 )
| ( c_Type_Otyping @ SV77 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV904 ) @ SV357 ) @ SV798 ) @ SV951 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2145]) ).
thf(2326,plain,
! [SV952: $i,SV905: $i,SV799: $i,SV608: $i,SV359: $i,SV79: $i] :
( ( ( SV79 = SV359 )
| ( c_ListOrder_Ostep1 @ SV608 @ SV79 @ SV359 @ SV799 )
| ~ ( c_ListOrder_Ostep1 @ SV608 @ ( c_List_Oappend @ SV79 @ ( c_List_Olist_OCons @ SV905 @ ( c_List_Olist_ONil @ SV799 ) @ SV799 ) @ SV799 ) @ ( c_List_Oappend @ SV359 @ ( c_List_Olist_OCons @ SV952 @ ( c_List_Olist_ONil @ SV799 ) @ SV799 ) @ SV799 ) @ SV799 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2146]) ).
thf(2327,plain,
! [SV363: $i,SV84: $i] :
( ( ( class_Int_Onumber__ring @ SV84 )
= $false )
| ( ( SV363
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV363 ) @ ( c_HOL_Ozero__class_Ozero @ SV84 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2147]) ).
thf(2328,plain,
! [SV370: $i,SV800: $i,SV91: $i,SV609: $i] :
( ( ( c_OrderedGroup_Omonoid__add @ SV609 @ SV91 @ SV800 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV91 @ SV370 ) @ SV609 )
= SV370 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2148]) ).
thf(2329,plain,
! [SV610: $i,SV801: $i,SV92: $i,SV371: $i] :
( ( ( c_OrderedGroup_Omonoid__add @ SV371 @ SV92 @ SV801 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV92 @ SV371 ) @ SV610 )
= SV610 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2149]) ).
thf(2330,plain,
! [SV372: $i,SV93: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV372 ) @ SV372 ) @ SV93 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV372 @ SV93 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2150]) ).
thf(2331,plain,
! [SV373: $i,SV94: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV373 @ SV94 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV373 ) @ SV373 ) @ SV94 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV94 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2151]) ).
thf(2332,plain,
! [SV611: $i,SV374: $i,SV802: $i,SV95: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV95 ) @ SV802 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV95 ) @ SV374 ) @ SV611 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV802 ) @ SV374 ) @ SV611 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2152]) ).
thf(2333,plain,
! [SV612: $i,SV96: $i,SV803: $i,SV375: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV375 ) @ SV803 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV96 ) @ SV375 ) @ SV612 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV96 ) @ SV803 ) @ SV612 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2153]) ).
thf(2334,plain,
! [SV377: $i,SV804: $i,SV614: $i,SV98: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV98 @ SV614 ) @ SV804 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV98 @ SV377 ) @ SV614 ) @ SV804 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2155]) ).
thf(2335,plain,
! [SV101: $i,SV380: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV380 @ ( c_HOL_Ozero__class_Ozero @ SV101 ) @ SV101 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ SV380 ) @ SV380 ) @ ( c_HOL_Ozero__class_Ozero @ SV101 ) @ SV101 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2156]) ).
thf(2336,plain,
! [SV381: $i,SV102: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SV381 ) @ SV381 ) @ ( c_HOL_Ozero__class_Ozero @ SV102 ) @ SV102 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV381 @ ( c_HOL_Ozero__class_Ozero @ SV102 ) @ SV102 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2157]) ).
thf(2337,plain,
! [SV382: $i,SV103: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV103 ) @ SV382 ) @ SV382 ) @ ( c_HOL_Ozero__class_Ozero @ SV103 ) @ SV103 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV382 @ ( c_HOL_Ozero__class_Ozero @ SV103 ) @ SV103 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2158]) ).
thf(2338,plain,
! [SV104: $i,SV383: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV383 @ ( c_HOL_Ozero__class_Ozero @ SV104 ) @ SV104 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV104 ) @ SV383 ) @ SV383 ) @ ( c_HOL_Ozero__class_Ozero @ SV104 ) @ SV104 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV104 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2159]) ).
thf(2339,plain,
! [SV805: $i,SV385: $i,SV618: $i,SV106: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV106 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV618 @ tc_Type_Otype ) @ SV385 @ SV805 )
= $false )
| ( ( c_Type_Otyping @ SV106 @ ( c_Lambda_OdB_OAbs @ SV385 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV618 ) @ SV805 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2161]) ).
thf(2340,plain,
! [SV622: $i,SV393: $i,SV117: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV393 ) @ SV622 ) @ SV117 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV622 @ SV117 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV393 @ SV117 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2168]) ).
thf(2341,plain,
! [SV953: $i,SV906: $i,SV807: $i,SV623: $i,SV394: $i,SV118: $i] :
( ( ( c_ListOrder_Ostep1 @ SV118 @ SV394 @ SV623 @ SV807 )
| ( SV623 = SV394 )
| ~ ( c_ListOrder_Ostep1 @ SV118 @ ( c_List_Olist_OCons @ SV906 @ SV394 @ SV807 ) @ ( c_List_Olist_OCons @ SV953 @ SV623 @ SV807 ) @ SV807 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2169]) ).
thf(2342,plain,
! [SV907: $i,SV808: $i,SV624: $i,SV395: $i,SV119: $i] :
( ( ( ( hAPP @ ( hAPP @ SV119 @ ( hAPP @ ( hAPP @ SV119 @ SV395 ) @ SV624 ) ) @ SV808 )
= ( hAPP @ ( hAPP @ SV119 @ SV395 ) @ ( hAPP @ ( hAPP @ SV119 @ SV624 ) @ SV808 ) ) )
= $true )
| ( ( ~ ( c_OrderedGroup_Osemigroup__add @ SV119 @ SV907 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2170]) ).
thf(2343,plain,
! [SV122: $i,SV626: $i,SV397: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV397 @ SV626 @ SV122 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV626 @ SV397 @ SV122 )
| ( SV626 = SV397 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2173]) ).
thf(2344,plain,
! [SV123: $i,SV627: $i,SV398: $i] :
( ( ( SV398 = SV627 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV627 @ SV398 @ SV123 )
| ( c_HOL_Oord__class_Oless @ SV398 @ SV627 @ SV123 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2174]) ).
thf(2345,plain,
! [SV125: $i,SV400: $i,SV628: $i] :
( ( ( SV628 = SV400 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV628 @ SV400 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV400 @ SV628 @ tc_nat )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV125 @ SV400 ) @ SV628 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2175]) ).
thf(2346,plain,
! [SV127: $i,SV629: $i,SV402: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV402 @ SV629 @ SV127 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV629 @ SV402 @ SV127 )
| ( SV629 = SV402 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV127 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2176]) ).
thf(2347,plain,
! [SV128: $i,SV630: $i,SV403: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV403 @ SV630 @ SV128 )
= $true )
| ( ( ( SV630 = SV403 )
| ( c_HOL_Oord__class_Oless @ SV630 @ SV403 @ SV128 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV128 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2177]) ).
thf(2348,plain,
! [SV129: $i,SV631: $i,SV404: $i] :
( ( ( SV404 = SV631 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV404 @ SV631 @ SV129 )
| ( c_HOL_Oord__class_Oless @ SV631 @ SV404 @ SV129 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2178]) ).
thf(2349,plain,
! [SV909: $i,SV810: $i,SV632: $i,SV405: $i,SV130: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV130 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SV405 ) @ SV632 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SV810 ) @ SV909 ) @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SV632 @ SV909 @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SV405 @ SV810 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2179]) ).
thf(2350,plain,
! [SV910: $i,SV811: $i,SV633: $i,SV406: $i,SV131: $i] :
( ( ( c_Type_Otyping @ SV131 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV406 ) @ SV633 ) @ SV811 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV131 @ SV633 @ SV910 )
| ~ ( c_Type_Otyping @ SV131 @ SV406 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV910 ) @ SV811 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2180]) ).
thf(2351,plain,
! [SV954: $i,SV911: $i,SV812: $i,SV634: $i,SV408: $i,SV134: $i] :
( ( ( SV134 = SV408 )
| ( SV634 = SV812 )
| ~ ( c_ListOrder_Ostep1 @ SV911 @ ( c_List_Oappend @ SV134 @ ( c_List_Olist_OCons @ SV634 @ ( c_List_Olist_ONil @ SV954 ) @ SV954 ) @ SV954 ) @ ( c_List_Oappend @ SV408 @ ( c_List_Olist_OCons @ SV812 @ ( c_List_Olist_ONil @ SV954 ) @ SV954 ) @ SV954 ) @ SV954 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2182]) ).
thf(2352,plain,
! [SV410: $i,SV813: $i,SV636: $i,SV137: $i] :
( ( ( ~ ( c_List_Olistsp @ SV137 @ SV636 @ SV813 ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV137 @ SV410 @ SV813 ) )
= $true )
| ( ( c_List_Olistsp @ SV137 @ ( c_List_Oappend @ SV410 @ SV636 @ SV813 ) @ SV813 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2183]) ).
thf(2353,plain,
! [SV913: $i,SV815: $i,SV638: $i,SV413: $i,SV141: $i] :
( ( ( ( hAPP @ ( c_Type_Oshift @ SV141 @ SV413 @ SV638 @ SV815 ) @ SV913 )
= ( hAPP @ SV141 @ SV913 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV913 @ SV413 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2185]) ).
thf(2354,plain,
! [SV955: $i,SV914: $i,SV816: $i,SV639: $i,SV414: $i,SV142: $i] :
( ( ! [SY2402: $i] :
( ( SV142
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV414 @ SV142 @ SV639 @ SV816 ) @ SV414 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV639 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV914 ) @ SV955 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV142 )
| ~ ( c_Type_Otypings @ SV639 @ SV955 @ SY2402 )
| ~ ( c_Type_Otyping @ SV639 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV914 ) @ SV955 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV816 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2186]) ).
thf(2355,plain,
! [SV817: $i,SV640: $i,SV416: $i,SV144: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV144 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV416 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ SV640 ) @ SV817 ) @ SV144 )
| ~ ( c_HOL_Oord__class_Oless @ SV416 @ SV817 @ SV144 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV144 ) @ SV640 @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2187]) ).
thf(2356,plain,
! [SV956: $i,SV915: $i,SV818: $i,SV641: $i,SV417: $i,SV145: $i] :
( ( ( c_List_Ofoldr @ SV145 @ ( c_List_Olist_OCons @ SV417 @ SV641 @ SV818 ) @ SV915 @ SV818 @ SV956 )
= ( hAPP @ ( hAPP @ SV145 @ SV417 ) @ ( c_List_Ofoldr @ SV145 @ SV641 @ SV915 @ SV818 @ SV956 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2188]) ).
thf(2357,plain,
! [SV916: $i,SV819: $i,SV642: $i,SV418: $i,SV146: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV146 @ ( c_Lambda_OdB_OdB__case @ SV418 @ SV642 @ SV819 @ ( c_Lambda_OdB_OAbs @ SV916 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV146 @ ( hAPP @ SV819 @ SV916 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2189]) ).
thf(2358,plain,
! [SV917: $i,SV820: $i,SV643: $i,SV419: $i,SV147: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV147 @ ( c_Lambda_OdB_OdB__case @ SV419 @ SV643 @ SV820 @ ( c_Lambda_OdB_OAbs @ SV917 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV147 @ ( hAPP @ SV820 @ SV917 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2190]) ).
thf(2359,plain,
! [SV821: $i,SV645: $i,SV421: $i,SV149: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV149 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV421 ) @ SV645 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV821 ) @ SV645 ) @ SV149 )
| ~ ( c_HOL_Oord__class_Oless @ SV421 @ SV821 @ SV149 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2191]) ).
thf(2360,plain,
! [SV822: $i,SV646: $i,SV422: $i,SV150: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV150 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV150 ) @ SV422 ) @ SV646 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV150 ) @ SV822 ) @ SV646 ) @ SV150 )
| ~ ( c_HOL_Oord__class_Oless @ SV422 @ SV822 @ SV150 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2192]) ).
thf(2361,plain,
! [SV823: $i,SV647: $i,SV423: $i,SV151: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV151 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV423 @ SV647 @ SV151 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV423 ) @ SV823 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV647 ) @ SV823 ) @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2193]) ).
thf(2362,plain,
! [SV824: $i,SV648: $i,SV424: $i,SV152: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV152 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV424 ) @ SV648 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV424 ) @ SV824 ) @ SV152 )
| ~ ( c_HOL_Oord__class_Oless @ SV648 @ SV824 @ SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2194]) ).
thf(2363,plain,
! [SV825: $i,SV649: $i,SV425: $i,SV153: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV153 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV425 ) @ SV649 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV425 ) @ SV825 ) @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SV649 @ SV825 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2195]) ).
thf(2364,plain,
! [SV826: $i,SV650: $i,SV426: $i,SV154: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV154 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV426 @ SV650 @ SV154 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SV826 ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SV826 ) @ SV650 ) @ SV154 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2196]) ).
thf(2365,plain,
! [SV651: $i,SV156: $i,SV427: $i,SV827: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV827 ) @ SV427 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV156 @ SV827 @ SV651 ) )
= $true )
| ( ( c_Type_Otyping @ SV156 @ SV427 @ SV651 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2198]) ).
