%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL785-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 10:30:32 AM UTC 2026
% Result : Unsatisfiable 75.62s 12.96s
% Output : CNFRefutation 75.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 419
% Syntax : Number of formulae : 3351 (2357 unt; 0 typ; 0 def)
% Number of atoms : 15134 (6877 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 48321 (3072 ~;3899 |; 0 &;41350 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 105 ( 102 usr; 24 con; 0-5 aty)
% Number of variables : 11483 ( 0 ^;11483 !; 0 ?;11483 :)
% Comments :
%------------------------------------------------------------------------------
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 > $i > $i ).
thf(tp_c_Lambda_Oliftn,type,
c_Lambda_Oliftn: $i > $i > $i > $i ).
thf(tp_c_Lambda_Osubst,type,
c_Lambda_Osubst: $i > $i > $i > $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_Obutlast,type,
c_List_Obutlast: $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_Olast,type,
c_List_Olast: $i > $i > $i ).
thf(tp_c_List_Olist_OCons,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(tp_c_List_Olist_ONil,type,
c_List_Olist_ONil: $i > $i ).
thf(tp_c_List_Olistsp,type,
c_List_Olistsp: $i > $i > $i > $o ).
thf(tp_c_List_Olistsum,type,
c_List_Olistsum: $i > $i > $i ).
thf(tp_c_List_Oreplicate,type,
c_List_Oreplicate: $i > $i > $i > $i ).
thf(tp_c_List_Orev,type,
c_List_Orev: $i > $i > $i ).
thf(tp_c_List_Orotate1,type,
c_List_Orotate1: $i > $i > $i ).
thf(tp_c_List_Osko__List__XCons__eq__append__conv__1__1,type,
c_List_Osko__List__XCons__eq__append__conv__1__1: $i > $i > $i > $i > $i > $i ).
thf(tp_c_List_Osko__List__Xappend__eq__Cons__conv__1__1,type,
c_List_Osko__List__Xappend__eq__Cons__conv__1__1: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Nat_Osemiring__1__class_Oof__nat,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i > $i ).
thf(tp_c_Nat_Osize__class_Osize,type,
c_Nat_Osize__class_Osize: $i > $i > $i ).
thf(tp_c_OrderedGroup_Omonoid__add,type,
c_OrderedGroup_Omonoid__add: $i > $i > $i > $o ).
thf(tp_c_OrderedGroup_Osemigroup__add,type,
c_OrderedGroup_Osemigroup__add: $i > $i > $o ).
thf(tp_c_Predicate_Oconversep,type,
c_Predicate_Oconversep: $i > $i > $i > $i ).
thf(tp_c_Transitive__Closure_Ortranclp,type,
c_Transitive__Closure_Ortranclp: $i > $i > $i ).
thf(tp_c_Type_Oshift,type,
c_Type_Oshift: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Osko__Type__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__Xtypes__snocE__1__2,type,
c_Type_Osko__Type__Xtypes__snocE__1__2: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xtyping__elims__2__1,type,
c_Type_Osko__Type__Xtyping__elims__2__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_Wellfounded_Oaccp,type,
c_Wellfounded_Oaccp: $i > $i > $i > $o ).
thf(tp_c_fequal,type,
c_fequal: $i > $i ).
thf(tp_class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $i > $o ).
thf(tp_class_Nat_Osemiring__char__0,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(tp_class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(tp_class_OrderedGroup_Oab__semigroup__add,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Ocancel__ab__semigroup__add,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Ocancel__semigroup__add,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Ocomm__monoid__add,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(tp_class_OrderedGroup_Olordered__ab__group__add,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(tp_class_OrderedGroup_Omonoid__add,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(tp_class_OrderedGroup_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_class_Ring__and__Field_Osemiring__1,type,
class_Ring__and__Field_Osemiring__1: $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_List_Olist,type,
tc_List_Olist: $i > $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_a____,type,
v_a____: $i ).
thf(tp_v_as____,type,
v_as____: $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_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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_X ) @ V_Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(2,axiom,
! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_x ) @ V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(3,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(4,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(5,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(6,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(7,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(8,axiom,
class_Nat_Osemiring__char__0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
thf(9,axiom,
class_OrderedGroup_Omonoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(10,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(11,axiom,
class_OrderedGroup_Osemigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).
thf(12,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(13,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(14,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(15,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(16,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(17,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(18,axiom,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(19,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(20,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(21,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Oorder @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(22,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Opreorder @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(23,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/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
thf(24,axiom,
( v_rs____
= ( c_List_Olist_OCons @ v_a____ @ v_as____ @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(25,axiom,
! [V_dB1_H: $i,V_dB2_H: $i,V_nat: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
thf(26,axiom,
! [V_e: $i,V_t: $i,V_T: $i,V_u: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ V_T @ V_e @ V_t @ V_u ) ) @ V_T ) )
| ~ ( c_Type_Otyping @ V_e @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I2_J_0) ).
thf(27,axiom,
! [V_f: $i,V_a: $i,V_xs: $i,V_ys: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ T_a @ T_b )
= ( c_List_Ofoldl @ V_f @ ( c_List_Ofoldl @ V_f @ V_a @ V_xs @ T_a @ T_b ) @ V_ys @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__append_0) ).
thf(28,axiom,
! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_s @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ V_t @ V_s @ V_k ) ) @ ( c_Lambda_Osubstn @ V_u @ V_s @ V_k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I2_J_0) ).
thf(29,axiom,
! [V_s: $i,V_t: $i,V_n: $i,V_ss: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_t )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
thf(30,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 @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lemma_0) ).
thf(31,axiom,
! [V_rs: $i,V_n: $i,V_v: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ V_rs @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_v ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_0) ).
thf(32,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/sandbox/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).
thf(33,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/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_0) ).
thf(34,axiom,
! [V_m: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OVar @ V_m )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_1) ).
thf(35,axiom,
! [V_r: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ V_r ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_2) ).
thf(36,axiom,
( v_rs____
= ( c_List_Olist_OCons @ v_a____ @ v_as____ @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons_0) ).
thf(37,axiom,
! [V_n: $i,V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ V_n @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ V_n @ V_s @ V_k ) ) @ ( c_Lambda_Oliftn @ V_n @ V_t @ V_k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I2_J_0) ).
thf(38,axiom,
! [V_s: $i,V_u: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_u ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appL_0) ).
thf(39,axiom,
! [V_u: $i,V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_s ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appR_0) ).
thf(40,axiom,
! [V_e: $i,V_us: $i,V_T: $i,V_U: $i,V_i: $i,V_ts: $i,V_Ts: $i] :
( ( c_Type_Otypings @ V_e @ V_us @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ V_T @ V_U @ V_e @ V_us ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_U )
| ~ ( c_Type_Otypings @ V_e @ V_ts @ V_Ts )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_us @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__types_1) ).
thf(41,axiom,
! [V_r: $i,V_ts: $i,V_s: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).
thf(42,axiom,
! [V_s: $i,V_ss: $i,V_r: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ V_r ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_1) ).
thf(43,axiom,
! [V_t: $i] :
( V_t
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2 @ V_t ) @ ( c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1 @ V_t ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__head__tail_0) ).
thf(44,axiom,
! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB1: $i,V_dB2: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ V_f2 @ V_dB1 ) @ V_dB2 ) @ ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ V_dB1 @ T_a ) ) @ ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ V_dB2 @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Orecs_I2_J_0) ).
thf(45,axiom,
! [V_r: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_r )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ V_r )
= V_s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).
thf(46,axiom,
! [V_env: $i,V_x: $i] : ( c_Type_Otyping @ V_env @ ( c_Lambda_OdB_OVar @ V_x ) @ ( hAPP @ V_env @ V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
thf(47,axiom,
! [V_r: $i,V_s: $i,V_t: $i,V_ts: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ V_r @ V_s @ V_t @ V_ts ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_2) ).
thf(48,axiom,
! [V_r: $i] :
( ( c_Lambda_OdB_OAbs @ V_r )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_2) ).
thf(49,axiom,
! [V_f: $i,V_a: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_a @ T_b )
= ( c_List_Ofoldl @ V_f @ ( hAPP @ ( hAPP @ V_f @ V_a ) @ V_x ) @ V_xs @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).
thf(50,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/sandbox/benchmark/theBenchmark.p',cls_list__app__typeE_1) ).
thf(51,axiom,
! [V_f1: $i,V_f2: $i,V_f3: $i,V_nat: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OVar @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I10_J_0) ).
thf(52,axiom,
! [V_m: $i] :
( ( c_Lambda_OdB_OVar @ V_m )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_2) ).
thf(53,axiom,
! [V_e: $i,V_u: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_u @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ V_T @ V_e @ V_t @ V_u ) )
| ~ ( c_Type_Otyping @ V_e @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I2_J_1) ).
thf(54,axiom,
! [V_plus: $i,V_x: $i,V_zero: $i,V_zs: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_plus @ V_x ) @ ( c_List_Ofoldl @ V_plus @ V_zero @ V_zs @ T_a @ T_a ) )
= ( c_List_Ofoldl @ V_plus @ V_x @ V_zs @ T_a @ T_a ) )
| ~ ( c_OrderedGroup_Omonoid__add @ V_zero @ V_plus @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add_Ofoldl__absorb0_0) ).
thf(55,axiom,
! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB1: $i,V_dB2: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) @ T_a )
= ( hAPP @ ( hAPP @ V_f2 @ V_dB1 ) @ V_dB2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I11_J_0) ).
thf(56,axiom,
! [V_v: $i,V_n: $i,V_rs: $i] :
( ( V_v
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_v ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_1) ).
thf(57,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/sandbox/benchmark/theBenchmark.p',cls_list__app__typeI_0) ).
thf(58,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/sandbox/benchmark/theBenchmark.p',cls_nT_0) ).
thf(59,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/sandbox/benchmark/theBenchmark.p',cls_var__app__typesE_0) ).
thf(60,axiom,
c_Type_Otyping @ v_ea______ @ v_ua______ @ v_T____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_I4_J_0) ).
thf(61,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/sandbox/benchmark/theBenchmark.p',cls_list__app__typeE_0) ).
thf(62,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/sandbox/benchmark/theBenchmark.p',cls_Var_I2_J_0) ).
thf(63,axiom,
! [V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ V_s @ V_k ) ) @ ( c_Lambda_Olift @ V_t @ V_k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
thf(64,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_zs: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ T_a )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) @ V_zs @ T_a @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y @ V_zs @ T_a @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__assoc_0) ).
thf(65,axiom,
! [V_e: $i,V_i: $i,V_T: $i] :
( ( ( hAPP @ V_e @ V_i )
= V_T )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OVar @ V_i ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
thf(66,axiom,
! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__IT_0) ).
thf(67,axiom,
! [V_nat: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
thf(68,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_True_0) ).
thf(69,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/sandbox/benchmark/theBenchmark.p',cls_Abs_0) ).
thf(70,axiom,
! [V_f: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Olist_ONil @ T_b ) @ T_a @ T_b )
= V_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
thf(71,axiom,
! [V_e: $i,V_x: $i,V_T: $i,T_a: $i] :
( ( hAPP @ ( c_Type_Oshift @ V_e @ V_x @ V_T @ T_a ) @ V_x )
= V_T ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__eq_0) ).
thf(72,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 @ ( 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/sandbox/benchmark/theBenchmark.p',cls_MI1_0) ).
thf(73,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 @ ( 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/sandbox/benchmark/theBenchmark.p',cls_MI2_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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).
thf(89,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/sandbox/benchmark/theBenchmark.p',cls_App_0) ).
thf(90,axiom,
! [V_i: $i,V_t: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
thf(91,axiom,
! [V_r: $i,V_s: $i,V_t: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_0) ).
thf(92,axiom,
! [V_r: $i,V_ss: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta2_0) ).
thf(93,axiom,
! [V_e: $i,V_i: $i,V_T: $i,T_a: $i,V_j: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ V_e @ V_i @ V_T @ T_a ) @ V_j )
= ( hAPP @ V_e @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__gt_0) ).
thf(94,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/sandbox/benchmark/theBenchmark.p',cls_var__app__types_0) ).
thf(95,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/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_1) ).
thf(96,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_dB1: $i,V_dB2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_dB1 ) @ V_dB2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit_1) ).
thf(97,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_xb: $i,V_xc: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_xb ) @ V_xc ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_xb ) @ V_xc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit__asm_1) ).
thf(98,axiom,
! [V_k: $i,V_u: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_k ) @ V_u @ V_k )
= V_u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).
thf(99,axiom,
! [V_m: $i,V_rs: $i,V_n: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_rs = V_ss ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).
thf(100,axiom,
! [V_m: $i,V_rs: $i,V_n: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).
thf(101,axiom,
! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_t ) @ V_t_H ) )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
thf(102,axiom,
! [V_dB_H: $i,V_dB1: $i,V_dB2: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
thf(103,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_nat: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OVar @ V_nat ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit_0) ).
thf(104,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_xd: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OVar @ V_xd ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_xd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit__asm_0) ).
thf(105,axiom,
! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OVar @ V_nat_H ) )
| ( V_nat = V_nat_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
thf(106,axiom,
! [V_e: $i,V_ts: $i,V_T: $i,V_i: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ V_T @ V_e @ V_i @ V_ts ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__typesE_1) ).
thf(107,axiom,
! [V_dB1: $i,V_dB2: $i,V_dB_H: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
thf(108,axiom,
! [V_dB_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
thf(109,axiom,
! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_s @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ V_t @ V_s @ V_k ) ) @ ( c_Lambda_Osubst @ V_u @ V_s @ V_k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__App_0) ).
thf(110,axiom,
! [V_r: $i,V_s: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_4) ).
thf(111,axiom,
c_Type_Otyping @ v_e____ @ v_u____ @ v_T____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uT_0) ).
thf(112,axiom,
! [V_plus: $i,V_x: $i,V_y: $i,V_zs: $i,T_a: $i] :
( ( ( c_List_Ofoldl @ V_plus @ ( hAPP @ ( hAPP @ V_plus @ V_x ) @ V_y ) @ V_zs @ T_a @ T_a )
= ( hAPP @ ( hAPP @ V_plus @ V_x ) @ ( c_List_Ofoldl @ V_plus @ V_y @ V_zs @ T_a @ T_a ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ V_plus @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_semigroup__add_Ofoldl__assoc_0) ).
thf(113,axiom,
! [V_P: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ V_P ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ V_P ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ V_P @ V_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lem_3) ).
thf(114,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 ) @ ( c_Lambda_Olift @ V_t @ V_i ) @ V_T )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__type_0) ).
thf(115,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(116,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(117,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(118,axiom,
! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__into__rtrancl_0) ).
thf(119,axiom,
! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclp__into__rtranclp_0) ).
thf(120,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(121,axiom,
! [V_xs: $i,V_x: $i,V_ts: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_x @ V_ts @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_x @ T_a ) @ V_ts @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).
thf(122,axiom,
! [V_zs: $i,V_x: $i,T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ V_zs @ V_x @ T_a ) @ V_ys @ T_a )
= ( c_List_Oappend @ V_zs @ ( c_List_Oappend @ V_x @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).
thf(123,axiom,
! [V_xs: $i,V_xs1: $i,V_us: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_xs1 @ V_us @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_xs1 @ T_a ) @ V_us @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).
thf(124,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i,V_zs: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_zs @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_ys @ V_zs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__assoc_0) ).
thf(125,axiom,
! [T_a: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).
thf(126,axiom,
! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
( ( ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
!= ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).
thf(127,axiom,
! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
( ( ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
!= ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_xs = V_ys ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).
thf(128,axiom,
! [V_r: $i,V_x: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_5) ).
thf(129,axiom,
! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_1) ).
thf(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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(132,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
thf(133,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
thf(134,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
thf(135,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
thf(136,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
thf(137,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
thf(138,axiom,
! [T_a: $i,V_x: $i,V_xs: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).
thf(139,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/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_0) ).
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_type2 = V_type2_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_1) ).
thf(141,axiom,
! [V_ys: $i,V_xs: $i,T_a: $i] :
( ( V_ys
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).
thf(142,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= V_ys )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).
thf(143,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( V_xs
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_0) ).
thf(144,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= V_xs )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__self__conv_0) ).
thf(145,axiom,
! [V_r: $i,V_i: $i,V_j: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_r @ ( c_Lambda_OdB_OVar @ V_i ) @ V_j ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).
thf(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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_foldr_Osimps_I2_J_0) ).
thf(149,axiom,
! [V_j: $i,V_u: $i,V_i: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_j ) @ V_u @ V_i )
= ( c_Lambda_OdB_OVar @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lt_0) ).
thf(150,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
thf(151,axiom,
! [V_t: $i,V_s: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_Lambda_Osubst @ V_t @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn__subst__0_0) ).
thf(152,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ T_a )
| ( c_OrderedGroup_Osemigroup__add @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_semigroup__add__class_Oaxioms_0) ).
thf(153,axiom,
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
thf(154,axiom,
! [V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_t @ V_k )
= V_t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn__0_0) ).
thf(155,axiom,
! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OAbs @ V_dB ) @ T_a )
= ( hAPP @ ( hAPP @ V_f3 @ V_dB ) @ ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ V_dB @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Orecs_I3_J_0) ).
thf(156,axiom,
! [V_A: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_ys @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_xs @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_2) ).
thf(157,axiom,
! [V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(158,axiom,
! [V_ys: $i,V_xs: $i,V_y: $i,V_x: $i,V_r: $i,T_a: $i] :
( ( V_ys = V_xs )
| ( V_y = V_x )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_2) ).
thf(159,axiom,
! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_xs @ T_a @ T_a )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__foldr1_0) ).
thf(160,axiom,
! [T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
thf(161,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
thf(162,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(163,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(164,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(165,axiom,
! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(166,axiom,
! [V_P: $i,V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_n ) @ V_m ) )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).
thf(167,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(168,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(169,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(170,axiom,
! [V_plus: $i,V_a: $i,V_b: $i,V_c: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_plus @ ( hAPP @ ( hAPP @ V_plus @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ V_plus @ V_a ) @ ( hAPP @ ( hAPP @ V_plus @ V_b ) @ V_c ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ V_plus @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_semigroup__add_Oadd__assoc_0) ).
thf(171,axiom,
! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( V_xs = V_ys )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_3) ).
thf(172,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
thf(173,axiom,
! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ V_r @ V_i ) ) @ ( c_Lambda_Olift @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_H_0) ).
thf(174,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 ) ) @ ( c_Lambda_Osubst @ V_s @ V_t @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta_0) ).
thf(175,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(176,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(177,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(178,axiom,
! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(179,axiom,
! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(180,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).
thf(181,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).
thf(182,axiom,
! [V_dB: $i,V_dB_H: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_dB )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) )
| ( V_dB = V_dB_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
thf(183,axiom,
! [T_a: $i,V_xs: $i,V_ys: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).
thf(184,axiom,
! [T_a: $i,V_xs: $i,V_ys: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).
thf(185,axiom,
! [V_t: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ V_t @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__IT_0) ).
thf(186,axiom,
! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ( V_i = V_k )
| ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_2) ).
thf(187,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 @ ( c_Lambda_Osubst @ V_r @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Beta_0) ).
thf(188,axiom,
! [T_a: $i,V_x: $i,V_zs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_zs @ T_a @ T_a ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x @ V_zs @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__absorb0_0) ).
thf(189,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
thf(190,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
thf(191,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
thf(192,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
thf(193,axiom,
! [V_r: $i,V_xs: $i,T_a: $i] :
~ ( c_ListOrder_Ostep1 @ V_r @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__step1__Nil_0) ).
thf(194,axiom,
! [V_r: $i,T_a: $i,V_xs: $i] :
~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_ONil @ T_a ) @ V_xs @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Nil__step1_0) ).
thf(195,axiom,
! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtranclp_0) ).
thf(196,axiom,
! [T_a: $i,V_xs: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T_a )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ V_a @ T_a @ T_a )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a @ V_xs @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr__conv__foldl_0) ).
thf(197,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
thf(198,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 ) @ ( c_Lambda_Osubst @ V_t @ V_r @ V_i ) ) @ ( c_Lambda_Osubst @ V_t @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta2_H_0) ).
thf(199,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 ) @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) ) @ ( c_Lambda_Osubst @ V_s @ V_t @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_H_0) ).
thf(200,axiom,
! [T_a: $i,V_x: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
thf(201,axiom,
! [V_r: $i,V_y: $i,V_x: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ( V_y = V_x )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_3) ).
thf(202,axiom,
! [V_f: $i,V_xs: $i,V_ys: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ V_a @ T_b @ T_a )
= ( c_List_Ofoldr @ V_f @ V_xs @ ( c_List_Ofoldr @ V_f @ V_ys @ V_a @ T_b @ T_a ) @ T_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr__append_0) ).
thf(203,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(204,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(205,axiom,
! [T_a: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(206,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 ) @ ( c_Lambda_Osubst @ V_t @ V_r @ V_i ) ) @ ( c_Lambda_Osubst @ V_t @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta2_0) ).
thf(207,axiom,
! [V_ys: $i,T_a: $i] :
( V_ys
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).
thf(208,axiom,
! [T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a )
= V_ys ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil_0) ).
thf(209,axiom,
! [V_xs: $i,T_a: $i] :
( V_xs
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_1) ).
thf(210,axiom,
! [V_x: $i,T_a: $i] :
( V_x
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).
thf(211,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil2_0) ).
thf(212,axiom,
! [V_r: $i,T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__trans_0) ).
thf(213,axiom,
! [V_r: $i,T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Ortranclp__def_1) ).
thf(214,axiom,
! [V_r: $i,T_a: $i,V_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__refl_0) ).
thf(215,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
thf(216,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
thf(217,axiom,
! [V_plus: $i,V_zero: $i,V_a: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_plus @ V_zero ) @ V_a )
= V_a )
| ~ ( c_OrderedGroup_Omonoid__add @ V_zero @ V_plus @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add_Oadd__0__left_0) ).
thf(218,axiom,
! [V_plus: $i,V_a: $i,V_zero: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_plus @ V_a ) @ V_zero )
= V_a )
| ~ ( c_OrderedGroup_Omonoid__add @ V_zero @ V_plus @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add_Oadd__0__right_0) ).
thf(219,axiom,
! [V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ ( c_Lambda_OdB_OAbs @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs_0) ).
thf(220,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(221,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(222,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(223,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(224,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(225,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
thf(226,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(227,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_x )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(228,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__idemp_0) ).
thf(229,axiom,
! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).
thf(230,axiom,
! [V_ys: $i,V_xs: $i,V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( V_ys = V_xs )
| ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_0) ).
thf(231,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).
thf(232,axiom,
! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= ( c_Lambda_Oliftn @ V_x @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_1) ).
thf(233,axiom,
! [V_xs: $i,V_x: $i,T_a: $i] :
( V_xs
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(234,axiom,
! [V_x: $i,V_t: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_t @ T_a )
!= V_t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(235,axiom,
! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ V_r @ V_i ) ) @ ( c_Lambda_Olift @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
thf(236,axiom,
! [V_i: $i,V_k: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
thf(237,axiom,
! [V_t: $i,V_k: $i,V_s: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ V_k ) @ V_s @ V_k )
= V_t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lift_0) ).
thf(238,axiom,
! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_H_0) ).
thf(239,axiom,
! [V_n: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_0) ).
thf(240,axiom,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_u____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uIT_0) ).
thf(241,axiom,
! [V_s: $i,V_t: $i,V_s_H: $i,V_t_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s_H ) @ V_t_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__App_0) ).
thf(242,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(243,axiom,
! [V_r: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ V_r ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).
thf(244,axiom,
! [V_x: $i,V_y: $i,V_r: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( V_x = V_y )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_0) ).
thf(245,axiom,
! [V_a_H: $i,V_list_H: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
thf(246,axiom,
! [V_x: $i,V_xa: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xa @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
thf(247,axiom,
! [V_x: $i,V_xs1: $i,V_zs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xs1 @ V_zs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xs1 @ T_a ) @ V_zs @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).
thf(248,axiom,
! [V_x: $i,V_xa: $i,V_zs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xa @ V_zs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ V_zs @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).
thf(249,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_a )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) )
| ( V_b = V_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
thf(250,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) )
| ( V_b = V_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
thf(251,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) )
| ( V_b = V_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(252,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) )
| ( V_y = V_z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
thf(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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
thf(259,axiom,
! [V_r: $i,V_y: $i,V_x: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_1) ).
thf(260,axiom,
! [V_f: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Olist_ONil @ T_b ) @ V_a @ T_b @ T_a )
= V_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr_Osimps_I1_J_0) ).
thf(261,axiom,
! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= V_s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_1) ).
thf(262,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i,V_u: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_u ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z )
= V_u ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(263,axiom,
! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).
thf(264,axiom,
! [V_m: $i] :
~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
thf(265,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(266,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_d ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(267,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(268,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ V_d ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(269,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(270,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(271,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(272,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(273,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) ) @ V_z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(274,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(275,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(276,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
thf(277,axiom,
! [V_t: $i,V_s: $i,V_n: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ V_n )
= ( c_Lambda_Osubst @ V_t @ ( c_Lambda_Oliftn @ V_n @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn__subst__n_0) ).
thf(278,axiom,
! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_x: $i] :
( ~ ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ V_x @ T_a ) @ ( c_List_Oappend @ V_xs @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__step1I_0) ).
thf(279,axiom,
! [V_r: $i,V_x: $i,V_vs: $i,T_a: $i,V_us: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_x @ V_vs @ T_a ) @ ( c_List_Oappend @ V_x @ V_us @ T_a ) @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ V_vs @ V_us @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__step1I_1) ).
thf(280,axiom,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_ua______ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_I3_J_0) ).
thf(281,axiom,
! [V_s: $i,V_s_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ ( c_Lambda_OdB_OAbs @ V_s_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__Abs_0) ).
thf(282,axiom,
! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ( V_i = V_k )
| ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_2) ).
thf(283,axiom,
! [V_A: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Olistsp @ V_A @ V_xs @ T_a )
| ~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_0) ).
thf(284,axiom,
! [V_A: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_List_Olistsp @ V_A @ V_ys @ T_a )
| ~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_1) ).
thf(285,axiom,
! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OAbs @ V_dB ) @ T_a )
= ( hAPP @ V_f3 @ V_dB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I12_J_0) ).
thf(286,axiom,
! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) ) @ ( c_Lambda_Osubst @ V_s @ V_t @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
thf(287,axiom,
! [V_x: $i,V_y: $i,V_xs: $i,V_ys: $i,V_r: $i,T_a: $i] :
( ( V_x = V_y )
| ( V_xs = V_ys )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_2) ).
thf(288,axiom,
! [V_r: $i,V_y: $i,V_xa: $i,V_x: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_xa ) )
| ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_xa @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_4) ).
thf(289,axiom,
! [V_A: $i,T_a: $i] : ( c_List_Olistsp @ V_A @ ( c_List_Olist_ONil @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).
thf(290,axiom,
! [V_ys: $i,V_xs: $i,T_a: $i,V_zs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_xs @ T_a )
!= ( c_List_Oappend @ V_zs @ V_xs @ T_a ) )
| ( V_ys = V_zs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
thf(291,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i,V_zs: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Oappend @ V_xs @ V_zs @ T_a ) )
| ( V_ys = V_zs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
thf(292,axiom,
! [V_P: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_t ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ V_P ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4 @ V_P ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ V_P ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ V_P ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Apps__dB__induct_5) ).
thf(293,axiom,
! [V_P: $i,V_t: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ V_P ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__4 @ V_P ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ V_P ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ V_P ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ V_P @ V_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lem_5) ).
thf(294,axiom,
! [V_r: $i,V_s: $i,V_t: $i,V_ts: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ V_r @ V_s @ V_t @ V_ts ) @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_1) ).
thf(295,axiom,
! [V_r: $i,V_s: $i,V_xa: $i] :
( ( V_r
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s ) @ V_xa @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s ) @ ( c_List_Oappend @ V_xa @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_5) ).
thf(296,axiom,
! [V_t: $i,V_ts: $i,V_u: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_u )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Oappend @ V_ts @ ( c_List_Olist_OCons @ V_u @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_app__last_0) ).
thf(297,axiom,
! [V_x: $i,V_s: $i,V_t: $i] :
( ( ( c_List_Oappend @ V_x @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_x @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_s )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Oappend @ V_x @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_3) ).
thf(298,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
thf(299,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
thf(300,axiom,
! [V_n: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_n ) ) )
| ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_1) ).
thf(301,axiom,
! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ V_xs @ T_a )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsum__foldr_0) ).
thf(302,axiom,
! [V_r: $i,V_s: $i,V_ss: $i] :
( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ V_r @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_s @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) ) @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__induction__lemma_0) ).
thf(303,axiom,
! [V_i: $i,V_x: $i,T_a: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_i @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oreplicate @ V_i @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__append__same_0) ).
thf(304,axiom,
! [V_x: $i,V_xs: $i,T_b: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_b )
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_b ) @ T_b ) @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__simps_1) ).
thf(305,axiom,
! [V_ys: $i,T_a: $i,V_y: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_1) ).
thf(306,axiom,
! [V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_0) ).
thf(307,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Orev @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev_Osimps_I2_J_0) ).
thf(308,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i,V_zs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
!= ( c_List_Oappend @ V_ys @ V_zs @ T_a ) )
| ( ( c_List_Olist_OCons @ V_x @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ T_a )
= V_ys )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_0) ).
thf(309,axiom,
! [V_ys: $i,V_zs: $i,T_a: $i,V_x: $i,V_xs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_zs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ V_zs @ T_a )
= V_xs )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_1) ).
thf(310,axiom,
! [V_xs: $i,V_x: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__snoc_0) ).
thf(311,axiom,
! [V_xs: $i,V_x: $i,T_a: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= V_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__snoc_0) ).
thf(312,axiom,
! [V_ys: $i,V_zs: $i,T_a: $i,V_x: $i,V_xs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_zs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( V_ys
= ( c_List_Olist_OCons @ V_x @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_0) ).
thf(313,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i,V_zs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
!= ( c_List_Oappend @ V_ys @ V_zs @ T_a ) )
| ( V_xs
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ V_zs @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_1) ).
thf(314,axiom,
! [T_a: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__greater__0__conv_0) ).
thf(315,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Obutlast @ V_ys @ T_a ) @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__append_1) ).
thf(316,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__append_0) ).
thf(317,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Olast @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__append_1) ).
thf(318,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Obutlast @ V_xs @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__append_0) ).
thf(319,axiom,
! [V_n: $i,V_x: $i,T_a: $i,V_xs: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__app__Cons__same_0) ).
thf(320,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i,V_zs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
!= ( c_List_Oappend @ V_ys @ V_zs @ T_a ) )
| ( V_xs
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ V_zs @ T_a ) )
| ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
= V_zs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_3) ).
thf(321,axiom,
! [V_ys: $i,V_zs: $i,T_a: $i,V_x: $i,V_xs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_zs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( V_ys
= ( c_List_Olist_OCons @ V_x @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ T_a ) )
| ( V_zs
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_2) ).
thf(322,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i,V_zs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
!= ( c_List_Oappend @ V_ys @ V_zs @ T_a ) )
| ( ( c_List_Olist_OCons @ V_x @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ T_a )
= V_ys )
| ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
= V_zs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_2) ).
thf(323,axiom,
! [V_ys: $i,V_zs: $i,T_a: $i,V_x: $i,V_xs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_zs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ V_zs @ T_a )
= V_xs )
| ( V_zs
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_3) ).
thf(324,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_1) ).
thf(325,axiom,
! [V_x: $i,T_a: $i] :
( ( c_List_Olast @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= V_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last_Osimps_0) ).
thf(326,axiom,
! [V_x: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_0) ).
thf(327,axiom,
! [V_xs: $i,T_a: $i,V_x: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__singleton__conv_0) ).
thf(328,axiom,
! [V_x: $i,T_a: $i,V_xs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a )
!= ( c_List_Orev @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__rev__conv_0) ).
thf(329,axiom,
! [V_x: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__singleton__conv_1) ).
thf(330,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last_Osimps_1) ).
thf(331,axiom,
! [V_x: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__rev__conv_1) ).
thf(332,axiom,
! [T_a: $i,V_xs: $i,V_ys: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_List_Olistsum @ V_xs @ T_a ) ) @ ( c_List_Olistsum @ V_ys @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsum__append_0) ).
thf(333,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__0__conv_0) ).
thf(334,axiom,
! [T_a: $i,V_n: $i,V_x: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_x @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__replicate_0) ).
thf(335,axiom,
! [V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Oreplicate @ V_n @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__empty_0) ).
thf(336,axiom,
! [T_a: $i,V_x: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__replicate_1) ).
thf(337,axiom,
! [T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__0__conv_1) ).
thf(338,axiom,
! [V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__empty_1) ).
thf(339,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
thf(340,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_2) ).
thf(341,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_1) ).
thf(342,axiom,
! [T_a: $i,V_x: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_List_Olistsum @ V_xs @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsum_Osimps_I2_J_0) ).
thf(343,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsum_Osimps_I1_J_0) ).
thf(344,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
thf(345,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
thf(346,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
thf(347,axiom,
! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
thf(348,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_List_Oappend @ ( c_List_Obutlast @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= V_xs )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__butlast__last__id_0) ).
thf(349,axiom,
! [V_r: $i,V_a: $i,T_a: $i,V_b: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__downward_0) ).
thf(350,axiom,
! [V_r: $i,V_y: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_y @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_a ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp_Ocases_0) ).
thf(351,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__add_0) ).
thf(352,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orev @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__rev_0) ).
thf(353,axiom,
! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Orev @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_1) ).
thf(354,axiom,
! [T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast_Osimps_I1_J_0) ).
thf(355,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
thf(356,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
thf(357,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_k ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
thf(358,axiom,
! [V_j: $i,V_i: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_i ) @ V_i @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
thf(359,axiom,
! [V_i: $i,V_j: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_i @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
thf(360,axiom,
! [V_r: $i,T_a: $i,T_b: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ T_b @ T_a )
= V_r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep__conversep_0) ).
thf(361,axiom,
! [T_a: $i,V_xs: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Orev @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_0) ).
thf(362,axiom,
! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( tc_List_Olist @ T_a ) )
= V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__replicate_0) ).
thf(363,axiom,
! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Olistsum @ V_xs @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsum__rev_0) ).
thf(364,axiom,
! [V_xs: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Orev @ V_ys @ T_a ) )
| ( V_xs = V_ys ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__rev__conv_0) ).
thf(365,axiom,
! [V_n: $i,V_m: $i,V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_m @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__add_0) ).
thf(366,axiom,
! [V_i: $i,V_k: $i,V_j: $i,V_l: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_l ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_l @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
thf(367,axiom,
! [V_n: $i,V_x: $i,T_a: $i,V_k: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__replicate__commute_0) ).
thf(368,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) @ ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__append_0) ).
thf(369,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate1 @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__rotate1_0) ).
thf(370,axiom,
! [T_a: $i] :
( ( c_Predicate_Oconversep @ ( c_fequal @ T_a ) @ T_a @ T_a )
= ( c_fequal @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep__eq_0) ).
thf(371,axiom,
! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).
thf(372,axiom,
! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).
thf(373,axiom,
! [V_x: $i,V_a: $i] :
( ( V_x
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
thf(374,axiom,
! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= V_m )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
thf(375,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
thf(376,axiom,
! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= ( c_List_Oreplicate @ V_n @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__replicate_0) ).
thf(377,axiom,
! [V_m: $i,V_l: $i,V_k: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_l )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_l @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
thf(378,axiom,
! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
thf(379,axiom,
! [V_i: $i,V_m: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_j ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
thf(380,axiom,
! [V_i: $i,V_j: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_m ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).
thf(381,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
thf(382,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_z @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
thf(383,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
thf(384,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__rev__ident_0) ).
thf(385,axiom,
! [V_ys: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Orev @ V_ys @ T_a ) @ T_a )
= V_ys ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__swap_1) ).
thf(386,axiom,
! [V_xs: $i,T_a: $i] :
( V_xs
= ( c_List_Orev @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__swap_0) ).
thf(387,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_List_Orotate1 @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate1__is__Nil__conv_0) ).
thf(388,axiom,
! [V_r: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_r @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termi__implies__IT_0) ).
thf(389,axiom,
! [V_t: $i] :
( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_t @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT__implies__termi_0) ).
thf(390,axiom,
! [V_r: $i,V_b: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__downwards__aux_0) ).
thf(391,axiom,
! [V_r: $i,V_b: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__downwards_0) ).
thf(392,axiom,
! [V_m: $i,V_x: $i,T_a: $i,V_n: $i,V_y: $i] :
( ( ( c_List_Oreplicate @ V_m @ V_x @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_y @ T_a ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).
thf(393,axiom,
! [T_a: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__simps_0) ).
thf(394,axiom,
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_2) ).
thf(395,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
thf(396,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) ) @ V_k )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
thf(397,axiom,
! [V_r: $i,T_a: $i,T_b: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep_Ointros_0) ).
thf(398,axiom,
! [V_r: $i,V_a2: $i,V_a1: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a2 ) @ V_a1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a1 ) @ V_a2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep_Ocases_0) ).
thf(399,axiom,
! [V_r: $i,T_a: $i,T_b: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep__iff_1) ).
thf(400,axiom,
! [V_r: $i,V_b: $i,V_a: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversepD_0) ).
thf(401,axiom,
! [V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__converseD_0) ).
thf(402,axiom,
! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__converseI_0) ).
thf(403,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_y )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_z ) )
| ( V_y = V_z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
thf(404,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_k )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
thf(405,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
thf(406,axiom,
! [V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= V_x )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__replicate_0) ).
thf(407,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_2) ).
thf(408,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_0) ).
thf(409,axiom,
! [V_m: $i,V_x: $i,T_a: $i,V_n: $i,V_y: $i] :
( ( ( c_List_Oreplicate @ V_m @ V_x @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_y @ T_a ) )
| ( V_x = V_y )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_1) ).