thf(2366,plain,
! [SV957: $i,SV918: $i,SV828: $i,SV652: $i,SV428: $i,SV157: $i] :
( ( ( c_ListOrder_Ostep1 @ SV157 @ SV428 @ SV652 @ SV828 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV157 @ SV918 ) @ SV957 ) )
| ~ ( c_ListOrder_Ostep1 @ SV157 @ ( c_List_Olist_OCons @ SV918 @ SV428 @ SV828 ) @ ( c_List_Olist_OCons @ SV957 @ SV652 @ SV828 ) @ SV828 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2199]) ).
thf(2367,plain,
! [SV919: $i,SV829: $i,SV653: $i,SV429: $i,SV158: $i] :
( ( ( c_ListOrder_Ostep1 @ SV158 @ ( c_List_Olist_OCons @ SV429 @ SV653 @ SV829 ) @ ( c_List_Olist_OCons @ SV429 @ SV919 @ SV829 ) @ SV829 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV158 @ SV653 @ SV919 @ SV829 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2200]) ).
thf(2368,plain,
! [SV920: $i,SV834: $i,SV658: $i,SV434: $i,SV165: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV165 @ SV434 @ SV658 @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV834 ) @ SV434 ) @ SV920 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV165 @ SV834 @ SV920 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2201]) ).
thf(2369,plain,
! [SV166: $i,SV659: $i,SV435: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV435 @ SV659 @ SV166 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV659 @ SV435 @ SV166 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV166 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2202]) ).
thf(2370,plain,
! [SV921: $i,SV835: $i,SV660: $i,SV436: $i,SV167: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV167 @ SV436 ) @ SV660 ) @ SV835 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV167 @ SV436 ) @ SV921 ) @ SV835 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV167 @ SV660 ) @ SV921 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2203]) ).
thf(2371,plain,
! [SV922: $i,SV836: $i,SV661: $i,SV437: $i,SV168: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV168 @ SV437 ) @ SV661 ) @ SV836 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV168 @ SV922 ) @ SV836 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV168 @ SV437 ) @ SV661 ) @ SV922 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2204]) ).
thf(2372,plain,
! [SV169: $i,SV662: $i,SV438: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV438 @ SV662 @ SV169 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV662 @ SV438 @ SV169 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2205]) ).
thf(2373,plain,
! [SV170: $i,SV663: $i,SV439: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV439 @ SV663 @ SV170 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV663 @ SV439 @ SV170 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2206]) ).
thf(2374,plain,
! [SV171: $i,SV664: $i,SV440: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV440 @ SV664 @ SV171 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV664 @ SV440 @ SV171 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV171 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2207]) ).
thf(2375,plain,
! [SV923: $i,SV837: $i,SV665: $i,SV442: $i,SV173: $i] :
( ( ( ( c_List_Ofoldl @ SV173 @ ( hAPP @ ( hAPP @ SV173 @ SV442 ) @ SV665 ) @ SV837 @ SV923 @ SV923 )
= ( hAPP @ ( hAPP @ SV173 @ SV442 ) @ ( c_List_Ofoldl @ SV173 @ SV665 @ SV837 @ SV923 @ SV923 ) ) )
= $true )
| ( ( ~ ( c_OrderedGroup_Osemigroup__add @ SV173 @ SV923 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2209]) ).
thf(2376,plain,
! [SV667: $i,SV445: $i,SV839: $i,SV176: $i] :
( ( ( c_Type_Otyping @ SV176 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV839 ) @ SV445 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV667 )
= $false )
| ( ( c_Type_Otypings @ SV176 @ SV445 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV667 @ SV176 @ SV839 @ SV445 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2210]) ).
thf(2377,plain,
! [SV924: $i,SV840: $i,SV668: $i,SV446: $i,SV177: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV177 @ ( c_Lambda_OdB_OdB__case @ SV446 @ SV668 @ SV840 @ ( c_Lambda_OdB_OVar @ SV924 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV177 @ ( hAPP @ SV446 @ SV924 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2211]) ).
thf(2378,plain,
! [SV925: $i,SV841: $i,SV669: $i,SV447: $i,SV178: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV178 @ ( c_Lambda_OdB_OdB__case @ SV447 @ SV669 @ SV841 @ ( c_Lambda_OdB_OVar @ SV925 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV178 @ ( hAPP @ SV447 @ SV925 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2212]) ).
thf(2379,plain,
! [SV958: $i,SV926: $i,SV842: $i,SV670: $i,SV449: $i,SV180: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV180 @ ( c_Lambda_OdB_OdB__case @ SV449 @ SV670 @ SV842 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV926 ) @ SV958 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV180 @ ( hAPP @ ( hAPP @ SV670 @ SV926 ) @ SV958 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2213]) ).
thf(2380,plain,
! [SV959: $i,SV927: $i,SV843: $i,SV671: $i,SV450: $i,SV181: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV181 @ ( c_Lambda_OdB_OdB__case @ SV450 @ SV671 @ SV843 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV927 ) @ SV959 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV181 @ ( hAPP @ ( hAPP @ SV671 @ SV927 ) @ SV959 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2214]) ).
thf(2381,plain,
! [SV928: $i,SV844: $i,SV675: $i,SV456: $i,SV187: $i] :
( ( ( SV187 = SV456 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV675 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV844 ) @ SV928 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV456 )
| ~ ( c_Type_Otyping @ SV675 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV844 ) @ SV928 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2218]) ).
thf(2382,plain,
! [SV680: $i,SV194: $i,SV463: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV463 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV194 ) @ SV463 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV680 @ 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 @ SV194 ) ) @ SV463 ) @ SV680 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2223]) ).
thf(2383,plain,
! [SV847: $i,SV682: $i,SV465: $i,SV198: $i] :
( ( ( class_OrderedGroup_Osemigroup__add @ SV198 )
= $false )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ SV465 ) @ SV682 ) @ SV847 @ SV198 @ SV198 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ SV465 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ SV682 @ SV847 @ SV198 @ SV198 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2226]) ).
thf(2384,plain,
! [SV685: $i,SV468: $i,SV849: $i,SV202: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV202 ) @ SV849 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV202 ) @ SV468 ) @ SV685 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV849 ) @ SV468 ) @ SV685 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2228]) ).
thf(2385,plain,
! [SV687: $i,SV850: $i,SV470: $i,SV204: $i] :
( ( ( c_Type_Otyping @ SV204 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV470 ) @ SV850 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV687 )
= $false )
| ( ( c_Type_Otyping @ SV204 @ ( c_Lambda_OdB_OVar @ SV470 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV687 @ SV204 @ SV470 @ SV850 ) @ SV687 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2230]) ).
thf(2386,plain,
! [SV960: $i,SV930: $i,SV851: $i,SV689: $i,SV472: $i,SV206: $i] :
( ( ( c_Lambda_OdB_OdB__case @ SV206 @ SV472 @ SV689 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV851 ) @ SV930 ) @ SV960 )
= ( hAPP @ ( hAPP @ SV472 @ SV851 ) @ SV930 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2232]) ).
thf(2387,plain,
! [SV931: $i,SV852: $i,SV690: $i,SV473: $i,SV207: $i] :
( ( ( ( hAPP @ ( hAPP @ SV207 @ SV473 ) @ ( c_List_Ofoldl @ SV207 @ SV690 @ SV852 @ SV931 @ SV931 ) )
= ( c_List_Ofoldl @ SV207 @ SV473 @ SV852 @ SV931 @ SV931 ) )
= $true )
| ( ( ~ ( c_OrderedGroup_Omonoid__add @ SV690 @ SV207 @ SV931 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2233]) ).
thf(2388,plain,
! [SV961: $i,SV933: $i,SV854: $i,SV692: $i,SV476: $i,SV212: $i] :
( ( ( c_List_Ofoldl @ SV212 @ SV476 @ ( c_List_Olist_OCons @ SV692 @ SV854 @ SV933 ) @ SV961 @ SV933 )
= ( c_List_Ofoldl @ SV212 @ ( hAPP @ ( hAPP @ SV212 @ SV476 ) @ SV692 ) @ SV854 @ SV961 @ SV933 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2236]) ).
thf(2389,plain,
! [SV962: $i,SV934: $i,SV855: $i,SV693: $i,SV478: $i,SV215: $i] :
( ( ( c_Lambda_OdB_OdB__rec @ SV215 @ SV478 @ SV693 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV855 ) @ SV934 ) @ SV962 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV478 @ SV855 ) @ SV934 ) @ ( c_Lambda_OdB_OdB__rec @ SV215 @ SV478 @ SV693 @ SV855 @ SV962 ) ) @ ( c_Lambda_OdB_OdB__rec @ SV215 @ SV478 @ SV693 @ SV934 @ SV962 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2237]) ).
thf(2390,plain,
! [SV963: $i,SV935: $i,SV856: $i,SV694: $i,SV479: $i,SV217: $i] :
( ( ! [SY2403: $i] :
( ( c_Type_Otypings @ SV217 @ SV479 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV694 @ SV856 @ SV217 @ SV479 ) )
| ~ ( c_Type_Otyping @ SV217 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV935 ) @ SV963 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV856 )
| ~ ( c_Type_Otypings @ SV217 @ SV963 @ SY2403 )
| ~ ( c_Type_Otyping @ SV217 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV935 ) @ SV963 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV479 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV694 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2238]) ).
thf(2391,plain,
! [SV964: $i,SV936: $i,SV859: $i,SV701: $i,SV487: $i,SV227: $i] :
( ( ( c_List_Ofoldl @ SV227 @ SV487 @ ( c_List_Oappend @ SV701 @ SV859 @ SV936 ) @ SV964 @ SV936 )
= ( c_List_Ofoldl @ SV227 @ ( c_List_Ofoldl @ SV227 @ SV487 @ SV701 @ SV964 @ SV936 ) @ SV859 @ SV964 @ SV936 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2242]) ).
thf(2392,plain,
! [SV860: $i,SV704: $i,SV493: $i,SV233: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV233 ) @ SV493 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV704 ) @ SV860 ) )
= $false )
| ( ( SV233 = SV704 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2244]) ).
thf(2393,plain,
! [SV861: $i,SV705: $i,SV494: $i,SV234: $i] :
( ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV234 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV494 ) @ SV705 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV494 ) @ SV861 ) )
| ( SV705 = SV861 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2245]) ).
thf(2394,plain,
! [SV862: $i,SV707: $i,SV496: $i,SV236: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV236 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV236 ) @ SV496 ) @ SV707 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV236 ) @ SV862 ) @ SV707 ) )
| ( SV496 = SV862 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2247]) ).
thf(2395,plain,
! [SV863: $i,SV708: $i,SV497: $i,SV237: $i] :
( ( ( ( c_List_Oappend @ SV237 @ SV497 @ SV708 )
= ( c_List_Oappend @ SV237 @ SV863 @ SV708 ) )
= $false )
| ( ( SV497 = SV863 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2248]) ).
thf(2396,plain,
! [SV864: $i,SV709: $i,SV498: $i,SV238: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV238 ) @ SV498 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV709 ) @ SV864 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV238 = SV709 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2249]) ).
thf(2397,plain,
! [SV865: $i,SV710: $i,SV499: $i,SV239: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV239 ) @ SV499 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV710 ) @ SV865 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV499 = SV865 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2250]) ).
thf(2398,plain,
! [SV937: $i,SV866: $i,SV711: $i,SV500: $i,SV240: $i] :
( ( ( ( c_List_Olist_OCons @ SV240 @ SV500 @ SV711 )
!= ( c_List_Olist_OCons @ SV866 @ SV937 @ SV711 ) )
= $true )
| ( ( SV240 = SV866 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2251]) ).
thf(2399,plain,
! [SV867: $i,SV712: $i,SV501: $i,SV241: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV241 ) @ SV501 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV712 ) @ SV867 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV241 = SV712 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2252]) ).
thf(2400,plain,
! [SV868: $i,SV713: $i,SV502: $i,SV242: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV242 ) @ SV502 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV713 @ SV868 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( SV242
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV713 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV242 @ SV502 @ SV713 @ SV868 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV868
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2253]) ).
thf(2401,plain,
! [SV965: $i,SV938: $i,SV869: $i,SV714: $i,SV503: $i,SV243: $i] :
( ( ! [SY2404: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV243 ) @ SV503 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV714 ) @ SV869 ) @ SV938 ) ) )
| ~ ( c_Type_Otyping @ SV965 @ SV869 @ SV243 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV869 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV965 @ SV938 @ SV243 @ tc_Type_Otype ) @ SV714 @ SY2404 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV714 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2254]) ).
thf(2402,plain,
! [SV870: $i,SV715: $i,SV504: $i,SV244: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV244 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV244 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV244 ) @ SV504 ) @ SV715 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV244 ) @ SV504 ) @ SV870 ) )
| ( SV715 = SV870 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2255]) ).
thf(2403,plain,
! [SV871: $i,SV716: $i,SV505: $i,SV245: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV245 ) @ SV505 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV716 ) @ SV871 ) )
= $false )
| ( ( SV505 = SV871 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2256]) ).
thf(2404,plain,
! [SV939: $i,SV873: $i,SV720: $i,SV509: $i,SV249: $i] :
( ( ( ( c_List_Oappend @ SV249 @ ( c_List_Olist_OCons @ SV509 @ ( c_List_Olist_ONil @ SV720 ) @ SV720 ) @ SV720 )
!= ( c_List_Oappend @ SV873 @ ( c_List_Olist_OCons @ SV939 @ ( c_List_Olist_ONil @ SV720 ) @ SV720 ) @ SV720 ) )
= $true )
| ( ( SV249 = SV873 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2259]) ).