thf(410,axiom,
! [V_x: $i] :
( V_x
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
thf(411,axiom,
! [V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n )
= V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
thf(412,axiom,
! [V_m: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= V_m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(413,axiom,
! [T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_1) ).
thf(414,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__append_0) ).
thf(415,axiom,
! [V_e: $i,V_t: $i,V_Ts: $i,V_ts: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ V_Ts @ V_e @ V_t @ V_ts ) )
| ~ ( c_Type_Otypings @ V_e @ ( c_List_Oappend @ V_ts @ ( c_List_Olist_OCons @ V_t @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ V_Ts ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_types__snocE_2) ).
thf(416,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__greater__0__conv_1) ).
thf(417,axiom,
! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ V_xs @ T_a )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_xs @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsum_0) ).
thf(418,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(419,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[418]) ).
thf(420,negated_conjecture,
~ ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) ) @ v_a____ ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_T_H____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(421,plain,
$false = $false,
inference(unfold_def,[status(thm)],[419]) ).
thf(422,plain,
( ( ! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_X ) @ V_Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(423,plain,
( ( ! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_x ) @ V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(424,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(425,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(426,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(427,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(428,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(429,plain,
( ( class_Nat_Osemiring__char__0 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(430,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(431,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(432,plain,
( ( class_OrderedGroup_Osemigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(433,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(434,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(435,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(436,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(437,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(438,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(439,plain,
( ( class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(440,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(441,plain,
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(442,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)],[21]) ).
thf(443,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)],[22]) ).
thf(444,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)],[23]) ).
thf(445,plain,
( ( v_rs____
= ( c_List_Olist_OCons @ v_a____ @ v_as____ @ tc_Lambda_OdB ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(446,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)],[25]) ).
thf(447,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i,V_u: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ V_T @ V_e @ V_t @ V_u ) ) @ V_T ) )
| ~ ( c_Type_Otyping @ V_e @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(448,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)],[27]) ).
thf(449,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)],[28]) ).
thf(450,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)],[29]) ).
thf(451,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 @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(452,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)],[31]) ).
thf(453,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)],[32]) ).
thf(454,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)],[33]) ).
thf(455,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)],[34]) ).
thf(456,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)],[35]) ).
thf(457,plain,
( ( v_rs____
= ( c_List_Olist_OCons @ v_a____ @ v_as____ @ tc_Lambda_OdB ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(458,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)],[37]) ).
thf(459,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)],[38]) ).
thf(460,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)],[39]) ).
thf(461,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)],[40]) ).
thf(462,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)],[41]) ).
thf(463,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)],[42]) ).
thf(464,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)],[43]) ).
thf(465,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)],[44]) ).
thf(466,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)],[45]) ).
thf(467,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)],[46]) ).
thf(468,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)],[47]) ).
thf(469,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)],[48]) ).
thf(470,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)],[49]) ).
thf(471,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)],[50]) ).
thf(472,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)],[51]) ).
thf(473,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)],[52]) ).
thf(474,plain,
( ( ! [V_e: $i,V_u: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_u @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ V_T @ V_e @ V_t @ V_u ) )
| ~ ( c_Type_Otyping @ V_e @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(475,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)],[54]) ).
thf(476,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)],[55]) ).
thf(477,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)],[56]) ).
thf(478,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)],[57]) ).
thf(479,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)],[58]) ).
thf(480,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)],[59]) ).
thf(481,plain,
( ( c_Type_Otyping @ v_ea______ @ v_ua______ @ v_T____ )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(482,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)],[61]) ).
thf(483,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)],[62]) ).
thf(484,plain,
( ( ! [V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ V_s @ V_k ) ) @ ( c_Lambda_Olift @ V_t @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(485,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)],[64]) ).
thf(486,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)],[65]) ).
thf(487,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(488,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)],[67]) ).
thf(489,plain,
( ( v_n____ = v_i____ )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(490,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)],[69]) ).
thf(491,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)],[70]) ).
thf(492,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)],[71]) ).
thf(493,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 @ ( 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)],[72]) ).
thf(494,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 @ ( 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)],[73]) ).
thf(495,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(496,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(497,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(498,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(499,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(500,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(501,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(502,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(503,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(504,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(505,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(506,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(507,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(508,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(509,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(510,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)],[89]) ).
thf(511,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)],[90]) ).
thf(512,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)],[91]) ).
thf(513,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)],[92]) ).
thf(514,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)],[93]) ).
thf(515,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)],[94]) ).
thf(516,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)],[95]) ).
thf(517,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)],[96]) ).
thf(518,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)],[97]) ).
thf(519,plain,
( ( ! [V_k: $i,V_u: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_k ) @ V_u @ V_k )
= V_u ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(520,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)],[99]) ).
thf(521,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)],[100]) ).
thf(522,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)],[101]) ).
thf(523,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)],[102]) ).
thf(524,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)],[103]) ).
thf(525,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)],[104]) ).
thf(526,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)],[105]) ).
thf(527,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)],[106]) ).
thf(528,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)],[107]) ).
thf(529,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)],[108]) ).
thf(530,plain,
( ( ! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_s @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ V_t @ V_s @ V_k ) ) @ ( c_Lambda_Osubst @ V_u @ V_s @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(531,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)],[110]) ).
thf(532,plain,
( ( c_Type_Otyping @ v_e____ @ v_u____ @ v_T____ )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(533,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)],[112]) ).
thf(534,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)],[113]) ).
thf(535,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 ) @ ( c_Lambda_Olift @ V_t @ V_i ) @ V_T )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(536,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)],[115]) ).
thf(537,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)],[116]) ).
thf(538,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)],[117]) ).
thf(539,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)],[118]) ).
thf(540,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)],[119]) ).
thf(541,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)],[120]) ).
thf(542,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)],[121]) ).
thf(543,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)],[122]) ).
thf(544,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)],[123]) ).
thf(545,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)],[124]) ).
thf(546,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)],[125]) ).
thf(547,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)],[126]) ).
thf(548,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)],[127]) ).
thf(549,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)],[128]) ).
thf(550,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)],[129]) ).
thf(551,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(552,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(553,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)],[132]) ).
thf(554,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)],[133]) ).
thf(555,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)],[134]) ).
thf(556,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)],[135]) ).
thf(557,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)],[136]) ).
thf(558,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)],[137]) ).
thf(559,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)],[138]) ).
thf(560,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)],[139]) ).
thf(561,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)],[140]) ).
thf(562,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)],[141]) ).
thf(563,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)],[142]) ).
thf(564,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)],[143]) ).
thf(565,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)],[144]) ).
thf(566,plain,
( ( ! [V_r: $i,V_i: $i,V_j: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( 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)],[145]) ).
thf(567,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(568,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(569,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(570,plain,
( ( ! [V_j: $i,V_u: $i,V_i: $i] :
( ( ( 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)],[149]) ).
thf(571,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)],[150]) ).
thf(572,plain,
( ( ! [V_t: $i,V_s: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_Lambda_Osubst @ V_t @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(573,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)],[152]) ).
thf(574,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)],[153]) ).
thf(575,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)],[154]) ).
thf(576,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)],[155]) ).
thf(577,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)],[156]) ).
thf(578,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)],[157]) ).
thf(579,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)],[158]) ).
thf(580,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)],[159]) ).
thf(581,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)],[160]) ).
thf(582,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)],[161]) ).
thf(583,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)],[162]) ).
thf(584,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)],[163]) ).
thf(585,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)],[164]) ).
thf(586,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)],[165]) ).
thf(587,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)],[166]) ).
thf(588,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)],[167]) ).
thf(589,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)],[168]) ).
thf(590,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)],[169]) ).
thf(591,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)],[170]) ).
thf(592,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)],[171]) ).
thf(593,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)],[172]) ).
thf(594,plain,
( ( ! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ V_r @ V_i ) ) @ ( 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)],[173]) ).
thf(595,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 ) ) @ ( c_Lambda_Osubst @ V_s @ V_t @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(596,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)],[175]) ).
thf(597,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)],[176]) ).
thf(598,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)],[177]) ).
thf(599,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(600,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(601,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)],[180]) ).
thf(602,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)],[181]) ).
thf(603,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)],[182]) ).
thf(604,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)],[183]) ).
thf(605,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)],[184]) ).
thf(606,plain,
( ( ! [V_t: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ V_t @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(607,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)],[186]) ).
thf(608,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 @ ( 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)],[187]) ).
thf(609,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)],[188]) ).
thf(610,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)],[189]) ).
thf(611,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)],[190]) ).
thf(612,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)],[191]) ).
thf(613,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)],[192]) ).
thf(614,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)],[193]) ).
thf(615,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)],[194]) ).
thf(616,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)],[195]) ).
thf(617,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)],[196]) ).
thf(618,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)],[197]) ).
thf(619,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 ) @ ( c_Lambda_Osubst @ V_t @ V_r @ V_i ) ) @ ( 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)],[198]) ).
thf(620,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 ) @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) ) @ ( 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)],[199]) ).
thf(621,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)],[200]) ).
thf(622,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)],[201]) ).
thf(623,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)],[202]) ).
thf(624,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)],[203]) ).
thf(625,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)],[204]) ).
thf(626,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)],[205]) ).
thf(627,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 ) @ ( c_Lambda_Osubst @ V_t @ V_r @ V_i ) ) @ ( 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)],[206]) ).
thf(628,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)],[207]) ).
thf(629,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)],[208]) ).
thf(630,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)],[209]) ).
thf(631,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)],[210]) ).
thf(632,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)],[211]) ).
thf(633,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)],[212]) ).
thf(634,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)],[213]) ).
thf(635,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)],[214]) ).
thf(636,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)],[215]) ).
thf(637,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)],[216]) ).
thf(638,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)],[217]) ).
thf(639,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)],[218]) ).
thf(640,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)],[219]) ).
thf(641,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)],[220]) ).
thf(642,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)],[221]) ).
thf(643,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)],[222]) ).
thf(644,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)],[223]) ).
thf(645,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)],[224]) ).
thf(646,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)],[225]) ).
thf(647,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)],[226]) ).
thf(648,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)],[227]) ).
thf(649,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)],[228]) ).
thf(650,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)],[229]) ).
thf(651,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)],[230]) ).
thf(652,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)],[231]) ).
thf(653,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)],[232]) ).
thf(654,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)],[233]) ).
thf(655,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)],[234]) ).
thf(656,plain,
( ( ! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ V_r @ V_i ) ) @ ( c_Lambda_Olift @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(657,plain,
( ( ! [V_i: $i,V_k: $i] :
( ( ( 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)],[236]) ).
thf(658,plain,
( ( ! [V_t: $i,V_k: $i,V_s: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ V_k ) @ V_s @ V_k )
= V_t ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(659,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)],[238]) ).
thf(660,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)],[239]) ).
thf(661,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_u____ ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(662,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)],[241]) ).
thf(663,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)],[242]) ).
thf(664,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)],[243]) ).
thf(665,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)],[244]) ).
thf(666,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)],[245]) ).
thf(667,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)],[246]) ).
thf(668,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)],[247]) ).
thf(669,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)],[248]) ).
thf(670,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)],[249]) ).
thf(671,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)],[250]) ).
thf(672,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)],[251]) ).
thf(673,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)],[252]) ).
thf(674,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(675,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(676,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(677,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(678,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(679,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(680,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)],[259]) ).
thf(681,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)],[260]) ).
thf(682,plain,
( ( ! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(683,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)],[262]) ).
thf(684,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)],[263]) ).
thf(685,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)],[264]) ).
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 ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
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(unfold_def,[status(thm)],[266]) ).
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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(689,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)],[268]) ).
thf(690,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)],[269]) ).
thf(691,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)],[270]) ).
thf(692,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)],[271]) ).
thf(693,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)],[272]) ).
thf(694,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)],[273]) ).
thf(695,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)],[274]) ).
thf(696,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)],[275]) ).
thf(697,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)],[276]) ).
thf(698,plain,
( ( ! [V_t: $i,V_s: $i,V_n: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ V_n )
= ( 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)],[277]) ).
thf(699,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)],[278]) ).
thf(700,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)],[279]) ).
thf(701,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_ua______ ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(702,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)],[281]) ).
thf(703,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( 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)],[282]) ).
thf(704,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)],[283]) ).
thf(705,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)],[284]) ).
thf(706,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)],[285]) ).
thf(707,plain,
( ( ! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) ) @ ( 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)],[286]) ).
thf(708,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)],[287]) ).
thf(709,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)],[288]) ).
thf(710,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)],[289]) ).
thf(711,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)],[290]) ).
thf(712,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)],[291]) ).
thf(713,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)],[292]) ).
thf(714,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)],[293]) ).
thf(715,plain,
( ( ! [V_r: $i,V_s: $i,V_t: $i,V_ts: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ V_r @ V_s @ V_t @ V_ts ) @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(716,plain,
( ( ! [V_r: $i,V_s: $i,V_xa: $i] :
( ( V_r
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s ) @ V_xa @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s ) @ ( c_List_Oappend @ V_xa @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(717,plain,
( ( ! [V_t: $i,V_ts: $i,V_u: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_u )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Oappend @ V_ts @ ( c_List_Olist_OCons @ V_u @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(718,plain,
( ( ! [V_x: $i,V_s: $i,V_t: $i] :
( ( ( c_List_Oappend @ V_x @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_x @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_s )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Oappend @ V_x @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(719,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(720,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(721,plain,
( ( ! [V_n: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_n ) ) )
| ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(722,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ V_xs @ T_a )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(723,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ V_r @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_s @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) ) @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(724,plain,
( ( ! [V_i: $i,V_x: $i,T_a: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_i @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oreplicate @ V_i @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(725,plain,
( ( ! [V_x: $i,V_xs: $i,T_b: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_b )
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_b ) @ T_b ) @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(726,plain,
( ( ! [V_ys: $i,T_a: $i,V_y: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(727,plain,
( ( ! [V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(728,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Orev @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(729,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i,V_zs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
!= ( c_List_Oappend @ V_ys @ V_zs @ T_a ) )
| ( ( c_List_Olist_OCons @ V_x @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ T_a )
= V_ys )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(730,plain,
( ( ! [V_ys: $i,V_zs: $i,T_a: $i,V_x: $i,V_xs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_zs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ V_zs @ T_a )
= V_xs )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(731,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(732,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(733,plain,
( ( ! [V_ys: $i,V_zs: $i,T_a: $i,V_x: $i,V_xs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_zs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( V_ys
= ( c_List_Olist_OCons @ V_x @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(734,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i,V_zs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
!= ( c_List_Oappend @ V_ys @ V_zs @ T_a ) )
| ( V_xs
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ V_zs @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(735,plain,
( ( ! [T_a: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(736,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Obutlast @ V_ys @ T_a ) @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(737,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(738,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Olast @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(739,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Obutlast @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318]) ).
thf(740,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i,V_xs: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(741,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i,V_zs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
!= ( c_List_Oappend @ V_ys @ V_zs @ T_a ) )
| ( V_xs
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ V_zs @ T_a ) )
| ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
= V_zs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(742,plain,
( ( ! [V_ys: $i,V_zs: $i,T_a: $i,V_x: $i,V_xs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_zs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( V_ys
= ( c_List_Olist_OCons @ V_x @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ T_a ) )
| ( V_zs
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[321]) ).
thf(743,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i,V_zs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
!= ( c_List_Oappend @ V_ys @ V_zs @ T_a ) )
| ( ( c_List_Olist_OCons @ V_x @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ T_a )
= V_ys )
| ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
= V_zs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(744,plain,
( ( ! [V_ys: $i,V_zs: $i,T_a: $i,V_x: $i,V_xs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_zs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ V_zs @ T_a )
= V_xs )
| ( V_zs
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(745,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(746,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Olast @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(747,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(748,plain,
( ( ! [V_xs: $i,T_a: $i,V_x: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(749,plain,
( ( ! [V_x: $i,T_a: $i,V_xs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a )
!= ( c_List_Orev @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[328]) ).
thf(750,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(751,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(752,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(753,plain,
( ( ! [T_a: $i,V_xs: $i,V_ys: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_List_Olistsum @ V_xs @ T_a ) ) @ ( c_List_Olistsum @ V_ys @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(754,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(755,plain,
( ( ! [T_a: $i,V_n: $i,V_x: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_x @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(756,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Oreplicate @ V_n @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(757,plain,
( ( ! [T_a: $i,V_x: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(758,plain,
( ( ! [T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(759,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(760,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(761,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(762,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(763,plain,
( ( ! [T_a: $i,V_x: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_List_Olistsum @ V_xs @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(764,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(765,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[344]) ).
thf(766,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(767,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(768,plain,
( ( ! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(769,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Oappend @ ( c_List_Obutlast @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= V_xs )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(770,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i,V_b: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(771,plain,
( ( ! [V_r: $i,V_y: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_y @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_a ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(772,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(773,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orev @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(774,plain,
( ( ! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Orev @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(775,plain,
( ( ! [T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(776,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(777,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(778,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_k ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357]) ).
thf(779,plain,
( ( ! [V_j: $i,V_i: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_i ) @ V_i @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(780,plain,
( ( ! [V_i: $i,V_j: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_i @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(781,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ T_b @ T_a )
= V_r ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(782,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Orev @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361]) ).
thf(783,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( tc_List_Olist @ T_a ) )
= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[362]) ).
thf(784,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Olistsum @ V_xs @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[363]) ).
thf(785,plain,
( ( ! [V_xs: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Orev @ V_ys @ T_a ) )
| ( V_xs = V_ys ) ) )
= $true ),
inference(unfold_def,[status(thm)],[364]) ).
thf(786,plain,
( ( ! [V_n: $i,V_m: $i,V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_m @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[365]) ).
thf(787,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i,V_l: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_l ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_l @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(788,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i,V_k: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(789,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) @ ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368]) ).
thf(790,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate1 @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[369]) ).
thf(791,plain,
( ( ! [T_a: $i] :
( ( c_Predicate_Oconversep @ ( c_fequal @ T_a ) @ T_a @ T_a )
= ( c_fequal @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370]) ).
thf(792,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371]) ).
thf(793,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[372]) ).
thf(794,plain,
( ( ! [V_x: $i,V_a: $i] :
( ( V_x
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[373]) ).
thf(795,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= V_m )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374]) ).
thf(796,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375]) ).
thf(797,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= ( c_List_Oreplicate @ V_n @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[376]) ).
thf(798,plain,
( ( ! [V_m: $i,V_l: $i,V_k: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_l )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_l @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377]) ).
thf(799,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378]) ).
thf(800,plain,
( ( ! [V_i: $i,V_m: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_j ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379]) ).
thf(801,plain,
( ( ! [V_i: $i,V_j: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_m ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(802,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[381]) ).
thf(803,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_z @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382]) ).
thf(804,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383]) ).
thf(805,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[384]) ).
thf(806,plain,
( ( ! [V_ys: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Orev @ V_ys @ T_a ) @ T_a )
= V_ys ) )
= $true ),
inference(unfold_def,[status(thm)],[385]) ).
thf(807,plain,
( ( ! [V_xs: $i,T_a: $i] :
( V_xs
= ( c_List_Orev @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[386]) ).
thf(808,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Orotate1 @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387]) ).
thf(809,plain,
( ( ! [V_r: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_r @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388]) ).
thf(810,plain,
( ( ! [V_t: $i] :
( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_t @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389]) ).
thf(811,plain,
( ( ! [V_r: $i,V_b: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(812,plain,
( ( ! [V_r: $i,V_b: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(813,plain,
( ( ! [V_m: $i,V_x: $i,T_a: $i,V_n: $i,V_y: $i] :
( ( ( c_List_Oreplicate @ V_m @ V_x @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_y @ T_a ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[392]) ).
thf(814,plain,
( ( ! [T_a: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[393]) ).
thf(815,plain,
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(816,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395]) ).
thf(817,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) ) @ V_k )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396]) ).
thf(818,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[397]) ).
thf(819,plain,
( ( ! [V_r: $i,V_a2: $i,V_a1: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a2 ) @ V_a1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a1 ) @ V_a2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398]) ).
thf(820,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[399]) ).
thf(821,plain,
( ( ! [V_r: $i,V_b: $i,V_a: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[400]) ).
thf(822,plain,
( ( ! [V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[401]) ).
thf(823,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[402]) ).
thf(824,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_y )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_z ) )
| ( V_y = V_z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[403]) ).
thf(825,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_k )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[404]) ).
thf(826,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[405]) ).
thf(827,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= V_x )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[406]) ).
thf(828,plain,
( ( ! [V_x: $i,T_a: $i,V_y: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[407]) ).
thf(829,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[408]) ).
thf(830,plain,
( ( ! [V_m: $i,V_x: $i,T_a: $i,V_n: $i,V_y: $i] :
( ( ( c_List_Oreplicate @ V_m @ V_x @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_y @ T_a ) )
| ( V_x = V_y )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[409]) ).
thf(831,plain,
( ( ! [V_x: $i] :
( V_x
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[410]) ).
thf(832,plain,
( ( ! [V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n )
= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[411]) ).
thf(833,plain,
( ( ! [V_m: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= V_m ) )
= $true ),
inference(unfold_def,[status(thm)],[412]) ).
thf(834,plain,
( ( ! [T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[413]) ).
thf(835,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[414]) ).
thf(836,plain,
( ( ! [V_e: $i,V_t: $i,V_Ts: $i,V_ts: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ V_Ts @ V_e @ V_t @ V_ts ) )
| ~ ( c_Type_Otypings @ V_e @ ( c_List_Oappend @ V_ts @ ( c_List_Olist_OCons @ V_t @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ V_Ts ) ) )
= $true ),
inference(unfold_def,[status(thm)],[415]) ).
thf(837,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[416]) ).
thf(838,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ V_xs @ T_a )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_xs @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[417]) ).
thf(839,plain,
( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) ) @ v_a____ ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_T_H____ ) )
= $true ),
inference(unfold_def,[status(thm)],[420]) ).
thf(840,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[421]) ).
thf(841,plain,
( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) ) @ v_a____ ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_T_H____ ) )
= $true ),
inference(copy,[status(thm)],[839]) ).
thf(842,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ V_xs @ T_a )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_xs @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[838]) ).
thf(843,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[837]) ).
thf(844,plain,
( ( ! [V_e: $i,V_t: $i,V_Ts: $i,V_ts: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ V_Ts @ V_e @ V_t @ V_ts ) )
| ~ ( c_Type_Otypings @ V_e @ ( c_List_Oappend @ V_ts @ ( c_List_Olist_OCons @ V_t @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ V_Ts ) ) )
= $true ),
inference(copy,[status(thm)],[836]) ).
thf(845,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[835]) ).
thf(846,plain,
( ( ! [T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[834]) ).
thf(847,plain,
( ( ! [V_m: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= V_m ) )
= $true ),
inference(copy,[status(thm)],[833]) ).
thf(848,plain,
( ( ! [V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n )
= V_n ) )
= $true ),
inference(copy,[status(thm)],[832]) ).
thf(849,plain,
( ( ! [V_x: $i] :
( V_x
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[831]) ).
thf(850,plain,
( ( ! [V_m: $i,V_x: $i,T_a: $i,V_n: $i,V_y: $i] :
( ( ( c_List_Oreplicate @ V_m @ V_x @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_y @ T_a ) )
| ( V_x = V_y )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[830]) ).
thf(851,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[829]) ).
thf(852,plain,
( ( ! [V_x: $i,T_a: $i,V_y: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[828]) ).
thf(853,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= V_x )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[827]) ).
thf(854,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[826]) ).
thf(855,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_k )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[825]) ).
thf(856,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_y )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_z ) )
| ( V_y = V_z ) ) )
= $true ),
inference(copy,[status(thm)],[824]) ).
thf(857,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[823]) ).
thf(858,plain,
( ( ! [V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[822]) ).
thf(859,plain,
( ( ! [V_r: $i,V_b: $i,V_a: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[821]) ).
thf(860,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[820]) ).
thf(861,plain,
( ( ! [V_r: $i,V_a2: $i,V_a1: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a2 ) @ V_a1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a1 ) @ V_a2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[819]) ).
thf(862,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[818]) ).
thf(863,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) ) @ V_k )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[817]) ).
thf(864,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_z ) ) ) )
= $true ),
inference(copy,[status(thm)],[816]) ).
thf(865,plain,
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[815]) ).
thf(866,plain,
( ( ! [T_a: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[814]) ).
thf(867,plain,
( ( ! [V_m: $i,V_x: $i,T_a: $i,V_n: $i,V_y: $i] :
( ( ( c_List_Oreplicate @ V_m @ V_x @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_y @ T_a ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[813]) ).
thf(868,plain,
( ( ! [V_r: $i,V_b: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[812]) ).
thf(869,plain,
( ( ! [V_r: $i,V_b: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[811]) ).
thf(870,plain,
( ( ! [V_t: $i] :
( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_t @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[810]) ).
thf(871,plain,
( ( ! [V_r: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_r @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[809]) ).
thf(872,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Orotate1 @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[808]) ).
thf(873,plain,
( ( ! [V_xs: $i,T_a: $i] :
( V_xs
= ( c_List_Orev @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[807]) ).
thf(874,plain,
( ( ! [V_ys: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Orev @ V_ys @ T_a ) @ T_a )
= V_ys ) )
= $true ),
inference(copy,[status(thm)],[806]) ).
thf(875,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[805]) ).
thf(876,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[804]) ).
thf(877,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_z @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[803]) ).
thf(878,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[802]) ).
thf(879,plain,
( ( ! [V_i: $i,V_j: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_m ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[801]) ).
thf(880,plain,
( ( ! [V_i: $i,V_m: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_j ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[800]) ).
thf(881,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) ) )
= $true ),
inference(copy,[status(thm)],[799]) ).
thf(882,plain,
( ( ! [V_m: $i,V_l: $i,V_k: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_l )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_l @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[798]) ).
thf(883,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= ( c_List_Oreplicate @ V_n @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[797]) ).
thf(884,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[796]) ).
thf(885,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= V_m )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[795]) ).
thf(886,plain,
( ( ! [V_x: $i,V_a: $i] :
( ( V_x
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[794]) ).
thf(887,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[793]) ).
thf(888,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[792]) ).
thf(889,plain,
( ( ! [T_a: $i] :
( ( c_Predicate_Oconversep @ ( c_fequal @ T_a ) @ T_a @ T_a )
= ( c_fequal @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[791]) ).
thf(890,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate1 @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[790]) ).
thf(891,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) @ ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[789]) ).
thf(892,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i,V_k: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[788]) ).
thf(893,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i,V_l: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_l ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_l @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[787]) ).
thf(894,plain,
( ( ! [V_n: $i,V_m: $i,V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_m @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[786]) ).
thf(895,plain,
( ( ! [V_xs: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Orev @ V_ys @ T_a ) )
| ( V_xs = V_ys ) ) )
= $true ),
inference(copy,[status(thm)],[785]) ).
thf(896,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Olistsum @ V_xs @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[784]) ).
thf(897,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( tc_List_Olist @ T_a ) )
= V_n ) )
= $true ),
inference(copy,[status(thm)],[783]) ).
thf(898,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Orev @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[782]) ).
thf(899,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ T_b @ T_a )
= V_r ) )
= $true ),
inference(copy,[status(thm)],[781]) ).
thf(900,plain,
( ( ! [V_i: $i,V_j: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_i @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[780]) ).
thf(901,plain,
( ( ! [V_j: $i,V_i: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_i ) @ V_i @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[779]) ).
thf(902,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_k ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[778]) ).
thf(903,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[777]) ).
thf(904,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[776]) ).
thf(905,plain,
( ( ! [T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[775]) ).
thf(906,plain,
( ( ! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Orev @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[774]) ).
thf(907,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orev @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[773]) ).
thf(908,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[772]) ).
thf(909,plain,
( ( ! [V_r: $i,V_y: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_y @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_a ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[771]) ).
thf(910,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i,V_b: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[770]) ).
thf(911,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Oappend @ ( c_List_Obutlast @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= V_xs )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[769]) ).
thf(912,plain,
( ( ! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[768]) ).
thf(913,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[767]) ).
thf(914,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[766]) ).
thf(915,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[765]) ).
thf(916,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[764]) ).
thf(917,plain,
( ( ! [T_a: $i,V_x: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_List_Olistsum @ V_xs @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[763]) ).
thf(918,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[762]) ).
thf(919,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[761]) ).
thf(920,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[760]) ).
thf(921,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[759]) ).
thf(922,plain,
( ( ! [T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[758]) ).
thf(923,plain,
( ( ! [T_a: $i,V_x: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[757]) ).
thf(924,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Oreplicate @ V_n @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[756]) ).
thf(925,plain,
( ( ! [T_a: $i,V_n: $i,V_x: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_x @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[755]) ).
thf(926,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[754]) ).
thf(927,plain,
( ( ! [T_a: $i,V_xs: $i,V_ys: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_List_Olistsum @ V_xs @ T_a ) ) @ ( c_List_Olistsum @ V_ys @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[753]) ).
thf(928,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[752]) ).
thf(929,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[751]) ).
thf(930,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[750]) ).
thf(931,plain,
( ( ! [V_x: $i,T_a: $i,V_xs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a )
!= ( c_List_Orev @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[749]) ).
thf(932,plain,
( ( ! [V_xs: $i,T_a: $i,V_x: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[748]) ).
thf(933,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[747]) ).
thf(934,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Olast @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[746]) ).
thf(935,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[745]) ).
thf(936,plain,
( ( ! [V_ys: $i,V_zs: $i,T_a: $i,V_x: $i,V_xs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_zs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ V_zs @ T_a )
= V_xs )
| ( V_zs
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[744]) ).
thf(937,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i,V_zs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
!= ( c_List_Oappend @ V_ys @ V_zs @ T_a ) )
| ( ( c_List_Olist_OCons @ V_x @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ T_a )
= V_ys )
| ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
= V_zs ) ) )
= $true ),
inference(copy,[status(thm)],[743]) ).
thf(938,plain,
( ( ! [V_ys: $i,V_zs: $i,T_a: $i,V_x: $i,V_xs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_zs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( V_ys
= ( c_List_Olist_OCons @ V_x @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ T_a ) )
| ( V_zs
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[742]) ).
thf(939,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i,V_zs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
!= ( c_List_Oappend @ V_ys @ V_zs @ T_a ) )
| ( V_xs
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ V_zs @ T_a ) )
| ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
= V_zs ) ) )
= $true ),
inference(copy,[status(thm)],[741]) ).
thf(940,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i,V_xs: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[740]) ).
thf(941,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Obutlast @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[739]) ).
thf(942,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Olast @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[738]) ).
thf(943,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[737]) ).
thf(944,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Obutlast @ V_ys @ T_a ) @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[736]) ).
thf(945,plain,
( ( ! [T_a: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[735]) ).
thf(946,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i,V_zs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
!= ( c_List_Oappend @ V_ys @ V_zs @ T_a ) )
| ( V_xs
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ V_zs @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[734]) ).
thf(947,plain,
( ( ! [V_ys: $i,V_zs: $i,T_a: $i,V_x: $i,V_xs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_zs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( V_ys
= ( c_List_Olist_OCons @ V_x @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[733]) ).
thf(948,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[732]) ).
thf(949,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[731]) ).
thf(950,plain,
( ( ! [V_ys: $i,V_zs: $i,T_a: $i,V_x: $i,V_xs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_zs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ V_zs @ T_a )
= V_xs )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[730]) ).
thf(951,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i,V_zs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
!= ( c_List_Oappend @ V_ys @ V_zs @ T_a ) )
| ( ( c_List_Olist_OCons @ V_x @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ T_a )
= V_ys )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[729]) ).
thf(952,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Orev @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[728]) ).
thf(953,plain,
( ( ! [V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[727]) ).
thf(954,plain,
( ( ! [V_ys: $i,T_a: $i,V_y: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[726]) ).
thf(955,plain,
( ( ! [V_x: $i,V_xs: $i,T_b: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_b )
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_b ) @ T_b ) @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[725]) ).
thf(956,plain,
( ( ! [V_i: $i,V_x: $i,T_a: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_i @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oreplicate @ V_i @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[724]) ).
thf(957,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ V_r @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_s @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) ) @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[723]) ).
thf(958,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ V_xs @ T_a )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[722]) ).
thf(959,plain,
( ( ! [V_n: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_n ) ) )
| ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[721]) ).
thf(960,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[720]) ).
thf(961,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[719]) ).
thf(962,plain,
( ( ! [V_x: $i,V_s: $i,V_t: $i] :
( ( ( c_List_Oappend @ V_x @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_x @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_s )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Oappend @ V_x @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(copy,[status(thm)],[718]) ).
thf(963,plain,
( ( ! [V_t: $i,V_ts: $i,V_u: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_u )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Oappend @ V_ts @ ( c_List_Olist_OCons @ V_u @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[717]) ).
thf(964,plain,
( ( ! [V_r: $i,V_s: $i,V_xa: $i] :
( ( V_r
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s ) @ V_xa @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s ) @ ( c_List_Oappend @ V_xa @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(copy,[status(thm)],[716]) ).
thf(965,plain,
( ( ! [V_r: $i,V_s: $i,V_t: $i,V_ts: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ V_r @ V_s @ V_t @ V_ts ) @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(copy,[status(thm)],[715]) ).
thf(966,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)],[714]) ).
thf(967,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)],[713]) ).
thf(968,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)],[712]) ).
thf(969,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)],[711]) ).
thf(970,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)],[710]) ).
thf(971,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)],[709]) ).
thf(972,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)],[708]) ).
thf(973,plain,
( ( ! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) ) @ ( c_Lambda_Osubst @ V_s @ V_t @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[707]) ).
thf(974,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)],[706]) ).
thf(975,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)],[705]) ).
thf(976,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)],[704]) ).
thf(977,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( 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)],[703]) ).
thf(978,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)],[702]) ).
thf(979,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_ua______ ) )
= $true ),
inference(copy,[status(thm)],[701]) ).
thf(980,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)],[700]) ).
thf(981,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)],[699]) ).
thf(982,plain,
( ( ! [V_t: $i,V_s: $i,V_n: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ V_n )
= ( 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)],[698]) ).
thf(983,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)],[697]) ).
thf(984,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)],[696]) ).
thf(985,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)],[695]) ).
thf(986,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)],[694]) ).
thf(987,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)],[693]) ).
thf(988,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)],[692]) ).
thf(989,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)],[691]) ).
thf(990,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)],[690]) ).
thf(991,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)],[689]) ).
thf(992,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)],[688]) ).
thf(993,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)],[687]) ).
thf(994,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)],[686]) ).
thf(995,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)],[685]) ).
thf(996,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)],[684]) ).
thf(997,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)],[683]) ).
thf(998,plain,
( ( ! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= V_s ) ) )
= $true ),
inference(copy,[status(thm)],[682]) ).
thf(999,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)],[681]) ).
thf(1000,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)],[680]) ).
thf(1001,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)],[679]) ).
thf(1002,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)],[678]) ).
thf(1003,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)],[677]) ).
thf(1004,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)],[676]) ).
thf(1005,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)],[675]) ).
thf(1006,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)],[674]) ).
thf(1007,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)],[673]) ).
thf(1008,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)],[672]) ).
thf(1009,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)],[671]) ).
thf(1010,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)],[670]) ).
thf(1011,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)],[669]) ).
thf(1012,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)],[668]) ).
thf(1013,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)],[667]) ).
thf(1014,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)],[666]) ).
thf(1015,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)],[665]) ).
thf(1016,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)],[664]) ).
thf(1017,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)],[663]) ).
thf(1018,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)],[662]) ).
thf(1019,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_u____ ) )
= $true ),
inference(copy,[status(thm)],[661]) ).
thf(1020,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)],[660]) ).
thf(1021,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)],[659]) ).
thf(1022,plain,
( ( ! [V_t: $i,V_k: $i,V_s: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ V_k ) @ V_s @ V_k )
= V_t ) )
= $true ),
inference(copy,[status(thm)],[658]) ).
thf(1023,plain,
( ( ! [V_i: $i,V_k: $i] :
( ( ( 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)],[657]) ).
thf(1024,plain,
( ( ! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ V_r @ V_i ) ) @ ( c_Lambda_Olift @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[656]) ).
thf(1025,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)],[655]) ).
thf(1026,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)],[654]) ).
thf(1027,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)],[653]) ).
thf(1028,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)],[652]) ).
thf(1029,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)],[651]) ).
thf(1030,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)],[650]) ).
thf(1031,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)],[649]) ).
thf(1032,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)],[648]) ).
thf(1033,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)],[647]) ).
thf(1034,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)],[646]) ).
thf(1035,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)],[645]) ).
thf(1036,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)],[644]) ).
thf(1037,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)],[643]) ).
thf(1038,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)],[642]) ).
thf(1039,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)],[641]) ).
thf(1040,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)],[640]) ).
thf(1041,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)],[639]) ).
thf(1042,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)],[638]) ).
thf(1043,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)],[637]) ).
thf(1044,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)],[636]) ).
thf(1045,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)],[635]) ).
thf(1046,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)],[634]) ).
thf(1047,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)],[633]) ).
thf(1048,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)],[632]) ).
thf(1049,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)],[631]) ).
thf(1050,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)],[630]) ).
thf(1051,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)],[629]) ).
thf(1052,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)],[628]) ).
thf(1053,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 ) @ ( c_Lambda_Osubst @ V_t @ V_r @ V_i ) ) @ ( c_Lambda_Osubst @ V_t @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[627]) ).
thf(1054,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)],[626]) ).
thf(1055,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)],[625]) ).
thf(1056,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)],[624]) ).
thf(1057,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)],[623]) ).
thf(1058,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)],[622]) ).
thf(1059,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)],[621]) ).
thf(1060,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 ) @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) ) @ ( 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)],[620]) ).
thf(1061,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 ) @ ( c_Lambda_Osubst @ V_t @ V_r @ V_i ) ) @ ( 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)],[619]) ).