thf(2405,plain,
! [SV875: $i,SV728: $i,SV517: $i,SV257: $i] :
( ( ( ( c_List_Omap @ SV257 @ SV517 @ SV728 @ SV875 )
= ( c_List_Olist_ONil @ SV875 ) )
= $false )
| ( ( SV517
= ( c_List_Olist_ONil @ SV728 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2265]) ).
thf(2406,plain,
! [SV518: $i,SV258: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SV518 ) @ SV518 )
= ( c_HOL_Ozero__class_Ozero @ SV258 ) )
= $false )
| ( ( SV518
= ( c_HOL_Ozero__class_Ozero @ SV258 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV258 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2266]) ).
thf(2407,plain,
! [SV876: $i,SV733: $i,SV523: $i,SV263: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV263 ) @ SV523 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV733 ) @ SV876 ) )
= $false )
| ( ( SV263 = SV733 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2270]) ).
thf(2408,plain,
! [SV877: $i,SV736: $i,SV526: $i,SV266: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV266 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV266 ) @ SV526 ) @ SV736 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV266 ) @ SV526 ) @ SV877 ) )
| ( SV736 = SV877 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2272]) ).
thf(2409,plain,
! [SV966: $i,SV940: $i,SV878: $i,SV738: $i,SV528: $i,SV268: $i] :
( ( ! [SY2405: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV268 ) @ SV528 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV738 ) @ SV878 ) @ SV940 ) ) )
| ~ ( c_Type_Otyping @ SV966 @ SV878 @ SV528 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV878 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV966 @ SV940 @ SV528 @ tc_Type_Otype ) @ SV738 @ SY2405 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV738 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2274]) ).
thf(2410,plain,
! [SV879: $i,SV739: $i,SV529: $i,SV269: $i] :
( ( ( ( c_List_Oappend @ SV269 @ SV529 @ SV739 )
= ( c_List_Oappend @ SV879 @ SV529 @ SV739 ) )
= $false )
| ( ( SV269 = SV879 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2275]) ).
thf(2411,plain,
! [SV880: $i,SV740: $i,SV531: $i,SV271: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV271 ) @ SV531 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV740 ) @ SV880 ) )
= $false )
| ( ( SV531 = SV880 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2276]) ).
thf(2412,plain,
! [SV881: $i,SV742: $i,SV534: $i,SV274: $i] :
( ( ( ( c_List_Olist_ONil @ SV274 )
= ( c_List_Omap @ SV534 @ SV742 @ SV881 @ SV274 ) )
= $false )
| ( ( SV742
= ( c_List_Olist_ONil @ SV881 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2277]) ).
thf(2413,plain,
! [SV941: $i,SV882: $i,SV743: $i,SV535: $i,SV275: $i] :
( ( ( ( c_List_Oappend @ SV275 @ ( c_List_Olist_OCons @ SV535 @ ( c_List_Olist_ONil @ SV743 ) @ SV743 ) @ SV743 )
!= ( c_List_Oappend @ SV882 @ ( c_List_Olist_OCons @ SV941 @ ( c_List_Olist_ONil @ SV743 ) @ SV743 ) @ SV743 ) )
= $true )
| ( ( SV535 = SV941 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2278]) ).
thf(2414,plain,
! [SV883: $i,SV747: $i,SV540: $i,SV280: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV280 ) @ SV540 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV747 ) @ SV883 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV540 = SV883 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2282]) ).
thf(2415,plain,
! [SV942: $i,SV884: $i,SV750: $i,SV543: $i,SV283: $i] :
( ( ( ( c_List_Olist_OCons @ SV283 @ SV543 @ SV750 )
!= ( c_List_Olist_OCons @ SV884 @ SV942 @ SV750 ) )
= $true )
| ( ( SV543 = SV942 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2283]) ).
thf(2416,plain,
! [SV753: $i,SV546: $i,SV286: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV286 ) )
= $true )
| ( ( ( SV546
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV286 ) @ SV546 ) @ SV753 ) )
| ( SV753
= ( c_HOL_Ozero__class_Ozero @ SV286 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV286 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2286]) ).
thf(2417,plain,
! [SV943: $i,SV885: $i,SV754: $i,SV548: $i,SV288: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV288 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV548 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV754 ) @ SV885 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV754 ) @ SV943 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV548 ) @ SV885 )
= SV943 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2287]) ).
thf(2418,plain,
! [SV944: $i,SV886: $i,SV759: $i,SV553: $i,SV295: $i,SV7: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV7 @ SV295 ) @ SV553 ) )
= $true )
| ( ( ( SV295 = SV553 )
| ~ ( c_ListOrder_Ostep1 @ SV7 @ ( c_List_Oappend @ SV759 @ ( c_List_Olist_OCons @ SV295 @ ( c_List_Olist_ONil @ SV886 ) @ SV886 ) @ SV886 ) @ ( c_List_Oappend @ SV944 @ ( c_List_Olist_OCons @ SV553 @ ( c_List_Olist_ONil @ SV886 ) @ SV886 ) @ SV886 ) @ SV886 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2294]) ).
thf(2419,plain,
! [SV559: $i,SV762: $i,SV888: $i,SV306: $i,SV19: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV19 @ SV306 ) @ SV888 ) @ SV762 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV19 @ SV306 ) @ SV559 ) @ SV888 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV19 @ SV306 ) @ SV559 ) @ SV762 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2297]) ).
thf(2420,plain,
! [SV889: $i,SV763: $i,SV562: $i,SV310: $i,SV23: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV23 @ SV310 ) @ SV562 ) )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV23 @ ( c_List_Olist_OCons @ SV310 @ SV763 @ SV889 ) @ ( c_List_Olist_OCons @ SV562 @ SV763 @ SV889 ) @ SV889 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2298]) ).
thf(2421,plain,
! [SV946: $i,SV890: $i,SV764: $i,SV563: $i,SV311: $i,SV24: $i] :
( ( ( SV24 = SV311 )
= $true )
| ( ( ( SV563 = SV764 )
| ~ ( c_ListOrder_Ostep1 @ SV890 @ ( c_List_Olist_OCons @ SV311 @ SV764 @ SV946 ) @ ( c_List_Olist_OCons @ SV24 @ SV563 @ SV946 ) @ SV946 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2299]) ).
thf(2422,plain,
! [SV316: $i,SV768: $i,SV892: $i,SV567: $i,SV30: $i] :
( ( ( c_ListOrder_Ostep1 @ SV30 @ SV567 @ SV892 @ SV768 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV30 @ ( c_List_Oappend @ SV316 @ SV567 @ SV768 ) @ ( c_List_Oappend @ SV316 @ SV892 @ SV768 ) @ SV768 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2302]) ).
thf(2423,plain,
! [SV893: $i,SV769: $i,SV568: $i,SV317: $i,SV31: $i] :
( ( ( c_ListOrder_Ostep1 @ SV31 @ SV317 @ SV568 @ SV769 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV31 @ ( c_List_Oappend @ SV317 @ SV893 @ SV769 ) @ ( c_List_Oappend @ SV568 @ SV893 @ SV769 ) @ SV769 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2303]) ).
thf(2424,plain,
! [SV770: $i,SV319: $i,SV894: $i,SV570: $i,SV34: $i] :
( ( ( ~ ( c_Type_Otypings @ SV34 @ SV570 @ SV894 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV34 @ SV319 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV894 @ SV770 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true )
| ( ( c_Type_Otyping @ SV34 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV319 @ SV570 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV770 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2304]) ).
thf(2425,plain,
! [SV771: $i,SV35: $i,SV571: $i,SV320: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV320 @ SV571 @ SV35 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV771 @ SV571 @ SV35 )
| ~ ( c_HOL_Oord__class_Oless @ SV320 @ SV771 @ SV35 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2305]) ).
thf(2426,plain,
! [SV772: $i,SV36: $i,SV572: $i,SV321: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV321 @ SV572 @ SV36 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV321 @ SV772 @ SV36 )
| ~ ( c_HOL_Oord__class_Oless @ SV772 @ SV572 @ SV36 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2306]) ).
thf(2427,plain,
! [SV948: $i,SV896: $i,SV784: $i,SV585: $i,SV334: $i,SV51: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV51 @ SV334 ) @ SV585 ) )
= $true )
| ( ( ( c_ListOrder_Ostep1 @ SV51 @ SV784 @ SV896 @ SV948 )
| ~ ( c_ListOrder_Ostep1 @ SV51 @ ( c_List_Oappend @ SV784 @ ( c_List_Olist_OCons @ SV334 @ ( c_List_Olist_ONil @ SV948 ) @ SV948 ) @ SV948 ) @ ( c_List_Oappend @ SV896 @ ( c_List_Olist_OCons @ SV585 @ ( c_List_Olist_ONil @ SV948 ) @ SV948 ) @ SV948 ) @ SV948 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2317]) ).
thf(2428,plain,
! [SV949: $i,SV897: $i,SV785: $i,SV586: $i,SV335: $i,SV53: $i] :
( ( ( c_Type_Otypings @ SV53 @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SV335 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV586 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV785 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV897 )
= $true )
| ( ( ~ ( c_Type_Otypings @ ( c_Type_Oshift @ SV53 @ SV586 @ SV949 @ tc_Type_Otype ) @ SV785 @ SV897 )
| ~ ( c_Type_Otyping @ SV53 @ SV335 @ SV949 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2318]) ).
thf(2429,plain,
! [SV336: $i,SV54: $i,SV587: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV587 @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV54 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV336 @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV54 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV336 ) @ SV587 ) @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV54 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2319]) ).
thf(2430,plain,
! [SV950: $i,SV901: $i,SV793: $i,SV598: $i,SV347: $i,SV66: $i] :
( ( ( SV66 = SV347 )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV598 @ SV347 ) @ SV66 ) )
| ~ ( c_ListOrder_Ostep1 @ SV598 @ ( c_List_Olist_OCons @ SV347 @ SV793 @ SV901 ) @ ( c_List_Olist_OCons @ SV66 @ SV950 @ SV901 ) @ SV901 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2320]) ).
thf(2431,plain,
! [SV902: $i,SV794: $i,SV599: $i,SV348: $i,SV67: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV67 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ SV348 ) @ SV599 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ SV794 ) @ SV902 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ SV348 ) @ SV794 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ SV599 ) @ SV902 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2321]) ).
thf(2432,plain,
! [SV600: $i,SV68: $i,SV795: $i,SV349: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV349 ) @ SV795 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV68 ) @ SV600 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV68 ) @ SV349 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV600 ) @ SV795 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2322]) ).
thf(2433,plain,
! [SV351: $i,SV602: $i,SV796: $i,SV70: $i] :
( ( ( c_Type_Otyping @ SV70 @ SV796 @ SV602 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV796 ) @ SV351 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV70 @ SV351 @ SV602 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2323]) ).
thf(2434,plain,
! [SV603: $i,SV352: $i,SV903: $i,SV797: $i,SV71: $i] :
( ( ( c_Type_Otypings @ SV71 @ SV797 @ SV903 )
= $false )
| ( ( c_Type_Otypings @ ( c_Type_Oshift @ SV71 @ SV352 @ SV603 @ tc_Type_Otype ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ SV352 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV797 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV903 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2324]) ).
thf(2435,plain,
! [SV951: $i,SV904: $i,SV798: $i,SV606: $i,SV357: $i,SV77: $i] :
( ( ( ~ ( c_Type_Otyping @ SV77 @ SV357 @ SV606 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV77 @ SV798 @ SV606 @ tc_Type_Otype ) @ SV904 @ SV951 )
| ( c_Type_Otyping @ SV77 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV904 ) @ SV357 ) @ SV798 ) @ SV951 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2325]) ).
thf(2436,plain,
! [SV952: $i,SV905: $i,SV799: $i,SV608: $i,SV359: $i,SV79: $i] :
( ( ( SV79 = SV359 )
= $true )
| ( ( ( c_ListOrder_Ostep1 @ SV608 @ SV79 @ SV359 @ SV799 )
| ~ ( c_ListOrder_Ostep1 @ SV608 @ ( c_List_Oappend @ SV79 @ ( c_List_Olist_OCons @ SV905 @ ( c_List_Olist_ONil @ SV799 ) @ SV799 ) @ SV799 ) @ ( c_List_Oappend @ SV359 @ ( c_List_Olist_OCons @ SV952 @ ( c_List_Olist_ONil @ SV799 ) @ SV799 ) @ SV799 ) @ SV799 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2326]) ).
thf(2437,plain,
! [SV393: $i,SV622: $i,SV117: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV622 @ SV117 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV393 @ SV117 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV393 ) @ SV622 ) @ SV117 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2340]) ).
thf(2438,plain,
! [SV953: $i,SV906: $i,SV807: $i,SV623: $i,SV394: $i,SV118: $i] :
( ( ( c_ListOrder_Ostep1 @ SV118 @ SV394 @ SV623 @ SV807 )
= $true )
| ( ( ( SV623 = SV394 )
| ~ ( c_ListOrder_Ostep1 @ SV118 @ ( c_List_Olist_OCons @ SV906 @ SV394 @ SV807 ) @ ( c_List_Olist_OCons @ SV953 @ SV623 @ SV807 ) @ SV807 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2341]) ).
thf(2439,plain,
! [SV808: $i,SV624: $i,SV395: $i,SV907: $i,SV119: $i] :
( ( ( c_OrderedGroup_Osemigroup__add @ SV119 @ SV907 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV119 @ ( hAPP @ ( hAPP @ SV119 @ SV395 ) @ SV624 ) ) @ SV808 )
= ( hAPP @ ( hAPP @ SV119 @ SV395 ) @ ( hAPP @ ( hAPP @ SV119 @ SV624 ) @ SV808 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2342]) ).
thf(2440,plain,
! [SV122: $i,SV397: $i,SV626: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV626 @ SV397 @ SV122 )
= $true )
| ( ( SV626 = SV397 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV397 @ SV626 @ SV122 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2343]) ).
thf(2441,plain,
! [SV123: $i,SV398: $i,SV627: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV627 @ SV398 @ SV123 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV398 @ SV627 @ SV123 )
= $true )
| ( ( SV398 = SV627 )
= $true )
| ( ( class_Orderings_Olinorder @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2344]) ).
thf(2442,plain,
! [SV127: $i,SV402: $i,SV629: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV629 @ SV402 @ SV127 )
= $true )
| ( ( SV629 = SV402 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV402 @ SV629 @ SV127 )
= $true )
| ( ( class_Orderings_Olinorder @ SV127 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2346]) ).
thf(2443,plain,
! [SV128: $i,SV403: $i,SV630: $i] :
( ( ( SV630 = SV403 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV630 @ SV403 @ SV128 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV403 @ SV630 @ SV128 )
= $true )
| ( ( class_Orderings_Olinorder @ SV128 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2347]) ).
thf(2444,plain,
! [SV129: $i,SV631: $i,SV404: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV404 @ SV631 @ SV129 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV631 @ SV404 @ SV129 )
= $true )
| ( ( SV404 = SV631 )
= $true )
| ( ( class_Orderings_Olinorder @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2348]) ).
thf(2445,plain,
! [SV909: $i,SV810: $i,SV632: $i,SV405: $i,SV130: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV130 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SV405 ) @ SV632 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SV810 ) @ SV909 ) @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SV632 @ SV909 @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SV405 @ SV810 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2349]) ).
thf(2446,plain,
! [SV811: $i,SV406: $i,SV910: $i,SV633: $i,SV131: $i] :
( ( ( ~ ( c_Type_Otyping @ SV131 @ SV633 @ SV910 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV131 @ SV406 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV910 ) @ SV811 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV131 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV406 ) @ SV633 ) @ SV811 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2350]) ).
thf(2447,plain,
! [SV954: $i,SV911: $i,SV812: $i,SV634: $i,SV408: $i,SV134: $i] :
( ( ( SV134 = SV408 )
= $true )
| ( ( ( SV634 = SV812 )
| ~ ( c_ListOrder_Ostep1 @ SV911 @ ( c_List_Oappend @ SV134 @ ( c_List_Olist_OCons @ SV634 @ ( c_List_Olist_ONil @ SV954 ) @ SV954 ) @ SV954 ) @ ( c_List_Oappend @ SV408 @ ( c_List_Olist_OCons @ SV812 @ ( c_List_Olist_ONil @ SV954 ) @ SV954 ) @ SV954 ) @ SV954 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2351]) ).
thf(2448,plain,
! [SV410: $i,SV813: $i,SV636: $i,SV137: $i] :
( ( ( c_List_Olistsp @ SV137 @ SV636 @ SV813 )
= $false )
| ( ( ~ ( c_List_Olistsp @ SV137 @ SV410 @ SV813 ) )
= $true )
| ( ( c_List_Olistsp @ SV137 @ ( c_List_Oappend @ SV410 @ SV636 @ SV813 ) @ SV813 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2352]) ).
thf(2449,plain,
! [SV815: $i,SV638: $i,SV141: $i,SV413: $i,SV913: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV913 @ SV413 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( c_Type_Oshift @ SV141 @ SV413 @ SV638 @ SV815 ) @ SV913 )
= ( hAPP @ SV141 @ SV913 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2353]) ).
thf(2450,plain,
! [SV967: $i,SV955: $i,SV914: $i,SV816: $i,SV639: $i,SV414: $i,SV142: $i] :
( ( ( SV142
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV414 @ SV142 @ SV639 @ SV816 ) @ SV414 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV639 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV914 ) @ SV955 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV142 )
| ~ ( c_Type_Otypings @ SV639 @ SV955 @ SV967 )
| ~ ( c_Type_Otyping @ SV639 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV914 ) @ SV955 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV816 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV414 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2354]) ).
thf(2451,plain,
! [SV817: $i,SV640: $i,SV144: $i,SV416: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV416 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ SV640 ) @ SV817 ) @ SV144 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV416 @ SV817 @ SV144 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV144 ) @ SV640 @ SV144 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV144 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2355]) ).
thf(2452,plain,
! [SV916: $i,SV819: $i,SV642: $i,SV418: $i,SV146: $i] :
( ( ( hBOOL @ ( hAPP @ SV146 @ ( c_Lambda_OdB_OdB__case @ SV418 @ SV642 @ SV819 @ ( c_Lambda_OdB_OAbs @ SV916 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV146 @ ( hAPP @ SV819 @ SV916 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2357]) ).
thf(2453,plain,
! [SV917: $i,SV820: $i,SV643: $i,SV419: $i,SV147: $i] :
( ( ( hBOOL @ ( hAPP @ SV147 @ ( c_Lambda_OdB_OdB__case @ SV419 @ SV643 @ SV820 @ ( c_Lambda_OdB_OAbs @ SV917 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV147 @ ( hAPP @ SV820 @ SV917 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2358]) ).
thf(2454,plain,
! [SV821: $i,SV645: $i,SV421: $i,SV149: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV421 ) @ SV645 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV821 ) @ SV645 ) @ SV149 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV421 @ SV821 @ SV149 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV149 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2359]) ).
thf(2455,plain,
! [SV822: $i,SV646: $i,SV422: $i,SV150: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV150 ) @ SV422 ) @ SV646 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV150 ) @ SV822 ) @ SV646 ) @ SV150 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV422 @ SV822 @ SV150 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV150 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2360]) ).
thf(2456,plain,
! [SV823: $i,SV151: $i,SV647: $i,SV423: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV423 @ SV647 @ SV151 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV423 ) @ SV823 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV647 ) @ SV823 ) @ SV151 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2361]) ).
thf(2457,plain,
! [SV824: $i,SV648: $i,SV424: $i,SV152: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV424 ) @ SV648 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV424 ) @ SV824 ) @ SV152 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV648 @ SV824 @ SV152 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV152 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2362]) ).
thf(2458,plain,
! [SV825: $i,SV649: $i,SV425: $i,SV153: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV425 ) @ SV649 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV425 ) @ SV825 ) @ SV153 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV649 @ SV825 @ SV153 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2363]) ).
thf(2459,plain,
! [SV826: $i,SV154: $i,SV650: $i,SV426: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV426 @ SV650 @ SV154 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SV826 ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SV826 ) @ SV650 ) @ SV154 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2364]) ).
thf(2460,plain,
! [SV651: $i,SV156: $i,SV427: $i,SV827: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV827 ) @ SV427 ) )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV156 @ SV827 @ SV651 ) )
= $true )
| ( ( c_Type_Otyping @ SV156 @ SV427 @ SV651 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2365]) ).
thf(2461,plain,
! [SV957: $i,SV918: $i,SV828: $i,SV652: $i,SV428: $i,SV157: $i] :
( ( ( c_ListOrder_Ostep1 @ SV157 @ SV428 @ SV652 @ SV828 )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV157 @ SV918 ) @ SV957 ) )
| ~ ( c_ListOrder_Ostep1 @ SV157 @ ( c_List_Olist_OCons @ SV918 @ SV428 @ SV828 ) @ ( c_List_Olist_OCons @ SV957 @ SV652 @ SV828 ) @ SV828 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2366]) ).
thf(2462,plain,
! [SV429: $i,SV829: $i,SV919: $i,SV653: $i,SV158: $i] :
( ( ( c_ListOrder_Ostep1 @ SV158 @ SV653 @ SV919 @ SV829 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV158 @ ( c_List_Olist_OCons @ SV429 @ SV653 @ SV829 ) @ ( c_List_Olist_OCons @ SV429 @ SV919 @ SV829 ) @ SV829 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2367]) ).
thf(2463,plain,
! [SV658: $i,SV434: $i,SV920: $i,SV834: $i,SV165: $i] :
( ( ( c_Type_Otyping @ SV165 @ SV834 @ SV920 )
= $false )
| ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV165 @ SV434 @ SV658 @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV834 ) @ SV434 ) @ SV920 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2368]) ).
thf(2464,plain,
! [SV166: $i,SV659: $i,SV435: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV435 @ SV659 @ SV166 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV659 @ SV435 @ SV166 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2369]) ).
thf(2465,plain,
! [SV660: $i,SV835: $i,SV921: $i,SV436: $i,SV167: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV167 @ SV436 ) @ SV921 ) @ SV835 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV167 @ SV660 ) @ SV921 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV167 @ SV436 ) @ SV660 ) @ SV835 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2370]) ).
thf(2466,plain,
! [SV661: $i,SV437: $i,SV836: $i,SV922: $i,SV168: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV168 @ SV922 ) @ SV836 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV168 @ SV437 ) @ SV661 ) @ SV922 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV168 @ SV437 ) @ SV661 ) @ SV836 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2371]) ).
thf(2467,plain,
! [SV169: $i,SV662: $i,SV438: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV438 @ SV662 @ SV169 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV662 @ SV438 @ SV169 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2372]) ).
thf(2468,plain,
! [SV170: $i,SV663: $i,SV439: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV439 @ SV663 @ SV170 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV663 @ SV439 @ SV170 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2373]) ).
thf(2469,plain,
! [SV171: $i,SV664: $i,SV440: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV440 @ SV664 @ SV171 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV664 @ SV440 @ SV171 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2374]) ).
thf(2470,plain,
! [SV837: $i,SV665: $i,SV442: $i,SV923: $i,SV173: $i] :
( ( ( c_OrderedGroup_Osemigroup__add @ SV173 @ SV923 )
= $false )
| ( ( ( c_List_Ofoldl @ SV173 @ ( hAPP @ ( hAPP @ SV173 @ SV442 ) @ SV665 ) @ SV837 @ SV923 @ SV923 )
= ( hAPP @ ( hAPP @ SV173 @ SV442 ) @ ( c_List_Ofoldl @ SV173 @ SV665 @ SV837 @ SV923 @ SV923 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2375]) ).
thf(2471,plain,
! [SV924: $i,SV840: $i,SV668: $i,SV446: $i,SV177: $i] :
( ( ( hBOOL @ ( hAPP @ SV177 @ ( c_Lambda_OdB_OdB__case @ SV446 @ SV668 @ SV840 @ ( c_Lambda_OdB_OVar @ SV924 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV177 @ ( hAPP @ SV446 @ SV924 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2377]) ).
thf(2472,plain,
! [SV925: $i,SV841: $i,SV669: $i,SV447: $i,SV178: $i] :
( ( ( hBOOL @ ( hAPP @ SV178 @ ( c_Lambda_OdB_OdB__case @ SV447 @ SV669 @ SV841 @ ( c_Lambda_OdB_OVar @ SV925 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV178 @ ( hAPP @ SV447 @ SV925 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2378]) ).
thf(2473,plain,
! [SV958: $i,SV926: $i,SV842: $i,SV670: $i,SV449: $i,SV180: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV180 @ ( c_Lambda_OdB_OdB__case @ SV449 @ SV670 @ SV842 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV926 ) @ SV958 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV180 @ ( hAPP @ ( hAPP @ SV670 @ SV926 ) @ SV958 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2379]) ).
thf(2474,plain,
! [SV959: $i,SV927: $i,SV843: $i,SV671: $i,SV450: $i,SV181: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV181 @ ( c_Lambda_OdB_OdB__case @ SV450 @ SV671 @ SV843 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV927 ) @ SV959 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV181 @ ( hAPP @ ( hAPP @ SV671 @ SV927 ) @ SV959 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2380]) ).
thf(2475,plain,
! [SV187: $i,SV456: $i,SV928: $i,SV844: $i,SV675: $i] :
( ( ( ~ ( c_Type_Otyping @ SV675 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV844 ) @ SV928 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV456 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV675 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV844 ) @ SV928 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV187 ) )
= $true )
| ( ( SV187 = SV456 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2381]) ).
thf(2476,plain,
! [SV680: $i,SV463: $i,SV194: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV194 ) @ SV463 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV680 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV463 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV194 ) ) @ SV463 ) @ SV680 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2382]) ).
thf(2477,plain,
! [SV852: $i,SV473: $i,SV931: $i,SV207: $i,SV690: $i] :
( ( ( c_OrderedGroup_Omonoid__add @ SV690 @ SV207 @ SV931 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV207 @ SV473 ) @ ( c_List_Ofoldl @ SV207 @ SV690 @ SV852 @ SV931 @ SV931 ) )
= ( c_List_Ofoldl @ SV207 @ SV473 @ SV852 @ SV931 @ SV931 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2387]) ).