thf(1062,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)],[618]) ).
thf(1063,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)],[617]) ).
thf(1064,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)],[616]) ).
thf(1065,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)],[615]) ).
thf(1066,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)],[614]) ).
thf(1067,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)],[613]) ).
thf(1068,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)],[612]) ).
thf(1069,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)],[611]) ).
thf(1070,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)],[610]) ).
thf(1071,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)],[609]) ).
thf(1072,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 @ ( 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)],[608]) ).
thf(1073,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)],[607]) ).
thf(1074,plain,
( ( ! [V_t: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ V_t @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[606]) ).
thf(1075,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)],[605]) ).
thf(1076,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)],[604]) ).
thf(1077,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)],[603]) ).
thf(1078,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)],[602]) ).
thf(1079,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)],[601]) ).
thf(1080,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[600]) ).
thf(1081,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[599]) ).
thf(1082,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)],[598]) ).
thf(1083,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)],[597]) ).
thf(1084,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)],[596]) ).
thf(1085,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 ) ) @ ( c_Lambda_Osubst @ V_s @ V_t @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[595]) ).
thf(1086,plain,
( ( ! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ V_r @ V_i ) ) @ ( 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)],[594]) ).
thf(1087,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)],[593]) ).
thf(1088,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)],[592]) ).
thf(1089,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)],[591]) ).
thf(1090,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)],[590]) ).
thf(1091,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)],[589]) ).
thf(1092,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)],[588]) ).
thf(1093,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)],[587]) ).
thf(1094,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)],[586]) ).
thf(1095,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)],[585]) ).
thf(1096,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)],[584]) ).
thf(1097,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)],[583]) ).
thf(1098,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)],[582]) ).
thf(1099,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)],[581]) ).
thf(1100,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)],[580]) ).
thf(1101,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)],[579]) ).
thf(1102,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)],[578]) ).
thf(1103,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)],[577]) ).
thf(1104,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)],[576]) ).
thf(1105,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)],[575]) ).
thf(1106,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)],[574]) ).
thf(1107,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)],[573]) ).
thf(1108,plain,
( ( ! [V_t: $i,V_s: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_Lambda_Osubst @ V_t @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[572]) ).
thf(1109,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)],[571]) ).
thf(1110,plain,
( ( ! [V_j: $i,V_u: $i,V_i: $i] :
( ( ( 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)],[570]) ).
thf(1111,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)],[569]) ).
thf(1112,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)],[568]) ).
thf(1113,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)],[567]) ).
thf(1114,plain,
( ( ! [V_r: $i,V_i: $i,V_j: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( 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)],[566]) ).
thf(1115,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)],[565]) ).
thf(1116,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)],[564]) ).
thf(1117,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)],[563]) ).
thf(1118,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)],[562]) ).
thf(1119,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)],[561]) ).
thf(1120,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)],[560]) ).
thf(1121,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)],[559]) ).
thf(1122,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)],[558]) ).
thf(1123,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)],[557]) ).
thf(1124,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)],[556]) ).
thf(1125,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)],[555]) ).
thf(1126,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)],[554]) ).
thf(1127,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)],[553]) ).
thf(1128,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)],[552]) ).
thf(1129,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)],[551]) ).
thf(1130,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)],[550]) ).
thf(1131,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)],[549]) ).
thf(1132,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)],[548]) ).
thf(1133,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)],[547]) ).
thf(1134,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)],[546]) ).
thf(1135,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)],[545]) ).
thf(1136,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)],[544]) ).
thf(1137,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)],[543]) ).
thf(1138,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)],[542]) ).
thf(1139,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)],[541]) ).
thf(1140,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)],[540]) ).
thf(1141,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)],[539]) ).
thf(1142,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)],[538]) ).
thf(1143,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)],[537]) ).
thf(1144,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)],[536]) ).
thf(1145,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 ) @ ( c_Lambda_Olift @ V_t @ V_i ) @ V_T )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[535]) ).
thf(1146,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)],[534]) ).
thf(1147,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)],[533]) ).
thf(1148,plain,
( ( c_Type_Otyping @ v_e____ @ v_u____ @ v_T____ )
= $true ),
inference(copy,[status(thm)],[532]) ).
thf(1149,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)],[531]) ).
thf(1150,plain,
( ( ! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_s @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ V_t @ V_s @ V_k ) ) @ ( c_Lambda_Osubst @ V_u @ V_s @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[530]) ).
thf(1151,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)],[529]) ).
thf(1152,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)],[528]) ).
thf(1153,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)],[527]) ).
thf(1154,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)],[526]) ).
thf(1155,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)],[525]) ).
thf(1156,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)],[524]) ).
thf(1157,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)],[523]) ).
thf(1158,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)],[522]) ).
thf(1159,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)],[521]) ).
thf(1160,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)],[520]) ).
thf(1161,plain,
( ( ! [V_k: $i,V_u: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_k ) @ V_u @ V_k )
= V_u ) )
= $true ),
inference(copy,[status(thm)],[519]) ).
thf(1162,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)],[518]) ).
thf(1163,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)],[517]) ).
thf(1164,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)],[516]) ).
thf(1165,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)],[515]) ).
thf(1166,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)],[514]) ).
thf(1167,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)],[513]) ).
thf(1168,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)],[512]) ).
thf(1169,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)],[511]) ).
thf(1170,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)],[510]) ).
thf(1171,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)],[509]) ).
thf(1172,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)],[508]) ).
thf(1173,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)],[507]) ).
thf(1174,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)],[506]) ).
thf(1175,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)],[505]) ).
thf(1176,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)],[504]) ).
thf(1177,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)],[503]) ).
thf(1178,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)],[502]) ).
thf(1179,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)],[501]) ).
thf(1180,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)],[500]) ).
thf(1181,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)],[499]) ).
thf(1182,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)],[498]) ).
thf(1183,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)],[497]) ).
thf(1184,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)],[496]) ).
thf(1185,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)],[495]) ).
thf(1186,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 @ ( 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)],[494]) ).
thf(1187,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 @ ( 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)],[493]) ).
thf(1188,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)],[492]) ).
thf(1189,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)],[491]) ).
thf(1190,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)],[490]) ).
thf(1191,plain,
( ( v_n____ = v_i____ )
= $true ),
inference(copy,[status(thm)],[489]) ).
thf(1192,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)],[488]) ).
thf(1193,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[487]) ).
thf(1194,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)],[486]) ).
thf(1195,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)],[485]) ).
thf(1196,plain,
( ( ! [V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ V_s @ V_k ) ) @ ( c_Lambda_Olift @ V_t @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[484]) ).
thf(1197,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)],[483]) ).
thf(1198,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)],[482]) ).
thf(1199,plain,
( ( c_Type_Otyping @ v_ea______ @ v_ua______ @ v_T____ )
= $true ),
inference(copy,[status(thm)],[481]) ).
thf(1200,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)],[480]) ).
thf(1201,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)],[479]) ).
thf(1202,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)],[478]) ).
thf(1203,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)],[477]) ).
thf(1204,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)],[476]) ).
thf(1205,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)],[475]) ).
thf(1206,plain,
( ( ! [V_e: $i,V_u: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_u @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ V_T @ V_e @ V_t @ V_u ) )
| ~ ( c_Type_Otyping @ V_e @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[474]) ).
thf(1207,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)],[473]) ).
thf(1208,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)],[472]) ).
thf(1209,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)],[471]) ).
thf(1210,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)],[470]) ).
thf(1211,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)],[469]) ).
thf(1212,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)],[468]) ).
thf(1213,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)],[467]) ).
thf(1214,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)],[466]) ).
thf(1215,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)],[465]) ).
thf(1216,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)],[464]) ).
thf(1217,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)],[463]) ).
thf(1218,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)],[462]) ).
thf(1219,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)],[461]) ).
thf(1220,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)],[460]) ).
thf(1221,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)],[459]) ).
thf(1222,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)],[458]) ).
thf(1223,plain,
( ( v_rs____
= ( c_List_Olist_OCons @ v_a____ @ v_as____ @ tc_Lambda_OdB ) )
= $true ),
inference(copy,[status(thm)],[457]) ).
thf(1224,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)],[456]) ).
thf(1225,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)],[455]) ).
thf(1226,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)],[454]) ).
thf(1227,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)],[453]) ).
thf(1228,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)],[452]) ).
thf(1229,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 @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[451]) ).
thf(1230,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)],[450]) ).
thf(1231,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)],[449]) ).
thf(1232,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)],[448]) ).
thf(1233,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i,V_u: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ V_T @ V_e @ V_t @ V_u ) ) @ V_T ) )
| ~ ( c_Type_Otyping @ V_e @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[447]) ).
thf(1234,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)],[446]) ).
thf(1235,plain,
( ( v_rs____
= ( c_List_Olist_OCons @ v_a____ @ v_as____ @ tc_Lambda_OdB ) )
= $true ),
inference(copy,[status(thm)],[445]) ).
thf(1236,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)],[444]) ).
thf(1237,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)],[443]) ).
thf(1238,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)],[442]) ).
thf(1239,plain,
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[441]) ).
thf(1240,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(1241,plain,
( ( class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[439]) ).
thf(1242,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[438]) ).
thf(1243,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(1244,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(copy,[status(thm)],[436]) ).
thf(1245,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(1246,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(1247,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(1248,plain,
( ( class_OrderedGroup_Osemigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(1249,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[431]) ).
thf(1250,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(1251,plain,
( ( class_Nat_Osemiring__char__0 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[429]) ).
thf(1252,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[428]) ).
thf(1253,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[427]) ).
thf(1254,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(1255,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[425]) ).
thf(1256,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[424]) ).
thf(1257,plain,
( ( ! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_x ) @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(1258,plain,
( ( ! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_X ) @ V_Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(1259,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[840]) ).
thf(1260,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Orev @ SX0 @ SX1 )
!= ( c_List_Orev @ SX2 @ SX1 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[895]) ).
thf(1261,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)],[1078]) ).
thf(1262,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)],[1008]) ).
thf(1263,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)],[1214]) ).
thf(1264,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[886]) ).
thf(1265,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Oreplicate @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_ONil @ SX2 ) )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[924]) ).
thf(1266,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oreplicate @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oreplicate @ SX3 @ SX4 @ SX2 ) )
| ( SX1 = SX4 )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[850]) ).
thf(1267,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) )
| ( SX0
= ( c_List_Olist_OCons @ SX3 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SX3 @ SX4 @ SX0 @ SX1 @ SX2 ) @ SX2 ) )
| ( SX0
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[947]) ).
thf(1268,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX2 ) @ SX3 ) )
| ~ ( c_HOL_Oord__class_Oless @ SX2 @ SX1 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SX0 @ SX3 @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[882]) ).
thf(1269,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)],[1234]) ).
thf(1270,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)],[1079]) ).
thf(1271,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)],[1099]) ).
thf(1272,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX2 @ SX3 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SX3
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( c_List_Olist_OCons @ SX1 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( SX3
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[965]) ).
thf(1273,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)],[1118]) ).
thf(1274,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oappend @ SX3 @ SX4 @ SX2 ) )
| ( SX1
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SX0 @ SX1 @ SX3 @ SX4 @ SX2 ) @ SX4 @ SX2 ) )
| ( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
= SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[939]) ).
thf(1275,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 )
!= SX0 )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[885]) ).
thf(1276,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[1025]) ).
thf(1277,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX0
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 ) @ SX2 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 ) @ ( c_List_Oappend @ SX2 @ ( c_List_Olist_OCons @ SX1 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[964]) ).
thf(1278,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)],[1128]) ).
thf(1279,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX2 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[854]) ).
thf(1280,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)],[969]) ).
thf(1281,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX2 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[856]) ).
thf(1282,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)],[1014]) ).
thf(1283,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)],[1010]) ).
thf(1284,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)],[1116]) ).
thf(1285,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)],[1009]) ).
thf(1286,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX2 ) @ SX1 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[855]) ).
thf(1287,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 @ ( 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)],[1186]) ).
thf(1288,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_Lambda_OdB_OVar @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1151]) ).
thf(1289,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_List_Orev @ SX0 @ SX1 )
!= ( c_List_Olist_ONil @ SX1 ) )
| ( SX0
= ( c_List_Olist_ONil @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[851]) ).
thf(1290,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oreplicate @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oreplicate @ SX3 @ SX4 @ SX2 ) )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[867]) ).
thf(1291,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_Lambda_OdB_OAbs @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1192]) ).
thf(1292,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)],[1171]) ).
thf(1293,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)],[1184]) ).
thf(1294,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Orev @ SX0 @ SX1 )
!= ( c_List_Olist_OCons @ SX2 @ ( c_List_Olist_ONil @ SX1 ) @ SX1 ) )
| ( SX0
= ( c_List_Olist_OCons @ SX2 @ ( c_List_Olist_ONil @ SX1 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[932]) ).
thf(1295,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( SX0
!= ( c_List_Olist_OCons @ SX1 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1026]) ).
thf(1296,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SX3 @ SX4 @ SX0 @ SX1 @ SX2 ) @ SX1 @ SX2 )
= SX4 )
| ( SX0
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[950]) ).
thf(1297,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)],[1059]) ).
thf(1298,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)],[968]) ).
thf(1299,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oappend @ SX3 @ SX4 @ SX2 ) )
| ( SX1
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SX0 @ SX1 @ SX3 @ SX4 @ SX2 ) @ SX4 @ SX2 ) )
| ( SX3
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[946]) ).
thf(1300,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)],[1119]) ).
thf(1301,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_Lambda_OdB_OAbs @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1077]) ).
thf(1302,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SX3 @ SX4 @ SX0 @ SX1 @ SX2 ) @ SX1 @ SX2 )
= SX4 )
| ( SX1
= ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[936]) ).
thf(1303,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_List_Orotate1 @ SX0 @ SX1 )
!= ( c_List_Olist_ONil @ SX1 ) )
| ( SX0
= ( c_List_Olist_ONil @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[872]) ).
thf(1304,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oappend @ SX3 @ SX4 @ SX2 ) )
| ( ( c_List_Olist_OCons @ SX0 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SX0 @ SX1 @ SX3 @ SX4 @ SX2 ) @ SX2 )
= SX3 )
| ( SX3
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[951]) ).
thf(1305,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Olist_ONil @ SX0 )
!= ( c_List_Oreplicate @ SX1 @ SX2 @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[925]) ).
thf(1306,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)],[1176]) ).
thf(1307,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ SX0 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SX1 @ SX0 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SX2 @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[884]) ).
thf(1308,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)],[1212]) ).
thf(1309,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)],[1133]) ).
thf(1310,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)],[1129]) ).
thf(1311,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)],[1182]) ).
thf(1312,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)],[1217]) ).
thf(1313,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)],[1181]) ).
thf(1314,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Olist_OCons @ SX0 @ ( c_List_Olist_ONil @ SX1 ) @ SX1 )
!= ( c_List_Orev @ SX2 @ SX1 ) )
| ( SX2
= ( c_List_Olist_OCons @ SX0 @ ( c_List_Olist_ONil @ SX1 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[931]) ).
thf(1315,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[887]) ).
thf(1316,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)],[997]) ).
thf(1317,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)],[1172]) ).
thf(1318,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_List_Olist_ONil @ SX0 )
!= ( c_List_Orev @ SX1 @ SX0 ) )
| ( SX1
= ( c_List_Olist_ONil @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[898]) ).
thf(1319,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oappend @ SX3 @ SX4 @ SX2 ) )
| ( ( c_List_Olist_OCons @ SX0 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SX0 @ SX1 @ SX3 @ SX4 @ SX2 ) @ SX2 )
= SX3 )
| ( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
= SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[937]) ).
thf(1320,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)],[1120]) ).
thf(1321,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Orev @ SX0 @ SX1 )
!= ( c_List_Olist_OCons @ SX2 @ SX3 @ SX1 ) )
| ( SX0
= ( c_List_Oappend @ ( c_List_Orev @ SX3 @ SX1 ) @ ( c_List_Olist_OCons @ SX2 @ ( c_List_Olist_ONil @ SX1 ) @ SX1 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[953]) ).
thf(1322,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)],[1117]) ).
thf(1323,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)],[1062]) ).
thf(1324,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)],[1168]) ).
thf(1325,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)],[1152]) ).
thf(1326,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) )
| ( SX0
= ( c_List_Olist_OCons @ SX3 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SX3 @ SX4 @ SX0 @ SX1 @ SX2 ) @ SX2 ) )
| ( SX1
= ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[938]) ).
thf(1327,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[888]) ).
thf(1328,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)],[1159]) ).
thf(1329,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)],[1225]) ).
thf(1330,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)],[1075]) ).
thf(1331,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)],[1115]) ).
thf(1332,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)],[1185]) ).
thf(1333,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_Lambda_OdB_OVar @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1154]) ).
thf(1334,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)],[1218]) ).
thf(1335,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)],[1160]) ).
thf(1336,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)],[1007]) ).
thf(1337,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)],[1013]) ).
thf(1338,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 @ ( 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)],[1187]) ).
thf(1339,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)],[1076]) ).
thf(1340,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)],[1173]) ).
thf(1341,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)],[1157]) ).
thf(1342,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)],[1230]) ).
thf(1343,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX1 ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX0
= ( c_List_Olist_ONil @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[926]) ).
thf(1344,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)],[1132]) ).
thf(1345,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)],[1175]) ).
thf(1346,plain,
( ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) ) @ v_a____ ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_T_H____ )
= $false ),
inference(extcnf_not_pos,[status(thm)],[841]) ).
thf(1347,plain,
! [SV1: $i] :
( ( ! [SY1255: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV1 )
| ( ( c_List_Olistsum @ SY1255 @ SV1 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV1 ) @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SY1255 @ SV1 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(1348,plain,
! [SV2: $i] :
( ( ! [SY1256: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV2 @ ( tc_List_Olist @ SY1256 ) ) @ tc_nat )
| ( SV2
= ( c_List_Olist_ONil @ SY1256 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(1349,plain,
! [SV3: $i] :
( ( ! [SY1257: $i,SY1258: $i,SY1259: $i] :
( ( c_Type_Otyping @ SV3 @ SY1257 @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ SY1258 @ SV3 @ SY1257 @ SY1259 ) )
| ~ ( c_Type_Otypings @ SV3 @ ( c_List_Oappend @ SY1259 @ ( c_List_Olist_OCons @ SY1257 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SY1258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(1350,plain,
! [SV4: $i] :
( ( ! [SY1260: $i,SY1261: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ SV4 @ SY1260 @ SY1261 ) @ SY1261 )
= ( c_List_Oappend @ ( c_List_Orev @ SY1260 @ SY1261 ) @ ( c_List_Orev @ SV4 @ SY1261 ) @ SY1261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(1351,plain,
! [SV5: $i] :
( ( ( c_List_Orev @ ( c_List_Olist_ONil @ SV5 ) @ SV5 )
= ( c_List_Olist_ONil @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(1352,plain,
! [SV6: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV6 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(1353,plain,
! [SV7: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV7 )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(1354,plain,
! [SV8: $i] :
( ( SV8
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV8 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(1355,plain,
! [SV9: $i] :
( ( ! [SY1262: $i,SY1263: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV9 @ SY1262 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1263 @ SY1262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(1356,plain,
! [SV10: $i] :
( ( ! [SY1264: $i,SY1265: $i] :
( ( ( c_List_Olast @ ( c_List_Oreplicate @ SV10 @ SY1264 @ SY1265 ) @ SY1265 )
= SY1264 )
| ( SV10
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(1357,plain,
! [SV11: $i] :
( ( ! [SY1266: $i,SY1267: $i,SY1268: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV11 @ SY1266 @ SY1266 ) @ SY1266 ) @ SY1267 ) @ SY1268 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV11 @ SY1266 ) @ SY1268 ) @ SY1267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(1358,plain,
! [SV12: $i] :
( ( ! [SY1269: $i,SY1270: $i,SY1271: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV12 @ SY1269 ) @ SY1270 ) @ SY1271 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV12 @ SY1269 @ SY1269 ) @ SY1269 ) @ SY1271 ) @ SY1270 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(1359,plain,
! [SV13: $i] :
( ( ! [SY1272: $i,SY1273: $i,SY1274: $i,SY1275: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV13 @ SY1272 ) @ SY1273 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV13 @ SY1274 @ SY1275 ) @ SY1273 ) @ SY1272 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1360,plain,
! [SV14: $i] :
( ( ! [SY1276: $i,SY1277: $i,SY1278: $i,SY1279: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV14 @ SY1276 @ SY1277 ) @ SY1278 ) @ SY1279 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV14 @ SY1279 ) @ SY1278 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(1361,plain,
! [SV15: $i] :
( ( ! [SY1280: $i,SY1281: $i,SY1282: $i,SY1283: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV15 @ SY1280 ) @ SY1281 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV15 @ SY1282 @ SY1283 ) @ SY1281 ) @ SY1280 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1362,plain,
! [SV16: $i] :
( ( ! [SY1284: $i,SY1285: $i,SY1286: $i,SY1287: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV16 @ SY1284 @ SY1285 ) @ SY1286 ) @ SY1287 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV16 @ SY1287 ) @ SY1286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(1363,plain,
! [SV17: $i] :
( ( ! [SY1288: $i,SY1289: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV17 ) @ SY1288 ) ) @ SY1289 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV17 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1288 ) @ SY1289 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[863]) ).
thf(1364,plain,
! [SV18: $i] :
( ( ! [SY1290: $i,SY1291: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV18 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1290 ) @ SY1291 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1290 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV18 ) @ SY1291 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(1365,plain,
! [SV19: $i] :
( ( ( c_List_Orotate1 @ ( c_List_Olist_ONil @ SV19 ) @ SV19 )
= ( c_List_Olist_ONil @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(1366,plain,
! [SV20: $i] :
( ( ! [SY1292: $i,SY1293: $i,SY1294: $i] :
( ( c_Wellfounded_Oaccp @ SV20 @ SY1292 @ SY1293 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV20 @ SY1293 ) @ SY1292 ) @ SY1294 ) )
| ~ ( c_Wellfounded_Oaccp @ SV20 @ SY1294 @ SY1293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(1367,plain,
! [SV21: $i] :
( ( ! [SY1295: $i,SY1296: $i,SY1297: $i] :
( ( c_Wellfounded_Oaccp @ SV21 @ SY1295 @ SY1296 )
| ~ ( c_Wellfounded_Oaccp @ SV21 @ SY1297 @ SY1296 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV21 @ SY1296 ) @ SY1295 ) @ SY1297 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(1368,plain,
! [SV22: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV22 @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(1369,plain,
! [SV23: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV23 ) )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV23 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(1370,plain,
! [SV24: $i] :
( ( ! [SY1298: $i] :
( SV24
= ( c_List_Orev @ ( c_List_Orev @ SV24 @ SY1298 ) @ SY1298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(1371,plain,
! [SV25: $i] :
( ( ! [SY1299: $i] :
( ( c_List_Orev @ ( c_List_Orev @ SV25 @ SY1299 ) @ SY1299 )
= SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(1372,plain,
! [SV26: $i] :
( ( ! [SY1300: $i] :
( ( c_List_Orev @ ( c_List_Orev @ SV26 @ SY1300 ) @ SY1300 )
= SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(1373,plain,
! [SV27: $i] :
( ( ! [SY1301: $i,SY1302: $i] :
( ( c_HOL_Oord__class_Oless @ SV27 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1301 ) @ SY1302 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV27 @ SY1301 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(1374,plain,
! [SV28: $i] :
( ( ! [SY1303: $i,SY1304: $i] :
( ( c_HOL_Oord__class_Oless @ SV28 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1303 ) @ SY1304 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV28 @ SY1304 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[877]) ).
thf(1375,plain,
! [SV29: $i] :
( ( ! [SY1305: $i,SY1306: $i] :
( ( c_HOL_Oord__class_Oless @ SV29 @ SY1305 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV29 ) @ SY1306 ) @ SY1305 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[878]) ).
thf(1376,plain,
! [SV30: $i] :
( ( ! [SY1307: $i,SY1308: $i] :
( ( c_HOL_Oord__class_Oless @ SV30 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1307 ) @ SY1308 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV30 @ SY1307 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(1377,plain,
! [SV31: $i] :
( ( ! [SY1309: $i,SY1310: $i] :
( ( c_HOL_Oord__class_Oless @ SV31 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1309 ) @ SY1310 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV31 @ SY1310 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(1378,plain,
! [SV32: $i] :
( ( ! [SY1311: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV32 ) @ SY1311 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1311 ) @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(1379,plain,
! [SV33: $i] :
( ( ! [SY1312: $i,SY1313: $i] :
( ( c_List_Orev @ ( c_List_Oreplicate @ SV33 @ SY1312 @ SY1313 ) @ SY1313 )
= ( c_List_Oreplicate @ SV33 @ SY1312 @ SY1313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(1380,plain,
! [SV34: $i] :
( ( ( c_Predicate_Oconversep @ ( c_fequal @ SV34 ) @ SV34 @ SV34 )
= ( c_fequal @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(1381,plain,
! [SV35: $i] :
( ( ! [SY1314: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate1 @ SV35 @ SY1314 ) @ ( tc_List_Olist @ SY1314 ) )
= ( c_Nat_Osize__class_Osize @ SV35 @ ( tc_List_Olist @ SY1314 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(1382,plain,
! [SV36: $i] :
( ( ! [SY1315: $i,SY1316: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oappend @ SV36 @ SY1315 @ SY1316 ) @ ( tc_List_Olist @ SY1316 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV36 @ ( tc_List_Olist @ SY1316 ) ) ) @ ( c_Nat_Osize__class_Osize @ SY1315 @ ( tc_List_Olist @ SY1316 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(1383,plain,
! [SV37: $i] :
( ( ! [SY1317: $i,SY1318: $i,SY1319: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV37 @ SY1317 @ SY1318 ) @ ( c_List_Oreplicate @ SY1319 @ SY1317 @ SY1318 ) @ SY1318 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SY1319 @ SY1317 @ SY1318 ) @ ( c_List_Oreplicate @ SV37 @ SY1317 @ SY1318 ) @ SY1318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(1384,plain,
! [SV38: $i] :
( ( ! [SY1320: $i,SY1321: $i,SY1322: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV38 ) @ SY1320 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1321 ) @ SY1322 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY1320 @ SY1322 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV38 @ SY1321 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(1385,plain,
! [SV39: $i] :
( ( ! [SY1323: $i,SY1324: $i,SY1325: $i] :
( ( c_List_Oreplicate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV39 ) @ SY1323 ) @ SY1324 @ SY1325 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SV39 @ SY1324 @ SY1325 ) @ ( c_List_Oreplicate @ SY1323 @ SY1324 @ SY1325 ) @ SY1325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1386,plain,
! [SV40: $i] :
( ( ! [SY1326: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV40 )
| ( ( c_List_Olistsum @ ( c_List_Orev @ SY1326 @ SV40 ) @ SV40 )
= ( c_List_Olistsum @ SY1326 @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1387,plain,
! [SV41: $i] :
( ( ! [SY1327: $i,SY1328: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ SV41 @ SY1327 @ SY1328 ) @ ( tc_List_Olist @ SY1328 ) )
= SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1388,plain,
! [SV42: $i] :
( ( ! [SY1329: $i,SY1330: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ SV42 @ SY1329 @ SY1330 ) @ SY1330 @ SY1329 )
= SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(1389,plain,
! [SV43: $i] :
( ( ! [SY1331: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV43 ) @ SY1331 ) @ SV43 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(1390,plain,
! [SV44: $i] :
( ( ! [SY1332: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV44 ) @ SY1332 ) @ SY1332 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(1391,plain,
! [SV45: $i] :
( ( ! [SY1333: $i,SY1334: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV45 ) @ SY1333 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1334 ) @ SY1333 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV45 @ SY1334 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(1392,plain,
! [SV46: $i] :
( ( ! [SY1335: $i,SY1336: $i] :
( ( c_HOL_Oord__class_Oless @ SV46 @ SY1335 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1336 ) @ SV46 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1336 ) @ SY1335 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(1393,plain,
! [SV47: $i] :
( ( ! [SY1337: $i,SY1338: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV47 ) @ SY1337 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV47 ) @ SY1338 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY1337 @ SY1338 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(1394,plain,
! [SV48: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_ONil @ SV48 ) @ SV48 )
= ( c_List_Olist_ONil @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(1395,plain,
! [SV49: $i] :
( ( ( c_List_Olist_ONil @ SV49 )
= ( c_List_Orev @ ( c_List_Olist_ONil @ SV49 ) @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(1396,plain,
! [SV50: $i] :
( ( ! [SY1339: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orev @ SV50 @ SY1339 ) @ ( tc_List_Olist @ SY1339 ) )
= ( c_Nat_Osize__class_Osize @ SV50 @ ( tc_List_Olist @ SY1339 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(1397,plain,
! [SV51: $i] :
( ( ! [SY1340: $i,SY1341: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV51 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1340 ) @ SY1341 ) @ SV51 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV51 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1340 @ SV51 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1341 @ SV51 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(1398,plain,
! [SV52: $i] :
( ( ! [SY1342: $i,SY1343: $i,SY1344: $i] :
( ( c_Wellfounded_Oaccp @ SV52 @ SY1342 @ SY1343 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV52 @ SY1342 ) @ SY1344 ) )
| ~ ( c_Wellfounded_Oaccp @ SV52 @ SY1344 @ SY1343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1399,plain,
! [SV53: $i] :
( ( ! [SY1345: $i,SY1346: $i,SY1347: $i] :
( ( c_Wellfounded_Oaccp @ SV53 @ SY1345 @ SY1346 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV53 @ SY1345 ) @ SY1347 ) )
| ~ ( c_Wellfounded_Oaccp @ SV53 @ SY1347 @ SY1346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1400,plain,
! [SV54: $i] :
( ( ! [SY1348: $i] :
( ( ( c_List_Oappend @ ( c_List_Obutlast @ SV54 @ SY1348 ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ SV54 @ SY1348 ) @ ( c_List_Olist_ONil @ SY1348 ) @ SY1348 ) @ SY1348 )
= SV54 )
| ( SV54
= ( c_List_Olist_ONil @ SY1348 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1401,plain,
! [SV55: $i] :
( ( ! [SY1349: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV55 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1349 @ SV55 ) @ ( c_HOL_Ozero__class_Ozero @ SV55 ) @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[912]) ).
thf(1402,plain,
! [SV56: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV56 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV56 )
= ( c_HOL_Ozero__class_Ozero @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1403,plain,
! [SV57: $i] :
( ( ! [SY1350: $i,SY1351: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV57 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1350 @ SV57 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1351 @ SV57 ) @ SV57 )
| ~ ( c_HOL_Oord__class_Oless @ SY1350 @ SY1351 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(1404,plain,
! [SV58: $i] :
( ( ! [SY1352: $i,SY1353: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV58 )
| ( c_HOL_Oord__class_Oless @ SY1352 @ SY1353 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1352 @ SV58 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1353 @ SV58 ) @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1405,plain,
! [SV59: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV59 )
| ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ SV59 ) @ SV59 )
= ( c_HOL_Ozero__class_Ozero @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1406,plain,
! [SV60: $i] :
( ( ! [SY1354: $i,SY1355: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV60 )
| ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ SY1354 @ SY1355 @ SV60 ) @ SV60 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SY1354 ) @ ( c_List_Olistsum @ SY1355 @ SV60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(1407,plain,
! [SV61: $i] :
( ( ! [SY1356: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV61 ) @ SY1356 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV61 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1408,plain,
! [SV62: $i] :
( ( ! [SY1357: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV62 ) @ SY1357 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1357 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1409,plain,
! [SV63: $i] :
( ( ! [SY1358: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV63 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1358 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1358 ) @ SV63 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1410,plain,
! [SV64: $i] :
( ( ! [SY1359: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV64 @ SY1359 )
= ( c_List_Olist_ONil @ SY1359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1411,plain,
! [SV65: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ SV65 ) @ ( tc_List_Olist @ SV65 ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[922]) ).