thf(2478,plain,
! [SV968: $i,SV963: $i,SV935: $i,SV856: $i,SV694: $i,SV479: $i,SV217: $i] :
( ( ( c_Type_Otypings @ SV217 @ SV479 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV694 @ SV856 @ SV217 @ SV479 ) )
| ~ ( c_Type_Otyping @ SV217 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV935 ) @ SV963 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV856 )
| ~ ( c_Type_Otypings @ SV217 @ SV963 @ SV968 )
| ~ ( c_Type_Otyping @ SV217 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV935 ) @ SV963 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV479 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV694 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2390]) ).
thf(2479,plain,
! [SV861: $i,SV705: $i,SV494: $i,SV234: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV494 ) @ SV705 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV494 ) @ SV861 ) )
= $true )
| ( ( SV705 = SV861 )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV234 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2393]) ).
thf(2480,plain,
! [SV862: $i,SV707: $i,SV496: $i,SV236: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV236 ) @ SV496 ) @ SV707 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV236 ) @ SV862 ) @ SV707 ) )
= $true )
| ( ( SV496 = SV862 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV236 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2394]) ).
thf(2481,plain,
! [SV937: $i,SV866: $i,SV711: $i,SV500: $i,SV240: $i] :
( ( ( ( c_List_Olist_OCons @ SV240 @ SV500 @ SV711 )
= ( c_List_Olist_OCons @ SV866 @ SV937 @ SV711 ) )
= $false )
| ( ( SV240 = SV866 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2398]) ).
thf(2482,plain,
! [SV868: $i,SV502: $i,SV713: $i,SV242: $i] :
( ( ( SV242
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV713 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV242 @ SV502 @ SV713 @ SV868 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV868
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV242 ) @ SV502 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV713 @ SV868 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2400]) ).
thf(2483,plain,
! [SV969: $i,SV965: $i,SV938: $i,SV869: $i,SV714: $i,SV503: $i,SV243: $i] :
( ( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV243 ) @ SV503 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV714 ) @ SV869 ) @ SV938 ) ) )
| ~ ( c_Type_Otyping @ SV965 @ SV869 @ SV243 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV869 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV965 @ SV938 @ SV243 @ tc_Type_Otype ) @ SV714 @ SV969 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV714 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2401]) ).
thf(2484,plain,
! [SV870: $i,SV715: $i,SV504: $i,SV244: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV244 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV244 ) @ SV504 ) @ SV715 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV244 ) @ SV504 ) @ SV870 ) )
| ( SV715 = SV870 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV244 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2402]) ).
thf(2485,plain,
! [SV939: $i,SV873: $i,SV720: $i,SV509: $i,SV249: $i] :
( ( ( ( c_List_Oappend @ SV249 @ ( c_List_Olist_OCons @ SV509 @ ( c_List_Olist_ONil @ SV720 ) @ SV720 ) @ SV720 )
= ( c_List_Oappend @ SV873 @ ( c_List_Olist_OCons @ SV939 @ ( c_List_Olist_ONil @ SV720 ) @ SV720 ) @ SV720 ) )
= $false )
| ( ( SV249 = SV873 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2404]) ).
thf(2486,plain,
! [SV877: $i,SV736: $i,SV526: $i,SV266: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV266 ) @ SV526 ) @ SV736 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV266 ) @ SV526 ) @ SV877 ) )
= $true )
| ( ( SV736 = SV877 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV266 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2408]) ).
thf(2487,plain,
! [SV970: $i,SV966: $i,SV940: $i,SV878: $i,SV738: $i,SV528: $i,SV268: $i] :
( ( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV268 ) @ SV528 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV738 ) @ SV878 ) @ SV940 ) ) )
| ~ ( c_Type_Otyping @ SV966 @ SV878 @ SV528 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV878 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV966 @ SV940 @ SV528 @ tc_Type_Otype ) @ SV738 @ SV970 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV738 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2409]) ).
thf(2488,plain,
! [SV941: $i,SV882: $i,SV743: $i,SV535: $i,SV275: $i] :
( ( ( ( c_List_Oappend @ SV275 @ ( c_List_Olist_OCons @ SV535 @ ( c_List_Olist_ONil @ SV743 ) @ SV743 ) @ SV743 )
= ( c_List_Oappend @ SV882 @ ( c_List_Olist_OCons @ SV941 @ ( c_List_Olist_ONil @ SV743 ) @ SV743 ) @ SV743 ) )
= $false )
| ( ( SV535 = SV941 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2413]) ).
thf(2489,plain,
! [SV942: $i,SV884: $i,SV750: $i,SV543: $i,SV283: $i] :
( ( ( ( c_List_Olist_OCons @ SV283 @ SV543 @ SV750 )
= ( c_List_Olist_OCons @ SV884 @ SV942 @ SV750 ) )
= $false )
| ( ( SV543 = SV942 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2415]) ).
thf(2490,plain,
! [SV753: $i,SV546: $i,SV286: $i] :
( ( ( class_Int_Onumber__ring @ SV286 )
= $false )
| ( ( ( SV546
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV286 ) @ SV546 ) @ SV753 ) )
| ( SV753
= ( c_HOL_Ozero__class_Ozero @ SV286 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV286 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2416]) ).
thf(2491,plain,
! [SV943: $i,SV885: $i,SV754: $i,SV548: $i,SV288: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV288 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV548 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV754 ) @ SV885 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV754 ) @ SV943 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV548 ) @ SV885 )
= SV943 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2417]) ).
thf(2492,plain,
! [SV944: $i,SV886: $i,SV759: $i,SV7: $i,SV553: $i,SV295: $i] :
( ( ( SV295 = SV553 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV7 @ ( c_List_Oappend @ SV759 @ ( c_List_Olist_OCons @ SV295 @ ( c_List_Olist_ONil @ SV886 ) @ SV886 ) @ SV886 ) @ ( c_List_Oappend @ SV944 @ ( c_List_Olist_OCons @ SV553 @ ( c_List_Olist_ONil @ SV886 ) @ SV886 ) @ SV886 ) @ SV886 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV7 @ SV295 ) @ SV553 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2418]) ).
thf(2493,plain,
! [SV559: $i,SV762: $i,SV888: $i,SV306: $i,SV19: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV19 @ SV306 ) @ SV888 ) @ SV762 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV19 @ SV306 ) @ SV559 ) @ SV888 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV19 @ SV306 ) @ SV559 ) @ SV762 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2419]) ).
thf(2494,plain,
! [SV24: $i,SV946: $i,SV311: $i,SV890: $i,SV764: $i,SV563: $i] :
( ( ( SV563 = SV764 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV890 @ ( c_List_Olist_OCons @ SV311 @ SV764 @ SV946 ) @ ( c_List_Olist_OCons @ SV24 @ SV563 @ SV946 ) @ SV946 ) )
= $true )
| ( ( SV24 = SV311 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2421]) ).
thf(2495,plain,
! [SV770: $i,SV319: $i,SV894: $i,SV570: $i,SV34: $i] :
( ( ( c_Type_Otypings @ SV34 @ SV570 @ SV894 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV34 @ SV319 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV894 @ SV770 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true )
| ( ( c_Type_Otyping @ SV34 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV319 @ SV570 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV770 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2424]) ).
thf(2496,plain,
! [SV320: $i,SV35: $i,SV571: $i,SV771: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV771 @ SV571 @ SV35 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV320 @ SV771 @ SV35 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV320 @ SV571 @ SV35 )
= $true )
| ( ( class_Orderings_Opreorder @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2425]) ).
thf(2497,plain,
! [SV572: $i,SV36: $i,SV772: $i,SV321: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV321 @ SV772 @ SV36 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV772 @ SV572 @ SV36 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV321 @ SV572 @ SV36 )
= $true )
| ( ( class_Orderings_Oorder @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2426]) ).
thf(2498,plain,
! [SV585: $i,SV334: $i,SV948: $i,SV896: $i,SV784: $i,SV51: $i] :
( ( ( c_ListOrder_Ostep1 @ SV51 @ SV784 @ SV896 @ SV948 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV51 @ ( c_List_Oappend @ SV784 @ ( c_List_Olist_OCons @ SV334 @ ( c_List_Olist_ONil @ SV948 ) @ SV948 ) @ SV948 ) @ ( c_List_Oappend @ SV896 @ ( c_List_Olist_OCons @ SV585 @ ( c_List_Olist_ONil @ SV948 ) @ SV948 ) @ SV948 ) @ SV948 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV51 @ SV334 ) @ SV585 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2427]) ).
thf(2499,plain,
! [SV335: $i,SV897: $i,SV785: $i,SV949: $i,SV586: $i,SV53: $i] :
( ( ( ~ ( c_Type_Otypings @ ( c_Type_Oshift @ SV53 @ SV586 @ SV949 @ tc_Type_Otype ) @ SV785 @ SV897 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV53 @ SV335 @ SV949 ) )
= $true )
| ( ( c_Type_Otypings @ SV53 @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SV335 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV586 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV785 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV897 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2428]) ).
thf(2500,plain,
! [SV336: $i,SV54: $i,SV587: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV587 @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV54 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV336 @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV54 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV336 ) @ SV587 ) @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV54 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2429]) ).
thf(2501,plain,
! [SV950: $i,SV901: $i,SV793: $i,SV66: $i,SV347: $i,SV598: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV598 @ SV347 ) @ SV66 ) )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV598 @ ( c_List_Olist_OCons @ SV347 @ SV793 @ SV901 ) @ ( c_List_Olist_OCons @ SV66 @ SV950 @ SV901 ) @ SV901 ) )
= $true )
| ( ( SV66 = SV347 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2430]) ).
thf(2502,plain,
! [SV795: $i,SV349: $i,SV600: $i,SV68: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV68 ) @ SV600 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV349 ) @ SV795 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV68 ) @ SV349 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV600 ) @ SV795 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2432]) ).
thf(2503,plain,
! [SV602: $i,SV70: $i,SV351: $i,SV796: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV796 ) @ SV351 ) )
= $false )
| ( ( c_Type_Otyping @ SV70 @ SV796 @ SV602 )
= $false )
| ( ( c_Type_Otyping @ SV70 @ SV351 @ SV602 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2433]) ).
thf(2504,plain,
! [SV951: $i,SV904: $i,SV798: $i,SV606: $i,SV357: $i,SV77: $i] :
( ( ( c_Type_Otyping @ SV77 @ SV357 @ SV606 )
= $false )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV77 @ SV798 @ SV606 @ tc_Type_Otype ) @ SV904 @ SV951 )
| ( c_Type_Otyping @ SV77 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV904 ) @ SV357 ) @ SV798 ) @ SV951 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2435]) ).
thf(2505,plain,
! [SV952: $i,SV905: $i,SV799: $i,SV359: $i,SV79: $i,SV608: $i] :
( ( ( c_ListOrder_Ostep1 @ SV608 @ SV79 @ SV359 @ SV799 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV608 @ ( c_List_Oappend @ SV79 @ ( c_List_Olist_OCons @ SV905 @ ( c_List_Olist_ONil @ SV799 ) @ SV799 ) @ SV799 ) @ ( c_List_Oappend @ SV359 @ ( c_List_Olist_OCons @ SV952 @ ( c_List_Olist_ONil @ SV799 ) @ SV799 ) @ SV799 ) @ SV799 ) )
= $true )
| ( ( SV79 = SV359 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2436]) ).
thf(2506,plain,
! [SV393: $i,SV622: $i,SV117: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV622 @ SV117 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV393 @ SV117 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV393 ) @ SV622 ) @ SV117 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2437]) ).
thf(2507,plain,
! [SV953: $i,SV807: $i,SV906: $i,SV118: $i,SV394: $i,SV623: $i] :
( ( ( SV623 = SV394 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV118 @ ( c_List_Olist_OCons @ SV906 @ SV394 @ SV807 ) @ ( c_List_Olist_OCons @ SV953 @ SV623 @ SV807 ) @ SV807 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV118 @ SV394 @ SV623 @ SV807 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2438]) ).
thf(2508,plain,
! [SV909: $i,SV810: $i,SV632: $i,SV405: $i,SV130: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SV405 ) @ SV632 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SV810 ) @ SV909 ) @ SV130 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV632 @ SV909 @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SV405 @ SV810 @ SV130 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV130 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2445]) ).
thf(2509,plain,
! [SV811: $i,SV406: $i,SV910: $i,SV633: $i,SV131: $i] :
( ( ( c_Type_Otyping @ SV131 @ SV633 @ SV910 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV131 @ SV406 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV910 ) @ SV811 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV131 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV406 ) @ SV633 ) @ SV811 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2446]) ).
thf(2510,plain,
! [SV408: $i,SV954: $i,SV134: $i,SV911: $i,SV812: $i,SV634: $i] :
( ( ( SV634 = SV812 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV911 @ ( c_List_Oappend @ SV134 @ ( c_List_Olist_OCons @ SV634 @ ( c_List_Olist_ONil @ SV954 ) @ SV954 ) @ SV954 ) @ ( c_List_Oappend @ SV408 @ ( c_List_Olist_OCons @ SV812 @ ( c_List_Olist_ONil @ SV954 ) @ SV954 ) @ SV954 ) @ SV954 ) )
= $true )
| ( ( SV134 = SV408 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2447]) ).
thf(2511,plain,
! [SV636: $i,SV813: $i,SV410: $i,SV137: $i] :
( ( ( c_List_Olistsp @ SV137 @ SV410 @ SV813 )
= $false )
| ( ( c_List_Olistsp @ SV137 @ SV636 @ SV813 )
= $false )
| ( ( c_List_Olistsp @ SV137 @ ( c_List_Oappend @ SV410 @ SV636 @ SV813 ) @ SV813 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2448]) ).
thf(2512,plain,
! [SV967: $i,SV955: $i,SV914: $i,SV816: $i,SV639: $i,SV414: $i,SV142: $i] :
( ( ( SV142
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV414 @ SV142 @ SV639 @ SV816 ) @ SV414 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV639 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV914 ) @ SV955 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV142 )
| ~ ( c_Type_Otypings @ SV639 @ SV955 @ SV967 )
| ~ ( c_Type_Otyping @ SV639 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV914 ) @ SV955 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV816 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV414 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2450]) ).
thf(2513,plain,
! [SV640: $i,SV144: $i,SV817: $i,SV416: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV416 @ SV817 @ SV144 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV144 ) @ SV640 @ SV144 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV416 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ SV640 ) @ SV817 ) @ SV144 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV144 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2451]) ).
thf(2514,plain,
! [SV645: $i,SV149: $i,SV821: $i,SV421: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV421 @ SV821 @ SV149 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV421 ) @ SV645 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV821 ) @ SV645 ) @ SV149 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2454]) ).
thf(2515,plain,
! [SV646: $i,SV150: $i,SV822: $i,SV422: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV422 @ SV822 @ SV150 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV150 ) @ SV422 ) @ SV646 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV150 ) @ SV822 ) @ SV646 ) @ SV150 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV150 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2455]) ).
thf(2516,plain,
! [SV647: $i,SV823: $i,SV423: $i,SV151: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV423 ) @ SV823 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV647 ) @ SV823 ) @ SV151 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV423 @ SV647 @ SV151 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2456]) ).
thf(2517,plain,
! [SV424: $i,SV152: $i,SV824: $i,SV648: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV648 @ SV824 @ SV152 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV424 ) @ SV648 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV424 ) @ SV824 ) @ SV152 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV152 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2457]) ).
thf(2518,plain,
! [SV425: $i,SV153: $i,SV825: $i,SV649: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV649 @ SV825 @ SV153 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV425 ) @ SV649 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV425 ) @ SV825 ) @ SV153 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2458]) ).
thf(2519,plain,
! [SV650: $i,SV426: $i,SV826: $i,SV154: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SV826 ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SV826 ) @ SV650 ) @ SV154 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV426 @ SV650 @ SV154 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2459]) ).
thf(2520,plain,
! [SV427: $i,SV651: $i,SV827: $i,SV156: $i] :
( ( ( c_Type_Otyping @ SV156 @ SV827 @ SV651 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV827 ) @ SV427 ) )
= $false )
| ( ( c_Type_Otyping @ SV156 @ SV427 @ SV651 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2460]) ).
thf(2521,plain,
! [SV652: $i,SV828: $i,SV428: $i,SV957: $i,SV918: $i,SV157: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV157 @ SV918 ) @ SV957 ) )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV157 @ ( c_List_Olist_OCons @ SV918 @ SV428 @ SV828 ) @ ( c_List_Olist_OCons @ SV957 @ SV652 @ SV828 ) @ SV828 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV157 @ SV428 @ SV652 @ SV828 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2461]) ).
thf(2522,plain,
! [SV166: $i,SV435: $i,SV659: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV659 @ SV435 @ SV166 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV435 @ SV659 @ SV166 )
= $false )
| ( ( class_Orderings_Oorder @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2464]) ).
thf(2523,plain,
! [SV660: $i,SV835: $i,SV921: $i,SV436: $i,SV167: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV167 @ SV436 ) @ SV921 ) @ SV835 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV167 @ SV660 ) @ SV921 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV167 @ SV436 ) @ SV660 ) @ SV835 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2465]) ).
thf(2524,plain,
! [SV661: $i,SV437: $i,SV836: $i,SV922: $i,SV168: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV168 @ SV922 ) @ SV836 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV168 @ SV437 ) @ SV661 ) @ SV922 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV168 @ SV437 ) @ SV661 ) @ SV836 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2466]) ).
thf(2525,plain,
! [SV169: $i,SV438: $i,SV662: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV662 @ SV438 @ SV169 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV438 @ SV662 @ SV169 )
= $false )
| ( ( class_Orderings_Olinorder @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2467]) ).
thf(2526,plain,
! [SV170: $i,SV439: $i,SV663: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV663 @ SV439 @ SV170 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV439 @ SV663 @ SV170 )
= $false )
| ( ( class_Orderings_Opreorder @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2468]) ).
thf(2527,plain,
! [SV171: $i,SV440: $i,SV664: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV664 @ SV440 @ SV171 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV440 @ SV664 @ SV171 )
= $false )
| ( ( class_Orderings_Opreorder @ SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2469]) ).
thf(2528,plain,
! [SV958: $i,SV926: $i,SV842: $i,SV670: $i,SV449: $i,SV180: $i] :
( ( ( hBOOL @ ( hAPP @ SV180 @ ( c_Lambda_OdB_OdB__case @ SV449 @ SV670 @ SV842 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV926 ) @ SV958 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV180 @ ( hAPP @ ( hAPP @ SV670 @ SV926 ) @ SV958 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2473]) ).
thf(2529,plain,
! [SV959: $i,SV927: $i,SV843: $i,SV671: $i,SV450: $i,SV181: $i] :
( ( ( hBOOL @ ( hAPP @ SV181 @ ( c_Lambda_OdB_OdB__case @ SV450 @ SV671 @ SV843 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV927 ) @ SV959 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV181 @ ( hAPP @ ( hAPP @ SV671 @ SV927 ) @ SV959 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2474]) ).
thf(2530,plain,
! [SV187: $i,SV456: $i,SV928: $i,SV844: $i,SV675: $i] :
( ( ( c_Type_Otyping @ SV675 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV844 ) @ SV928 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV456 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV675 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV844 ) @ SV928 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV187 ) )
= $true )
| ( ( SV187 = SV456 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2475]) ).
thf(2531,plain,
! [SV968: $i,SV963: $i,SV935: $i,SV856: $i,SV694: $i,SV479: $i,SV217: $i] :
( ( ( c_Type_Otypings @ SV217 @ SV479 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV694 @ SV856 @ SV217 @ SV479 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV217 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV935 ) @ SV963 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV856 )
| ~ ( c_Type_Otypings @ SV217 @ SV963 @ SV968 )
| ~ ( c_Type_Otyping @ SV217 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV935 ) @ SV963 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV479 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV694 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2478]) ).
thf(2532,plain,
! [SV861: $i,SV705: $i,SV494: $i,SV234: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV494 ) @ SV705 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV494 ) @ SV861 ) )
= $false )
| ( ( SV705 = SV861 )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV234 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2479]) ).
thf(2533,plain,
! [SV862: $i,SV707: $i,SV496: $i,SV236: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV236 ) @ SV496 ) @ SV707 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV236 ) @ SV862 ) @ SV707 ) )
= $false )
| ( ( SV496 = SV862 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2480]) ).
thf(2534,plain,
! [SV969: $i,SV965: $i,SV938: $i,SV869: $i,SV714: $i,SV503: $i,SV243: $i] :
( ( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV243 ) @ SV503 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV714 ) @ SV869 ) @ SV938 ) ) )
| ~ ( c_Type_Otyping @ SV965 @ SV869 @ SV243 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV869 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV965 @ SV938 @ SV243 @ tc_Type_Otype ) @ SV714 @ SV969 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV714 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2483]) ).
thf(2535,plain,
! [SV870: $i,SV715: $i,SV504: $i,SV244: $i] :
( ( ( class_Int_Onumber__ring @ SV244 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV244 ) @ SV504 ) @ SV715 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV244 ) @ SV504 ) @ SV870 ) )
| ( SV715 = SV870 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV244 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2484]) ).
thf(2536,plain,
! [SV877: $i,SV736: $i,SV526: $i,SV266: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV266 ) @ SV526 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV266 ) @ SV526 ) @ SV877 ) )
= $false )
| ( ( SV736 = SV877 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV266 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2486]) ).
thf(2537,plain,
! [SV970: $i,SV966: $i,SV940: $i,SV878: $i,SV738: $i,SV528: $i,SV268: $i] :
( ( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV268 ) @ SV528 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV738 ) @ SV878 ) @ SV940 ) ) )
| ~ ( c_Type_Otyping @ SV966 @ SV878 @ SV528 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV878 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV966 @ SV940 @ SV528 @ tc_Type_Otype ) @ SV738 @ SV970 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV738 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2487]) ).
thf(2538,plain,
! [SV753: $i,SV286: $i,SV546: $i] :
( ( ( SV546
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV286 ) @ SV546 ) @ SV753 ) )
= $true )
| ( ( SV753
= ( c_HOL_Ozero__class_Ozero @ SV286 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV286 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV286 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2490]) ).
thf(2539,plain,
! [SV943: $i,SV885: $i,SV754: $i,SV548: $i,SV288: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV548 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV754 ) @ SV885 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV754 ) @ SV943 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV548 ) @ SV885 )
= SV943 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV288 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2491]) ).
thf(2540,plain,
! [SV553: $i,SV944: $i,SV886: $i,SV295: $i,SV759: $i,SV7: $i] :
( ( ( c_ListOrder_Ostep1 @ SV7 @ ( c_List_Oappend @ SV759 @ ( c_List_Olist_OCons @ SV295 @ ( c_List_Olist_ONil @ SV886 ) @ SV886 ) @ SV886 ) @ ( c_List_Oappend @ SV944 @ ( c_List_Olist_OCons @ SV553 @ ( c_List_Olist_ONil @ SV886 ) @ SV886 ) @ SV886 ) @ SV886 )
= $false )
| ( ( SV295 = SV553 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV7 @ SV295 ) @ SV553 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2492]) ).
thf(2541,plain,
! [SV762: $i,SV888: $i,SV559: $i,SV306: $i,SV19: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV19 @ SV306 ) @ SV559 ) @ SV888 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV19 @ SV306 ) @ SV888 ) @ SV762 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV19 @ SV306 ) @ SV559 ) @ SV762 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2493]) ).
thf(2542,plain,
! [SV563: $i,SV24: $i,SV946: $i,SV764: $i,SV311: $i,SV890: $i] :
( ( ( c_ListOrder_Ostep1 @ SV890 @ ( c_List_Olist_OCons @ SV311 @ SV764 @ SV946 ) @ ( c_List_Olist_OCons @ SV24 @ SV563 @ SV946 ) @ SV946 )
= $false )
| ( ( SV563 = SV764 )
= $true )
| ( ( SV24 = SV311 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2494]) ).
thf(2543,plain,
! [SV570: $i,SV770: $i,SV894: $i,SV319: $i,SV34: $i] :
( ( ( c_Type_Otyping @ SV34 @ SV319 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV894 @ SV770 @ tc_Type_Otype @ tc_Type_Otype ) )
= $false )
| ( ( c_Type_Otypings @ SV34 @ SV570 @ SV894 )
= $false )
| ( ( c_Type_Otyping @ SV34 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV319 @ SV570 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV770 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2495]) ).
thf(2544,plain,
! [SV320: $i,SV35: $i,SV571: $i,SV771: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV771 @ SV571 @ SV35 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV320 @ SV771 @ SV35 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV320 @ SV571 @ SV35 )
= $true )
| ( ( class_Orderings_Opreorder @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2496]) ).
thf(2545,plain,
! [SV572: $i,SV36: $i,SV772: $i,SV321: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV321 @ SV772 @ SV36 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV772 @ SV572 @ SV36 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV321 @ SV572 @ SV36 )
= $true )
| ( ( class_Orderings_Oorder @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2497]) ).
thf(2546,plain,
! [SV585: $i,SV896: $i,SV948: $i,SV334: $i,SV784: $i,SV51: $i] :
( ( ( c_ListOrder_Ostep1 @ SV51 @ ( c_List_Oappend @ SV784 @ ( c_List_Olist_OCons @ SV334 @ ( c_List_Olist_ONil @ SV948 ) @ SV948 ) @ SV948 ) @ ( c_List_Oappend @ SV896 @ ( c_List_Olist_OCons @ SV585 @ ( c_List_Olist_ONil @ SV948 ) @ SV948 ) @ SV948 ) @ SV948 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV51 @ SV784 @ SV896 @ SV948 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV51 @ SV334 ) @ SV585 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2498]) ).
thf(2547,plain,
! [SV335: $i,SV897: $i,SV785: $i,SV949: $i,SV586: $i,SV53: $i] :
( ( ( c_Type_Otypings @ ( c_Type_Oshift @ SV53 @ SV586 @ SV949 @ tc_Type_Otype ) @ SV785 @ SV897 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV53 @ SV335 @ SV949 ) )
= $true )
| ( ( c_Type_Otypings @ SV53 @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SV335 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV586 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV785 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV897 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2499]) ).
thf(2548,plain,
! [SV587: $i,SV54: $i,SV336: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV336 @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV54 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV587 @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV54 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV336 ) @ SV587 ) @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV54 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2500]) ).