thf(1412,plain,
! [SV66: $i] :
( ( ! [SY1360: $i] :
( ( c_List_Olist_ONil @ SV66 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1360 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1413,plain,
! [SV67: $i] :
( ( ! [SY1361: $i,SY1362: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV67 )
| ( ( c_List_Olistsum @ ( c_List_Oappend @ SY1361 @ SY1362 @ SV67 ) @ SV67 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ ( c_List_Olistsum @ SY1361 @ SV67 ) ) @ ( c_List_Olistsum @ SY1362 @ SV67 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1414,plain,
! [SV68: $i] :
( ( ! [SY1363: $i] :
( ( c_List_Olist_OCons @ SV68 @ ( c_List_Olist_ONil @ SY1363 ) @ SY1363 )
= ( c_List_Orev @ ( c_List_Olist_OCons @ SV68 @ ( c_List_Olist_ONil @ SY1363 ) @ SY1363 ) @ SY1363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1415,plain,
! [SV69: $i] :
( ( ! [SY1364: $i,SY1365: $i] :
( ( ( c_List_Olast @ ( c_List_Olist_OCons @ SV69 @ SY1364 @ SY1365 ) @ SY1365 )
= ( c_List_Olast @ SY1364 @ SY1365 ) )
| ( SY1364
= ( c_List_Olist_ONil @ SY1365 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1416,plain,
! [SV70: $i] :
( ( ! [SY1366: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ SV70 @ ( c_List_Olist_ONil @ SY1366 ) @ SY1366 ) @ SY1366 )
= ( c_List_Olist_OCons @ SV70 @ ( c_List_Olist_ONil @ SY1366 ) @ SY1366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(1417,plain,
! [SV71: $i] :
( ( ! [SY1367: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV71 @ ( c_List_Olist_ONil @ SY1367 ) @ SY1367 ) @ SY1367 )
= ( c_List_Olist_ONil @ SY1367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1418,plain,
! [SV72: $i] :
( ( ! [SY1368: $i] :
( ( c_List_Olast @ ( c_List_Olist_OCons @ SV72 @ ( c_List_Olist_ONil @ SY1368 ) @ SY1368 ) @ SY1368 )
= SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1419,plain,
! [SV73: $i] :
( ( ! [SY1369: $i,SY1370: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV73 @ SY1369 @ SY1370 ) @ SY1370 )
= ( c_List_Olist_OCons @ SV73 @ ( c_List_Obutlast @ SY1369 @ SY1370 ) @ SY1370 ) )
| ( SY1369
= ( c_List_Olist_ONil @ SY1370 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1420,plain,
! [SV74: $i] :
( ( ! [SY1371: $i,SY1372: $i,SY1373: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV74 @ SY1371 @ SY1372 ) @ ( c_List_Olist_OCons @ SY1371 @ SY1373 @ SY1372 ) @ SY1372 )
= ( c_List_Olist_OCons @ SY1371 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV74 @ SY1371 @ SY1372 ) @ SY1373 @ SY1372 ) @ SY1372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1421,plain,
! [SV75: $i] :
( ( ! [SY1374: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ SV75 @ ( c_List_Olist_ONil @ SY1374 ) @ SY1374 ) @ SY1374 )
= ( c_List_Obutlast @ SV75 @ SY1374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1422,plain,
! [SV76: $i] :
( ( ! [SY1375: $i,SY1376: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ SV76 @ SY1375 @ SY1376 ) @ SY1376 )
= ( c_List_Olast @ SY1375 @ SY1376 ) )
| ( SY1375
= ( c_List_Olist_ONil @ SY1376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1423,plain,
! [SV77: $i] :
( ( ! [SY1377: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ SV77 @ ( c_List_Olist_ONil @ SY1377 ) @ SY1377 ) @ SY1377 )
= ( c_List_Olast @ SV77 @ SY1377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1424,plain,
! [SV78: $i] :
( ( ! [SY1378: $i,SY1379: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV78 @ SY1378 @ SY1379 ) @ SY1379 )
= ( c_List_Oappend @ SV78 @ ( c_List_Obutlast @ SY1378 @ SY1379 ) @ SY1379 ) )
| ( SY1378
= ( c_List_Olist_ONil @ SY1379 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(1425,plain,
! [SV79: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ SV79 ) @ ( tc_List_Olist @ SV79 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1426,plain,
! [SV80: $i] :
( ( ! [SY1380: $i,SY1381: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ SV80 @ ( c_List_Olist_OCons @ SY1380 @ ( c_List_Olist_ONil @ SY1381 ) @ SY1381 ) @ SY1381 ) @ SY1381 )
= SY1380 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1427,plain,
! [SV81: $i] :
( ( ! [SY1382: $i,SY1383: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ SV81 @ ( c_List_Olist_OCons @ SY1382 @ ( c_List_Olist_ONil @ SY1383 ) @ SY1383 ) @ SY1383 ) @ SY1383 )
= SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(1428,plain,
! [SV82: $i] :
( ( ! [SY1384: $i,SY1385: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ SV82 @ SY1384 @ SY1385 ) @ SY1385 )
= ( c_List_Oappend @ ( c_List_Orev @ SY1384 @ SY1385 ) @ ( c_List_Olist_OCons @ SV82 @ ( c_List_Olist_ONil @ SY1385 ) @ SY1385 ) @ SY1385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1429,plain,
! [SV83: $i] :
( ( ! [SY1386: $i,SY1387: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ SV83 @ SY1386 ) @ ( c_List_Olist_OCons @ SY1387 @ ( c_List_Olist_ONil @ SY1386 ) @ SY1386 ) @ SY1386 ) @ SY1386 )
= ( c_List_Olist_OCons @ SY1387 @ SV83 @ SY1386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1430,plain,
! [SV84: $i] :
( ( ! [SY1388: $i,SY1389: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ SV84 @ SY1388 @ SY1389 ) @ SY1389 )
= ( c_List_Oappend @ SY1388 @ ( c_List_Olist_OCons @ SV84 @ ( c_List_Olist_ONil @ SY1389 ) @ SY1389 ) @ SY1389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1431,plain,
! [SV85: $i] :
( ( ! [SY1390: $i,SY1391: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV85 @ SY1390 @ SY1391 ) @ ( c_List_Olist_OCons @ SY1390 @ ( c_List_Olist_ONil @ SY1391 ) @ SY1391 ) @ SY1391 )
= ( c_List_Olist_OCons @ SY1390 @ ( c_List_Oreplicate @ SV85 @ SY1390 @ SY1391 ) @ SY1391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1432,plain,
! [SV86: $i] :
( ( ! [SY1392: $i,SY1393: $i] :
( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV86 @ SY1392 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1393 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1392 @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV86 ) ) @ SY1392 ) @ SY1393 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1433,plain,
! [SV87: $i] :
( ( ! [SY1394: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV87 )
| ( ( c_List_Olistsum @ SY1394 @ SV87 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV87 ) @ SY1394 @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1434,plain,
! [SV88: $i] :
( ( ! [SY1395: $i,SY1396: $i] :
( ( ( c_Lambda_Oliftn @ SV88 @ ( c_Lambda_OdB_OVar @ SY1395 ) @ SY1396 )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1395 ) @ SV88 ) ) )
| ( c_HOL_Oord__class_Oless @ SY1395 @ SY1396 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1435,plain,
! [SV89: $i] :
( ( ! [SY1397: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV89 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1397 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1397 @ SV89 ) @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1436,plain,
! [SV90: $i] :
( ( ! [SY1398: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV90 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1398 @ SV90 ) @ SV90 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1398 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1437,plain,
! [SV91: $i] :
( ( ! [SY1399: $i,SY1400: $i] :
( ( ( c_List_Oappend @ SV91 @ ( c_List_Olist_OCons @ SY1399 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1400 @ SV91 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1399 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1400 @ ( c_List_Oappend @ SV91 @ ( c_List_Olist_OCons @ SY1399 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1438,plain,
! [SV92: $i] :
( ( ! [SY1401: $i,SY1402: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV92 @ SY1401 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1402 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV92 @ ( c_List_Oappend @ SY1401 @ ( c_List_Olist_OCons @ SY1402 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(1439,plain,
! [SV93: $i] :
( ( ! [SY1403: $i] :
( ~ ( hBOOL @ ( hAPP @ SV93 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV93 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__4 @ SV93 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ SV93 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV93 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV93 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ SV93 @ SY1403 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1440,plain,
! [SV94: $i] :
( ( ! [SY1404: $i] :
( ( hBOOL @ ( hAPP @ SV94 @ SY1404 ) )
| ~ ( hBOOL @ ( hAPP @ SV94 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV94 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4 @ SV94 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ SV94 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV94 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV94 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1441,plain,
! [SV95: $i] :
( ( ! [SY1405: $i] : ( c_List_Olistsp @ SV95 @ ( c_List_Olist_ONil @ SY1405 ) @ SY1405 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1442,plain,
! [SV96: $i] :
( ( ! [SY1406: $i,SY1407: $i,SY1408: $i,SY1409: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV96 @ SY1406 ) @ SY1407 ) )
| ( c_ListOrder_Ostep1 @ SV96 @ ( c_List_Olist_OCons @ SY1406 @ SY1408 @ SY1409 ) @ ( c_List_Olist_OCons @ SY1407 @ SY1408 @ SY1409 ) @ SY1409 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1443,plain,
! [SV97: $i] :
( ( ! [SY1410: $i,SY1411: $i,SY1412: $i,SY1413: $i,SY1414: $i] :
( ( SV97 = SY1410 )
| ( SY1411 = SY1412 )
| ~ ( c_ListOrder_Ostep1 @ SY1413 @ ( c_List_Olist_OCons @ SY1410 @ SY1412 @ SY1414 ) @ ( c_List_Olist_OCons @ SV97 @ SY1411 @ SY1414 ) @ SY1414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1444,plain,
! [SV98: $i] :
( ( ! [SY1415: $i,SY1416: $i,SY1417: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV98 @ SY1415 @ SY1416 ) ) @ ( c_Lambda_Osubst @ SY1417 @ SY1415 @ SY1416 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV98 ) @ SY1417 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1445,plain,
! [SV99: $i] :
( ( ! [SY1418: $i,SY1419: $i,SY1420: $i,SY1421: $i] :
( ( c_Lambda_OdB_OdB__case @ SV99 @ SY1418 @ SY1419 @ ( c_Lambda_OdB_OAbs @ SY1420 ) @ SY1421 )
= ( hAPP @ SY1419 @ SY1420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1446,plain,
! [SV100: $i] :
( ( ! [SY1422: $i,SY1423: $i,SY1424: $i] :
( ( c_List_Olistsp @ SV100 @ SY1422 @ SY1423 )
| ~ ( c_List_Olistsp @ SV100 @ ( c_List_Oappend @ SY1424 @ SY1422 @ SY1423 ) @ SY1423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1447,plain,
! [SV101: $i] :
( ( ! [SY1425: $i,SY1426: $i,SY1427: $i] :
( ( c_List_Olistsp @ SV101 @ SY1425 @ SY1426 )
| ~ ( c_List_Olistsp @ SV101 @ ( c_List_Oappend @ SY1425 @ SY1427 @ SY1426 ) @ SY1426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1448,plain,
! [SV102: $i] :
( ( ! [SY1428: $i,SY1429: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV102 ) @ SY1428 @ SY1429 )
= ( c_Lambda_OdB_OVar @ SV102 ) )
| ( SV102 = SY1429 )
| ( c_HOL_Oord__class_Oless @ SY1429 @ SV102 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1449,plain,
! [SV103: $i] :
( ( ! [SY1430: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV103 ) ) @ ( c_Lambda_OdB_OAbs @ SY1430 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV103 ) @ SY1430 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1450,plain,
! [SV104: $i] :
( ( ! [SY1431: $i,SY1432: $i,SY1433: $i,SY1434: $i] :
( ( c_ListOrder_Ostep1 @ SV104 @ ( c_List_Oappend @ SY1431 @ SY1432 @ SY1433 ) @ ( c_List_Oappend @ SY1431 @ SY1434 @ SY1433 ) @ SY1433 )
| ~ ( c_ListOrder_Ostep1 @ SV104 @ SY1432 @ SY1434 @ SY1433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1451,plain,
! [SV105: $i] :
( ( ! [SY1435: $i,SY1436: $i,SY1437: $i,SY1438: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV105 @ SY1435 @ SY1436 @ SY1437 )
| ( c_ListOrder_Ostep1 @ SV105 @ ( c_List_Oappend @ SY1435 @ SY1438 @ SY1437 ) @ ( c_List_Oappend @ SY1436 @ SY1438 @ SY1437 ) @ SY1437 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1452,plain,
! [SV106: $i] :
( ( ! [SY1439: $i,SY1440: $i] :
( ( c_Lambda_Osubstn @ SV106 @ SY1439 @ SY1440 )
= ( c_Lambda_Osubst @ SV106 @ ( c_Lambda_Oliftn @ SY1440 @ SY1439 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1453,plain,
! [SV107: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV107 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Ozero__class_Ozero @ SV107 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV107 ) )
= ( c_HOL_Ozero__class_Ozero @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1454,plain,
! [SV108: $i] :
( ( ! [SY1441: $i,SY1442: $i,SY1443: $i] :
( ~ ( class_Orderings_Opreorder @ SV108 )
| ( c_HOL_Oord__class_Oless @ SY1441 @ SY1442 @ SV108 )
| ~ ( c_HOL_Oord__class_Oless @ SY1443 @ SY1442 @ SV108 )
| ~ ( c_HOL_Oord__class_Oless @ SY1441 @ SY1443 @ SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1455,plain,
! [SV109: $i] :
( ( ! [SY1444: $i,SY1445: $i,SY1446: $i] :
( ~ ( class_Orderings_Oorder @ SV109 )
| ( c_HOL_Oord__class_Oless @ SY1444 @ SY1445 @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ SY1444 @ SY1446 @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ SY1446 @ SY1445 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1456,plain,
! [SV110: $i] :
( ( ! [SY1447: $i,SY1448: $i,SY1449: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV110 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SY1447 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SY1448 ) @ SY1449 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SY1447 ) @ SY1448 ) ) @ SY1449 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1457,plain,
! [SV111: $i] :
( ( ! [SY1450: $i,SY1451: $i,SY1452: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV111 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SY1450 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SY1451 ) @ SY1452 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SY1451 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SY1450 ) @ SY1452 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1458,plain,
! [SV112: $i] :
( ( ! [SY1453: $i,SY1454: $i,SY1455: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV112 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SY1453 ) @ SY1454 ) ) @ SY1455 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SY1453 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SY1454 ) @ SY1455 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1459,plain,
! [SV113: $i] :
( ( ! [SY1456: $i,SY1457: $i,SY1458: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV113 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SY1456 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SY1457 ) @ SY1458 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SY1457 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SY1456 ) @ SY1458 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1460,plain,
! [SV114: $i] :
( ( ! [SY1459: $i,SY1460: $i,SY1461: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV114 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SY1459 ) @ SY1460 ) ) @ SY1461 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SY1459 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SY1460 ) @ SY1461 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1461,plain,
! [SV115: $i] :
( ( ! [SY1462: $i,SY1463: $i,SY1464: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV115 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SY1462 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SY1463 ) @ SY1464 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SY1462 ) @ SY1463 ) ) @ SY1464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1462,plain,
! [SV116: $i] :
( ( ! [SY1465: $i,SY1466: $i,SY1467: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV116 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SY1465 ) @ SY1466 ) ) @ SY1467 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SY1465 ) @ SY1467 ) ) @ SY1466 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1463,plain,
! [SV117: $i] :
( ( ! [SY1468: $i,SY1469: $i,SY1470: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV117 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SY1468 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SY1469 ) @ SY1470 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SY1469 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SY1468 ) @ SY1470 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1464,plain,
! [SV118: $i] :
( ( ! [SY1471: $i,SY1472: $i,SY1473: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV118 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SY1471 ) @ SY1472 ) ) @ SY1473 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SY1471 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SY1472 ) @ SY1473 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1465,plain,
! [SV119: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV119 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1466,plain,
! [SV120: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV120 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1467,plain,
! [SV121: $i] :
( ( ! [SY1474: $i] :
( ( c_HOL_Oord__class_Oless @ SV121 @ SV121 @ tc_nat )
| ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV121 ) @ SY1474 @ SV121 )
= SY1474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1468,plain,
! [SV122: $i] :
( ( ! [SY1475: $i,SY1476: $i,SY1477: $i] :
( ( c_List_Ofoldr @ SV122 @ ( c_List_Olist_ONil @ SY1475 ) @ SY1476 @ SY1475 @ SY1477 )
= SY1476 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1469,plain,
! [SV123: $i] :
( ( ! [SY1478: $i,SY1479: $i,SY1480: $i,SY1481: $i,SY1482: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SY1478 ) @ SY1479 ) )
| ( c_ListOrder_Ostep1 @ SV123 @ SY1480 @ SY1481 @ SY1482 )
| ~ ( c_ListOrder_Ostep1 @ SV123 @ ( c_List_Oappend @ SY1480 @ ( c_List_Olist_OCons @ SY1478 @ ( c_List_Olist_ONil @ SY1482 ) @ SY1482 ) @ SY1482 ) @ ( c_List_Oappend @ SY1481 @ ( c_List_Olist_OCons @ SY1479 @ ( c_List_Olist_ONil @ SY1482 ) @ SY1482 ) @ SY1482 ) @ SY1482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1470,plain,
! [SV124: $i] :
( ( ! [SY1483: $i,SY1484: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV124 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV124 ) @ SY1483 ) @ SY1484 ) @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ SV124 )
| ~ ( c_HOL_Oord__class_Oless @ SY1484 @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ SV124 )
| ~ ( c_HOL_Oord__class_Oless @ SY1483 @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1471,plain,
! [SV125: $i] :
( ( ! [SY1485: $i,SY1486: $i,SY1487: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV125 @ SY1485 @ SY1486 ) @ SY1487 @ SY1486 )
= ( c_List_Olist_OCons @ SV125 @ ( c_List_Oappend @ SY1485 @ SY1487 @ SY1486 ) @ SY1486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1472,plain,
! [SV126: $i] :
( ( ! [SY1488: $i,SY1489: $i,SY1490: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV126 @ SY1488 @ SY1489 ) @ SY1490 @ SY1489 )
= ( c_List_Olist_OCons @ SV126 @ ( c_List_Oappend @ SY1488 @ SY1490 @ SY1489 ) @ SY1489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1473,plain,
! [SV127: $i] :
( ( ! [SY1491: $i,SY1492: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV127 ) @ SY1491 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV127 ) @ SY1492 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1491 ) @ SY1492 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1474,plain,
! [SV128: $i] :
( ( ! [SY1493: $i,SY1494: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV128 ) @ SY1493 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1494 ) @ SY1493 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV128 ) @ SY1494 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1475,plain,
! [SV129: $i] :
( ( ! [SY1495: $i,SY1496: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV129 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV129 ) @ SY1495 @ SY1496 @ SV129 @ SV129 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV129 ) @ SY1495 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV129 ) @ SY1496 @ ( c_HOL_Ozero__class_Ozero @ SV129 ) @ SV129 @ SV129 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1476,plain,
! [SV130: $i] :
( ( ! [SY1497: $i,SY1498: $i,SY1499: $i] :
( ( c_List_Olist_OCons @ SV130 @ ( c_List_Oappend @ SY1497 @ SY1498 @ SY1499 ) @ SY1499 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV130 @ SY1497 @ SY1499 ) @ SY1498 @ SY1499 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1477,plain,
! [SV131: $i] :
( ( ! [SY1500: $i,SY1501: $i,SY1502: $i] :
( ( c_List_Olist_OCons @ SV131 @ ( c_List_Oappend @ SY1500 @ SY1501 @ SY1502 ) @ SY1502 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV131 @ SY1500 @ SY1502 ) @ SY1501 @ SY1502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1478,plain,
! [SV132: $i] :
( ( ! [SY1503: $i,SY1504: $i,SY1505: $i,SY1506: $i,SY1507: $i] :
( ( SV132 = SY1503 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1504 @ SY1503 ) @ SV132 ) )
| ~ ( c_ListOrder_Ostep1 @ SY1504 @ ( c_List_Olist_OCons @ SY1503 @ SY1505 @ SY1506 ) @ ( c_List_Olist_OCons @ SV132 @ SY1507 @ SY1506 ) @ SY1506 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1479,plain,
! [SV133: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV133 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1480,plain,
! [SV134: $i] :
( ( ! [SY1508: $i,SY1509: $i,SY1510: $i,SY1511: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV134 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ SY1508 ) @ SY1509 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ SY1510 ) @ SY1511 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ SY1508 ) @ SY1510 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ SY1509 ) @ SY1511 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1481,plain,
! [SV135: $i] :
( ( ! [SY1512: $i,SY1513: $i,SY1514: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV135 ) @ SY1512 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1513 ) @ SY1514 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1512 ) @ SY1514 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV135 ) @ SY1513 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1482,plain,
! [SV136: $i] :
( ( ! [SY1515: $i,SY1516: $i] :
( ( ( c_Lambda_Oliftn @ SV136 @ ( c_Lambda_OdB_OVar @ SY1515 ) @ SY1516 )
= ( c_Lambda_OdB_OVar @ SY1515 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1515 @ SY1516 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1483,plain,
! [SV137: $i] :
( ( ! [SY1517: $i,SY1518: $i,SY1519: $i] :
( ( c_Type_Otyping @ SV137 @ SY1517 @ SY1518 )
| ~ ( c_Type_Otyping @ SV137 @ SY1519 @ SY1518 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1519 ) @ SY1517 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1484,plain,
! [SV138: $i] :
( ( ! [SY1520: $i,SY1521: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV138 @ SY1520 ) @ SY1521 @ SY1520 )
= SV138 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1485,plain,
! [SV139: $i] :
( ( ! [SY1522: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV139 ) @ SY1522 )
= ( c_Lambda_OdB_OVar @ SV139 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV139 @ SY1522 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1486,plain,
! [SV140: $i] :
( ( ! [SY1523: $i,SY1524: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV140 @ SY1523 ) ) @ ( c_Lambda_Olift @ SY1524 @ SY1523 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV140 ) @ SY1524 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1487,plain,
! [SV141: $i] :
( ( ! [SY1525: $i] :
( ( c_HOL_Oord__class_Oless @ SV141 @ SV141 @ tc_nat )
| ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV141 ) @ SY1525 @ SV141 )
= ( c_Lambda_Oliftn @ SV141 @ SY1525 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1488,plain,
! [SV142: $i] :
( ( ! [SY1526: $i,SY1527: $i] :
( ( c_List_Olist_OCons @ SV142 @ SY1526 @ SY1527 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY1527 ) @ ( c_List_Olist_OCons @ SV142 @ SY1526 @ SY1527 ) @ SY1527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1489,plain,
! [SV143: $i] :
( ( ! [SY1528: $i,SY1529: $i,SY1530: $i,SY1531: $i,SY1532: $i] :
( ( SV143 = SY1528 )
| ( c_ListOrder_Ostep1 @ SY1529 @ SV143 @ SY1528 @ SY1530 )
| ~ ( c_ListOrder_Ostep1 @ SY1529 @ ( c_List_Oappend @ SV143 @ ( c_List_Olist_OCons @ SY1531 @ ( c_List_Olist_ONil @ SY1530 ) @ SY1530 ) @ SY1530 ) @ ( c_List_Oappend @ SY1528 @ ( c_List_Olist_OCons @ SY1532 @ ( c_List_Olist_ONil @ SY1530 ) @ SY1530 ) @ SY1530 ) @ SY1530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1490,plain,
! [SV144: $i] :
( ( ( c_List_Olist_ONil @ SV144 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV144 ) @ ( c_List_Olist_ONil @ SV144 ) @ SV144 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1030]) ).
thf(1491,plain,
! [SV145: $i] :
( ( ! [SY1533: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ SV145 @ SY1533 ) @ SY1533 )
= ( c_Transitive__Closure_Ortranclp @ SV145 @ SY1533 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1492,plain,
! [SV146: $i] :
( ( ! [SY1534: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV146 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ ( c_HOL_Ozero__class_Ozero @ SV146 ) ) @ SY1534 )
= SY1534 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1493,plain,
! [SV147: $i] :
( ( ! [SY1535: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV147 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ ( c_HOL_Ozero__class_Ozero @ SV147 ) ) @ SY1535 )
= SY1535 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1494,plain,
! [SV148: $i] :
( ( ! [SY1536: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV148 )
| ~ ( class_Int_Onumber__ring @ SV148 )
| ( SY1536
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SY1536 ) @ ( c_HOL_Ozero__class_Ozero @ SV148 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1034]) ).
thf(1495,plain,
! [SV149: $i] :
( ( ! [SY1537: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV149 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SY1537 ) @ ( c_HOL_Ozero__class_Ozero @ SV149 ) )
= SY1537 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1496,plain,
! [SV150: $i] :
( ( ! [SY1538: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV150 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV150 ) @ ( c_HOL_Ozero__class_Ozero @ SV150 ) ) @ SY1538 )
= SY1538 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1036]) ).
thf(1497,plain,
! [SV151: $i] :
( ( ! [SY1539: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV151 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SY1539 ) @ ( c_HOL_Ozero__class_Ozero @ SV151 ) )
= SY1539 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1498,plain,
! [SV152: $i] :
( ( ! [SY1540: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV152 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SY1540 ) @ ( c_HOL_Ozero__class_Ozero @ SV152 ) )
= SY1540 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1499,plain,
! [SV153: $i] :
( ( ! [SY1541: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV153 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ ( c_HOL_Ozero__class_Ozero @ SV153 ) ) @ SY1541 )
= SY1541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1500,plain,
! [SV154: $i] :
( ( ! [SY1542: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV154 ) ) @ ( c_Lambda_OdB_OAbs @ SY1542 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV154 ) @ SY1542 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1501,plain,
! [SV155: $i] :
( ( ! [SY1543: $i,SY1544: $i,SY1545: $i] :
( ( ( hAPP @ ( hAPP @ SV155 @ SY1543 ) @ SY1544 )
= SY1543 )
| ~ ( c_OrderedGroup_Omonoid__add @ SY1544 @ SV155 @ SY1545 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1502,plain,
! [SV156: $i] :
( ( ! [SY1546: $i,SY1547: $i,SY1548: $i] :
( ( ( hAPP @ ( hAPP @ SV156 @ SY1546 ) @ SY1547 )
= SY1547 )
| ~ ( c_OrderedGroup_Omonoid__add @ SY1546 @ SV156 @ SY1548 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1503,plain,
! [SV157: $i] :
( ( ! [SY1549: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV157 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV157 ) @ SY1549 @ SV157 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV157 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SY1549 ) @ SY1549 ) @ SV157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1504,plain,
! [SV158: $i] :
( ( ! [SY1550: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV158 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SY1550 ) @ SY1550 ) @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SY1550 @ SV158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1505,plain,
! [SV159: $i] :
( ( ! [SY1551: $i,SY1552: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV159 @ SY1551 ) @ SY1552 ) @ SY1552 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1506,plain,
! [SV160: $i] :
( ( ! [SY1553: $i,SY1554: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV160 @ SY1553 ) @ SY1554 ) @ SY1554 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1507,plain,
! [SV161: $i] :
( ( ! [SY1555: $i,SY1556: $i,SY1557: $i,SY1558: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV161 @ SY1555 ) @ SY1556 ) @ SY1557 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV161 @ SY1555 ) @ SY1558 ) @ SY1557 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV161 @ SY1555 ) @ SY1556 ) @ SY1558 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1508,plain,
! [SV162: $i] :
( ( ! [SY1559: $i] :
( ( c_List_Oappend @ SV162 @ ( c_List_Olist_ONil @ SY1559 ) @ SY1559 )
= SV162 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1509,plain,
! [SV163: $i] :
( ( ! [SY1560: $i] :
( SV163
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY1560 ) @ SV163 @ SY1560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1510,plain,
! [SV164: $i] :
( ( ! [SY1561: $i] :
( SV164
= ( c_List_Oappend @ SV164 @ ( c_List_Olist_ONil @ SY1561 ) @ SY1561 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1511,plain,
! [SV165: $i] :
( ( ! [SY1562: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV165 ) @ SY1562 @ SV165 )
= SY1562 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1512,plain,
! [SV166: $i] :
( ( ! [SY1563: $i] :
( SV166
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY1563 ) @ SV166 @ SY1563 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1513,plain,
! [SV167: $i] :
( ( ! [SY1564: $i,SY1565: $i,SY1566: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV167 @ SY1564 @ SY1565 ) ) @ ( c_Lambda_Osubst @ SV167 @ SY1566 @ SY1565 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1564 ) @ SY1566 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1514,plain,
! [SV168: $i] :
( ( ! [SY1567: $i,SY1568: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV168 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV168 ) @ SY1567 ) @ SY1568 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV168 ) @ SY1568 ) @ SY1567 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1515,plain,
! [SV169: $i] :
( ( ! [SY1569: $i,SY1570: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV169 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV169 ) @ SY1569 ) @ SY1570 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV169 ) @ SY1570 ) @ SY1569 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1516,plain,
! [SV170: $i] :
( ( ! [SY1571: $i,SY1572: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV170 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV170 ) @ SY1571 ) @ SY1572 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV170 ) @ SY1572 ) @ SY1571 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1517,plain,
! [SV171: $i] :
( ( ! [SY1573: $i,SY1574: $i,SY1575: $i,SY1576: $i,SY1577: $i] :
( ( c_List_Ofoldr @ SV171 @ ( c_List_Oappend @ SY1573 @ SY1574 @ SY1575 ) @ SY1576 @ SY1575 @ SY1577 )
= ( c_List_Ofoldr @ SV171 @ SY1573 @ ( c_List_Ofoldr @ SV171 @ SY1574 @ SY1576 @ SY1575 @ SY1577 ) @ SY1575 @ SY1577 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1518,plain,
! [SV172: $i] :
( ( ! [SY1578: $i,SY1579: $i,SY1580: $i,SY1581: $i,SY1582: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV172 @ SY1578 ) @ SY1579 ) )
| ( SY1578 = SY1579 )
| ~ ( c_ListOrder_Ostep1 @ SV172 @ ( c_List_Oappend @ SY1580 @ ( c_List_Olist_OCons @ SY1578 @ ( c_List_Olist_ONil @ SY1581 ) @ SY1581 ) @ SY1581 ) @ ( c_List_Oappend @ SY1582 @ ( c_List_Olist_OCons @ SY1579 @ ( c_List_Olist_ONil @ SY1581 ) @ SY1581 ) @ SY1581 ) @ SY1581 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1519,plain,
! [SV173: $i] :
( ( ! [SY1583: $i,SY1584: $i,SY1585: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV173 @ SY1583 @ SY1584 ) ) @ ( c_Lambda_Osubst @ SY1585 @ SY1583 @ SY1584 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV173 ) @ SY1585 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1520,plain,
! [SV174: $i] :
( ( ! [SY1586: $i,SY1587: $i,SY1588: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV174 @ SY1586 @ SY1587 ) ) @ ( c_Lambda_Osubst @ SV174 @ SY1588 @ SY1587 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1586 ) @ SY1588 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1521,plain,
! [SV175: $i] :
( ( ! [SY1589: $i,SY1590: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV175 )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV175 ) @ SY1589 @ SY1590 @ SV175 @ SV175 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV175 ) @ SY1590 @ SY1589 @ SV175 @ SV175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1522,plain,
! [SV176: $i] :
( ( ! [SY1591: $i,SY1592: $i,SY1593: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV176 @ SY1591 ) @ SY1592 ) @ SY1593 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV176 @ SY1592 ) @ SY1593 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1523,plain,
! [SV177: $i] :
( ( ! [SY1594: $i,SY1595: $i] :
~ ( c_ListOrder_Ostep1 @ SV177 @ ( c_List_Olist_ONil @ SY1594 ) @ SY1595 @ SY1594 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1065]) ).
thf(1524,plain,
! [SV178: $i] :
( ( ! [SY1596: $i,SY1597: $i] :
~ ( c_ListOrder_Ostep1 @ SV178 @ SY1596 @ ( c_List_Olist_ONil @ SY1597 ) @ SY1597 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1525,plain,
! [SV179: $i] :
( ( ! [SY1598: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV179 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV179 ) @ SY1598 ) @ SY1598 ) @ ( c_HOL_Ozero__class_Ozero @ SV179 ) @ SV179 )
| ~ ( c_HOL_Oord__class_Oless @ SY1598 @ ( c_HOL_Ozero__class_Ozero @ SV179 ) @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1526,plain,
! [SV180: $i] :
( ( ! [SY1599: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV180 )
| ( c_HOL_Oord__class_Oless @ SY1599 @ ( c_HOL_Ozero__class_Ozero @ SV180 ) @ SV180 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV180 ) @ SY1599 ) @ SY1599 ) @ ( c_HOL_Ozero__class_Ozero @ SV180 ) @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1527,plain,
! [SV181: $i] :
( ( ! [SY1600: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV181 )
| ( c_HOL_Oord__class_Oless @ SY1600 @ ( c_HOL_Ozero__class_Ozero @ SV181 ) @ SV181 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV181 ) @ SY1600 ) @ SY1600 ) @ ( c_HOL_Ozero__class_Ozero @ SV181 ) @ SV181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1528,plain,
! [SV182: $i] :
( ( ! [SY1601: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV182 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV182 ) @ SY1601 ) @ SY1601 ) @ ( c_HOL_Ozero__class_Ozero @ SV182 ) @ SV182 )
| ~ ( c_HOL_Oord__class_Oless @ SY1601 @ ( c_HOL_Ozero__class_Ozero @ SV182 ) @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1529,plain,
! [SV183: $i] :
( ( ! [SY1602: $i,SY1603: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV183 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ SY1602 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ ( c_HOL_Ozero__class_Ozero @ SV183 ) @ SY1603 @ SV183 @ SV183 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ SY1602 @ SY1603 @ SV183 @ SV183 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1530,plain,
! [SV184: $i] :
( ( ! [SY1604: $i,SY1605: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV184 ) ) @ SY1604 ) @ SY1605 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1604 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV184 @ SY1604 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1605 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1072]) ).
thf(1531,plain,
! [SV185: $i] :
( ( ! [SY1606: $i,SY1607: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV185 ) @ SY1606 @ SY1607 )
= ( c_Lambda_OdB_OVar @ SV185 ) )
| ( SV185 = SY1607 )
| ( c_HOL_Oord__class_Oless @ SY1607 @ SV185 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1532,plain,
! [SV186: $i] :
( ( ! [SY1608: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV186 @ SY1608 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1533,plain,
! [SV187: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV187 @ SV187 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1534,plain,
! [SV188: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV188 @ SV188 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1535,plain,
! [SV189: $i] :
( ( ! [SY1609: $i] :
( ~ ( class_Orderings_Oorder @ SV189 )
| ~ ( c_HOL_Oord__class_Oless @ SY1609 @ SY1609 @ SV189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1536,plain,
! [SV190: $i] :
( ( ! [SY1610: $i] :
( ~ ( class_Orderings_Olinorder @ SV190 )
| ~ ( c_HOL_Oord__class_Oless @ SY1610 @ SY1610 @ SV190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1537,plain,
! [SV191: $i] :
( ( ! [SY1611: $i] :
( ~ ( class_Orderings_Opreorder @ SV191 )
| ~ ( c_HOL_Oord__class_Oless @ SY1611 @ SY1611 @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1538,plain,
! [SV192: $i] :
( ( ! [SY1612: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV192 ) ) @ SY1612 ) ) @ ( c_Lambda_Osubst @ SV192 @ SY1612 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1539,plain,
! [SV193: $i] :
( ( ! [SY1613: $i,SY1614: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV193 @ SY1613 ) ) @ ( c_Lambda_Olift @ SY1614 @ SY1613 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV193 ) @ SY1614 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1540,plain,
! [SV194: $i] :
( ( ! [SY1615: $i,SY1616: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV194 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV194 ) @ SY1615 ) @ SY1616 ) @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SY1616 @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SY1615 @ SV194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1541,plain,
! [SV195: $i] :
( ( ! [SY1617: $i,SY1618: $i,SY1619: $i,SY1620: $i,SY1621: $i] :
( ( c_ListOrder_Ostep1 @ SV195 @ SY1617 @ SY1618 @ SY1619 )
| ( SY1618 = SY1617 )
| ~ ( c_ListOrder_Ostep1 @ SV195 @ ( c_List_Olist_OCons @ SY1620 @ SY1617 @ SY1619 ) @ ( c_List_Olist_OCons @ SY1621 @ SY1618 @ SY1619 ) @ SY1619 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1542,plain,
! [SV196: $i] :
( ( ! [SY1622: $i,SY1623: $i,SY1624: $i,SY1625: $i] :
( ( ( hAPP @ ( hAPP @ SV196 @ ( hAPP @ ( hAPP @ SV196 @ SY1622 ) @ SY1623 ) ) @ SY1624 )
= ( hAPP @ ( hAPP @ SV196 @ SY1622 ) @ ( hAPP @ ( hAPP @ SV196 @ SY1623 ) @ SY1624 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV196 @ SY1625 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1543,plain,
! [SV197: $i] :
( ( ! [SY1626: $i,SY1627: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV197 )
| ( c_HOL_Oord__class_Oless @ SY1626 @ SY1627 @ SV197 )
| ( c_HOL_Oord__class_Oless @ SY1627 @ SY1626 @ SV197 )
| ( SY1627 = SY1626 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1544,plain,
! [SV198: $i] :
( ( ! [SY1628: $i,SY1629: $i] :
( ~ ( class_Orderings_Olinorder @ SV198 )
| ( SY1628 = SY1629 )
| ( c_HOL_Oord__class_Oless @ SY1629 @ SY1628 @ SV198 )
| ( c_HOL_Oord__class_Oless @ SY1628 @ SY1629 @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1545,plain,
! [SV199: $i] :
( ( ! [SY1630: $i] :
( ( c_HOL_Oord__class_Oless @ SV199 @ SY1630 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY1630 @ SV199 @ tc_nat )
| ( SY1630 = SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1546,plain,
! [SV200: $i] :
( ( ! [SY1631: $i,SY1632: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV200 @ SY1631 ) @ SY1632 ) )
| ( c_HOL_Oord__class_Oless @ SY1631 @ SY1632 @ tc_nat )
| ( SY1632 = SY1631 )
| ( c_HOL_Oord__class_Oless @ SY1632 @ SY1631 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1093]) ).
thf(1547,plain,
! [SV201: $i] :
( ( ! [SY1633: $i] :
( ( c_HOL_Oord__class_Oless @ SV201 @ SY1633 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY1633 @ SV201 @ tc_nat )
| ( SY1633 = SV201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1548,plain,
! [SV202: $i] :
( ( ! [SY1634: $i,SY1635: $i] :
( ~ ( class_Orderings_Olinorder @ SV202 )
| ( c_HOL_Oord__class_Oless @ SY1634 @ SY1635 @ SV202 )
| ( c_HOL_Oord__class_Oless @ SY1635 @ SY1634 @ SV202 )
| ( SY1635 = SY1634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1549,plain,
! [SV203: $i] :
( ( ! [SY1636: $i,SY1637: $i] :
( ~ ( class_Orderings_Olinorder @ SV203 )
| ( c_HOL_Oord__class_Oless @ SY1636 @ SY1637 @ SV203 )
| ( SY1637 = SY1636 )
| ( c_HOL_Oord__class_Oless @ SY1637 @ SY1636 @ SV203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1550,plain,
! [SV204: $i] :
( ( ! [SY1638: $i,SY1639: $i] :
( ~ ( class_Orderings_Olinorder @ SV204 )
| ( SY1638 = SY1639 )
| ( c_HOL_Oord__class_Oless @ SY1638 @ SY1639 @ SV204 )
| ( c_HOL_Oord__class_Oless @ SY1639 @ SY1638 @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1551,plain,
! [SV205: $i] :
( ( ! [SY1640: $i,SY1641: $i,SY1642: $i,SY1643: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV205 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV205 ) @ SY1640 ) @ SY1641 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV205 ) @ SY1642 ) @ SY1643 ) @ SV205 )
| ~ ( c_HOL_Oord__class_Oless @ SY1641 @ SY1643 @ SV205 )
| ~ ( c_HOL_Oord__class_Oless @ SY1640 @ SY1642 @ SV205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1552,plain,
! [SV206: $i] :
( ( ! [SY1644: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV206 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV206 ) @ ( c_HOL_Ozero__class_Ozero @ SV206 ) @ SY1644 @ SV206 @ SV206 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV206 ) @ SY1644 @ ( c_HOL_Ozero__class_Ozero @ SV206 ) @ SV206 @ SV206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1553,plain,
! [SV207: $i] :
( ( ! [SY1645: $i,SY1646: $i,SY1647: $i,SY1648: $i,SY1649: $i] :
( ( SV207 = SY1645 )
| ( SY1646 = SY1647 )
| ~ ( c_ListOrder_Ostep1 @ SY1648 @ ( c_List_Oappend @ SV207 @ ( c_List_Olist_OCons @ SY1646 @ ( c_List_Olist_ONil @ SY1649 ) @ SY1649 ) @ SY1649 ) @ ( c_List_Oappend @ SY1645 @ ( c_List_Olist_OCons @ SY1647 @ ( c_List_Olist_ONil @ SY1649 ) @ SY1649 ) @ SY1649 ) @ SY1649 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1554,plain,
! [SV208: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV208 @ tc_nat )
| ( SV208
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1555,plain,
! [SV209: $i] :
( ( ! [SY1650: $i,SY1651: $i,SY1652: $i] :
( ( c_List_Olistsp @ SV209 @ ( c_List_Oappend @ SY1650 @ SY1651 @ SY1652 ) @ SY1652 )
| ~ ( c_List_Olistsp @ SV209 @ SY1651 @ SY1652 )
| ~ ( c_List_Olistsp @ SV209 @ SY1650 @ SY1652 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1556,plain,
! [SV210: $i] :
( ( ! [SY1653: $i,SY1654: $i,SY1655: $i,SY1656: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV210 @ SY1653 @ SY1654 @ ( c_Lambda_OdB_OAbs @ SY1655 ) @ SY1656 )
= ( hAPP @ ( hAPP @ SY1654 @ SY1655 ) @ ( c_Lambda_OdB_OdB__rec @ SV210 @ SY1653 @ SY1654 @ SY1655 @ SY1656 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1557,plain,
! [SV211: $i] :
( ( ! [SY1657: $i] :
( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV211 @ SY1657 )
= SV211 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1558,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)],[1106]) ).