thf(2549,plain,
! [SV950: $i,SV66: $i,SV901: $i,SV793: $i,SV347: $i,SV598: $i] :
( ( ( c_ListOrder_Ostep1 @ SV598 @ ( c_List_Olist_OCons @ SV347 @ SV793 @ SV901 ) @ ( c_List_Olist_OCons @ SV66 @ SV950 @ SV901 ) @ SV901 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV598 @ SV347 ) @ SV66 ) )
= $true )
| ( ( SV66 = SV347 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2501]) ).
thf(2550,plain,
! [SV357: $i,SV951: $i,SV904: $i,SV606: $i,SV798: $i,SV77: $i] :
( ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV77 @ SV798 @ SV606 @ tc_Type_Otype ) @ SV904 @ SV951 ) )
= $true )
| ( ( c_Type_Otyping @ SV77 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV904 ) @ SV357 ) @ SV798 ) @ SV951 )
= $true )
| ( ( c_Type_Otyping @ SV77 @ SV357 @ SV606 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2504]) ).
thf(2551,plain,
! [SV952: $i,SV359: $i,SV799: $i,SV905: $i,SV79: $i,SV608: $i] :
( ( ( c_ListOrder_Ostep1 @ SV608 @ ( c_List_Oappend @ SV79 @ ( c_List_Olist_OCons @ SV905 @ ( c_List_Olist_ONil @ SV799 ) @ SV799 ) @ SV799 ) @ ( c_List_Oappend @ SV359 @ ( c_List_Olist_OCons @ SV952 @ ( c_List_Olist_ONil @ SV799 ) @ SV799 ) @ SV799 ) @ SV799 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV608 @ SV79 @ SV359 @ SV799 )
= $true )
| ( ( SV79 = SV359 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2505]) ).
thf(2552,plain,
! [SV622: $i,SV393: $i,SV117: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV393 @ SV117 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV622 @ SV117 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV393 ) @ SV622 ) @ SV117 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2506]) ).
thf(2553,plain,
! [SV623: $i,SV953: $i,SV807: $i,SV394: $i,SV906: $i,SV118: $i] :
( ( ( c_ListOrder_Ostep1 @ SV118 @ ( c_List_Olist_OCons @ SV906 @ SV394 @ SV807 ) @ ( c_List_Olist_OCons @ SV953 @ SV623 @ SV807 ) @ SV807 )
= $false )
| ( ( SV623 = SV394 )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV118 @ SV394 @ SV623 @ SV807 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2507]) ).
thf(2554,plain,
! [SV810: $i,SV405: $i,SV130: $i,SV909: $i,SV632: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV632 @ SV909 @ SV130 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV405 @ SV810 @ SV130 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SV405 ) @ SV632 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SV810 ) @ SV909 ) @ SV130 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV130 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2508]) ).
thf(2555,plain,
! [SV633: $i,SV811: $i,SV910: $i,SV406: $i,SV131: $i] :
( ( ( c_Type_Otyping @ SV131 @ SV406 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV910 ) @ SV811 ) )
= $false )
| ( ( c_Type_Otyping @ SV131 @ SV633 @ SV910 )
= $false )
| ( ( c_Type_Otyping @ SV131 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV406 ) @ SV633 ) @ SV811 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2509]) ).
thf(2556,plain,
! [SV812: $i,SV408: $i,SV954: $i,SV634: $i,SV134: $i,SV911: $i] :
( ( ( c_ListOrder_Ostep1 @ SV911 @ ( c_List_Oappend @ SV134 @ ( c_List_Olist_OCons @ SV634 @ ( c_List_Olist_ONil @ SV954 ) @ SV954 ) @ SV954 ) @ ( c_List_Oappend @ SV408 @ ( c_List_Olist_OCons @ SV812 @ ( c_List_Olist_ONil @ SV954 ) @ SV954 ) @ SV954 ) @ SV954 )
= $false )
| ( ( SV634 = SV812 )
= $true )
| ( ( SV134 = SV408 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2510]) ).
thf(2557,plain,
! [SV414: $i,SV816: $i,SV967: $i,SV142: $i,SV955: $i,SV914: $i,SV639: $i] :
( ( ( ~ ( c_Type_Otyping @ SV639 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV914 ) @ SV955 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV142 ) )
= $true )
| ( ( ~ ( c_Type_Otypings @ SV639 @ SV955 @ SV967 )
| ~ ( c_Type_Otyping @ SV639 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV914 ) @ SV955 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV816 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV414 ) )
= $true )
| ( ( SV142
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV414 @ SV142 @ SV639 @ SV816 ) @ SV414 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2512]) ).
thf(2558,plain,
! [SV640: $i,SV144: $i,SV817: $i,SV416: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV416 @ SV817 @ SV144 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV144 ) @ SV640 @ SV144 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV416 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ SV640 ) @ SV817 ) @ SV144 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2513]) ).
thf(2559,plain,
! [SV652: $i,SV957: $i,SV828: $i,SV428: $i,SV918: $i,SV157: $i] :
( ( ( c_ListOrder_Ostep1 @ SV157 @ ( c_List_Olist_OCons @ SV918 @ SV428 @ SV828 ) @ ( c_List_Olist_OCons @ SV957 @ SV652 @ SV828 ) @ SV828 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV157 @ SV918 ) @ SV957 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV157 @ SV428 @ SV652 @ SV828 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2521]) ).
thf(2560,plain,
! [SV835: $i,SV436: $i,SV921: $i,SV660: $i,SV167: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV167 @ SV660 ) @ SV921 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV167 @ SV436 ) @ SV921 ) @ SV835 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV167 @ SV436 ) @ SV660 ) @ SV835 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2523]) ).
thf(2561,plain,
! [SV836: $i,SV922: $i,SV661: $i,SV437: $i,SV168: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV168 @ SV437 ) @ SV661 ) @ SV922 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV168 @ SV922 ) @ SV836 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV168 @ SV437 ) @ SV661 ) @ SV836 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2524]) ).
thf(2562,plain,
! [SV456: $i,SV187: $i,SV928: $i,SV844: $i,SV675: $i] :
( ( ( c_Type_Otyping @ SV675 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV844 ) @ SV928 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV187 )
= $false )
| ( ( c_Type_Otyping @ SV675 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV844 ) @ SV928 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV456 )
= $false )
| ( ( SV187 = SV456 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2530]) ).
thf(2563,plain,
! [SV694: $i,SV479: $i,SV968: $i,SV856: $i,SV963: $i,SV935: $i,SV217: $i] :
( ( ( ~ ( c_Type_Otyping @ SV217 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV935 ) @ SV963 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV856 ) )
= $true )
| ( ( ~ ( c_Type_Otypings @ SV217 @ SV963 @ SV968 )
| ~ ( c_Type_Otyping @ SV217 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV935 ) @ SV963 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV479 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV694 ) )
= $true )
| ( ( c_Type_Otypings @ SV217 @ SV479 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV694 @ SV856 @ SV217 @ SV479 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2531]) ).
thf(2564,plain,
! [SV969: $i,SV965: $i,SV938: $i,SV869: $i,SV714: $i,SV503: $i,SV243: $i] :
( ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV243 ) @ SV503 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV714 ) @ SV869 ) @ SV938 ) ) )
| ~ ( c_Type_Otyping @ SV965 @ SV869 @ SV243 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV869 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV965 @ SV938 @ SV243 @ tc_Type_Otype ) @ SV714 @ SV969 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV714 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2534]) ).
thf(2565,plain,
! [SV870: $i,SV715: $i,SV504: $i,SV244: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV244 ) @ SV504 ) @ SV715 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV244 ) @ SV504 ) @ SV870 ) )
= $true )
| ( ( SV715 = SV870 )
= $true )
| ( ( class_Int_Onumber__ring @ SV244 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV244 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2535]) ).
thf(2566,plain,
! [SV970: $i,SV966: $i,SV940: $i,SV878: $i,SV738: $i,SV528: $i,SV268: $i] :
( ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV268 ) @ SV528 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV738 ) @ SV878 ) @ SV940 ) ) )
| ~ ( c_Type_Otyping @ SV966 @ SV878 @ SV528 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV878 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV966 @ SV940 @ SV528 @ tc_Type_Otype ) @ SV738 @ SV970 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV738 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2537]) ).
thf(2567,plain,
! [SV753: $i,SV286: $i,SV546: $i] :
( ( ( SV546
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV286 ) @ SV546 ) @ SV753 ) )
= $false )
| ( ( SV753
= ( c_HOL_Ozero__class_Ozero @ SV286 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV286 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV286 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2538]) ).
thf(2568,plain,
! [SV943: $i,SV885: $i,SV754: $i,SV548: $i,SV288: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV548 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV754 ) @ SV885 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV754 ) @ SV943 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV288 ) @ SV548 ) @ SV885 )
= SV943 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV288 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2539]) ).
thf(2569,plain,
! [SV571: $i,SV35: $i,SV771: $i,SV320: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV320 @ SV771 @ SV35 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV771 @ SV571 @ SV35 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV320 @ SV571 @ SV35 )
= $true )
| ( ( class_Orderings_Opreorder @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2544]) ).
thf(2570,plain,
! [SV321: $i,SV36: $i,SV572: $i,SV772: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV772 @ SV572 @ SV36 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV321 @ SV772 @ SV36 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV321 @ SV572 @ SV36 )
= $true )
| ( ( class_Orderings_Oorder @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2545]) ).
thf(2571,plain,
! [SV897: $i,SV785: $i,SV586: $i,SV949: $i,SV335: $i,SV53: $i] :
( ( ( c_Type_Otyping @ SV53 @ SV335 @ SV949 )
= $false )
| ( ( c_Type_Otypings @ ( c_Type_Oshift @ SV53 @ SV586 @ SV949 @ tc_Type_Otype ) @ SV785 @ SV897 )
= $false )
| ( ( c_Type_Otypings @ SV53 @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SV335 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV586 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV785 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV897 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2547]) ).
thf(2572,plain,
! [SV357: $i,SV951: $i,SV904: $i,SV606: $i,SV798: $i,SV77: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV77 @ SV798 @ SV606 @ tc_Type_Otype ) @ SV904 @ SV951 )
= $false )
| ( ( c_Type_Otyping @ SV77 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV904 ) @ SV357 ) @ SV798 ) @ SV951 )
= $true )
| ( ( c_Type_Otyping @ SV77 @ SV357 @ SV606 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2550]) ).
thf(2573,plain,
! [SV810: $i,SV405: $i,SV130: $i,SV909: $i,SV632: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV632 @ SV909 @ SV130 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV405 @ SV810 @ SV130 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SV405 ) @ SV632 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SV810 ) @ SV909 ) @ SV130 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV130 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2554]) ).
thf(2574,plain,
! [SV414: $i,SV816: $i,SV967: $i,SV142: $i,SV955: $i,SV914: $i,SV639: $i] :
( ( ( c_Type_Otyping @ SV639 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV914 ) @ SV955 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV142 )
= $false )
| ( ( ~ ( c_Type_Otypings @ SV639 @ SV955 @ SV967 )
| ~ ( c_Type_Otyping @ SV639 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV914 ) @ SV955 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV816 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV414 ) )
= $true )
| ( ( SV142
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV414 @ SV142 @ SV639 @ SV816 ) @ SV414 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2557]) ).
thf(2575,plain,
! [SV817: $i,SV416: $i,SV640: $i,SV144: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV144 ) @ SV640 @ SV144 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV416 @ SV817 @ SV144 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV416 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ SV640 ) @ SV817 ) @ SV144 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2558]) ).
thf(2576,plain,
! [SV694: $i,SV479: $i,SV968: $i,SV856: $i,SV963: $i,SV935: $i,SV217: $i] :
( ( ( c_Type_Otyping @ SV217 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV935 ) @ SV963 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV856 )
= $false )
| ( ( ~ ( c_Type_Otypings @ SV217 @ SV963 @ SV968 )
| ~ ( c_Type_Otyping @ SV217 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV935 ) @ SV963 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV479 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV694 ) )
= $true )
| ( ( c_Type_Otypings @ SV217 @ SV479 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV694 @ SV856 @ SV217 @ SV479 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2563]) ).
thf(2577,plain,
! [SV503: $i,SV969: $i,SV243: $i,SV965: $i,SV938: $i,SV869: $i,SV714: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV714 ) @ SV869 ) @ SV938 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV965 @ SV869 @ SV243 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV869 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV965 @ SV938 @ SV243 @ tc_Type_Otype ) @ SV714 @ SV969 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV714 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV243 ) @ SV503 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2564]) ).
thf(2578,plain,
! [SV870: $i,SV715: $i,SV504: $i,SV244: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV244 ) @ SV504 ) @ SV715 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV244 ) @ SV504 ) @ SV870 ) )
= $false )
| ( ( SV715 = SV870 )
= $true )
| ( ( class_Int_Onumber__ring @ SV244 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV244 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2565]) ).
thf(2579,plain,
! [SV268: $i,SV970: $i,SV528: $i,SV966: $i,SV940: $i,SV878: $i,SV738: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV738 ) @ SV878 ) @ SV940 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV966 @ SV878 @ SV528 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV878 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV966 @ SV940 @ SV528 @ tc_Type_Otype ) @ SV738 @ SV970 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV738 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV268 ) @ SV528 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2566]) ).