thf(1559,plain,
! [SV212: $i] :
( ( ~ ( class_OrderedGroup_Osemigroup__add @ SV212 )
| ( c_OrderedGroup_Osemigroup__add @ ( c_HOL_Oplus__class_Oplus @ SV212 ) @ SV212 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1560,plain,
! [SV213: $i] :
( ( ! [SY1658: $i] :
( ( c_Lambda_Osubstn @ SV213 @ SY1658 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_Lambda_Osubst @ SV213 @ SY1658 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1561,plain,
! [SV214: $i] :
( ( ! [SY1659: $i,SY1660: $i,SY1661: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV214 )
| ( c_HOL_Oord__class_Oless @ SY1659 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV214 ) @ SY1660 ) @ SY1661 ) @ SV214 )
| ~ ( c_HOL_Oord__class_Oless @ SY1659 @ SY1661 @ SV214 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV214 ) @ SY1660 @ SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1562,plain,
! [SV215: $i] :
( ( ! [SY1662: $i,SY1663: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV215 ) @ SY1662 @ SY1663 )
= ( c_Lambda_OdB_OVar @ SV215 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV215 @ SY1663 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1563,plain,
! [SV216: $i] :
( ( ! [SY1664: $i,SY1665: $i,SY1666: $i,SY1667: $i,SY1668: $i] :
( ( c_List_Ofoldr @ SV216 @ ( c_List_Olist_OCons @ SY1664 @ SY1665 @ SY1666 ) @ SY1667 @ SY1666 @ SY1668 )
= ( hAPP @ ( hAPP @ SV216 @ SY1664 ) @ ( c_List_Ofoldr @ SV216 @ SY1665 @ SY1667 @ SY1666 @ SY1668 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1564,plain,
! [SV217: $i] :
( ( ! [SY1669: $i,SY1670: $i,SY1671: $i,SY1672: $i] :
( ~ ( hBOOL @ ( hAPP @ SV217 @ ( c_Lambda_OdB_OdB__case @ SY1669 @ SY1670 @ SY1671 @ ( c_Lambda_OdB_OAbs @ SY1672 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV217 @ ( hAPP @ SY1671 @ SY1672 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1565,plain,
! [SV218: $i] :
( ( ! [SY1673: $i,SY1674: $i,SY1675: $i,SY1676: $i] :
( ~ ( hBOOL @ ( hAPP @ SV218 @ ( c_Lambda_OdB_OdB__case @ SY1673 @ SY1674 @ SY1675 @ ( c_Lambda_OdB_OAbs @ SY1676 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV218 @ ( hAPP @ SY1675 @ SY1676 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1113]) ).
thf(1566,plain,
! [SV219: $i] :
( ( ! [SY1677: $i,SY1678: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV219 @ ( c_Lambda_OdB_OVar @ SY1677 ) @ SY1678 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV219 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1567,plain,
! [SV220: $i] :
( ( ! [SY1679: $i,SY1680: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV220 ) @ ( c_List_Olist_OCons @ SY1679 @ SY1680 @ SV220 ) @ SV220 )
= ( c_List_Olist_OCons @ SY1679 @ SY1680 @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1568,plain,
! [SV221: $i] :
( ( ! [SY1681: $i,SY1682: $i,SY1683: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV221 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV221 ) @ SY1681 ) @ SY1682 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV221 ) @ SY1683 ) @ SY1682 ) @ SV221 )
| ~ ( c_HOL_Oord__class_Oless @ SY1681 @ SY1683 @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1569,plain,
! [SV222: $i] :
( ( ! [SY1684: $i,SY1685: $i,SY1686: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV222 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV222 ) @ SY1684 ) @ SY1685 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV222 ) @ SY1686 ) @ SY1685 ) @ SV222 )
| ~ ( c_HOL_Oord__class_Oless @ SY1684 @ SY1686 @ SV222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1570,plain,
! [SV223: $i] :
( ( ! [SY1687: $i,SY1688: $i,SY1689: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV223 )
| ( c_HOL_Oord__class_Oless @ SY1687 @ SY1688 @ SV223 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV223 ) @ SY1687 ) @ SY1689 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV223 ) @ SY1688 ) @ SY1689 ) @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1571,plain,
! [SV224: $i] :
( ( ! [SY1690: $i,SY1691: $i,SY1692: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV224 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV224 ) @ SY1690 ) @ SY1691 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV224 ) @ SY1690 ) @ SY1692 ) @ SV224 )
| ~ ( c_HOL_Oord__class_Oless @ SY1691 @ SY1692 @ SV224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1125]) ).
thf(1572,plain,
! [SV225: $i] :
( ( ! [SY1693: $i,SY1694: $i,SY1695: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV225 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV225 ) @ SY1693 ) @ SY1694 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV225 ) @ SY1693 ) @ SY1695 ) @ SV225 )
| ~ ( c_HOL_Oord__class_Oless @ SY1694 @ SY1695 @ SV225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1573,plain,
! [SV226: $i] :
( ( ! [SY1696: $i,SY1697: $i,SY1698: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV226 )
| ( c_HOL_Oord__class_Oless @ SY1696 @ SY1697 @ SV226 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV226 ) @ SY1698 ) @ SY1696 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV226 ) @ SY1698 ) @ SY1697 ) @ SV226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1574,plain,
! [SV227: $i] :
( ( ! [SY1699: $i,SY1700: $i,SY1701: $i,SY1702: $i,SY1703: $i] :
( ( c_ListOrder_Ostep1 @ SV227 @ SY1699 @ SY1700 @ SY1701 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV227 @ SY1702 ) @ SY1703 ) )
| ~ ( c_ListOrder_Ostep1 @ SV227 @ ( c_List_Olist_OCons @ SY1702 @ SY1699 @ SY1701 ) @ ( c_List_Olist_OCons @ SY1703 @ SY1700 @ SY1701 ) @ SY1701 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1575,plain,
! [SV228: $i] :
( ( ! [SY1704: $i,SY1705: $i,SY1706: $i,SY1707: $i] :
( ( c_ListOrder_Ostep1 @ SV228 @ ( c_List_Olist_OCons @ SY1704 @ SY1705 @ SY1706 ) @ ( c_List_Olist_OCons @ SY1704 @ SY1707 @ SY1706 ) @ SY1706 )
| ~ ( c_ListOrder_Ostep1 @ SV228 @ SY1705 @ SY1707 @ SY1706 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1576,plain,
! [SV229: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV229 ) @ ( c_List_Olist_ONil @ SV229 ) @ SV229 )
= ( c_List_Olist_ONil @ SV229 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1577,plain,
! [SV230: $i] :
( ( ! [SY1708: $i,SY1709: $i,SY1710: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV230 @ SY1708 @ SY1709 ) @ SY1710 @ SY1709 )
= ( c_List_Oappend @ SV230 @ ( c_List_Oappend @ SY1708 @ SY1710 @ SY1709 ) @ SY1709 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1578,plain,
! [SV231: $i] :
( ( ! [SY1711: $i,SY1712: $i,SY1713: $i] :
( ( c_List_Oappend @ SV231 @ ( c_List_Oappend @ SY1711 @ SY1712 @ SY1713 ) @ SY1713 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV231 @ SY1711 @ SY1713 ) @ SY1712 @ SY1713 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1579,plain,
! [SV232: $i] :
( ( ! [SY1714: $i,SY1715: $i,SY1716: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV232 @ SY1714 @ SY1715 ) @ SY1716 @ SY1715 )
= ( c_List_Oappend @ SV232 @ ( c_List_Oappend @ SY1714 @ SY1716 @ SY1715 ) @ SY1715 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1580,plain,
! [SV233: $i] :
( ( ! [SY1717: $i,SY1718: $i,SY1719: $i] :
( ( c_List_Oappend @ SV233 @ ( c_List_Oappend @ SY1717 @ SY1718 @ SY1719 ) @ SY1719 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV233 @ SY1717 @ SY1719 ) @ SY1718 @ SY1719 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1581,plain,
! [SV234: $i] :
( ( ! [SY1720: $i,SY1721: $i] :
( ~ ( class_Orderings_Oorder @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SY1720 @ SY1721 @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SY1721 @ SY1720 @ SV234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1582,plain,
! [SV235: $i] :
( ( ! [SY1722: $i,SY1723: $i,SY1724: $i,SY1725: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV235 @ SY1722 ) @ SY1723 ) @ SY1724 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV235 @ SY1722 ) @ SY1725 ) @ SY1724 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SY1723 ) @ SY1725 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1583,plain,
! [SV236: $i] :
( ( ! [SY1726: $i,SY1727: $i,SY1728: $i,SY1729: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV236 @ SY1726 ) @ SY1727 ) @ SY1728 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV236 @ SY1729 ) @ SY1728 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV236 @ SY1726 ) @ SY1727 ) @ SY1729 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1584,plain,
! [SV237: $i] :
( ( ! [SY1730: $i,SY1731: $i] :
( ~ ( class_Orderings_Olinorder @ SV237 )
| ~ ( c_HOL_Oord__class_Oless @ SY1730 @ SY1731 @ SV237 )
| ~ ( c_HOL_Oord__class_Oless @ SY1731 @ SY1730 @ SV237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1585,plain,
! [SV238: $i] :
( ( ! [SY1732: $i,SY1733: $i] :
( ~ ( class_Orderings_Opreorder @ SV238 )
| ~ ( c_HOL_Oord__class_Oless @ SY1732 @ SY1733 @ SV238 )
| ~ ( c_HOL_Oord__class_Oless @ SY1733 @ SY1732 @ SV238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1586,plain,
! [SV239: $i] :
( ( ! [SY1734: $i,SY1735: $i] :
( ~ ( class_Orderings_Opreorder @ SV239 )
| ~ ( c_HOL_Oord__class_Oless @ SY1734 @ SY1735 @ SV239 )
| ~ ( c_HOL_Oord__class_Oless @ SY1735 @ SY1734 @ SV239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1587,plain,
! [SV240: $i] :
( ( ! [SY1736: $i,SY1737: $i,SY1738: $i,SY1739: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV240 @ SY1736 @ SY1737 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SY1738 @ SY1736 ) @ SY1739 )
| ~ ( c_Type_Otyping @ SV240 @ SY1738 @ SY1739 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1588,plain,
! [SV241: $i] :
( ( ! [SY1740: $i] :
( ( hBOOL @ ( hAPP @ SV241 @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV241 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV241 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV241 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV241 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ SV241 @ SY1740 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1589,plain,
! [SV242: $i] :
( ( ! [SY1741: $i,SY1742: $i,SY1743: $i,SY1744: $i] :
( ( ( c_List_Ofoldl @ SV242 @ ( hAPP @ ( hAPP @ SV242 @ SY1741 ) @ SY1742 ) @ SY1743 @ SY1744 @ SY1744 )
= ( hAPP @ ( hAPP @ SV242 @ SY1741 ) @ ( c_List_Ofoldl @ SV242 @ SY1742 @ SY1743 @ SY1744 @ SY1744 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV242 @ SY1744 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1590,plain,
! [SV243: $i] :
( ( ! [SY1745: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV243 ) @ SY1745 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV243 ) @ SY1745 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1149]) ).
thf(1591,plain,
! [SV244: $i] :
( ( ! [SY1746: $i,SY1747: $i,SY1748: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV244 ) @ SY1746 ) @ SY1747 @ SY1748 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV244 @ SY1747 @ SY1748 ) ) @ ( c_Lambda_Osubst @ SY1746 @ SY1747 @ SY1748 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1150]) ).
thf(1592,plain,
! [SV245: $i] :
( ( ! [SY1749: $i,SY1750: $i,SY1751: $i] :
( ( c_Type_Otypings @ SV245 @ SY1749 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SY1750 @ SV245 @ SY1751 @ SY1749 ) )
| ~ ( c_Type_Otyping @ SV245 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1751 ) @ SY1749 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1750 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1593,plain,
! [SV246: $i] :
( ( ! [SY1752: $i,SY1753: $i,SY1754: $i,SY1755: $i] :
( ~ ( hBOOL @ ( hAPP @ SV246 @ ( c_Lambda_OdB_OdB__case @ SY1752 @ SY1753 @ SY1754 @ ( c_Lambda_OdB_OVar @ SY1755 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV246 @ ( hAPP @ SY1752 @ SY1755 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1594,plain,
! [SV247: $i] :
( ( ! [SY1756: $i,SY1757: $i,SY1758: $i,SY1759: $i] :
( ~ ( hBOOL @ ( hAPP @ SV247 @ ( c_Lambda_OdB_OdB__case @ SY1756 @ SY1757 @ SY1758 @ ( c_Lambda_OdB_OVar @ SY1759 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV247 @ ( hAPP @ SY1756 @ SY1759 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1595,plain,
! [SV248: $i] :
( ( ! [SY1760: $i,SY1761: $i,SY1762: $i] :
( ( c_Type_Otyping @ SV248 @ SY1760 @ SY1761 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1762 ) @ SY1760 ) )
| ~ ( c_Type_Otyping @ SV248 @ SY1762 @ SY1761 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1158]) ).
thf(1596,plain,
! [SV249: $i] :
( ( ! [SY1763: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV249 ) @ SY1763 @ SV249 )
= SY1763 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1597,plain,
! [SV250: $i] :
( ( ! [SY1764: $i,SY1765: $i,SY1766: $i,SY1767: $i,SY1768: $i] :
( ~ ( hBOOL @ ( hAPP @ SV250 @ ( c_Lambda_OdB_OdB__case @ SY1764 @ SY1765 @ SY1766 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1767 ) @ SY1768 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV250 @ ( hAPP @ ( hAPP @ SY1765 @ SY1767 ) @ SY1768 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1598,plain,
! [SV251: $i] :
( ( ! [SY1769: $i,SY1770: $i,SY1771: $i,SY1772: $i,SY1773: $i] :
( ~ ( hBOOL @ ( hAPP @ SV251 @ ( c_Lambda_OdB_OdB__case @ SY1769 @ SY1770 @ SY1771 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1772 ) @ SY1773 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV251 @ ( hAPP @ ( hAPP @ SY1770 @ SY1772 ) @ SY1773 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1599,plain,
! [SV252: $i] :
( ( ! [SY1774: $i,SY1775: $i,SY1776: $i] :
( ( c_Type_Otypings @ SV252 @ SY1774 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SY1775 @ SV252 @ SY1776 @ SY1774 ) )
| ~ ( c_Type_Otyping @ SV252 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1776 @ SY1774 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1775 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1600,plain,
! [SV253: $i] :
( ( ! [SY1777: $i,SY1778: $i,SY1779: $i,SY1780: $i,SY1781: $i,SY1782: $i] :
( ( SV253
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SY1777 @ SV253 @ SY1778 @ SY1779 ) @ SY1777 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SY1778 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1780 ) @ SY1781 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV253 )
| ~ ( c_Type_Otypings @ SY1778 @ SY1781 @ SY1782 )
| ~ ( c_Type_Otyping @ SY1778 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1780 ) @ SY1781 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1779 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1777 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1601,plain,
! [SV254: $i] :
( ( ! [SY1783: $i,SY1784: $i,SY1785: $i,SY1786: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV254 @ SY1783 @ SY1784 @ SY1785 ) @ SY1786 )
= ( hAPP @ SV254 @ SY1786 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1786 @ SY1783 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1602,plain,
! [SV255: $i] :
( ( ! [SY1787: $i,SY1788: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV255 @ SY1787 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1788 @ SY1787 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV255 ) @ SY1788 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1167]) ).
thf(1603,plain,
! [SV256: $i] :
( ( ! [SY1789: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV256 ) ) @ SY1789 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1604,plain,
! [SV257: $i] :
( ( ! [SY1790: $i,SY1791: $i,SY1792: $i,SY1793: $i] :
( ( c_Type_Otyping @ SV257 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1790 ) @ SY1791 ) @ SY1792 )
| ~ ( c_Type_Otyping @ SV257 @ SY1791 @ SY1793 )
| ~ ( c_Type_Otyping @ SV257 @ SY1790 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1793 ) @ SY1792 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1170]) ).
thf(1605,plain,
! [SV258: $i] :
( ( ! [SY1794: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV258 ) @ SY1794 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SY1794 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1606,plain,
! [SV259: $i] :
( ( ! [SY1795: $i,SY1796: $i,SY1797: $i,SY1798: $i] :
( ( SV259 = SY1795 )
| ~ ( c_Type_Otyping @ SY1796 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1797 ) @ SY1798 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1795 )
| ~ ( c_Type_Otyping @ SY1796 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1797 ) @ SY1798 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1607,plain,
! [SV260: $i] :
( ( ! [SY1799: $i,SY1800: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV260 @ SY1799 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV260 @ SY1800 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SY1799 @ SY1800 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1608,plain,
! [SV261: $i] :
( ( ! [SY1801: $i] :
( ( hBOOL @ ( hAPP @ SV261 @ SY1801 ) )
| ( hBOOL @ ( hAPP @ SV261 @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV261 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV261 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV261 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV261 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1609,plain,
! [SV262: $i] :
( ( ! [SY1802: $i,SY1803: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV262 @ SY1802 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1803 @ SY1802 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV262 ) @ SY1803 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1180]) ).
thf(1610,plain,
! [SV263: $i] :
( ( ! [SY1804: $i,SY1805: $i,SY1806: $i,SY1807: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV263 @ SY1804 @ SY1805 @ ( c_Lambda_OdB_OVar @ SY1806 ) @ SY1807 )
= ( hAPP @ SV263 @ SY1806 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1183]) ).
thf(1611,plain,
! [SV264: $i] :
( ( ! [SY1808: $i,SY1809: $i,SY1810: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV264 @ SY1808 @ SY1809 @ SY1810 ) @ SY1808 )
= SY1809 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1612,plain,
! [SV265: $i] :
( ( ! [SY1811: $i,SY1812: $i,SY1813: $i] :
( ( c_List_Ofoldl @ SV265 @ SY1811 @ ( c_List_Olist_ONil @ SY1812 ) @ SY1813 @ SY1812 )
= SY1811 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1613,plain,
! [SV266: $i] :
( ( ! [SY1814: $i,SY1815: $i,SY1816: $i] :
( ( c_Type_Otyping @ SV266 @ ( c_Lambda_OdB_OAbs @ SY1814 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1815 ) @ SY1816 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV266 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1815 @ tc_Type_Otype ) @ SY1814 @ SY1816 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1190]) ).
thf(1614,plain,
! [SV267: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ SV267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1193]) ).
thf(1615,plain,
! [SV268: $i] :
( ( ! [SY1817: $i,SY1818: $i] :
( ( ( hAPP @ SV268 @ SY1817 )
= SY1818 )
| ~ ( c_Type_Otyping @ SV268 @ ( c_Lambda_OdB_OVar @ SY1817 ) @ SY1818 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1616,plain,
! [SV269: $i] :
( ( ! [SY1819: $i,SY1820: $i,SY1821: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ SV269 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV269 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV269 ) @ SY1819 ) @ SY1820 ) @ SY1821 @ SV269 @ SV269 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV269 ) @ SY1819 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV269 ) @ SY1820 @ SY1821 @ SV269 @ SV269 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1617,plain,
! [SV270: $i] :
( ( ! [SY1822: $i,SY1823: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV270 ) @ SY1822 ) @ SY1823 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV270 @ SY1823 ) ) @ ( c_Lambda_Olift @ SY1822 @ SY1823 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1618,plain,
! [SV271: $i] :
( ( ! [SY1824: $i,SY1825: $i,SY1826: $i] :
( ( c_Type_Otyping @ SV271 @ SY1824 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SY1825 @ SV271 @ SY1824 @ SY1826 ) @ SY1825 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV271 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1824 @ SY1826 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1825 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1619,plain,
! [SV272: $i] :
( ( ! [SY1827: $i,SY1828: $i,SY1829: $i] :
( ( c_Type_Otyping @ SV272 @ ( c_Lambda_OdB_OVar @ SY1827 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SY1828 @ SV272 @ SY1827 @ SY1829 ) @ SY1828 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV272 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1827 ) @ SY1829 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1828 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1620,plain,
! [SV273: $i] :
( ( ! [SY1830: $i,SY1831: $i,SY1832: $i,SY1833: $i] :
( ( c_Type_Otyping @ SV273 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1830 @ SY1831 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1832 )
| ~ ( c_Type_Otypings @ SV273 @ SY1831 @ SY1833 )
| ~ ( c_Type_Otyping @ SV273 @ SY1830 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY1833 @ SY1832 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1202]) ).
thf(1621,plain,
! [SV274: $i] :
( ( ! [SY1834: $i,SY1835: $i] :
( ( SV274
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1834 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SY1834 @ SY1835 @ SV274 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1834 ) @ SY1835 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV274 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1622,plain,
! [SV275: $i] :
( ( ! [SY1836: $i,SY1837: $i,SY1838: $i,SY1839: $i,SY1840: $i] :
( ( c_Lambda_OdB_OdB__case @ SV275 @ SY1836 @ SY1837 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1838 ) @ SY1839 ) @ SY1840 )
= ( hAPP @ ( hAPP @ SY1836 @ SY1838 ) @ SY1839 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1623,plain,
! [SV276: $i] :
( ( ! [SY1841: $i,SY1842: $i,SY1843: $i,SY1844: $i] :
( ( ( hAPP @ ( hAPP @ SV276 @ SY1841 ) @ ( c_List_Ofoldl @ SV276 @ SY1842 @ SY1843 @ SY1844 @ SY1844 ) )
= ( c_List_Ofoldl @ SV276 @ SY1841 @ SY1843 @ SY1844 @ SY1844 ) )
| ~ ( c_OrderedGroup_Omonoid__add @ SY1842 @ SV276 @ SY1844 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1624,plain,
! [SV277: $i] :
( ( ! [SY1845: $i,SY1846: $i,SY1847: $i] :
( ( c_Type_Otyping @ SV277 @ SY1845 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SY1846 @ SV277 @ SY1847 @ SY1845 ) )
| ~ ( c_Type_Otyping @ SV277 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1847 ) @ SY1845 ) @ SY1846 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1206]) ).
thf(1625,plain,
! [SV278: $i] :
( ( ( c_Lambda_OdB_OVar @ SV278 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV278 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1626,plain,
! [SV279: $i] :
( ( ! [SY1848: $i,SY1849: $i,SY1850: $i,SY1851: $i] :
( ( c_Lambda_OdB_OdB__case @ SV279 @ SY1848 @ SY1849 @ ( c_Lambda_OdB_OVar @ SY1850 ) @ SY1851 )
= ( hAPP @ SV279 @ SY1850 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1208]) ).
thf(1627,plain,
! [SV280: $i] :
( ( ! [SY1852: $i,SY1853: $i,SY1854: $i] :
( ( c_Type_Otypings @ SV280 @ SY1852 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SY1853 @ SV280 @ SY1854 @ SY1852 ) )
| ~ ( c_Type_Otyping @ SV280 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1854 @ SY1852 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1853 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1628,plain,
! [SV281: $i] :
( ( ! [SY1855: $i,SY1856: $i,SY1857: $i,SY1858: $i,SY1859: $i] :
( ( c_List_Ofoldl @ SV281 @ SY1855 @ ( c_List_Olist_OCons @ SY1856 @ SY1857 @ SY1858 ) @ SY1859 @ SY1858 )
= ( c_List_Ofoldl @ SV281 @ ( hAPP @ ( hAPP @ SV281 @ SY1855 ) @ SY1856 ) @ SY1857 @ SY1859 @ SY1858 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1629,plain,
! [SV282: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV282 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV282 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1630,plain,
! [SV283: $i] :
( ( ! [SY1860: $i] : ( c_Type_Otyping @ SV283 @ ( c_Lambda_OdB_OVar @ SY1860 ) @ ( hAPP @ SV283 @ SY1860 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1631,plain,
! [SV284: $i] :
( ( ! [SY1861: $i,SY1862: $i,SY1863: $i,SY1864: $i,SY1865: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV284 @ SY1861 @ SY1862 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1863 ) @ SY1864 ) @ SY1865 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SY1861 @ SY1863 ) @ SY1864 ) @ ( c_Lambda_OdB_OdB__rec @ SV284 @ SY1861 @ SY1862 @ SY1863 @ SY1865 ) ) @ ( c_Lambda_OdB_OdB__rec @ SV284 @ SY1861 @ SY1862 @ SY1864 @ SY1865 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1632,plain,
! [SV285: $i] :
( ( SV285
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2 @ SV285 ) @ ( c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1 @ SV285 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1216]) ).
thf(1633,plain,
! [SV286: $i] :
( ( ! [SY1866: $i,SY1867: $i,SY1868: $i,SY1869: $i,SY1870: $i,SY1871: $i] :
( ( c_Type_Otypings @ SV286 @ SY1866 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SY1867 @ SY1868 @ SV286 @ SY1866 ) )
| ~ ( c_Type_Otyping @ SV286 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1869 ) @ SY1870 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1868 )
| ~ ( c_Type_Otypings @ SV286 @ SY1870 @ SY1871 )
| ~ ( c_Type_Otyping @ SV286 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1869 ) @ SY1870 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1866 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1867 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1219]) ).
thf(1634,plain,
! [SV287: $i] :
( ( ! [SY1872: $i,SY1873: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV287 ) @ SY1872 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV287 ) @ SY1873 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1872 ) @ SY1873 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1635,plain,
! [SV288: $i] :
( ( ! [SY1874: $i,SY1875: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV288 ) @ SY1874 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1875 ) @ SY1874 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV288 ) @ SY1875 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1636,plain,
! [SV289: $i] :
( ( ! [SY1876: $i,SY1877: $i,SY1878: $i] :
( ( c_Lambda_Oliftn @ SV289 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1876 ) @ SY1877 ) @ SY1878 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ SV289 @ SY1876 @ SY1878 ) ) @ ( c_Lambda_Oliftn @ SV289 @ SY1877 @ SY1878 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1637,plain,
! [SV290: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV290 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV290 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1638,plain,
! [SV291: $i] :
( ( ! [SY1879: $i,SY1880: $i,SY1881: $i] :
( ( c_Type_Otyping @ SV291 @ SY1879 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SY1880 @ SV291 @ SY1879 @ SY1881 ) @ SY1880 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV291 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1879 @ SY1881 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1880 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1639,plain,
! [SV292: $i] :
( ( ! [SY1882: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV292 ) @ ( c_Lambda_OdB_OVar @ SY1882 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV292 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1640,plain,
! [SV293: $i] :
( ( ! [SY1883: $i,SY1884: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV293 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SY1883 @ SV293 @ SY1884 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1883 ) @ SV293 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1884 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1228]) ).
thf(1641,plain,
! [SV294: $i] :
( ( ! [SY1885: $i,SY1886: $i,SY1887: $i,SY1888: $i,SY1889: $i] :
( ~ ( c_Type_Otyping @ SV294 @ SY1885 @ SY1886 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV294 @ SY1887 @ SY1886 @ tc_Type_Otype ) @ SY1888 @ SY1889 )
| ( c_Type_Otyping @ SV294 @ ( c_Lambda_Osubst @ SY1888 @ SY1885 @ SY1887 ) @ SY1889 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1642,plain,
! [SV295: $i] :
( ( ! [SY1890: $i,SY1891: $i,SY1892: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV295 ) @ SY1890 ) @ SY1891 @ SY1892 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ SV295 @ SY1891 @ SY1892 ) ) @ ( c_Lambda_Osubstn @ SY1890 @ SY1891 @ SY1892 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1231]) ).
thf(1643,plain,
! [SV296: $i] :
( ( ! [SY1893: $i,SY1894: $i,SY1895: $i,SY1896: $i,SY1897: $i] :
( ( c_List_Ofoldl @ SV296 @ SY1893 @ ( c_List_Oappend @ SY1894 @ SY1895 @ SY1896 ) @ SY1897 @ SY1896 )
= ( c_List_Ofoldl @ SV296 @ ( c_List_Ofoldl @ SV296 @ SY1893 @ SY1894 @ SY1897 @ SY1896 ) @ SY1895 @ SY1897 @ SY1896 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1644,plain,
! [SV297: $i] :
( ( ! [SY1898: $i,SY1899: $i,SY1900: $i] :
( ( c_Type_Otyping @ SV297 @ SY1898 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SY1899 @ SV297 @ SY1898 @ SY1900 ) ) @ SY1899 ) )
| ~ ( c_Type_Otyping @ SV297 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1898 ) @ SY1900 ) @ SY1899 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1233]) ).
thf(1645,plain,
! [SV298: $i] :
( ( ! [SY1901: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ SV298 @ SY1901 ) )
| ~ ( class_Orderings_Opreorder @ SY1901 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1237]) ).
thf(1646,plain,
! [SV299: $i] :
( ( ! [SY1902: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ SV299 @ SY1902 ) )
| ~ ( class_Orderings_Oorder @ SY1902 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1238]) ).
thf(1647,plain,
! [SV300: $i] :
( ( ! [SY1903: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV300 ) @ SY1903 ) @ SY1903 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1648,plain,
! [SV301: $i] :
( ( ! [SY1904: $i,SY1905: $i] :
( ( SV301 = SY1904 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY1905 ) @ SV301 ) @ SY1904 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1649,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[1259]) ).
thf(1650,plain,
! [SV302: $i] :
( ( ! [SY1906: $i,SY1907: $i] :
( ( ( c_List_Orev @ SV302 @ SY1906 )
!= ( c_List_Orev @ SY1907 @ SY1906 ) )
| ( SV302 = SY1907 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1651,plain,
! [SV303: $i] :
( ( ! [SY1908: $i,SY1909: $i] :
( ( ( c_List_Oappend @ SV303 @ SY1908 @ SY1909 )
!= ( c_List_Olist_ONil @ SY1909 ) )
| ( SV303
= ( c_List_Olist_ONil @ SY1909 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1652,plain,
! [SV304: $i] :
( ( ! [SY1910: $i,SY1911: $i,SY1912: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV304 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV304 ) @ SY1910 ) @ SY1911 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV304 ) @ SY1910 ) @ SY1912 ) )
| ( SY1911 = SY1912 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1653,plain,
! [SV305: $i] :
( ( ! [SY1913: $i,SY1914: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV305 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1913 @ SY1914 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV305 )
= SY1913 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1654,plain,
! [SV306: $i] :
( ( ! [SY1915: $i] :
( ( SV306
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV306 ) @ SY1915 ) )
| ( SY1915
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1264]) ).
thf(1655,plain,
! [SV307: $i] :
( ( ! [SY1916: $i,SY1917: $i] :
( ( ( c_List_Oreplicate @ SV307 @ SY1916 @ SY1917 )
!= ( c_List_Olist_ONil @ SY1917 ) )
| ( SV307
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1656,plain,
! [SV308: $i] :
( ( ! [SY1918: $i,SY1919: $i,SY1920: $i,SY1921: $i] :
( ( ( c_List_Oreplicate @ SV308 @ SY1918 @ SY1919 )
!= ( c_List_Oreplicate @ SY1920 @ SY1921 @ SY1919 ) )
| ( SY1918 = SY1921 )
| ( SV308
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1657,plain,
! [SV309: $i] :
( ( ! [SY1922: $i,SY1923: $i,SY1924: $i,SY1925: $i] :
( ( ( c_List_Oappend @ SV309 @ SY1922 @ SY1923 )
!= ( c_List_Olist_OCons @ SY1924 @ SY1925 @ SY1923 ) )
| ( SV309
= ( c_List_Olist_OCons @ SY1924 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY1924 @ SY1925 @ SV309 @ SY1922 @ SY1923 ) @ SY1923 ) )
| ( SV309
= ( c_List_Olist_ONil @ SY1923 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1658,plain,
! [SV310: $i] :
( ( ! [SY1926: $i,SY1927: $i,SY1928: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV310 ) @ SY1926 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1927 ) @ SY1928 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1927 @ SY1926 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV310 @ SY1928 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1268]) ).
thf(1659,plain,
! [SV311: $i] :
( ( ! [SY1929: $i,SY1930: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV311 ) @ SY1929 )
!= ( c_Lambda_OdB_OVar @ SY1930 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1269]) ).
thf(1660,plain,
! [SV312: $i] :
( ( ! [SY1931: $i,SY1932: $i] :
( ( ( c_List_Oappend @ SV312 @ SY1931 @ SY1932 )
!= ( c_List_Olist_ONil @ SY1932 ) )
| ( SY1931
= ( c_List_Olist_ONil @ SY1932 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1661,plain,
! [SV313: $i] :
( ( ! [SY1933: $i,SY1934: $i] :
( ( c_List_Olist_ONil @ SV313 )
!= ( c_List_Olist_OCons @ SY1933 @ SY1934 @ SV313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1271]) ).
thf(1662,plain,
! [SV314: $i] :
( ( ! [SY1935: $i,SY1936: $i,SY1937: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV314 ) @ SY1935 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1936 @ SY1937 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1937
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV314 @ SY1935 @ SY1936 @ SY1937 ) @ ( c_List_Olist_OCons @ SY1935 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( SY1937
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1663,plain,
! [SV315: $i] :
( ( ! [SY1938: $i,SY1939: $i] :
( ( SV315
!= ( c_List_Oappend @ SY1938 @ SV315 @ SY1939 ) )
| ( SY1938
= ( c_List_Olist_ONil @ SY1939 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1664,plain,
! [SV316: $i] :
( ( ! [SY1940: $i,SY1941: $i,SY1942: $i,SY1943: $i] :
( ( ( c_List_Olist_OCons @ SV316 @ SY1940 @ SY1941 )
!= ( c_List_Oappend @ SY1942 @ SY1943 @ SY1941 ) )
| ( SY1940
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV316 @ SY1940 @ SY1942 @ SY1943 @ SY1941 ) @ SY1943 @ SY1941 ) )
| ( ( c_List_Olist_OCons @ SV316 @ SY1940 @ SY1941 )
= SY1943 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1274]) ).
thf(1665,plain,
! [SV317: $i] :
( ( ! [SY1944: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV317 ) @ SY1944 )
!= SV317 )
| ( SY1944
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(1666,plain,
! [SV318: $i] :
( ( ! [SY1945: $i,SY1946: $i] :
( ( c_List_Olist_OCons @ SV318 @ SY1945 @ SY1946 )
!= SY1945 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1667,plain,
! [SV319: $i] :
( ( ! [SY1947: $i,SY1948: $i] :
( ( SV319
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV319 ) @ SY1947 ) @ SY1948 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV319 ) @ SY1947 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV319 ) @ SY1947 ) @ ( c_List_Oappend @ SY1948 @ ( c_List_Olist_OCons @ SY1947 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1668,plain,
! [SV320: $i] :
( ( ! [SY1949: $i,SY1950: $i,SY1951: $i,SY1952: $i] :
( ( ( c_List_Olist_OCons @ SV320 @ SY1949 @ SY1950 )
!= ( c_List_Olist_OCons @ SY1951 @ SY1952 @ SY1950 ) )
| ( SV320 = SY1951 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1278]) ).
thf(1669,plain,
! [SV321: $i] :
( ( ! [SY1953: $i,SY1954: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV321 ) @ SY1953 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV321 ) @ SY1954 ) )
| ( SY1953 = SY1954 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1279]) ).
thf(1670,plain,
! [SV322: $i] :
( ( ! [SY1955: $i,SY1956: $i,SY1957: $i] :
( ( ( c_List_Oappend @ SV322 @ SY1955 @ SY1956 )
!= ( c_List_Oappend @ SY1957 @ SY1955 @ SY1956 ) )
| ( SV322 = SY1957 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1280]) ).
thf(1671,plain,
! [SV323: $i] :
( ( ! [SY1958: $i,SY1959: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV323 ) @ SY1958 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV323 ) @ SY1959 ) )
| ( SY1958 = SY1959 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1281]) ).
thf(1672,plain,
! [SV324: $i] :
( ( ! [SY1960: $i,SY1961: $i] :
( ( c_List_Olist_OCons @ SV324 @ SY1960 @ SY1961 )
!= ( c_List_Olist_ONil @ SY1961 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1673,plain,
! [SV325: $i] :
( ( ! [SY1962: $i,SY1963: $i,SY1964: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV325 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV325 ) @ SY1962 ) @ SY1963 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV325 ) @ SY1964 ) @ SY1963 ) )
| ( SY1962 = SY1964 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1674,plain,
! [SV326: $i] :
( ( ! [SY1965: $i,SY1966: $i] :
( ( SV326
!= ( c_List_Oappend @ SV326 @ SY1965 @ SY1966 ) )
| ( SY1965
= ( c_List_Olist_ONil @ SY1966 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1675,plain,
! [SV327: $i] :
( ( ! [SY1967: $i,SY1968: $i,SY1969: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV327 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SY1967 ) @ SY1968 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SY1967 ) @ SY1969 ) )
| ( SY1968 = SY1969 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1285]) ).
thf(1676,plain,
! [SV328: $i] :
( ( ! [SY1970: $i,SY1971: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV328 ) @ SY1970 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1971 ) @ SY1970 ) )
| ( SV328 = SY1971 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1286]) ).
thf(1677,plain,
! [SV329: $i] :
( ( ! [SY1972: $i,SY1973: $i,SY1974: $i,SY1975: $i,SY1976: $i,SY1977: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV329 ) @ SY1972 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SY1973 @ SY1974 @ SY1975 ) ) )
| ~ ( c_Type_Otyping @ SY1976 @ SY1974 @ SY1972 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1974 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY1976 @ SY1975 @ SY1972 @ tc_Type_Otype ) @ SY1973 @ SY1977 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1973 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1678,plain,
! [SV330: $i] :
( ( ! [SY1978: $i] :
( ( c_Lambda_OdB_OAbs @ SV330 )
!= ( c_Lambda_OdB_OVar @ SY1978 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1679,plain,
! [SV331: $i] :
( ( ! [SY1979: $i] :
( ( ( c_List_Orev @ SV331 @ SY1979 )
!= ( c_List_Olist_ONil @ SY1979 ) )
| ( SV331
= ( c_List_Olist_ONil @ SY1979 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1680,plain,
! [SV332: $i] :
( ( ! [SY1980: $i,SY1981: $i,SY1982: $i,SY1983: $i] :
( ( ( c_List_Oreplicate @ SV332 @ SY1980 @ SY1981 )
!= ( c_List_Oreplicate @ SY1982 @ SY1983 @ SY1981 ) )
| ( SV332 = SY1982 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1290]) ).
thf(1681,plain,
! [SV333: $i] :
( ( ! [SY1984: $i] :
( ( c_Lambda_OdB_OVar @ SV333 )
!= ( c_Lambda_OdB_OAbs @ SY1984 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1291]) ).