thf(2580,plain,
! [SV909: $i,SV632: $i,SV130: $i,SV810: $i,SV405: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV405 @ SV810 @ SV130 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV632 @ SV909 @ SV130 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SV405 ) @ SV632 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SV810 ) @ SV909 ) @ SV130 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV130 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2573]) ).
thf(2581,plain,
! [SV142: $i,SV414: $i,SV816: $i,SV914: $i,SV967: $i,SV955: $i,SV639: $i] :
( ( ( ~ ( c_Type_Otypings @ SV639 @ SV955 @ SV967 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV639 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV914 ) @ SV955 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV816 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV414 ) )
= $true )
| ( ( c_Type_Otyping @ SV639 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV914 ) @ SV955 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV142 )
= $false )
| ( ( SV142
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV414 @ SV142 @ SV639 @ SV816 ) @ SV414 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2574]) ).
thf(2582,plain,
! [SV856: $i,SV694: $i,SV479: $i,SV935: $i,SV968: $i,SV963: $i,SV217: $i] :
( ( ( ~ ( c_Type_Otypings @ SV217 @ SV963 @ SV968 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV217 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV935 ) @ SV963 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV479 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV694 ) )
= $true )
| ( ( c_Type_Otyping @ SV217 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV935 ) @ SV963 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV856 )
= $false )
| ( ( c_Type_Otypings @ SV217 @ SV479 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV694 @ SV856 @ SV217 @ SV479 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2576]) ).
thf(2583,plain,
! [SV503: $i,SV969: $i,SV714: $i,SV938: $i,SV243: $i,SV869: $i,SV965: $i] :
( ( ( ~ ( c_Type_Otyping @ SV965 @ SV869 @ SV243 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV869 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV965 @ SV938 @ SV243 @ tc_Type_Otype ) @ SV714 @ SV969 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV714 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV714 ) @ SV869 ) @ SV938 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV243 ) @ SV503 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2577]) ).
thf(2584,plain,
! [SV268: $i,SV970: $i,SV738: $i,SV940: $i,SV528: $i,SV878: $i,SV966: $i] :
( ( ( ~ ( c_Type_Otyping @ SV966 @ SV878 @ SV528 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV878 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV966 @ SV940 @ SV528 @ tc_Type_Otype ) @ SV738 @ SV970 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV738 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV738 ) @ SV878 ) @ SV940 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV268 ) @ SV528 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2579]) ).
thf(2585,plain,
! [SV142: $i,SV414: $i,SV816: $i,SV914: $i,SV967: $i,SV955: $i,SV639: $i] :
( ( ( c_Type_Otypings @ SV639 @ SV955 @ SV967 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV639 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV914 ) @ SV955 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV816 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV414 ) )
= $true )
| ( ( c_Type_Otyping @ SV639 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV914 ) @ SV955 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV142 )
= $false )
| ( ( SV142
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV414 @ SV142 @ SV639 @ SV816 ) @ SV414 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2581]) ).
thf(2586,plain,
! [SV856: $i,SV694: $i,SV479: $i,SV935: $i,SV968: $i,SV963: $i,SV217: $i] :
( ( ( c_Type_Otypings @ SV217 @ SV963 @ SV968 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV217 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV935 ) @ SV963 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV479 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV694 ) )
= $true )
| ( ( c_Type_Otyping @ SV217 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV935 ) @ SV963 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV856 )
= $false )
| ( ( c_Type_Otypings @ SV217 @ SV479 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV694 @ SV856 @ SV217 @ SV479 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2582]) ).
thf(2587,plain,
! [SV503: $i,SV969: $i,SV714: $i,SV938: $i,SV243: $i,SV869: $i,SV965: $i] :
( ( ( c_Type_Otyping @ SV965 @ SV869 @ SV243 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV869 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV965 @ SV938 @ SV243 @ tc_Type_Otype ) @ SV714 @ SV969 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV714 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV714 ) @ SV869 ) @ SV938 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV243 ) @ SV503 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2583]) ).
thf(2588,plain,
! [SV268: $i,SV970: $i,SV738: $i,SV940: $i,SV528: $i,SV878: $i,SV966: $i] :
( ( ( c_Type_Otyping @ SV966 @ SV878 @ SV528 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV878 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV966 @ SV940 @ SV528 @ tc_Type_Otype ) @ SV738 @ SV970 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV738 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV738 ) @ SV878 ) @ SV940 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV268 ) @ SV528 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2584]) ).
thf(2589,plain,
! [SV142: $i,SV967: $i,SV414: $i,SV816: $i,SV955: $i,SV914: $i,SV639: $i] :
( ( ( c_Type_Otyping @ SV639 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV914 ) @ SV955 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV816 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV414 )
= $false )
| ( ( c_Type_Otypings @ SV639 @ SV955 @ SV967 )
= $false )
| ( ( c_Type_Otyping @ SV639 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV914 ) @ SV955 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV142 )
= $false )
| ( ( SV142
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV414 @ SV142 @ SV639 @ SV816 ) @ SV414 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2585]) ).
thf(2590,plain,
! [SV856: $i,SV968: $i,SV694: $i,SV479: $i,SV963: $i,SV935: $i,SV217: $i] :
( ( ( c_Type_Otyping @ SV217 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV935 ) @ SV963 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV479 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV694 )
= $false )
| ( ( c_Type_Otypings @ SV217 @ SV963 @ SV968 )
= $false )
| ( ( c_Type_Otyping @ SV217 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV935 ) @ SV963 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV856 )
= $false )
| ( ( c_Type_Otypings @ SV217 @ SV479 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV694 @ SV856 @ SV217 @ SV479 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2586]) ).
thf(2591,plain,
! [SV503: $i,SV969: $i,SV714: $i,SV243: $i,SV938: $i,SV965: $i,SV869: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV869 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV965 @ SV938 @ SV243 @ tc_Type_Otype ) @ SV714 @ SV969 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV714 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV965 @ SV869 @ SV243 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV714 ) @ SV869 ) @ SV938 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV243 ) @ SV503 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2587]) ).
thf(2592,plain,
! [SV268: $i,SV970: $i,SV738: $i,SV528: $i,SV940: $i,SV966: $i,SV878: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV878 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV966 @ SV940 @ SV528 @ tc_Type_Otype ) @ SV738 @ SV970 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV738 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV966 @ SV878 @ SV528 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV738 ) @ SV878 ) @ SV940 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV268 ) @ SV528 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2588]) ).
thf(2593,plain,
! [SV503: $i,SV969: $i,SV714: $i,SV243: $i,SV938: $i,SV965: $i,SV869: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV869 ) )
= $false )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV965 @ SV938 @ SV243 @ tc_Type_Otype ) @ SV714 @ SV969 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV714 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV965 @ SV869 @ SV243 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV714 ) @ SV869 ) @ SV938 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV243 ) @ SV503 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2591]) ).
thf(2594,plain,
! [SV268: $i,SV970: $i,SV738: $i,SV528: $i,SV940: $i,SV966: $i,SV878: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV878 ) )
= $false )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV966 @ SV940 @ SV528 @ tc_Type_Otype ) @ SV738 @ SV970 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV738 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV966 @ SV878 @ SV528 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV738 ) @ SV878 ) @ SV940 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV268 ) @ SV528 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2592]) ).
thf(2595,plain,
! [SV503: $i,SV869: $i,SV969: $i,SV714: $i,SV243: $i,SV938: $i,SV965: $i] :
( ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV965 @ SV938 @ SV243 @ tc_Type_Otype ) @ SV714 @ SV969 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV714 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV869 ) )
= $false )
| ( ( c_Type_Otyping @ SV965 @ SV869 @ SV243 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV714 ) @ SV869 ) @ SV938 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV243 ) @ SV503 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2593]) ).
thf(2596,plain,
! [SV268: $i,SV878: $i,SV970: $i,SV738: $i,SV528: $i,SV940: $i,SV966: $i] :
( ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV966 @ SV940 @ SV528 @ tc_Type_Otype ) @ SV738 @ SV970 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV738 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV878 ) )
= $false )
| ( ( c_Type_Otyping @ SV966 @ SV878 @ SV528 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV738 ) @ SV878 ) @ SV940 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV268 ) @ SV528 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2594]) ).
thf(2597,plain,
! [SV503: $i,SV869: $i,SV969: $i,SV714: $i,SV243: $i,SV938: $i,SV965: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV965 @ SV938 @ SV243 @ tc_Type_Otype ) @ SV714 @ SV969 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV714 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV869 ) )
= $false )
| ( ( c_Type_Otyping @ SV965 @ SV869 @ SV243 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV714 ) @ SV869 ) @ SV938 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV243 ) @ SV503 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2595]) ).
thf(2598,plain,
! [SV268: $i,SV878: $i,SV970: $i,SV738: $i,SV528: $i,SV940: $i,SV966: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV966 @ SV940 @ SV528 @ tc_Type_Otype ) @ SV738 @ SV970 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV738 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV878 ) )
= $false )
| ( ( c_Type_Otyping @ SV966 @ SV878 @ SV528 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV738 ) @ SV878 ) @ SV940 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV268 ) @ SV528 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2596]) ).
thf(2599,plain,
! [SV503: $i,SV869: $i,SV969: $i,SV243: $i,SV938: $i,SV965: $i,SV714: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV714 ) )
= $false )
| ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV965 @ SV938 @ SV243 @ tc_Type_Otype ) @ SV714 @ SV969 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV869 ) )
= $false )
| ( ( c_Type_Otyping @ SV965 @ SV869 @ SV243 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV714 ) @ SV869 ) @ SV938 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV243 ) @ SV503 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2597]) ).
thf(2600,plain,
! [SV268: $i,SV878: $i,SV970: $i,SV528: $i,SV940: $i,SV966: $i,SV738: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV738 ) )
= $false )
| ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV966 @ SV940 @ SV528 @ tc_Type_Otype ) @ SV738 @ SV970 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV878 ) )
= $false )
| ( ( c_Type_Otyping @ SV966 @ SV878 @ SV528 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV738 ) @ SV878 ) @ SV940 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV268 ) @ SV528 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2598]) ).
thf(2601,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[662,2600,2599,2590,2589,2580,2578,2575,2572,2571,2570,2569,2568,2567,2562,2561,2560,2559,2556,2555,2553,2552,2551,2549,2548,2546,2543,2542,2541,2540,2536,2533,2532,2529,2528,2527,2526,2525,2522,2520,2519,2518,2517,2516,2515,2514,2511,2503,2502,2489,2488,2485,2482,2481,2477,2476,2472,2471,2470,2463,2462,2453,2452,2449,2444,2443,2442,2441,2440,2439,2434,2431,2423,2422,2420,2414,2412,2411,2410,2407,2406,2405,2403,2399,2397,2396,2395,2392,2391,2389,2388,2386,2385,2384,2383,2376,2356,2345,2339,2338,2337,2336,2335,2334,2333,2332,2331,2330,2329,2328,2327,2316,2315,2314,2313,2312,2311,2310,2309,2308,2307,2301,2300,2296,2295,2293,2292,2291,2290,2289,2288,2285,2284,2281,2280,2279,2273,2271,2269,2268,2267,2264,2263,2262,2261,2260,2258,2257,2246,2243,2241,2240,2239,2235,2234,2231,2229,2227,2225,2224,2222,2221,2220,2219,2217,2216,2215,2208,2197,2184,2181,2172,2171,2167,2166,2165,2164,2163,2162,2160,2154,2144,2143,2140,2136,2135,2134,2133,2132,2131,2130,2127,2108,2107,2103,2101,2100,2099,2089,2084,2083,2076,2074,2069,2063,2059,2058,2051,2036,2034,2033,2031,2029,2028,2014,2008,2007,2001,1992,1982,1981,1980,1979,1958,1952,1950,1936,1929,1928,1919,1918,1917,1916,1915,1914,1912,1911,1906,1899,1898,1890,1889,1884,1868,1838,1832,1783,1779,1775,1765,1751,1728,1717,1710,1707,1655,1653,1652,1627,1612,1611,1601,1600,1527,1513,1481,1476,1446,1442,1439,1418,1414,1413,1384,1351,1350,1326,1321,1320,1319,1318,1317,1247,1238,1231,1228,1224,1211,1174,1154,1094,1014,953,952,951,950,949,948,947,946,945,944,943,942,941,940,939,938,935,934,933,922,913,900,899,895,887,833]) ).
thf(2602,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2601]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL784-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n010.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 12:34:25 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 38.81/8.04 ..
% 38.81/8.04
% 38.81/8.04 No.of.Axioms: 317
% 38.81/8.04
% 38.81/8.04 Length.of.Defs: 0
% 38.81/8.04
% 38.81/8.04 Contains.Choice.Funs: false
% 38.81/8.04 ..................................................................................................
% 38.81/8.04
% 38.81/8.04 ********************************
% 38.81/8.04 * All subproblems solved! *
% 38.81/8.04 ********************************
% 38.81/8.04 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:317,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2601,loop_count:0,foatp_calls:1,translation:fof_full)
% 38.81/8.04
% 38.81/8.04 %**** Beginning of derivation protocol ****
% 38.81/8.04 % SZS output start CNFRefutation
% See solution above
% 38.81/8.06
% 38.81/8.06 %**** End of derivation protocol ****
% 38.81/8.06 %**** no. of clauses in derivation: 2602 ****
% 38.81/8.06 %**** clause counter: 2601 ****
% 38.81/8.06
% 38.81/8.06 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:317,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2601,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------