thf(1682,plain,
! [SV334: $i] :
( ( ! [SY1985: $i,SY1986: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV334 @ SY1985 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY1986 ) )
| ( SV334
= ( c_Lambda_OdB_OAbs @ SY1986 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1683,plain,
! [SV335: $i] :
( ( ! [SY1987: $i,SY1988: $i] :
( ( c_Lambda_OdB_OVar @ SV335 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1987 ) @ SY1988 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1684,plain,
! [SV336: $i] :
( ( ! [SY1989: $i,SY1990: $i] :
( ( ( c_List_Orev @ SV336 @ SY1989 )
!= ( c_List_Olist_OCons @ SY1990 @ ( c_List_Olist_ONil @ SY1989 ) @ SY1989 ) )
| ( SV336
= ( c_List_Olist_OCons @ SY1990 @ ( c_List_Olist_ONil @ SY1989 ) @ SY1989 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1685,plain,
! [SV337: $i] :
( ( ! [SY1991: $i,SY1992: $i] :
( SV337
!= ( c_List_Olist_OCons @ SY1991 @ SV337 @ SY1992 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1295]) ).
thf(1686,plain,
! [SV338: $i] :
( ( ! [SY1993: $i,SY1994: $i,SY1995: $i,SY1996: $i] :
( ( ( c_List_Oappend @ SV338 @ SY1993 @ SY1994 )
!= ( c_List_Olist_OCons @ SY1995 @ SY1996 @ SY1994 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY1995 @ SY1996 @ SV338 @ SY1993 @ SY1994 ) @ SY1993 @ SY1994 )
= SY1996 )
| ( SV338
= ( c_List_Olist_ONil @ SY1994 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1687,plain,
! [SV339: $i] :
( ( ! [SY1997: $i,SY1998: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV339 )
| ~ ( class_Int_Onumber__ring @ SV339 )
| ( SY1997
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV339 ) @ SY1997 ) @ SY1998 ) )
| ( SY1998
= ( c_HOL_Ozero__class_Ozero @ SV339 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1297]) ).
thf(1688,plain,
! [SV340: $i] :
( ( ! [SY1999: $i,SY2000: $i,SY2001: $i] :
( ( ( c_List_Oappend @ SV340 @ SY1999 @ SY2000 )
!= ( c_List_Oappend @ SV340 @ SY2001 @ SY2000 ) )
| ( SY1999 = SY2001 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1298]) ).
thf(1689,plain,
! [SV341: $i] :
( ( ! [SY2002: $i,SY2003: $i,SY2004: $i,SY2005: $i] :
( ( ( c_List_Olist_OCons @ SV341 @ SY2002 @ SY2003 )
!= ( c_List_Oappend @ SY2004 @ SY2005 @ SY2003 ) )
| ( SY2002
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV341 @ SY2002 @ SY2004 @ SY2005 @ SY2003 ) @ SY2005 @ SY2003 ) )
| ( SY2004
= ( c_List_Olist_ONil @ SY2003 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1690,plain,
! [SV342: $i] :
( ( ! [SY2006: $i,SY2007: $i,SY2008: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV342 ) @ SY2006 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY2007 ) @ SY2008 ) )
| ( SY2006 = SY2008 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1691,plain,
! [SV343: $i] :
( ( ! [SY2009: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV343 )
!= ( c_Lambda_OdB_OAbs @ SY2009 ) )
| ( SV343 = SY2009 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1692,plain,
! [SV344: $i] :
( ( ! [SY2010: $i,SY2011: $i,SY2012: $i,SY2013: $i] :
( ( ( c_List_Oappend @ SV344 @ SY2010 @ SY2011 )
!= ( c_List_Olist_OCons @ SY2012 @ SY2013 @ SY2011 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY2012 @ SY2013 @ SV344 @ SY2010 @ SY2011 ) @ SY2010 @ SY2011 )
= SY2013 )
| ( SY2010
= ( c_List_Olist_OCons @ SY2012 @ SY2013 @ SY2011 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1302]) ).
thf(1693,plain,
! [SV345: $i] :
( ( ! [SY2014: $i] :
( ( ( c_List_Orotate1 @ SV345 @ SY2014 )
!= ( c_List_Olist_ONil @ SY2014 ) )
| ( SV345
= ( c_List_Olist_ONil @ SY2014 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1303]) ).
thf(1694,plain,
! [SV346: $i] :
( ( ! [SY2015: $i,SY2016: $i,SY2017: $i,SY2018: $i] :
( ( ( c_List_Olist_OCons @ SV346 @ SY2015 @ SY2016 )
!= ( c_List_Oappend @ SY2017 @ SY2018 @ SY2016 ) )
| ( ( c_List_Olist_OCons @ SV346 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV346 @ SY2015 @ SY2017 @ SY2018 @ SY2016 ) @ SY2016 )
= SY2017 )
| ( SY2017
= ( c_List_Olist_ONil @ SY2016 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1304]) ).
thf(1695,plain,
! [SV347: $i] :
( ( ! [SY2019: $i,SY2020: $i] :
( ( ( c_List_Olist_ONil @ SV347 )
!= ( c_List_Oreplicate @ SY2019 @ SY2020 @ SV347 ) )
| ( SY2019
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1696,plain,
! [SV348: $i] :
( ( ! [SY2021: $i,SY2022: $i,SY2023: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV348 ) @ SY2021 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2022 ) @ SY2023 ) )
| ( SY2021 = SY2023 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1306]) ).
thf(1697,plain,
! [SV349: $i] :
( ( ! [SY2024: $i,SY2025: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ SV349 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SY2024 @ SV349 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY2025 @ SV349 ) )
| ( SY2024 = SY2025 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1698,plain,
! [SV350: $i] :
( ( ! [SY2026: $i,SY2027: $i,SY2028: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV350 ) @ SY2026 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2027 @ SY2028 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV350
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2027 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV350 @ SY2026 @ SY2027 @ SY2028 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2028
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1308]) ).
thf(1699,plain,
! [SV351: $i] :
( ( ! [SY2029: $i,SY2030: $i,SY2031: $i,SY2032: $i] :
( ( ( c_List_Oappend @ SV351 @ ( c_List_Olist_OCons @ SY2029 @ ( c_List_Olist_ONil @ SY2030 ) @ SY2030 ) @ SY2030 )
!= ( c_List_Oappend @ SY2031 @ ( c_List_Olist_OCons @ SY2032 @ ( c_List_Olist_ONil @ SY2030 ) @ SY2030 ) @ SY2030 ) )
| ( SY2029 = SY2032 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1309]) ).
thf(1700,plain,
! [SV352: $i] :
( ( ! [SY2033: $i,SY2034: $i,SY2035: $i,SY2036: $i] :
( ( ( c_List_Olist_OCons @ SV352 @ SY2033 @ SY2034 )
!= ( c_List_Olist_OCons @ SY2035 @ SY2036 @ SY2034 ) )
| ( SY2033 = SY2036 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1701,plain,
! [SV353: $i] :
( ( ! [SY2037: $i,SY2038: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV353 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2037 @ SY2038 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2038
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1702,plain,
! [SV354: $i] :
( ( ! [SY2039: $i,SY2040: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV354 @ SY2039 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY2040 ) )
| ( SY2039
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1312]) ).
thf(1703,plain,
! [SV355: $i] :
( ( ! [SY2041: $i,SY2042: $i] :
( ( ( c_Lambda_OdB_OVar @ SV355 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2041 @ SY2042 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV355 )
= SY2041 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1313]) ).
thf(1704,plain,
! [SV356: $i] :
( ( ! [SY2043: $i,SY2044: $i] :
( ( ( c_List_Olist_OCons @ SV356 @ ( c_List_Olist_ONil @ SY2043 ) @ SY2043 )
!= ( c_List_Orev @ SY2044 @ SY2043 ) )
| ( SY2044
= ( c_List_Olist_OCons @ SV356 @ ( c_List_Olist_ONil @ SY2043 ) @ SY2043 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1705,plain,
! [SV357: $i] :
( ( ! [SY2045: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV357 ) @ SY2045 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV357
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1706,plain,
! [SV358: $i] :
( ( ! [SY2046: $i,SY2047: $i,SY2048: $i,SY2049: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV358 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SY2046 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SY2047 ) @ SY2048 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SY2047 ) @ SY2049 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SY2046 ) @ SY2048 )
= SY2049 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1707,plain,
! [SV359: $i] :
( ( ! [SY2050: $i,SY2051: $i,SY2052: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV359 ) @ SY2050 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY2051 ) @ SY2052 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV359 = SY2051 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1317]) ).
thf(1708,plain,
! [SV360: $i] :
( ( ! [SY2053: $i] :
( ( ( c_List_Olist_ONil @ SV360 )
!= ( c_List_Orev @ SY2053 @ SV360 ) )
| ( SY2053
= ( c_List_Olist_ONil @ SV360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1318]) ).
thf(1709,plain,
! [SV361: $i] :
( ( ! [SY2054: $i,SY2055: $i,SY2056: $i,SY2057: $i] :
( ( ( c_List_Olist_OCons @ SV361 @ SY2054 @ SY2055 )
!= ( c_List_Oappend @ SY2056 @ SY2057 @ SY2055 ) )
| ( ( c_List_Olist_OCons @ SV361 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV361 @ SY2054 @ SY2056 @ SY2057 @ SY2055 ) @ SY2055 )
= SY2056 )
| ( ( c_List_Olist_OCons @ SV361 @ SY2054 @ SY2055 )
= SY2057 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1319]) ).
thf(1710,plain,
! [SV362: $i] :
( ( ! [SY2058: $i,SY2059: $i,SY2060: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV362 ) @ SY2058 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY2059 ) @ SY2060 ) )
| ( SV362 = SY2059 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1320]) ).
thf(1711,plain,
! [SV363: $i] :
( ( ! [SY2061: $i,SY2062: $i,SY2063: $i] :
( ( ( c_List_Orev @ SV363 @ SY2061 )
!= ( c_List_Olist_OCons @ SY2062 @ SY2063 @ SY2061 ) )
| ( SV363
= ( c_List_Oappend @ ( c_List_Orev @ SY2063 @ SY2061 ) @ ( c_List_Olist_OCons @ SY2062 @ ( c_List_Olist_ONil @ SY2061 ) @ SY2061 ) @ SY2061 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1712,plain,
! [SV364: $i] :
( ( ! [SY2064: $i,SY2065: $i] :
( ( ( c_List_Oappend @ SV364 @ SY2064 @ SY2065 )
!= SY2064 )
| ( SV364
= ( c_List_Olist_ONil @ SY2065 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1713,plain,
! [SV365: $i] :
( ( ! [SY2066: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV365 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV365 ) @ SY2066 ) @ SY2066 )
!= ( c_HOL_Ozero__class_Ozero @ SV365 ) )
| ( SY2066
= ( c_HOL_Ozero__class_Ozero @ SV365 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1714,plain,
! [SV366: $i] :
( ( ! [SY2067: $i,SY2068: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV366 ) @ SY2067 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2068 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV366 ) @ SY2067 )
= SY2068 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1715,plain,
! [SV367: $i] :
( ( ! [SY2069: $i,SY2070: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV367 ) @ SY2069 )
!= ( c_Lambda_OdB_OAbs @ SY2070 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1716,plain,
! [SV368: $i] :
( ( ! [SY2071: $i,SY2072: $i,SY2073: $i,SY2074: $i] :
( ( ( c_List_Oappend @ SV368 @ SY2071 @ SY2072 )
!= ( c_List_Olist_OCons @ SY2073 @ SY2074 @ SY2072 ) )
| ( SV368
= ( c_List_Olist_OCons @ SY2073 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY2073 @ SY2074 @ SV368 @ SY2071 @ SY2072 ) @ SY2072 ) )
| ( SY2071
= ( c_List_Olist_OCons @ SY2073 @ SY2074 @ SY2072 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1326]) ).
thf(1717,plain,
! [SV369: $i] :
( ( ! [SY2075: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV369 ) @ SY2075 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY2075
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1327]) ).
thf(1718,plain,
! [SV370: $i] :
( ( ! [SY2076: $i,SY2077: $i,SY2078: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV370 ) @ SY2076 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2077 ) @ SY2078 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV370 = SY2077 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1328]) ).
thf(1719,plain,
! [SV371: $i] :
( ( ! [SY2079: $i,SY2080: $i] :
( ( ( c_Lambda_OdB_OVar @ SV371 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2079 @ SY2080 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2080
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1329]) ).
thf(1720,plain,
! [SV372: $i] :
( ( ! [SY2081: $i,SY2082: $i] :
( ( ( c_List_Olist_ONil @ SV372 )
!= ( c_List_Oappend @ SY2081 @ SY2082 @ SV372 ) )
| ( SY2081
= ( c_List_Olist_ONil @ SV372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1330]) ).
thf(1721,plain,
! [SV373: $i] :
( ( ! [SY2083: $i,SY2084: $i] :
( ( ( c_List_Oappend @ SV373 @ SY2083 @ SY2084 )
!= SV373 )
| ( SY2083
= ( c_List_Olist_ONil @ SY2084 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1331]) ).
thf(1722,plain,
! [SV374: $i] :
( ( ! [SY2085: $i,SY2086: $i,SY2087: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV374 ) @ SY2085 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY2086 ) @ SY2087 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1332]) ).
thf(1723,plain,
! [SV375: $i] :
( ( ! [SY2088: $i] :
( ( ( c_Lambda_OdB_OVar @ SV375 )
!= ( c_Lambda_OdB_OVar @ SY2088 ) )
| ( SV375 = SY2088 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1333]) ).
thf(1724,plain,
! [SV376: $i] :
( ( ! [SY2089: $i,SY2090: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV376 @ SY2089 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2090 @ SY2089 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV376 = SY2090 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1334]) ).
thf(1725,plain,
! [SV377: $i] :
( ( ! [SY2091: $i,SY2092: $i,SY2093: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV377 ) @ SY2091 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2092 ) @ SY2093 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2091 = SY2093 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1335]) ).
thf(1726,plain,
! [SV378: $i] :
( ( ! [SY2094: $i,SY2095: $i,SY2096: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV378 )
| ~ ( class_Int_Onumber__ring @ SV378 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV378 ) @ SY2094 ) @ SY2095 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV378 ) @ SY2094 ) @ SY2096 ) )
| ( SY2095 = SY2096 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1727,plain,
! [SV379: $i] :
( ( ! [SY2097: $i,SY2098: $i] :
( ( c_List_Olist_OCons @ SV379 @ SY2097 @ SY2098 )
!= ( c_List_Olist_ONil @ SY2098 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1337]) ).
thf(1728,plain,
! [SV380: $i] :
( ( ! [SY2099: $i,SY2100: $i,SY2101: $i,SY2102: $i,SY2103: $i,SY2104: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV380 ) @ SY2099 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SY2100 @ SY2101 @ SY2102 ) ) )
| ~ ( c_Type_Otyping @ SY2103 @ SY2101 @ SV380 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY2101 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY2103 @ SY2102 @ SV380 @ tc_Type_Otype ) @ SY2100 @ SY2104 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY2100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(1729,plain,
! [SV381: $i] :
( ( ! [SY2105: $i,SY2106: $i] :
( ( ( c_List_Olist_ONil @ SV381 )
!= ( c_List_Oappend @ SY2105 @ SY2106 @ SV381 ) )
| ( SY2106
= ( c_List_Olist_ONil @ SV381 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1339]) ).
thf(1730,plain,
! [SV382: $i] :
( ( ! [SY2107: $i,SY2108: $i,SY2109: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV382 ) @ SY2107 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY2108 ) @ SY2109 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2107 = SY2109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1731,plain,
! [SV383: $i] :
( ( ! [SY2110: $i,SY2111: $i] :
( ( c_Lambda_OdB_OAbs @ SV383 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2110 ) @ SY2111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1341]) ).
thf(1732,plain,
! [SV384: $i] :
( ( ! [SY2112: $i,SY2113: $i,SY2114: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV384 ) ) @ SY2112 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2113 ) @ SY2114 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(1733,plain,
! [SV385: $i] :
( ( ! [SY2115: $i] :
( ( ( c_Nat_Osize__class_Osize @ SV385 @ ( tc_List_Olist @ SY2115 ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV385
= ( c_List_Olist_ONil @ SY2115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1343]) ).
thf(1734,plain,
! [SV386: $i] :
( ( ! [SY2116: $i,SY2117: $i,SY2118: $i,SY2119: $i] :
( ( ( c_List_Oappend @ SV386 @ ( c_List_Olist_OCons @ SY2116 @ ( c_List_Olist_ONil @ SY2117 ) @ SY2117 ) @ SY2117 )
!= ( c_List_Oappend @ SY2118 @ ( c_List_Olist_OCons @ SY2119 @ ( c_List_Olist_ONil @ SY2117 ) @ SY2117 ) @ SY2117 ) )
| ( SV386 = SY2118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1344]) ).
thf(1735,plain,
! [SV387: $i] :
( ( ! [SY2120: $i,SY2121: $i,SY2122: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV387 ) @ SY2120 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2121 ) @ SY2122 ) )
| ( SV387 = SY2121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1345]) ).
thf(1736,plain,
! [SV388: $i,SV1: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV1 )
| ( ( c_List_Olistsum @ SV388 @ SV1 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV1 ) @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SV388 @ SV1 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1347]) ).
thf(1737,plain,
! [SV389: $i,SV2: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV2 @ ( tc_List_Olist @ SV389 ) ) @ tc_nat )
| ( SV2
= ( c_List_Olist_ONil @ SV389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1348]) ).
thf(1738,plain,
! [SV390: $i,SV3: $i] :
( ( ! [SY2123: $i,SY2124: $i] :
( ( c_Type_Otyping @ SV3 @ SV390 @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ SY2123 @ SV3 @ SV390 @ SY2124 ) )
| ~ ( c_Type_Otypings @ SV3 @ ( c_List_Oappend @ SY2124 @ ( c_List_Olist_OCons @ SV390 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SY2123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1349]) ).
thf(1739,plain,
! [SV391: $i,SV4: $i] :
( ( ! [SY2125: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ SV4 @ SV391 @ SY2125 ) @ SY2125 )
= ( c_List_Oappend @ ( c_List_Orev @ SV391 @ SY2125 ) @ ( c_List_Orev @ SV4 @ SY2125 ) @ SY2125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1350]) ).
thf(1740,plain,
! [SV392: $i,SV9: $i] :
( ( ! [SY2126: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV9 @ SV392 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2126 @ SV392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1355]) ).
thf(1741,plain,
! [SV393: $i,SV10: $i] :
( ( ! [SY2127: $i] :
( ( ( c_List_Olast @ ( c_List_Oreplicate @ SV10 @ SV393 @ SY2127 ) @ SY2127 )
= SV393 )
| ( SV10
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1356]) ).
thf(1742,plain,
! [SV394: $i,SV11: $i] :
( ( ! [SY2128: $i,SY2129: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV11 @ SV394 @ SV394 ) @ SV394 ) @ SY2128 ) @ SY2129 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV11 @ SV394 ) @ SY2129 ) @ SY2128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1357]) ).
thf(1743,plain,
! [SV395: $i,SV12: $i] :
( ( ! [SY2130: $i,SY2131: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV12 @ SV395 ) @ SY2130 ) @ SY2131 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV12 @ SV395 @ SV395 ) @ SV395 ) @ SY2131 ) @ SY2130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1358]) ).
thf(1744,plain,
! [SV396: $i,SV13: $i] :
( ( ! [SY2132: $i,SY2133: $i,SY2134: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV13 @ SV396 ) @ SY2132 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV13 @ SY2133 @ SY2134 ) @ SY2132 ) @ SV396 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1359]) ).
thf(1745,plain,
! [SV397: $i,SV14: $i] :
( ( ! [SY2135: $i,SY2136: $i,SY2137: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV14 @ SV397 @ SY2135 ) @ SY2136 ) @ SY2137 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV14 @ SY2137 ) @ SY2136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1360]) ).
thf(1746,plain,
! [SV398: $i,SV15: $i] :
( ( ! [SY2138: $i,SY2139: $i,SY2140: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV15 @ SV398 ) @ SY2138 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV15 @ SY2139 @ SY2140 ) @ SY2138 ) @ SV398 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1361]) ).
thf(1747,plain,
! [SV399: $i,SV16: $i] :
( ( ! [SY2141: $i,SY2142: $i,SY2143: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV16 @ SV399 @ SY2141 ) @ SY2142 ) @ SY2143 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV16 @ SY2143 ) @ SY2142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1362]) ).
thf(1748,plain,
! [SV400: $i,SV17: $i] :
( ( ! [SY2144: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV17 ) @ SV400 ) ) @ SY2144 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV17 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV400 ) @ SY2144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1363]) ).
thf(1749,plain,
! [SV401: $i,SV18: $i] :
( ( ! [SY2145: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV18 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV401 ) @ SY2145 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV401 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV18 ) @ SY2145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1364]) ).
thf(1750,plain,
! [SV402: $i,SV20: $i] :
( ( ! [SY2146: $i,SY2147: $i] :
( ( c_Wellfounded_Oaccp @ SV20 @ SV402 @ SY2146 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV20 @ SY2146 ) @ SV402 ) @ SY2147 ) )
| ~ ( c_Wellfounded_Oaccp @ SV20 @ SY2147 @ SY2146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1366]) ).
thf(1751,plain,
! [SV403: $i,SV21: $i] :
( ( ! [SY2148: $i,SY2149: $i] :
( ( c_Wellfounded_Oaccp @ SV21 @ SV403 @ SY2148 )
| ~ ( c_Wellfounded_Oaccp @ SV21 @ SY2149 @ SY2148 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV21 @ SY2148 ) @ SV403 ) @ SY2149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1367]) ).
thf(1752,plain,
! [SV22: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV22 @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1368]) ).
thf(1753,plain,
! [SV23: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV23 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV23 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1369]) ).
thf(1754,plain,
! [SV404: $i,SV24: $i] :
( ( SV24
= ( c_List_Orev @ ( c_List_Orev @ SV24 @ SV404 ) @ SV404 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1755,plain,
! [SV405: $i,SV25: $i] :
( ( ( c_List_Orev @ ( c_List_Orev @ SV25 @ SV405 ) @ SV405 )
= SV25 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(1756,plain,
! [SV406: $i,SV26: $i] :
( ( ( c_List_Orev @ ( c_List_Orev @ SV26 @ SV406 ) @ SV406 )
= SV26 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1372]) ).
thf(1757,plain,
! [SV407: $i,SV27: $i] :
( ( ! [SY2150: $i] :
( ( c_HOL_Oord__class_Oless @ SV27 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV407 ) @ SY2150 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV27 @ SV407 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1373]) ).
thf(1758,plain,
! [SV408: $i,SV28: $i] :
( ( ! [SY2151: $i] :
( ( c_HOL_Oord__class_Oless @ SV28 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV408 ) @ SY2151 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV28 @ SY2151 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1374]) ).
thf(1759,plain,
! [SV409: $i,SV29: $i] :
( ( ! [SY2152: $i] :
( ( c_HOL_Oord__class_Oless @ SV29 @ SV409 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV29 ) @ SY2152 ) @ SV409 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1375]) ).
thf(1760,plain,
! [SV410: $i,SV30: $i] :
( ( ! [SY2153: $i] :
( ( c_HOL_Oord__class_Oless @ SV30 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV410 ) @ SY2153 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV30 @ SV410 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1376]) ).
thf(1761,plain,
! [SV411: $i,SV31: $i] :
( ( ! [SY2154: $i] :
( ( c_HOL_Oord__class_Oless @ SV31 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV411 ) @ SY2154 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV31 @ SY2154 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1377]) ).
thf(1762,plain,
! [SV412: $i,SV32: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV32 ) @ SV412 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV412 ) @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1378]) ).
thf(1763,plain,
! [SV413: $i,SV33: $i] :
( ( ! [SY2155: $i] :
( ( c_List_Orev @ ( c_List_Oreplicate @ SV33 @ SV413 @ SY2155 ) @ SY2155 )
= ( c_List_Oreplicate @ SV33 @ SV413 @ SY2155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1379]) ).
thf(1764,plain,
! [SV414: $i,SV35: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate1 @ SV35 @ SV414 ) @ ( tc_List_Olist @ SV414 ) )
= ( c_Nat_Osize__class_Osize @ SV35 @ ( tc_List_Olist @ SV414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1381]) ).
thf(1765,plain,
! [SV415: $i,SV36: $i] :
( ( ! [SY2156: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oappend @ SV36 @ SV415 @ SY2156 ) @ ( tc_List_Olist @ SY2156 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV36 @ ( tc_List_Olist @ SY2156 ) ) ) @ ( c_Nat_Osize__class_Osize @ SV415 @ ( tc_List_Olist @ SY2156 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1382]) ).
thf(1766,plain,
! [SV416: $i,SV37: $i] :
( ( ! [SY2157: $i,SY2158: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV37 @ SV416 @ SY2157 ) @ ( c_List_Oreplicate @ SY2158 @ SV416 @ SY2157 ) @ SY2157 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SY2158 @ SV416 @ SY2157 ) @ ( c_List_Oreplicate @ SV37 @ SV416 @ SY2157 ) @ SY2157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1383]) ).
thf(1767,plain,
! [SV417: $i,SV38: $i] :
( ( ! [SY2159: $i,SY2160: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV38 ) @ SV417 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2159 ) @ SY2160 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV417 @ SY2160 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV38 @ SY2159 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1384]) ).
thf(1768,plain,
! [SV418: $i,SV39: $i] :
( ( ! [SY2161: $i,SY2162: $i] :
( ( c_List_Oreplicate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV39 ) @ SV418 ) @ SY2161 @ SY2162 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SV39 @ SY2161 @ SY2162 ) @ ( c_List_Oreplicate @ SV418 @ SY2161 @ SY2162 ) @ SY2162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(1769,plain,
! [SV419: $i,SV40: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV40 )
| ( ( c_List_Olistsum @ ( c_List_Orev @ SV419 @ SV40 ) @ SV40 )
= ( c_List_Olistsum @ SV419 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1386]) ).
thf(1770,plain,
! [SV420: $i,SV41: $i] :
( ( ! [SY2163: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ SV41 @ SV420 @ SY2163 ) @ ( tc_List_Olist @ SY2163 ) )
= SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1387]) ).
thf(1771,plain,
! [SV421: $i,SV42: $i] :
( ( ! [SY2164: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ SV42 @ SV421 @ SY2164 ) @ SY2164 @ SV421 )
= SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1388]) ).
thf(1772,plain,
! [SV422: $i,SV43: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV43 ) @ SV422 ) @ SV43 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1389]) ).
thf(1773,plain,
! [SV423: $i,SV44: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV44 ) @ SV423 ) @ SV423 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1390]) ).
thf(1774,plain,
! [SV424: $i,SV45: $i] :
( ( ! [SY2165: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV45 ) @ SV424 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2165 ) @ SV424 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV45 @ SY2165 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1391]) ).
thf(1775,plain,
! [SV425: $i,SV46: $i] :
( ( ! [SY2166: $i] :
( ( c_HOL_Oord__class_Oless @ SV46 @ SV425 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2166 ) @ SV46 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2166 ) @ SV425 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1392]) ).
thf(1776,plain,
! [SV426: $i,SV47: $i] :
( ( ! [SY2167: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV47 ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV47 ) @ SY2167 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV426 @ SY2167 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1393]) ).
thf(1777,plain,
! [SV427: $i,SV50: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Orev @ SV50 @ SV427 ) @ ( tc_List_Olist @ SV427 ) )
= ( c_Nat_Osize__class_Osize @ SV50 @ ( tc_List_Olist @ SV427 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1396]) ).
thf(1778,plain,
! [SV428: $i,SV51: $i] :
( ( ! [SY2168: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV51 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV428 ) @ SY2168 ) @ SV51 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV51 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV428 @ SV51 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2168 @ SV51 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1397]) ).
thf(1779,plain,
! [SV429: $i,SV52: $i] :
( ( ! [SY2169: $i,SY2170: $i] :
( ( c_Wellfounded_Oaccp @ SV52 @ SV429 @ SY2169 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV52 @ SV429 ) @ SY2170 ) )
| ~ ( c_Wellfounded_Oaccp @ SV52 @ SY2170 @ SY2169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1398]) ).
thf(1780,plain,
! [SV430: $i,SV53: $i] :
( ( ! [SY2171: $i,SY2172: $i] :
( ( c_Wellfounded_Oaccp @ SV53 @ SV430 @ SY2171 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV53 @ SV430 ) @ SY2172 ) )
| ~ ( c_Wellfounded_Oaccp @ SV53 @ SY2172 @ SY2171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1399]) ).
thf(1781,plain,
! [SV431: $i,SV54: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Obutlast @ SV54 @ SV431 ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ SV54 @ SV431 ) @ ( c_List_Olist_ONil @ SV431 ) @ SV431 ) @ SV431 )
= SV54 )
| ( SV54
= ( c_List_Olist_ONil @ SV431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1400]) ).
thf(1782,plain,
! [SV432: $i,SV55: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV55 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV432 @ SV55 ) @ ( c_HOL_Ozero__class_Ozero @ SV55 ) @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1401]) ).
thf(1783,plain,
! [SV56: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV56 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV56 )
= ( c_HOL_Ozero__class_Ozero @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1402]) ).
thf(1784,plain,
! [SV433: $i,SV57: $i] :
( ( ! [SY2173: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV57 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV433 @ SV57 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2173 @ SV57 ) @ SV57 )
| ~ ( c_HOL_Oord__class_Oless @ SV433 @ SY2173 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1403]) ).
thf(1785,plain,
! [SV434: $i,SV58: $i] :
( ( ! [SY2174: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV58 )
| ( c_HOL_Oord__class_Oless @ SV434 @ SY2174 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV434 @ SV58 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2174 @ SV58 ) @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1404]) ).
thf(1786,plain,
! [SV59: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV59 ) )
= $true )
| ( ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ SV59 ) @ SV59 )
= ( c_HOL_Ozero__class_Ozero @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1405]) ).
thf(1787,plain,
! [SV435: $i,SV60: $i] :
( ( ! [SY2175: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV60 )
| ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ SV435 @ SY2175 @ SV60 ) @ SV60 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV435 ) @ ( c_List_Olistsum @ SY2175 @ SV60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(1788,plain,
! [SV436: $i,SV61: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV61 ) @ SV436 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV61 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1407]) ).
thf(1789,plain,
! [SV437: $i,SV62: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV62 ) @ SV437 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV437 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1408]) ).
thf(1790,plain,
! [SV438: $i,SV63: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV63 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV438 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV438 ) @ SV63 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1409]) ).
thf(1791,plain,
! [SV439: $i,SV64: $i] :
( ( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV64 @ SV439 )
= ( c_List_Olist_ONil @ SV439 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1410]) ).
thf(1792,plain,
! [SV440: $i,SV66: $i] :
( ( ( c_List_Olist_ONil @ SV66 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV440 @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1412]) ).
thf(1793,plain,
! [SV441: $i,SV67: $i] :
( ( ! [SY2176: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV67 )
| ( ( c_List_Olistsum @ ( c_List_Oappend @ SV441 @ SY2176 @ SV67 ) @ SV67 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ ( c_List_Olistsum @ SV441 @ SV67 ) ) @ ( c_List_Olistsum @ SY2176 @ SV67 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1413]) ).
thf(1794,plain,
! [SV442: $i,SV68: $i] :
( ( ( c_List_Olist_OCons @ SV68 @ ( c_List_Olist_ONil @ SV442 ) @ SV442 )
= ( c_List_Orev @ ( c_List_Olist_OCons @ SV68 @ ( c_List_Olist_ONil @ SV442 ) @ SV442 ) @ SV442 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1414]) ).
thf(1795,plain,
! [SV443: $i,SV69: $i] :
( ( ! [SY2177: $i] :
( ( ( c_List_Olast @ ( c_List_Olist_OCons @ SV69 @ SV443 @ SY2177 ) @ SY2177 )
= ( c_List_Olast @ SV443 @ SY2177 ) )
| ( SV443
= ( c_List_Olist_ONil @ SY2177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1415]) ).
thf(1796,plain,
! [SV444: $i,SV70: $i] :
( ( ( c_List_Orev @ ( c_List_Olist_OCons @ SV70 @ ( c_List_Olist_ONil @ SV444 ) @ SV444 ) @ SV444 )
= ( c_List_Olist_OCons @ SV70 @ ( c_List_Olist_ONil @ SV444 ) @ SV444 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1416]) ).
thf(1797,plain,
! [SV445: $i,SV71: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV71 @ ( c_List_Olist_ONil @ SV445 ) @ SV445 ) @ SV445 )
= ( c_List_Olist_ONil @ SV445 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1417]) ).
thf(1798,plain,
! [SV446: $i,SV72: $i] :
( ( ( c_List_Olast @ ( c_List_Olist_OCons @ SV72 @ ( c_List_Olist_ONil @ SV446 ) @ SV446 ) @ SV446 )
= SV72 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1418]) ).
thf(1799,plain,
! [SV447: $i,SV73: $i] :
( ( ! [SY2178: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV73 @ SV447 @ SY2178 ) @ SY2178 )
= ( c_List_Olist_OCons @ SV73 @ ( c_List_Obutlast @ SV447 @ SY2178 ) @ SY2178 ) )
| ( SV447
= ( c_List_Olist_ONil @ SY2178 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1419]) ).
thf(1800,plain,
! [SV448: $i,SV74: $i] :
( ( ! [SY2179: $i,SY2180: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV74 @ SV448 @ SY2179 ) @ ( c_List_Olist_OCons @ SV448 @ SY2180 @ SY2179 ) @ SY2179 )
= ( c_List_Olist_OCons @ SV448 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV74 @ SV448 @ SY2179 ) @ SY2180 @ SY2179 ) @ SY2179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(1801,plain,
! [SV449: $i,SV75: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV75 @ ( c_List_Olist_ONil @ SV449 ) @ SV449 ) @ SV449 )
= ( c_List_Obutlast @ SV75 @ SV449 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(1802,plain,
! [SV450: $i,SV76: $i] :
( ( ! [SY2181: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ SV76 @ SV450 @ SY2181 ) @ SY2181 )
= ( c_List_Olast @ SV450 @ SY2181 ) )
| ( SV450
= ( c_List_Olist_ONil @ SY2181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1422]) ).
thf(1803,plain,
! [SV451: $i,SV77: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ SV77 @ ( c_List_Olist_ONil @ SV451 ) @ SV451 ) @ SV451 )
= ( c_List_Olast @ SV77 @ SV451 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1423]) ).
thf(1804,plain,
! [SV452: $i,SV78: $i] :
( ( ! [SY2182: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV78 @ SV452 @ SY2182 ) @ SY2182 )
= ( c_List_Oappend @ SV78 @ ( c_List_Obutlast @ SV452 @ SY2182 ) @ SY2182 ) )
| ( SV452
= ( c_List_Olist_ONil @ SY2182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1424]) ).
thf(1805,plain,
! [SV79: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ SV79 ) @ ( tc_List_Olist @ SV79 ) ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1425]) ).
thf(1806,plain,
! [SV453: $i,SV80: $i] :
( ( ! [SY2183: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ SV80 @ ( c_List_Olist_OCons @ SV453 @ ( c_List_Olist_ONil @ SY2183 ) @ SY2183 ) @ SY2183 ) @ SY2183 )
= SV453 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1426]) ).
thf(1807,plain,
! [SV454: $i,SV81: $i] :
( ( ! [SY2184: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ SV81 @ ( c_List_Olist_OCons @ SV454 @ ( c_List_Olist_ONil @ SY2184 ) @ SY2184 ) @ SY2184 ) @ SY2184 )
= SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1427]) ).
thf(1808,plain,
! [SV455: $i,SV82: $i] :
( ( ! [SY2185: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ SV82 @ SV455 @ SY2185 ) @ SY2185 )
= ( c_List_Oappend @ ( c_List_Orev @ SV455 @ SY2185 ) @ ( c_List_Olist_OCons @ SV82 @ ( c_List_Olist_ONil @ SY2185 ) @ SY2185 ) @ SY2185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1428]) ).
thf(1809,plain,
! [SV456: $i,SV83: $i] :
( ( ! [SY2186: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ SV83 @ SV456 ) @ ( c_List_Olist_OCons @ SY2186 @ ( c_List_Olist_ONil @ SV456 ) @ SV456 ) @ SV456 ) @ SV456 )
= ( c_List_Olist_OCons @ SY2186 @ SV83 @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1429]) ).
thf(1810,plain,
! [SV457: $i,SV84: $i] :
( ( ! [SY2187: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ SV84 @ SV457 @ SY2187 ) @ SY2187 )
= ( c_List_Oappend @ SV457 @ ( c_List_Olist_OCons @ SV84 @ ( c_List_Olist_ONil @ SY2187 ) @ SY2187 ) @ SY2187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1430]) ).
thf(1811,plain,
! [SV458: $i,SV85: $i] :
( ( ! [SY2188: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV85 @ SV458 @ SY2188 ) @ ( c_List_Olist_OCons @ SV458 @ ( c_List_Olist_ONil @ SY2188 ) @ SY2188 ) @ SY2188 )
= ( c_List_Olist_OCons @ SV458 @ ( c_List_Oreplicate @ SV85 @ SV458 @ SY2188 ) @ SY2188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1431]) ).
thf(1812,plain,
! [SV459: $i,SV86: $i] :
( ( ! [SY2189: $i] :
( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV86 @ SV459 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY2189 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV459 @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV86 ) ) @ SV459 ) @ SY2189 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1432]) ).
thf(1813,plain,
! [SV460: $i,SV87: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV87 )
| ( ( c_List_Olistsum @ SV460 @ SV87 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV87 ) @ SV460 @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1433]) ).
thf(1814,plain,
! [SV461: $i,SV88: $i] :
( ( ! [SY2190: $i] :
( ( ( c_Lambda_Oliftn @ SV88 @ ( c_Lambda_OdB_OVar @ SV461 ) @ SY2190 )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV461 ) @ SV88 ) ) )
| ( c_HOL_Oord__class_Oless @ SV461 @ SY2190 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1434]) ).
thf(1815,plain,
! [SV462: $i,SV89: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV89 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV462 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV462 @ SV89 ) @ SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1435]) ).
thf(1816,plain,
! [SV463: $i,SV90: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV90 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV463 @ SV90 ) @ SV90 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV463 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1436]) ).
thf(1817,plain,
! [SV464: $i,SV91: $i] :
( ( ! [SY2191: $i] :
( ( ( c_List_Oappend @ SV91 @ ( c_List_Olist_OCons @ SV464 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2191 @ SV91 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV464 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2191 @ ( c_List_Oappend @ SV91 @ ( c_List_Olist_OCons @ SV464 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(1818,plain,
! [SV465: $i,SV92: $i] :
( ( ! [SY2192: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV92 @ SV465 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY2192 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV92 @ ( c_List_Oappend @ SV465 @ ( c_List_Olist_OCons @ SY2192 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1819,plain,
! [SV466: $i,SV93: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV93 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV93 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__4 @ SV93 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ SV93 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV93 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV93 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ SV93 @ SV466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1439]) ).
thf(1820,plain,
! [SV467: $i,SV94: $i] :
( ( ( hBOOL @ ( hAPP @ SV94 @ SV467 ) )
| ~ ( hBOOL @ ( hAPP @ SV94 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV94 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4 @ SV94 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ SV94 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV94 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV94 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1440]) ).
thf(1821,plain,
! [SV468: $i,SV95: $i] :
( ( c_List_Olistsp @ SV95 @ ( c_List_Olist_ONil @ SV468 ) @ SV468 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(1822,plain,
! [SV469: $i,SV96: $i] :
( ( ! [SY2193: $i,SY2194: $i,SY2195: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV96 @ SV469 ) @ SY2193 ) )
| ( c_ListOrder_Ostep1 @ SV96 @ ( c_List_Olist_OCons @ SV469 @ SY2194 @ SY2195 ) @ ( c_List_Olist_OCons @ SY2193 @ SY2194 @ SY2195 ) @ SY2195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1823,plain,
! [SV470: $i,SV97: $i] :
( ( ! [SY2196: $i,SY2197: $i,SY2198: $i,SY2199: $i] :
( ( SV97 = SV470 )
| ( SY2196 = SY2197 )
| ~ ( c_ListOrder_Ostep1 @ SY2198 @ ( c_List_Olist_OCons @ SV470 @ SY2197 @ SY2199 ) @ ( c_List_Olist_OCons @ SV97 @ SY2196 @ SY2199 ) @ SY2199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1443]) ).
thf(1824,plain,
! [SV471: $i,SV98: $i] :
( ( ! [SY2200: $i,SY2201: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV98 @ SV471 @ SY2200 ) ) @ ( c_Lambda_Osubst @ SY2201 @ SV471 @ SY2200 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV98 ) @ SY2201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1444]) ).
thf(1825,plain,
! [SV472: $i,SV99: $i] :
( ( ! [SY2202: $i,SY2203: $i,SY2204: $i] :
( ( c_Lambda_OdB_OdB__case @ SV99 @ SV472 @ SY2202 @ ( c_Lambda_OdB_OAbs @ SY2203 ) @ SY2204 )
= ( hAPP @ SY2202 @ SY2203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(1826,plain,
! [SV473: $i,SV100: $i] :
( ( ! [SY2205: $i,SY2206: $i] :
( ( c_List_Olistsp @ SV100 @ SV473 @ SY2205 )
| ~ ( c_List_Olistsp @ SV100 @ ( c_List_Oappend @ SY2206 @ SV473 @ SY2205 ) @ SY2205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(1827,plain,
! [SV474: $i,SV101: $i] :
( ( ! [SY2207: $i,SY2208: $i] :
( ( c_List_Olistsp @ SV101 @ SV474 @ SY2207 )
| ~ ( c_List_Olistsp @ SV101 @ ( c_List_Oappend @ SV474 @ SY2208 @ SY2207 ) @ SY2207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(1828,plain,
! [SV475: $i,SV102: $i] :
( ( ! [SY2209: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV102 ) @ SV475 @ SY2209 )
= ( c_Lambda_OdB_OVar @ SV102 ) )
| ( SV102 = SY2209 )
| ( c_HOL_Oord__class_Oless @ SY2209 @ SV102 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(1829,plain,
! [SV476: $i,SV103: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV103 ) ) @ ( c_Lambda_OdB_OAbs @ SV476 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV103 ) @ SV476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1449]) ).
thf(1830,plain,
! [SV477: $i,SV104: $i] :
( ( ! [SY2210: $i,SY2211: $i,SY2212: $i] :
( ( c_ListOrder_Ostep1 @ SV104 @ ( c_List_Oappend @ SV477 @ SY2210 @ SY2211 ) @ ( c_List_Oappend @ SV477 @ SY2212 @ SY2211 ) @ SY2211 )
| ~ ( c_ListOrder_Ostep1 @ SV104 @ SY2210 @ SY2212 @ SY2211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1450]) ).
thf(1831,plain,
! [SV478: $i,SV105: $i] :
( ( ! [SY2213: $i,SY2214: $i,SY2215: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV105 @ SV478 @ SY2213 @ SY2214 )
| ( c_ListOrder_Ostep1 @ SV105 @ ( c_List_Oappend @ SV478 @ SY2215 @ SY2214 ) @ ( c_List_Oappend @ SY2213 @ SY2215 @ SY2214 ) @ SY2214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(1832,plain,
! [SV479: $i,SV106: $i] :
( ( ! [SY2216: $i] :
( ( c_Lambda_Osubstn @ SV106 @ SV479 @ SY2216 )
= ( c_Lambda_Osubst @ SV106 @ ( c_Lambda_Oliftn @ SY2216 @ SV479 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY2216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(1833,plain,
! [SV107: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV107 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Ozero__class_Ozero @ SV107 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV107 ) )
= ( c_HOL_Ozero__class_Ozero @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1453]) ).
thf(1834,plain,
! [SV480: $i,SV108: $i] :
( ( ! [SY2217: $i,SY2218: $i] :
( ~ ( class_Orderings_Opreorder @ SV108 )
| ( c_HOL_Oord__class_Oless @ SV480 @ SY2217 @ SV108 )
| ~ ( c_HOL_Oord__class_Oless @ SY2218 @ SY2217 @ SV108 )
| ~ ( c_HOL_Oord__class_Oless @ SV480 @ SY2218 @ SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(1835,plain,
! [SV481: $i,SV109: $i] :
( ( ! [SY2219: $i,SY2220: $i] :
( ~ ( class_Orderings_Oorder @ SV109 )
| ( c_HOL_Oord__class_Oless @ SV481 @ SY2219 @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ SV481 @ SY2220 @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ SY2220 @ SY2219 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1455]) ).
thf(1836,plain,
! [SV482: $i,SV110: $i] :
( ( ! [SY2221: $i,SY2222: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV110 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV482 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SY2221 ) @ SY2222 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV482 ) @ SY2221 ) ) @ SY2222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(1837,plain,
! [SV483: $i,SV111: $i] :
( ( ! [SY2223: $i,SY2224: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV111 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV483 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SY2223 ) @ SY2224 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SY2223 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV483 ) @ SY2224 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1457]) ).
thf(1838,plain,
! [SV484: $i,SV112: $i] :
( ( ! [SY2225: $i,SY2226: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV112 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SV484 ) @ SY2225 ) ) @ SY2226 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SV484 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SY2225 ) @ SY2226 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1458]) ).
thf(1839,plain,
! [SV485: $i,SV113: $i] :
( ( ! [SY2227: $i,SY2228: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV113 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV485 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SY2227 ) @ SY2228 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SY2227 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV485 ) @ SY2228 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(1840,plain,
! [SV486: $i,SV114: $i] :
( ( ! [SY2229: $i,SY2230: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV114 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SV486 ) @ SY2229 ) ) @ SY2230 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SV486 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SY2229 ) @ SY2230 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1841,plain,
! [SV487: $i,SV115: $i] :
( ( ! [SY2231: $i,SY2232: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV115 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SV487 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SY2231 ) @ SY2232 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SV487 ) @ SY2231 ) ) @ SY2232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1461]) ).
thf(1842,plain,
! [SV488: $i,SV116: $i] :
( ( ! [SY2233: $i,SY2234: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV116 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV488 ) @ SY2233 ) ) @ SY2234 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV488 ) @ SY2234 ) ) @ SY2233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1462]) ).
thf(1843,plain,
! [SV489: $i,SV117: $i] :
( ( ! [SY2235: $i,SY2236: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV117 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV489 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SY2235 ) @ SY2236 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SY2235 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV489 ) @ SY2236 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(1844,plain,
! [SV490: $i,SV118: $i] :
( ( ! [SY2237: $i,SY2238: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV118 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV490 ) @ SY2237 ) ) @ SY2238 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV490 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SY2237 ) @ SY2238 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1464]) ).
thf(1845,plain,
! [SV119: $i] :
( ( c_HOL_Oord__class_Oless @ SV119 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1465]) ).
thf(1846,plain,
! [SV120: $i] :
( ( c_HOL_Oord__class_Oless @ SV120 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1466]) ).
thf(1847,plain,
! [SV491: $i,SV121: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV121 @ SV121 @ tc_nat )
| ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV121 ) @ SV491 @ SV121 )
= SV491 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1467]) ).
thf(1848,plain,
! [SV492: $i,SV122: $i] :
( ( ! [SY2239: $i,SY2240: $i] :
( ( c_List_Ofoldr @ SV122 @ ( c_List_Olist_ONil @ SV492 ) @ SY2239 @ SV492 @ SY2240 )
= SY2239 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(1849,plain,
! [SV493: $i,SV123: $i] :
( ( ! [SY2241: $i,SY2242: $i,SY2243: $i,SY2244: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SV493 ) @ SY2241 ) )
| ( c_ListOrder_Ostep1 @ SV123 @ SY2242 @ SY2243 @ SY2244 )
| ~ ( c_ListOrder_Ostep1 @ SV123 @ ( c_List_Oappend @ SY2242 @ ( c_List_Olist_OCons @ SV493 @ ( c_List_Olist_ONil @ SY2244 ) @ SY2244 ) @ SY2244 ) @ ( c_List_Oappend @ SY2243 @ ( c_List_Olist_OCons @ SY2241 @ ( c_List_Olist_ONil @ SY2244 ) @ SY2244 ) @ SY2244 ) @ SY2244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1469]) ).
thf(1850,plain,
! [SV494: $i,SV124: $i] :
( ( ! [SY2245: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV124 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV124 ) @ SV494 ) @ SY2245 ) @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ SV124 )
| ~ ( c_HOL_Oord__class_Oless @ SY2245 @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ SV124 )
| ~ ( c_HOL_Oord__class_Oless @ SV494 @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1470]) ).
thf(1851,plain,
! [SV495: $i,SV125: $i] :
( ( ! [SY2246: $i,SY2247: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV125 @ SV495 @ SY2246 ) @ SY2247 @ SY2246 )
= ( c_List_Olist_OCons @ SV125 @ ( c_List_Oappend @ SV495 @ SY2247 @ SY2246 ) @ SY2246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1471]) ).
thf(1852,plain,
! [SV496: $i,SV126: $i] :
( ( ! [SY2248: $i,SY2249: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV126 @ SV496 @ SY2248 ) @ SY2249 @ SY2248 )
= ( c_List_Olist_OCons @ SV126 @ ( c_List_Oappend @ SV496 @ SY2249 @ SY2248 ) @ SY2248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1472]) ).
thf(1853,plain,
! [SV497: $i,SV127: $i] :
( ( ! [SY2250: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV127 ) @ SV497 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV127 ) @ SY2250 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV497 ) @ SY2250 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1473]) ).
thf(1854,plain,
! [SV498: $i,SV128: $i] :
( ( ! [SY2251: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV128 ) @ SV498 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2251 ) @ SV498 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV128 ) @ SY2251 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1474]) ).
thf(1855,plain,
! [SV499: $i,SV129: $i] :
( ( ! [SY2252: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV129 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV129 ) @ SV499 @ SY2252 @ SV129 @ SV129 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV129 ) @ SV499 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV129 ) @ SY2252 @ ( c_HOL_Ozero__class_Ozero @ SV129 ) @ SV129 @ SV129 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(1856,plain,
! [SV500: $i,SV130: $i] :
( ( ! [SY2253: $i,SY2254: $i] :
( ( c_List_Olist_OCons @ SV130 @ ( c_List_Oappend @ SV500 @ SY2253 @ SY2254 ) @ SY2254 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV130 @ SV500 @ SY2254 ) @ SY2253 @ SY2254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1476]) ).
thf(1857,plain,
! [SV501: $i,SV131: $i] :
( ( ! [SY2255: $i,SY2256: $i] :
( ( c_List_Olist_OCons @ SV131 @ ( c_List_Oappend @ SV501 @ SY2255 @ SY2256 ) @ SY2256 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV131 @ SV501 @ SY2256 ) @ SY2255 @ SY2256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(1858,plain,
! [SV502: $i,SV132: $i] :
( ( ! [SY2257: $i,SY2258: $i,SY2259: $i,SY2260: $i] :
( ( SV132 = SV502 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2257 @ SV502 ) @ SV132 ) )
| ~ ( c_ListOrder_Ostep1 @ SY2257 @ ( c_List_Olist_OCons @ SV502 @ SY2258 @ SY2259 ) @ ( c_List_Olist_OCons @ SV132 @ SY2260 @ SY2259 ) @ SY2259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1478]) ).
thf(1859,plain,
! [SV133: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV133 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV133 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1479]) ).
thf(1860,plain,
! [SV503: $i,SV134: $i] :
( ( ! [SY2261: $i,SY2262: $i,SY2263: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV134 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ SV503 ) @ SY2261 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ SY2262 ) @ SY2263 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ SV503 ) @ SY2262 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ SY2261 ) @ SY2263 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1480]) ).
thf(1861,plain,
! [SV504: $i,SV135: $i] :
( ( ! [SY2264: $i,SY2265: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV135 ) @ SV504 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2264 ) @ SY2265 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV504 ) @ SY2265 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV135 ) @ SY2264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1481]) ).
thf(1862,plain,
! [SV505: $i,SV136: $i] :
( ( ! [SY2266: $i] :
( ( ( c_Lambda_Oliftn @ SV136 @ ( c_Lambda_OdB_OVar @ SV505 ) @ SY2266 )
= ( c_Lambda_OdB_OVar @ SV505 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV505 @ SY2266 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1482]) ).
thf(1863,plain,
! [SV506: $i,SV137: $i] :
( ( ! [SY2267: $i,SY2268: $i] :
( ( c_Type_Otyping @ SV137 @ SV506 @ SY2267 )
| ~ ( c_Type_Otyping @ SV137 @ SY2268 @ SY2267 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY2268 ) @ SV506 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1483]) ).
thf(1864,plain,
! [SV507: $i,SV138: $i] :
( ( ! [SY2269: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV138 @ SV507 ) @ SY2269 @ SV507 )
= SV138 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1484]) ).
thf(1865,plain,
! [SV508: $i,SV139: $i] :
( ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV139 ) @ SV508 )
= ( c_Lambda_OdB_OVar @ SV139 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV139 @ SV508 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1485]) ).
thf(1866,plain,
! [SV509: $i,SV140: $i] :
( ( ! [SY2270: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV140 @ SV509 ) ) @ ( c_Lambda_Olift @ SY2270 @ SV509 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV140 ) @ SY2270 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1486]) ).
thf(1867,plain,
! [SV510: $i,SV141: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV141 @ SV141 @ tc_nat )
| ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV141 ) @ SV510 @ SV141 )
= ( c_Lambda_Oliftn @ SV141 @ SV510 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1487]) ).
thf(1868,plain,
! [SV511: $i,SV142: $i] :
( ( ! [SY2271: $i] :
( ( c_List_Olist_OCons @ SV142 @ SV511 @ SY2271 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY2271 ) @ ( c_List_Olist_OCons @ SV142 @ SV511 @ SY2271 ) @ SY2271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1488]) ).
thf(1869,plain,
! [SV512: $i,SV143: $i] :
( ( ! [SY2272: $i,SY2273: $i,SY2274: $i,SY2275: $i] :
( ( SV143 = SV512 )
| ( c_ListOrder_Ostep1 @ SY2272 @ SV143 @ SV512 @ SY2273 )
| ~ ( c_ListOrder_Ostep1 @ SY2272 @ ( c_List_Oappend @ SV143 @ ( c_List_Olist_OCons @ SY2274 @ ( c_List_Olist_ONil @ SY2273 ) @ SY2273 ) @ SY2273 ) @ ( c_List_Oappend @ SV512 @ ( c_List_Olist_OCons @ SY2275 @ ( c_List_Olist_ONil @ SY2273 ) @ SY2273 ) @ SY2273 ) @ SY2273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1489]) ).
thf(1870,plain,
! [SV513: $i,SV145: $i] :
( ( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ SV145 @ SV513 ) @ SV513 )
= ( c_Transitive__Closure_Ortranclp @ SV145 @ SV513 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1491]) ).
thf(1871,plain,
! [SV514: $i,SV146: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV146 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ ( c_HOL_Ozero__class_Ozero @ SV146 ) ) @ SV514 )
= SV514 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1492]) ).
thf(1872,plain,
! [SV515: $i,SV147: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV147 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ ( c_HOL_Ozero__class_Ozero @ SV147 ) ) @ SV515 )
= SV515 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(1873,plain,
! [SV516: $i,SV148: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV148 )
| ~ ( class_Int_Onumber__ring @ SV148 )
| ( SV516
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV516 ) @ ( c_HOL_Ozero__class_Ozero @ SV148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(1874,plain,
! [SV517: $i,SV149: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV149 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV517 ) @ ( c_HOL_Ozero__class_Ozero @ SV149 ) )
= SV517 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1495]) ).
thf(1875,plain,
! [SV518: $i,SV150: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV150 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV150 ) @ ( c_HOL_Ozero__class_Ozero @ SV150 ) ) @ SV518 )
= SV518 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1496]) ).
thf(1876,plain,
! [SV519: $i,SV151: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV151 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV519 ) @ ( c_HOL_Ozero__class_Ozero @ SV151 ) )
= SV519 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1497]) ).
thf(1877,plain,
! [SV520: $i,SV152: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV152 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV520 ) @ ( c_HOL_Ozero__class_Ozero @ SV152 ) )
= SV520 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1498]) ).
thf(1878,plain,
! [SV521: $i,SV153: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV153 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ ( c_HOL_Ozero__class_Ozero @ SV153 ) ) @ SV521 )
= SV521 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1499]) ).
thf(1879,plain,
! [SV522: $i,SV154: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV154 ) ) @ ( c_Lambda_OdB_OAbs @ SV522 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV154 ) @ SV522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1500]) ).
thf(1880,plain,
! [SV523: $i,SV155: $i] :
( ( ! [SY2276: $i,SY2277: $i] :
( ( ( hAPP @ ( hAPP @ SV155 @ SV523 ) @ SY2276 )
= SV523 )
| ~ ( c_OrderedGroup_Omonoid__add @ SY2276 @ SV155 @ SY2277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1501]) ).
thf(1881,plain,
! [SV524: $i,SV156: $i] :
( ( ! [SY2278: $i,SY2279: $i] :
( ( ( hAPP @ ( hAPP @ SV156 @ SV524 ) @ SY2278 )
= SY2278 )
| ~ ( c_OrderedGroup_Omonoid__add @ SV524 @ SV156 @ SY2279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1502]) ).
thf(1882,plain,
! [SV525: $i,SV157: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV157 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV157 ) @ SV525 @ SV157 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV157 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV525 ) @ SV525 ) @ SV157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1503]) ).
thf(1883,plain,
! [SV526: $i,SV158: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV158 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV526 ) @ SV526 ) @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV526 @ SV158 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1504]) ).
thf(1884,plain,
! [SV527: $i,SV159: $i] :
( ( ! [SY2280: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV159 @ SV527 ) @ SY2280 ) @ SY2280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1505]) ).
thf(1885,plain,
! [SV528: $i,SV160: $i] :
( ( ! [SY2281: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV160 @ SV528 ) @ SY2281 ) @ SY2281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(1886,plain,
! [SV529: $i,SV161: $i] :
( ( ! [SY2282: $i,SY2283: $i,SY2284: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV161 @ SV529 ) @ SY2282 ) @ SY2283 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV161 @ SV529 ) @ SY2284 ) @ SY2283 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV161 @ SV529 ) @ SY2282 ) @ SY2284 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1507]) ).
thf(1887,plain,
! [SV530: $i,SV162: $i] :
( ( ( c_List_Oappend @ SV162 @ ( c_List_Olist_ONil @ SV530 ) @ SV530 )
= SV162 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(1888,plain,
! [SV531: $i,SV163: $i] :
( ( SV163
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV531 ) @ SV163 @ SV531 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1509]) ).
thf(1889,plain,
! [SV532: $i,SV164: $i] :
( ( SV164
= ( c_List_Oappend @ SV164 @ ( c_List_Olist_ONil @ SV532 ) @ SV532 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(1890,plain,
! [SV533: $i,SV165: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV165 ) @ SV533 @ SV165 )
= SV533 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1511]) ).
thf(1891,plain,
! [SV534: $i,SV166: $i] :
( ( SV166
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV534 ) @ SV166 @ SV534 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1512]) ).
thf(1892,plain,
! [SV535: $i,SV167: $i] :
( ( ! [SY2285: $i,SY2286: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV167 @ SV535 @ SY2285 ) ) @ ( c_Lambda_Osubst @ SV167 @ SY2286 @ SY2285 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV535 ) @ SY2286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(1893,plain,
! [SV536: $i,SV168: $i] :
( ( ! [SY2287: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV168 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV168 ) @ SV536 ) @ SY2287 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV168 ) @ SY2287 ) @ SV536 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1514]) ).
thf(1894,plain,
! [SV537: $i,SV169: $i] :
( ( ! [SY2288: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV169 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV169 ) @ SV537 ) @ SY2288 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV169 ) @ SY2288 ) @ SV537 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1515]) ).
thf(1895,plain,
! [SV538: $i,SV170: $i] :
( ( ! [SY2289: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV170 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV170 ) @ SV538 ) @ SY2289 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV170 ) @ SY2289 ) @ SV538 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1516]) ).
thf(1896,plain,
! [SV539: $i,SV171: $i] :
( ( ! [SY2290: $i,SY2291: $i,SY2292: $i,SY2293: $i] :
( ( c_List_Ofoldr @ SV171 @ ( c_List_Oappend @ SV539 @ SY2290 @ SY2291 ) @ SY2292 @ SY2291 @ SY2293 )
= ( c_List_Ofoldr @ SV171 @ SV539 @ ( c_List_Ofoldr @ SV171 @ SY2290 @ SY2292 @ SY2291 @ SY2293 ) @ SY2291 @ SY2293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1517]) ).
thf(1897,plain,
! [SV540: $i,SV172: $i] :
( ( ! [SY2294: $i,SY2295: $i,SY2296: $i,SY2297: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV172 @ SV540 ) @ SY2294 ) )
| ( SV540 = SY2294 )
| ~ ( c_ListOrder_Ostep1 @ SV172 @ ( c_List_Oappend @ SY2295 @ ( c_List_Olist_OCons @ SV540 @ ( c_List_Olist_ONil @ SY2296 ) @ SY2296 ) @ SY2296 ) @ ( c_List_Oappend @ SY2297 @ ( c_List_Olist_OCons @ SY2294 @ ( c_List_Olist_ONil @ SY2296 ) @ SY2296 ) @ SY2296 ) @ SY2296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(1898,plain,
! [SV541: $i,SV173: $i] :
( ( ! [SY2298: $i,SY2299: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV173 @ SV541 @ SY2298 ) ) @ ( c_Lambda_Osubst @ SY2299 @ SV541 @ SY2298 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV173 ) @ SY2299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1519]) ).
thf(1899,plain,
! [SV542: $i,SV174: $i] :
( ( ! [SY2300: $i,SY2301: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV174 @ SV542 @ SY2300 ) ) @ ( c_Lambda_Osubst @ SV174 @ SY2301 @ SY2300 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV542 ) @ SY2301 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(1900,plain,
! [SV543: $i,SV175: $i] :
( ( ! [SY2302: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV175 )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV175 ) @ SV543 @ SY2302 @ SV175 @ SV175 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV175 ) @ SY2302 @ SV543 @ SV175 @ SV175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1521]) ).
thf(1901,plain,
! [SV544: $i,SV176: $i] :
( ( ! [SY2303: $i,SY2304: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV176 @ SV544 ) @ SY2303 ) @ SY2304 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV176 @ SY2303 ) @ SY2304 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(1902,plain,
! [SV545: $i,SV177: $i] :
( ( ! [SY2305: $i] :
~ ( c_ListOrder_Ostep1 @ SV177 @ ( c_List_Olist_ONil @ SV545 ) @ SY2305 @ SV545 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(1903,plain,
! [SV546: $i,SV178: $i] :
( ( ! [SY2306: $i] :
~ ( c_ListOrder_Ostep1 @ SV178 @ SV546 @ ( c_List_Olist_ONil @ SY2306 ) @ SY2306 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1524]) ).
thf(1904,plain,
! [SV547: $i,SV179: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV179 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV179 ) @ SV547 ) @ SV547 ) @ ( c_HOL_Ozero__class_Ozero @ SV179 ) @ SV179 )
| ~ ( c_HOL_Oord__class_Oless @ SV547 @ ( c_HOL_Ozero__class_Ozero @ SV179 ) @ SV179 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1525]) ).
thf(1905,plain,
! [SV548: $i,SV180: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV180 )
| ( c_HOL_Oord__class_Oless @ SV548 @ ( c_HOL_Ozero__class_Ozero @ SV180 ) @ SV180 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV180 ) @ SV548 ) @ SV548 ) @ ( c_HOL_Ozero__class_Ozero @ SV180 ) @ SV180 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(1906,plain,
! [SV549: $i,SV181: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV181 )
| ( c_HOL_Oord__class_Oless @ SV549 @ ( c_HOL_Ozero__class_Ozero @ SV181 ) @ SV181 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV181 ) @ SV549 ) @ SV549 ) @ ( c_HOL_Ozero__class_Ozero @ SV181 ) @ SV181 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(1907,plain,
! [SV550: $i,SV182: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV182 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV182 ) @ SV550 ) @ SV550 ) @ ( c_HOL_Ozero__class_Ozero @ SV182 ) @ SV182 )
| ~ ( c_HOL_Oord__class_Oless @ SV550 @ ( c_HOL_Ozero__class_Ozero @ SV182 ) @ SV182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(1908,plain,
! [SV551: $i,SV183: $i] :
( ( ! [SY2307: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV183 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ SV551 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ ( c_HOL_Ozero__class_Ozero @ SV183 ) @ SY2307 @ SV183 @ SV183 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ SV551 @ SY2307 @ SV183 @ SV183 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(1909,plain,
! [SV552: $i,SV184: $i] :
( ( ! [SY2308: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV184 ) ) @ SV552 ) @ SY2308 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV552 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV184 @ SV552 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY2308 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1530]) ).
thf(1910,plain,
! [SV553: $i,SV185: $i] :
( ( ! [SY2309: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV185 ) @ SV553 @ SY2309 )
= ( c_Lambda_OdB_OVar @ SV185 ) )
| ( SV185 = SY2309 )
| ( c_HOL_Oord__class_Oless @ SY2309 @ SV185 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(1911,plain,
! [SV554: $i,SV186: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV186 @ SV554 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(1912,plain,
! [SV187: $i] :
( ( c_HOL_Oord__class_Oless @ SV187 @ SV187 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1533]) ).
thf(1913,plain,
! [SV188: $i] :
( ( c_HOL_Oord__class_Oless @ SV188 @ SV188 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1534]) ).
thf(1914,plain,
! [SV555: $i,SV189: $i] :
( ( ~ ( class_Orderings_Oorder @ SV189 )
| ~ ( c_HOL_Oord__class_Oless @ SV555 @ SV555 @ SV189 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1535]) ).
thf(1915,plain,
! [SV556: $i,SV190: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV190 )
| ~ ( c_HOL_Oord__class_Oless @ SV556 @ SV556 @ SV190 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1536]) ).
thf(1916,plain,
! [SV557: $i,SV191: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV191 )
| ~ ( c_HOL_Oord__class_Oless @ SV557 @ SV557 @ SV191 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(1917,plain,
! [SV558: $i,SV192: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV192 ) ) @ SV558 ) ) @ ( c_Lambda_Osubst @ SV192 @ SV558 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1538]) ).
thf(1918,plain,
! [SV559: $i,SV193: $i] :
( ( ! [SY2310: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV193 @ SV559 ) ) @ ( c_Lambda_Olift @ SY2310 @ SV559 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV193 ) @ SY2310 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1539]) ).
thf(1919,plain,
! [SV560: $i,SV194: $i] :
( ( ! [SY2311: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV194 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV194 ) @ SV560 ) @ SY2311 ) @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SY2311 @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV560 @ SV194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1540]) ).
thf(1920,plain,
! [SV561: $i,SV195: $i] :
( ( ! [SY2312: $i,SY2313: $i,SY2314: $i,SY2315: $i] :
( ( c_ListOrder_Ostep1 @ SV195 @ SV561 @ SY2312 @ SY2313 )
| ( SY2312 = SV561 )
| ~ ( c_ListOrder_Ostep1 @ SV195 @ ( c_List_Olist_OCons @ SY2314 @ SV561 @ SY2313 ) @ ( c_List_Olist_OCons @ SY2315 @ SY2312 @ SY2313 ) @ SY2313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(1921,plain,
! [SV562: $i,SV196: $i] :
( ( ! [SY2316: $i,SY2317: $i,SY2318: $i] :
( ( ( hAPP @ ( hAPP @ SV196 @ ( hAPP @ ( hAPP @ SV196 @ SV562 ) @ SY2316 ) ) @ SY2317 )
= ( hAPP @ ( hAPP @ SV196 @ SV562 ) @ ( hAPP @ ( hAPP @ SV196 @ SY2316 ) @ SY2317 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV196 @ SY2318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1542]) ).
thf(1922,plain,
! [SV563: $i,SV197: $i] :
( ( ! [SY2319: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV197 )
| ( c_HOL_Oord__class_Oless @ SV563 @ SY2319 @ SV197 )
| ( c_HOL_Oord__class_Oless @ SY2319 @ SV563 @ SV197 )
| ( SY2319 = SV563 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1543]) ).
thf(1923,plain,
! [SV564: $i,SV198: $i] :
( ( ! [SY2320: $i] :
( ~ ( class_Orderings_Olinorder @ SV198 )
| ( SV564 = SY2320 )
| ( c_HOL_Oord__class_Oless @ SY2320 @ SV564 @ SV198 )
| ( c_HOL_Oord__class_Oless @ SV564 @ SY2320 @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1544]) ).
thf(1924,plain,
! [SV565: $i,SV199: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV199 @ SV565 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV565 @ SV199 @ tc_nat )
| ( SV565 = SV199 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(1925,plain,
! [SV566: $i,SV200: $i] :
( ( ! [SY2321: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV200 @ SV566 ) @ SY2321 ) )
| ( c_HOL_Oord__class_Oless @ SV566 @ SY2321 @ tc_nat )
| ( SY2321 = SV566 )
| ( c_HOL_Oord__class_Oless @ SY2321 @ SV566 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(1926,plain,
! [SV567: $i,SV201: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV201 @ SV567 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV567 @ SV201 @ tc_nat )
| ( SV567 = SV201 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1547]) ).
thf(1927,plain,
! [SV568: $i,SV202: $i] :
( ( ! [SY2322: $i] :
( ~ ( class_Orderings_Olinorder @ SV202 )
| ( c_HOL_Oord__class_Oless @ SV568 @ SY2322 @ SV202 )
| ( c_HOL_Oord__class_Oless @ SY2322 @ SV568 @ SV202 )
| ( SY2322 = SV568 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1548]) ).
thf(1928,plain,
! [SV569: $i,SV203: $i] :
( ( ! [SY2323: $i] :
( ~ ( class_Orderings_Olinorder @ SV203 )
| ( c_HOL_Oord__class_Oless @ SV569 @ SY2323 @ SV203 )
| ( SY2323 = SV569 )
| ( c_HOL_Oord__class_Oless @ SY2323 @ SV569 @ SV203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(1929,plain,
! [SV570: $i,SV204: $i] :
( ( ! [SY2324: $i] :
( ~ ( class_Orderings_Olinorder @ SV204 )
| ( SV570 = SY2324 )
| ( c_HOL_Oord__class_Oless @ SV570 @ SY2324 @ SV204 )
| ( c_HOL_Oord__class_Oless @ SY2324 @ SV570 @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1550]) ).
thf(1930,plain,
! [SV571: $i,SV205: $i] :
( ( ! [SY2325: $i,SY2326: $i,SY2327: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV205 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV205 ) @ SV571 ) @ SY2325 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV205 ) @ SY2326 ) @ SY2327 ) @ SV205 )
| ~ ( c_HOL_Oord__class_Oless @ SY2325 @ SY2327 @ SV205 )
| ~ ( c_HOL_Oord__class_Oless @ SV571 @ SY2326 @ SV205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(1931,plain,
! [SV572: $i,SV206: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV206 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV206 ) @ ( c_HOL_Ozero__class_Ozero @ SV206 ) @ SV572 @ SV206 @ SV206 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV206 ) @ SV572 @ ( c_HOL_Ozero__class_Ozero @ SV206 ) @ SV206 @ SV206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1552]) ).
thf(1932,plain,
! [SV573: $i,SV207: $i] :
( ( ! [SY2328: $i,SY2329: $i,SY2330: $i,SY2331: $i] :
( ( SV207 = SV573 )
| ( SY2328 = SY2329 )
| ~ ( c_ListOrder_Ostep1 @ SY2330 @ ( c_List_Oappend @ SV207 @ ( c_List_Olist_OCons @ SY2328 @ ( c_List_Olist_ONil @ SY2331 ) @ SY2331 ) @ SY2331 ) @ ( c_List_Oappend @ SV573 @ ( c_List_Olist_OCons @ SY2329 @ ( c_List_Olist_ONil @ SY2331 ) @ SY2331 ) @ SY2331 ) @ SY2331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1553]) ).
thf(1933,plain,
! [SV208: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV208 @ tc_nat )
= $true )
| ( ( SV208
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1554]) ).
thf(1934,plain,
! [SV574: $i,SV209: $i] :
( ( ! [SY2332: $i,SY2333: $i] :
( ( c_List_Olistsp @ SV209 @ ( c_List_Oappend @ SV574 @ SY2332 @ SY2333 ) @ SY2333 )
| ~ ( c_List_Olistsp @ SV209 @ SY2332 @ SY2333 )
| ~ ( c_List_Olistsp @ SV209 @ SV574 @ SY2333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1555]) ).
thf(1935,plain,
! [SV575: $i,SV210: $i] :
( ( ! [SY2334: $i,SY2335: $i,SY2336: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV210 @ SV575 @ SY2334 @ ( c_Lambda_OdB_OAbs @ SY2335 ) @ SY2336 )
= ( hAPP @ ( hAPP @ SY2334 @ SY2335 ) @ ( c_Lambda_OdB_OdB__rec @ SV210 @ SV575 @ SY2334 @ SY2335 @ SY2336 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1556]) ).
thf(1936,plain,
! [SV576: $i,SV211: $i] :
( ( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV211 @ SV576 )
= SV211 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(1937,plain,
! [SV212: $i] :
( ( ( ~ ( class_OrderedGroup_Osemigroup__add @ SV212 ) )
= $true )
| ( ( c_OrderedGroup_Osemigroup__add @ ( c_HOL_Oplus__class_Oplus @ SV212 ) @ SV212 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1559]) ).
thf(1938,plain,
! [SV577: $i,SV213: $i] :
( ( ( c_Lambda_Osubstn @ SV213 @ SV577 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_Lambda_Osubst @ SV213 @ SV577 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1560]) ).
thf(1939,plain,
! [SV578: $i,SV214: $i] :
( ( ! [SY2337: $i,SY2338: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV214 )
| ( c_HOL_Oord__class_Oless @ SV578 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV214 ) @ SY2337 ) @ SY2338 ) @ SV214 )
| ~ ( c_HOL_Oord__class_Oless @ SV578 @ SY2338 @ SV214 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV214 ) @ SY2337 @ SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1561]) ).
thf(1940,plain,
! [SV579: $i,SV215: $i] :
( ( ! [SY2339: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV215 ) @ SV579 @ SY2339 )
= ( c_Lambda_OdB_OVar @ SV215 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV215 @ SY2339 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1562]) ).
thf(1941,plain,
! [SV580: $i,SV216: $i] :
( ( ! [SY2340: $i,SY2341: $i,SY2342: $i,SY2343: $i] :
( ( c_List_Ofoldr @ SV216 @ ( c_List_Olist_OCons @ SV580 @ SY2340 @ SY2341 ) @ SY2342 @ SY2341 @ SY2343 )
= ( hAPP @ ( hAPP @ SV216 @ SV580 ) @ ( c_List_Ofoldr @ SV216 @ SY2340 @ SY2342 @ SY2341 @ SY2343 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1563]) ).
thf(1942,plain,
! [SV581: $i,SV217: $i] :
( ( ! [SY2344: $i,SY2345: $i,SY2346: $i] :
( ~ ( hBOOL @ ( hAPP @ SV217 @ ( c_Lambda_OdB_OdB__case @ SV581 @ SY2344 @ SY2345 @ ( c_Lambda_OdB_OAbs @ SY2346 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV217 @ ( hAPP @ SY2345 @ SY2346 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(1943,plain,
! [SV582: $i,SV218: $i] :
( ( ! [SY2347: $i,SY2348: $i,SY2349: $i] :
( ~ ( hBOOL @ ( hAPP @ SV218 @ ( c_Lambda_OdB_OdB__case @ SV582 @ SY2347 @ SY2348 @ ( c_Lambda_OdB_OAbs @ SY2349 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV218 @ ( hAPP @ SY2348 @ SY2349 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1565]) ).
thf(1944,plain,
! [SV583: $i,SV219: $i] :
( ( ! [SY2350: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV219 @ ( c_Lambda_OdB_OVar @ SV583 ) @ SY2350 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV219 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1566]) ).
thf(1945,plain,
! [SV584: $i,SV220: $i] :
( ( ! [SY2351: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV220 ) @ ( c_List_Olist_OCons @ SV584 @ SY2351 @ SV220 ) @ SV220 )
= ( c_List_Olist_OCons @ SV584 @ SY2351 @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1567]) ).
thf(1946,plain,
! [SV585: $i,SV221: $i] :
( ( ! [SY2352: $i,SY2353: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV221 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV221 ) @ SV585 ) @ SY2352 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV221 ) @ SY2353 ) @ SY2352 ) @ SV221 )
| ~ ( c_HOL_Oord__class_Oless @ SV585 @ SY2353 @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1568]) ).
thf(1947,plain,
! [SV586: $i,SV222: $i] :
( ( ! [SY2354: $i,SY2355: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV222 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV222 ) @ SV586 ) @ SY2354 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV222 ) @ SY2355 ) @ SY2354 ) @ SV222 )
| ~ ( c_HOL_Oord__class_Oless @ SV586 @ SY2355 @ SV222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1569]) ).
thf(1948,plain,
! [SV587: $i,SV223: $i] :
( ( ! [SY2356: $i,SY2357: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV223 )
| ( c_HOL_Oord__class_Oless @ SV587 @ SY2356 @ SV223 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV223 ) @ SV587 ) @ SY2357 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV223 ) @ SY2356 ) @ SY2357 ) @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1570]) ).
thf(1949,plain,
! [SV588: $i,SV224: $i] :
( ( ! [SY2358: $i,SY2359: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV224 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV224 ) @ SV588 ) @ SY2358 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV224 ) @ SV588 ) @ SY2359 ) @ SV224 )
| ~ ( c_HOL_Oord__class_Oless @ SY2358 @ SY2359 @ SV224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1571]) ).
thf(1950,plain,
! [SV589: $i,SV225: $i] :
( ( ! [SY2360: $i,SY2361: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV225 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV225 ) @ SV589 ) @ SY2360 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV225 ) @ SV589 ) @ SY2361 ) @ SV225 )
| ~ ( c_HOL_Oord__class_Oless @ SY2360 @ SY2361 @ SV225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1572]) ).
thf(1951,plain,
! [SV590: $i,SV226: $i] :
( ( ! [SY2362: $i,SY2363: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV226 )
| ( c_HOL_Oord__class_Oless @ SV590 @ SY2362 @ SV226 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV226 ) @ SY2363 ) @ SV590 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV226 ) @ SY2363 ) @ SY2362 ) @ SV226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1573]) ).
thf(1952,plain,
! [SV591: $i,SV227: $i] :
( ( ! [SY2364: $i,SY2365: $i,SY2366: $i,SY2367: $i] :
( ( c_ListOrder_Ostep1 @ SV227 @ SV591 @ SY2364 @ SY2365 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV227 @ SY2366 ) @ SY2367 ) )
| ~ ( c_ListOrder_Ostep1 @ SV227 @ ( c_List_Olist_OCons @ SY2366 @ SV591 @ SY2365 ) @ ( c_List_Olist_OCons @ SY2367 @ SY2364 @ SY2365 ) @ SY2365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1574]) ).
thf(1953,plain,
! [SV592: $i,SV228: $i] :
( ( ! [SY2368: $i,SY2369: $i,SY2370: $i] :
( ( c_ListOrder_Ostep1 @ SV228 @ ( c_List_Olist_OCons @ SV592 @ SY2368 @ SY2369 ) @ ( c_List_Olist_OCons @ SV592 @ SY2370 @ SY2369 ) @ SY2369 )
| ~ ( c_ListOrder_Ostep1 @ SV228 @ SY2368 @ SY2370 @ SY2369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(1954,plain,
! [SV593: $i,SV230: $i] :
( ( ! [SY2371: $i,SY2372: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV230 @ SV593 @ SY2371 ) @ SY2372 @ SY2371 )
= ( c_List_Oappend @ SV230 @ ( c_List_Oappend @ SV593 @ SY2372 @ SY2371 ) @ SY2371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(1955,plain,
! [SV594: $i,SV231: $i] :
( ( ! [SY2373: $i,SY2374: $i] :
( ( c_List_Oappend @ SV231 @ ( c_List_Oappend @ SV594 @ SY2373 @ SY2374 ) @ SY2374 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV231 @ SV594 @ SY2374 ) @ SY2373 @ SY2374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(1956,plain,
! [SV595: $i,SV232: $i] :
( ( ! [SY2375: $i,SY2376: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV232 @ SV595 @ SY2375 ) @ SY2376 @ SY2375 )
= ( c_List_Oappend @ SV232 @ ( c_List_Oappend @ SV595 @ SY2376 @ SY2375 ) @ SY2375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(1957,plain,
! [SV596: $i,SV233: $i] :
( ( ! [SY2377: $i,SY2378: $i] :
( ( c_List_Oappend @ SV233 @ ( c_List_Oappend @ SV596 @ SY2377 @ SY2378 ) @ SY2378 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV233 @ SV596 @ SY2378 ) @ SY2377 @ SY2378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1580]) ).
thf(1958,plain,
! [SV597: $i,SV234: $i] :
( ( ! [SY2379: $i] :
( ~ ( class_Orderings_Oorder @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SV597 @ SY2379 @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SY2379 @ SV597 @ SV234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1581]) ).
thf(1959,plain,
! [SV598: $i,SV235: $i] :
( ( ! [SY2380: $i,SY2381: $i,SY2382: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV235 @ SV598 ) @ SY2380 ) @ SY2381 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV235 @ SV598 ) @ SY2382 ) @ SY2381 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SY2380 ) @ SY2382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1582]) ).
thf(1960,plain,
! [SV599: $i,SV236: $i] :
( ( ! [SY2383: $i,SY2384: $i,SY2385: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV236 @ SV599 ) @ SY2383 ) @ SY2384 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV236 @ SY2385 ) @ SY2384 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV236 @ SV599 ) @ SY2383 ) @ SY2385 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1583]) ).
thf(1961,plain,
! [SV600: $i,SV237: $i] :
( ( ! [SY2386: $i] :
( ~ ( class_Orderings_Olinorder @ SV237 )
| ~ ( c_HOL_Oord__class_Oless @ SV600 @ SY2386 @ SV237 )
| ~ ( c_HOL_Oord__class_Oless @ SY2386 @ SV600 @ SV237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1584]) ).
thf(1962,plain,
! [SV601: $i,SV238: $i] :
( ( ! [SY2387: $i] :
( ~ ( class_Orderings_Opreorder @ SV238 )
| ~ ( c_HOL_Oord__class_Oless @ SV601 @ SY2387 @ SV238 )
| ~ ( c_HOL_Oord__class_Oless @ SY2387 @ SV601 @ SV238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1585]) ).
thf(1963,plain,
! [SV602: $i,SV239: $i] :
( ( ! [SY2388: $i] :
( ~ ( class_Orderings_Opreorder @ SV239 )
| ~ ( c_HOL_Oord__class_Oless @ SV602 @ SY2388 @ SV239 )
| ~ ( c_HOL_Oord__class_Oless @ SY2388 @ SV602 @ SV239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(1964,plain,
! [SV603: $i,SV240: $i] :
( ( ! [SY2389: $i,SY2390: $i,SY2391: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV240 @ SV603 @ SY2389 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SY2390 @ SV603 ) @ SY2391 )
| ~ ( c_Type_Otyping @ SV240 @ SY2390 @ SY2391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1587]) ).
thf(1965,plain,
! [SV604: $i,SV241: $i] :
( ( ( hBOOL @ ( hAPP @ SV241 @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV241 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV241 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV241 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV241 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ SV241 @ SV604 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1588]) ).
thf(1966,plain,
! [SV605: $i,SV242: $i] :
( ( ! [SY2392: $i,SY2393: $i,SY2394: $i] :
( ( ( c_List_Ofoldl @ SV242 @ ( hAPP @ ( hAPP @ SV242 @ SV605 ) @ SY2392 ) @ SY2393 @ SY2394 @ SY2394 )
= ( hAPP @ ( hAPP @ SV242 @ SV605 ) @ ( c_List_Ofoldl @ SV242 @ SY2392 @ SY2393 @ SY2394 @ SY2394 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV242 @ SY2394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1589]) ).
thf(1967,plain,
! [SV606: $i,SV243: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV243 ) @ SV606 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV243 ) @ SV606 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(1968,plain,
! [SV607: $i,SV244: $i] :
( ( ! [SY2395: $i,SY2396: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV244 ) @ SV607 ) @ SY2395 @ SY2396 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV244 @ SY2395 @ SY2396 ) ) @ ( c_Lambda_Osubst @ SV607 @ SY2395 @ SY2396 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1591]) ).
thf(1969,plain,
! [SV608: $i,SV245: $i] :
( ( ! [SY2397: $i,SY2398: $i] :
( ( c_Type_Otypings @ SV245 @ SV608 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SY2397 @ SV245 @ SY2398 @ SV608 ) )
| ~ ( c_Type_Otyping @ SV245 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2398 ) @ SV608 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2397 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(1970,plain,
! [SV609: $i,SV246: $i] :
( ( ! [SY2399: $i,SY2400: $i,SY2401: $i] :
( ~ ( hBOOL @ ( hAPP @ SV246 @ ( c_Lambda_OdB_OdB__case @ SV609 @ SY2399 @ SY2400 @ ( c_Lambda_OdB_OVar @ SY2401 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV246 @ ( hAPP @ SV609 @ SY2401 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(1971,plain,
! [SV610: $i,SV247: $i] :
( ( ! [SY2402: $i,SY2403: $i,SY2404: $i] :
( ~ ( hBOOL @ ( hAPP @ SV247 @ ( c_Lambda_OdB_OdB__case @ SV610 @ SY2402 @ SY2403 @ ( c_Lambda_OdB_OVar @ SY2404 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV247 @ ( hAPP @ SV610 @ SY2404 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1594]) ).
thf(1972,plain,
! [SV611: $i,SV248: $i] :
( ( ! [SY2405: $i,SY2406: $i] :
( ( c_Type_Otyping @ SV248 @ SV611 @ SY2405 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY2406 ) @ SV611 ) )
| ~ ( c_Type_Otyping @ SV248 @ SY2406 @ SY2405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1595]) ).
thf(1973,plain,
! [SV612: $i,SV249: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV249 ) @ SV612 @ SV249 )
= SV612 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1596]) ).
thf(1974,plain,
! [SV613: $i,SV250: $i] :
( ( ! [SY2407: $i,SY2408: $i,SY2409: $i,SY2410: $i] :
( ~ ( hBOOL @ ( hAPP @ SV250 @ ( c_Lambda_OdB_OdB__case @ SV613 @ SY2407 @ SY2408 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2409 ) @ SY2410 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV250 @ ( hAPP @ ( hAPP @ SY2407 @ SY2409 ) @ SY2410 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1597]) ).
thf(1975,plain,
! [SV614: $i,SV251: $i] :
( ( ! [SY2411: $i,SY2412: $i,SY2413: $i,SY2414: $i] :
( ~ ( hBOOL @ ( hAPP @ SV251 @ ( c_Lambda_OdB_OdB__case @ SV614 @ SY2411 @ SY2412 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2413 ) @ SY2414 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV251 @ ( hAPP @ ( hAPP @ SY2411 @ SY2413 ) @ SY2414 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1598]) ).
thf(1976,plain,
! [SV615: $i,SV252: $i] :
( ( ! [SY2415: $i,SY2416: $i] :
( ( c_Type_Otypings @ SV252 @ SV615 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SY2415 @ SV252 @ SY2416 @ SV615 ) )
| ~ ( c_Type_Otyping @ SV252 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2416 @ SV615 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2415 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1599]) ).
thf(1977,plain,
! [SV616: $i,SV253: $i] :
( ( ! [SY2417: $i,SY2418: $i,SY2419: $i,SY2420: $i,SY2421: $i] :
( ( SV253
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV616 @ SV253 @ SY2417 @ SY2418 ) @ SV616 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SY2417 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2419 ) @ SY2420 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV253 )
| ~ ( c_Type_Otypings @ SY2417 @ SY2420 @ SY2421 )
| ~ ( c_Type_Otyping @ SY2417 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2419 ) @ SY2420 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2418 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV616 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1600]) ).
thf(1978,plain,
! [SV617: $i,SV254: $i] :
( ( ! [SY2422: $i,SY2423: $i,SY2424: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV254 @ SV617 @ SY2422 @ SY2423 ) @ SY2424 )
= ( hAPP @ SV254 @ SY2424 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2424 @ SV617 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1601]) ).
thf(1979,plain,
! [SV618: $i,SV255: $i] :
( ( ! [SY2425: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV255 @ SV618 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2425 @ SV618 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV255 ) @ SY2425 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(1980,plain,
! [SV619: $i,SV256: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV256 ) ) @ SV619 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(1981,plain,
! [SV620: $i,SV257: $i] :
( ( ! [SY2426: $i,SY2427: $i,SY2428: $i] :
( ( c_Type_Otyping @ SV257 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV620 ) @ SY2426 ) @ SY2427 )
| ~ ( c_Type_Otyping @ SV257 @ SY2426 @ SY2428 )
| ~ ( c_Type_Otyping @ SV257 @ SV620 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY2428 ) @ SY2427 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1604]) ).
thf(1982,plain,
! [SV621: $i,SV258: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV258 ) @ SV621 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV621 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1605]) ).
thf(1983,plain,
! [SV622: $i,SV259: $i] :
( ( ! [SY2429: $i,SY2430: $i,SY2431: $i] :
( ( SV259 = SV622 )
| ~ ( c_Type_Otyping @ SY2429 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2430 ) @ SY2431 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV622 )
| ~ ( c_Type_Otyping @ SY2429 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2430 ) @ SY2431 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1606]) ).
thf(1984,plain,
! [SV623: $i,SV260: $i] :
( ( ! [SY2432: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV260 @ SV623 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV260 @ SY2432 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV623 @ SY2432 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1607]) ).
thf(1985,plain,
! [SV624: $i,SV261: $i] :
( ( ( hBOOL @ ( hAPP @ SV261 @ SV624 ) )
| ( hBOOL @ ( hAPP @ SV261 @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV261 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV261 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV261 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV261 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1608]) ).
thf(1986,plain,
! [SV625: $i,SV262: $i] :
( ( ! [SY2433: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV262 @ SV625 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2433 @ SV625 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV262 ) @ SY2433 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(1987,plain,
! [SV626: $i,SV263: $i] :
( ( ! [SY2434: $i,SY2435: $i,SY2436: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV263 @ SV626 @ SY2434 @ ( c_Lambda_OdB_OVar @ SY2435 ) @ SY2436 )
= ( hAPP @ SV263 @ SY2435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1610]) ).
thf(1988,plain,
! [SV627: $i,SV264: $i] :
( ( ! [SY2437: $i,SY2438: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV264 @ SV627 @ SY2437 @ SY2438 ) @ SV627 )
= SY2437 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1611]) ).
thf(1989,plain,
! [SV628: $i,SV265: $i] :
( ( ! [SY2439: $i,SY2440: $i] :
( ( c_List_Ofoldl @ SV265 @ SV628 @ ( c_List_Olist_ONil @ SY2439 ) @ SY2440 @ SY2439 )
= SV628 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(1990,plain,
! [SV629: $i,SV266: $i] :
( ( ! [SY2441: $i,SY2442: $i] :
( ( c_Type_Otyping @ SV266 @ ( c_Lambda_OdB_OAbs @ SV629 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY2441 ) @ SY2442 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV266 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2441 @ tc_Type_Otype ) @ SV629 @ SY2442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(1991,plain,
! [SV630: $i,SV268: $i] :
( ( ! [SY2443: $i] :
( ( ( hAPP @ SV268 @ SV630 )
= SY2443 )
| ~ ( c_Type_Otyping @ SV268 @ ( c_Lambda_OdB_OVar @ SV630 ) @ SY2443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1615]) ).
thf(1992,plain,
! [SV631: $i,SV269: $i] :
( ( ! [SY2444: $i,SY2445: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ SV269 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV269 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV269 ) @ SV631 ) @ SY2444 ) @ SY2445 @ SV269 @ SV269 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV269 ) @ SV631 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV269 ) @ SY2444 @ SY2445 @ SV269 @ SV269 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1616]) ).
thf(1993,plain,
! [SV632: $i,SV270: $i] :
( ( ! [SY2446: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV270 ) @ SV632 ) @ SY2446 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV270 @ SY2446 ) ) @ ( c_Lambda_Olift @ SV632 @ SY2446 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1617]) ).
thf(1994,plain,
! [SV633: $i,SV271: $i] :
( ( ! [SY2447: $i,SY2448: $i] :
( ( c_Type_Otyping @ SV271 @ SV633 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SY2447 @ SV271 @ SV633 @ SY2448 ) @ SY2447 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV271 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV633 @ SY2448 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1618]) ).
thf(1995,plain,
! [SV634: $i,SV272: $i] :
( ( ! [SY2449: $i,SY2450: $i] :
( ( c_Type_Otyping @ SV272 @ ( c_Lambda_OdB_OVar @ SV634 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SY2449 @ SV272 @ SV634 @ SY2450 ) @ SY2449 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV272 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV634 ) @ SY2450 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1619]) ).
thf(1996,plain,
! [SV635: $i,SV273: $i] :
( ( ! [SY2451: $i,SY2452: $i,SY2453: $i] :
( ( c_Type_Otyping @ SV273 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV635 @ SY2451 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2452 )
| ~ ( c_Type_Otypings @ SV273 @ SY2451 @ SY2453 )
| ~ ( c_Type_Otyping @ SV273 @ SV635 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY2453 @ SY2452 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(1997,plain,
! [SV636: $i,SV274: $i] :
( ( ! [SY2454: $i] :
( ( SV274
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV636 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV636 @ SY2454 @ SV274 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV636 ) @ SY2454 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV274 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(1998,plain,
! [SV637: $i,SV275: $i] :
( ( ! [SY2455: $i,SY2456: $i,SY2457: $i,SY2458: $i] :
( ( c_Lambda_OdB_OdB__case @ SV275 @ SV637 @ SY2455 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2456 ) @ SY2457 ) @ SY2458 )
= ( hAPP @ ( hAPP @ SV637 @ SY2456 ) @ SY2457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1622]) ).
thf(1999,plain,
! [SV638: $i,SV276: $i] :
( ( ! [SY2459: $i,SY2460: $i,SY2461: $i] :
( ( ( hAPP @ ( hAPP @ SV276 @ SV638 ) @ ( c_List_Ofoldl @ SV276 @ SY2459 @ SY2460 @ SY2461 @ SY2461 ) )
= ( c_List_Ofoldl @ SV276 @ SV638 @ SY2460 @ SY2461 @ SY2461 ) )
| ~ ( c_OrderedGroup_Omonoid__add @ SY2459 @ SV276 @ SY2461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1623]) ).
thf(2000,plain,
! [SV639: $i,SV277: $i] :
( ( ! [SY2462: $i,SY2463: $i] :
( ( c_Type_Otyping @ SV277 @ SV639 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SY2462 @ SV277 @ SY2463 @ SV639 ) )
| ~ ( c_Type_Otyping @ SV277 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2463 ) @ SV639 ) @ SY2462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(2001,plain,
! [SV640: $i,SV279: $i] :
( ( ! [SY2464: $i,SY2465: $i,SY2466: $i] :
( ( c_Lambda_OdB_OdB__case @ SV279 @ SV640 @ SY2464 @ ( c_Lambda_OdB_OVar @ SY2465 ) @ SY2466 )
= ( hAPP @ SV279 @ SY2465 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1626]) ).
thf(2002,plain,
! [SV641: $i,SV280: $i] :
( ( ! [SY2467: $i,SY2468: $i] :
( ( c_Type_Otypings @ SV280 @ SV641 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SY2467 @ SV280 @ SY2468 @ SV641 ) )
| ~ ( c_Type_Otyping @ SV280 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2468 @ SV641 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1627]) ).
thf(2003,plain,
! [SV642: $i,SV281: $i] :
( ( ! [SY2469: $i,SY2470: $i,SY2471: $i,SY2472: $i] :
( ( c_List_Ofoldl @ SV281 @ SV642 @ ( c_List_Olist_OCons @ SY2469 @ SY2470 @ SY2471 ) @ SY2472 @ SY2471 )
= ( c_List_Ofoldl @ SV281 @ ( hAPP @ ( hAPP @ SV281 @ SV642 ) @ SY2469 ) @ SY2470 @ SY2472 @ SY2471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(2004,plain,
! [SV643: $i,SV283: $i] :
( ( c_Type_Otyping @ SV283 @ ( c_Lambda_OdB_OVar @ SV643 ) @ ( hAPP @ SV283 @ SV643 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1630]) ).
thf(2005,plain,
! [SV644: $i,SV284: $i] :
( ( ! [SY2473: $i,SY2474: $i,SY2475: $i,SY2476: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV284 @ SV644 @ SY2473 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2474 ) @ SY2475 ) @ SY2476 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV644 @ SY2474 ) @ SY2475 ) @ ( c_Lambda_OdB_OdB__rec @ SV284 @ SV644 @ SY2473 @ SY2474 @ SY2476 ) ) @ ( c_Lambda_OdB_OdB__rec @ SV284 @ SV644 @ SY2473 @ SY2475 @ SY2476 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1631]) ).
thf(2006,plain,
! [SV645: $i,SV286: $i] :
( ( ! [SY2477: $i,SY2478: $i,SY2479: $i,SY2480: $i,SY2481: $i] :
( ( c_Type_Otypings @ SV286 @ SV645 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SY2477 @ SY2478 @ SV286 @ SV645 ) )
| ~ ( c_Type_Otyping @ SV286 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2479 ) @ SY2480 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2478 )
| ~ ( c_Type_Otypings @ SV286 @ SY2480 @ SY2481 )
| ~ ( c_Type_Otyping @ SV286 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2479 ) @ SY2480 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV645 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(2007,plain,
! [SV646: $i,SV287: $i] :
( ( ! [SY2482: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV287 ) @ SV646 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV287 ) @ SY2482 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV646 ) @ SY2482 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(2008,plain,
! [SV647: $i,SV288: $i] :
( ( ! [SY2483: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV288 ) @ SV647 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2483 ) @ SV647 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV288 ) @ SY2483 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1635]) ).
thf(2009,plain,
! [SV648: $i,SV289: $i] :
( ( ! [SY2484: $i,SY2485: $i] :
( ( c_Lambda_Oliftn @ SV289 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV648 ) @ SY2484 ) @ SY2485 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ SV289 @ SV648 @ SY2485 ) ) @ ( c_Lambda_Oliftn @ SV289 @ SY2484 @ SY2485 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(2010,plain,
! [SV649: $i,SV291: $i] :
( ( ! [SY2486: $i,SY2487: $i] :
( ( c_Type_Otyping @ SV291 @ SV649 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SY2486 @ SV291 @ SV649 @ SY2487 ) @ SY2486 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV291 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV649 @ SY2487 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(2011,plain,
! [SV650: $i,SV292: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV292 ) @ ( c_Lambda_OdB_OVar @ SV650 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(2012,plain,
! [SV651: $i,SV293: $i] :
( ( ! [SY2488: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV293 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV651 @ SV293 @ SY2488 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV651 ) @ SV293 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY2488 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(2013,plain,
! [SV652: $i,SV294: $i] :
( ( ! [SY2489: $i,SY2490: $i,SY2491: $i,SY2492: $i] :
( ~ ( c_Type_Otyping @ SV294 @ SV652 @ SY2489 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV294 @ SY2490 @ SY2489 @ tc_Type_Otype ) @ SY2491 @ SY2492 )
| ( c_Type_Otyping @ SV294 @ ( c_Lambda_Osubst @ SY2491 @ SV652 @ SY2490 ) @ SY2492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1641]) ).
thf(2014,plain,
! [SV653: $i,SV295: $i] :
( ( ! [SY2493: $i,SY2494: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV295 ) @ SV653 ) @ SY2493 @ SY2494 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ SV295 @ SY2493 @ SY2494 ) ) @ ( c_Lambda_Osubstn @ SV653 @ SY2493 @ SY2494 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1642]) ).
thf(2015,plain,
! [SV654: $i,SV296: $i] :
( ( ! [SY2495: $i,SY2496: $i,SY2497: $i,SY2498: $i] :
( ( c_List_Ofoldl @ SV296 @ SV654 @ ( c_List_Oappend @ SY2495 @ SY2496 @ SY2497 ) @ SY2498 @ SY2497 )
= ( c_List_Ofoldl @ SV296 @ ( c_List_Ofoldl @ SV296 @ SV654 @ SY2495 @ SY2498 @ SY2497 ) @ SY2496 @ SY2498 @ SY2497 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1643]) ).
thf(2016,plain,
! [SV655: $i,SV297: $i] :
( ( ! [SY2499: $i,SY2500: $i] :
( ( c_Type_Otyping @ SV297 @ SV655 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SY2499 @ SV297 @ SV655 @ SY2500 ) ) @ SY2499 ) )
| ~ ( c_Type_Otyping @ SV297 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV655 ) @ SY2500 ) @ SY2499 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1644]) ).
thf(2017,plain,
! [SV656: $i,SV298: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV298 @ SV656 ) )
| ~ ( class_Orderings_Opreorder @ SV656 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1645]) ).
thf(2018,plain,
! [SV657: $i,SV299: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV299 @ SV657 ) )
| ~ ( class_Orderings_Oorder @ SV657 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1646]) ).
thf(2019,plain,
! [SV658: $i,SV300: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV300 ) @ SV658 ) @ SV658 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(2020,plain,
! [SV659: $i,SV301: $i] :
( ( ! [SY2501: $i] :
( ( SV301 = SV659 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY2501 ) @ SV301 ) @ SV659 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1648]) ).
thf(2021,plain,
! [SV660: $i,SV302: $i] :
( ( ! [SY2502: $i] :
( ( ( c_List_Orev @ SV302 @ SV660 )
!= ( c_List_Orev @ SY2502 @ SV660 ) )
| ( SV302 = SY2502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(2022,plain,
! [SV661: $i,SV303: $i] :
( ( ! [SY2503: $i] :
( ( ( c_List_Oappend @ SV303 @ SV661 @ SY2503 )
!= ( c_List_Olist_ONil @ SY2503 ) )
| ( SV303
= ( c_List_Olist_ONil @ SY2503 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(2023,plain,
! [SV662: $i,SV304: $i] :
( ( ! [SY2504: $i,SY2505: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV304 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV304 ) @ SV662 ) @ SY2504 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV304 ) @ SV662 ) @ SY2505 ) )
| ( SY2504 = SY2505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1652]) ).
thf(2024,plain,
! [SV663: $i,SV305: $i] :
( ( ! [SY2506: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV305 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV663 @ SY2506 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV305 )
= SV663 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(2025,plain,
! [SV664: $i,SV306: $i] :
( ( ( SV306
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV306 ) @ SV664 ) )
| ( SV664
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(2026,plain,
! [SV665: $i,SV307: $i] :
( ( ! [SY2507: $i] :
( ( ( c_List_Oreplicate @ SV307 @ SV665 @ SY2507 )
!= ( c_List_Olist_ONil @ SY2507 ) )
| ( SV307
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(2027,plain,
! [SV666: $i,SV308: $i] :
( ( ! [SY2508: $i,SY2509: $i,SY2510: $i] :
( ( ( c_List_Oreplicate @ SV308 @ SV666 @ SY2508 )
!= ( c_List_Oreplicate @ SY2509 @ SY2510 @ SY2508 ) )
| ( SV666 = SY2510 )
| ( SV308
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(2028,plain,
! [SV667: $i,SV309: $i] :
( ( ! [SY2511: $i,SY2512: $i,SY2513: $i] :
( ( ( c_List_Oappend @ SV309 @ SV667 @ SY2511 )
!= ( c_List_Olist_OCons @ SY2512 @ SY2513 @ SY2511 ) )
| ( SV309
= ( c_List_Olist_OCons @ SY2512 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY2512 @ SY2513 @ SV309 @ SV667 @ SY2511 ) @ SY2511 ) )
| ( SV309
= ( c_List_Olist_ONil @ SY2511 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1657]) ).
thf(2029,plain,
! [SV668: $i,SV310: $i] :
( ( ! [SY2514: $i,SY2515: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV310 ) @ SV668 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2514 ) @ SY2515 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2514 @ SV668 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV310 @ SY2515 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1658]) ).
thf(2030,plain,
! [SV669: $i,SV311: $i] :
( ( ! [SY2516: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV311 ) @ SV669 )
!= ( c_Lambda_OdB_OVar @ SY2516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1659]) ).
thf(2031,plain,
! [SV670: $i,SV312: $i] :
( ( ! [SY2517: $i] :
( ( ( c_List_Oappend @ SV312 @ SV670 @ SY2517 )
!= ( c_List_Olist_ONil @ SY2517 ) )
| ( SV670
= ( c_List_Olist_ONil @ SY2517 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1660]) ).
thf(2032,plain,
! [SV671: $i,SV313: $i] :
( ( ! [SY2518: $i] :
( ( c_List_Olist_ONil @ SV313 )
!= ( c_List_Olist_OCons @ SV671 @ SY2518 @ SV313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1661]) ).
thf(2033,plain,
! [SV672: $i,SV314: $i] :
( ( ! [SY2519: $i,SY2520: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV314 ) @ SV672 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2519 @ SY2520 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2520
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV314 @ SV672 @ SY2519 @ SY2520 ) @ ( c_List_Olist_OCons @ SV672 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( SY2520
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1662]) ).
thf(2034,plain,
! [SV673: $i,SV315: $i] :
( ( ! [SY2521: $i] :
( ( SV315
!= ( c_List_Oappend @ SV673 @ SV315 @ SY2521 ) )
| ( SV673
= ( c_List_Olist_ONil @ SY2521 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1663]) ).
thf(2035,plain,
! [SV674: $i,SV316: $i] :
( ( ! [SY2522: $i,SY2523: $i,SY2524: $i] :
( ( ( c_List_Olist_OCons @ SV316 @ SV674 @ SY2522 )
!= ( c_List_Oappend @ SY2523 @ SY2524 @ SY2522 ) )
| ( SV674
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV316 @ SV674 @ SY2523 @ SY2524 @ SY2522 ) @ SY2524 @ SY2522 ) )
| ( ( c_List_Olist_OCons @ SV316 @ SV674 @ SY2522 )
= SY2524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1664]) ).
thf(2036,plain,
! [SV675: $i,SV317: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV317 ) @ SV675 )
!= SV317 )
| ( SV675
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1665]) ).
thf(2037,plain,
! [SV676: $i,SV318: $i] :
( ( ! [SY2525: $i] :
( ( c_List_Olist_OCons @ SV318 @ SV676 @ SY2525 )
!= SV676 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1666]) ).
thf(2038,plain,
! [SV677: $i,SV319: $i] :
( ( ! [SY2526: $i] :
( ( SV319
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV319 ) @ SV677 ) @ SY2526 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV319 ) @ SV677 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV319 ) @ SV677 ) @ ( c_List_Oappend @ SY2526 @ ( c_List_Olist_OCons @ SV677 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1667]) ).
thf(2039,plain,
! [SV678: $i,SV320: $i] :
( ( ! [SY2527: $i,SY2528: $i,SY2529: $i] :
( ( ( c_List_Olist_OCons @ SV320 @ SV678 @ SY2527 )
!= ( c_List_Olist_OCons @ SY2528 @ SY2529 @ SY2527 ) )
| ( SV320 = SY2528 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1668]) ).
thf(2040,plain,
! [SV679: $i,SV321: $i] :
( ( ! [SY2530: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV321 ) @ SV679 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV321 ) @ SY2530 ) )
| ( SV679 = SY2530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(2041,plain,
! [SV680: $i,SV322: $i] :
( ( ! [SY2531: $i,SY2532: $i] :
( ( ( c_List_Oappend @ SV322 @ SV680 @ SY2531 )
!= ( c_List_Oappend @ SY2532 @ SV680 @ SY2531 ) )
| ( SV322 = SY2532 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1670]) ).
thf(2042,plain,
! [SV681: $i,SV323: $i] :
( ( ! [SY2533: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV323 ) @ SV681 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV323 ) @ SY2533 ) )
| ( SV681 = SY2533 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1671]) ).
thf(2043,plain,
! [SV682: $i,SV324: $i] :
( ( ! [SY2534: $i] :
( ( c_List_Olist_OCons @ SV324 @ SV682 @ SY2534 )
!= ( c_List_Olist_ONil @ SY2534 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1672]) ).
thf(2044,plain,
! [SV683: $i,SV325: $i] :
( ( ! [SY2535: $i,SY2536: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV325 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV325 ) @ SV683 ) @ SY2535 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV325 ) @ SY2536 ) @ SY2535 ) )
| ( SV683 = SY2536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1673]) ).
thf(2045,plain,
! [SV684: $i,SV326: $i] :
( ( ! [SY2537: $i] :
( ( SV326
!= ( c_List_Oappend @ SV326 @ SV684 @ SY2537 ) )
| ( SV684
= ( c_List_Olist_ONil @ SY2537 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(2046,plain,
! [SV685: $i,SV327: $i] :
( ( ! [SY2538: $i,SY2539: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV327 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SV685 ) @ SY2538 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SV685 ) @ SY2539 ) )
| ( SY2538 = SY2539 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1675]) ).
thf(2047,plain,
! [SV686: $i,SV328: $i] :
( ( ! [SY2540: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV328 ) @ SV686 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2540 ) @ SV686 ) )
| ( SV328 = SY2540 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1676]) ).
thf(2048,plain,
! [SV687: $i,SV329: $i] :
( ( ! [SY2541: $i,SY2542: $i,SY2543: $i,SY2544: $i,SY2545: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV329 ) @ SV687 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SY2541 @ SY2542 @ SY2543 ) ) )
| ~ ( c_Type_Otyping @ SY2544 @ SY2542 @ SV687 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY2542 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY2544 @ SY2543 @ SV687 @ tc_Type_Otype ) @ SY2541 @ SY2545 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY2541 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1677]) ).
thf(2049,plain,
! [SV688: $i,SV330: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV330 )
!= ( c_Lambda_OdB_OVar @ SV688 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1678]) ).
thf(2050,plain,
! [SV689: $i,SV331: $i] :
( ( ( ( c_List_Orev @ SV331 @ SV689 )
!= ( c_List_Olist_ONil @ SV689 ) )
| ( SV331
= ( c_List_Olist_ONil @ SV689 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1679]) ).
thf(2051,plain,
! [SV690: $i,SV332: $i] :
( ( ! [SY2546: $i,SY2547: $i,SY2548: $i] :
( ( ( c_List_Oreplicate @ SV332 @ SV690 @ SY2546 )
!= ( c_List_Oreplicate @ SY2547 @ SY2548 @ SY2546 ) )
| ( SV332 = SY2547 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1680]) ).
thf(2052,plain,
! [SV691: $i,SV333: $i] :
( ( ( c_Lambda_OdB_OVar @ SV333 )
!= ( c_Lambda_OdB_OAbs @ SV691 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1681]) ).
thf(2053,plain,
! [SV692: $i,SV334: $i] :
( ( ! [SY2549: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV334 @ SV692 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY2549 ) )
| ( SV334
= ( c_Lambda_OdB_OAbs @ SY2549 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(2054,plain,
! [SV693: $i,SV335: $i] :
( ( ! [SY2550: $i] :
( ( c_Lambda_OdB_OVar @ SV335 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV693 ) @ SY2550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1683]) ).
thf(2055,plain,
! [SV694: $i,SV336: $i] :
( ( ! [SY2551: $i] :
( ( ( c_List_Orev @ SV336 @ SV694 )
!= ( c_List_Olist_OCons @ SY2551 @ ( c_List_Olist_ONil @ SV694 ) @ SV694 ) )
| ( SV336
= ( c_List_Olist_OCons @ SY2551 @ ( c_List_Olist_ONil @ SV694 ) @ SV694 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1684]) ).
thf(2056,plain,
! [SV695: $i,SV337: $i] :
( ( ! [SY2552: $i] :
( SV337
!= ( c_List_Olist_OCons @ SV695 @ SV337 @ SY2552 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1685]) ).
thf(2057,plain,
! [SV696: $i,SV338: $i] :
( ( ! [SY2553: $i,SY2554: $i,SY2555: $i] :
( ( ( c_List_Oappend @ SV338 @ SV696 @ SY2553 )
!= ( c_List_Olist_OCons @ SY2554 @ SY2555 @ SY2553 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY2554 @ SY2555 @ SV338 @ SV696 @ SY2553 ) @ SV696 @ SY2553 )
= SY2555 )
| ( SV338
= ( c_List_Olist_ONil @ SY2553 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1686]) ).
thf(2058,plain,
! [SV697: $i,SV339: $i] :
( ( ! [SY2556: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV339 )
| ~ ( class_Int_Onumber__ring @ SV339 )
| ( SV697
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV339 ) @ SV697 ) @ SY2556 ) )
| ( SY2556
= ( c_HOL_Ozero__class_Ozero @ SV339 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1687]) ).
thf(2059,plain,
! [SV698: $i,SV340: $i] :
( ( ! [SY2557: $i,SY2558: $i] :
( ( ( c_List_Oappend @ SV340 @ SV698 @ SY2557 )
!= ( c_List_Oappend @ SV340 @ SY2558 @ SY2557 ) )
| ( SV698 = SY2558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1688]) ).
thf(2060,plain,
! [SV699: $i,SV341: $i] :
( ( ! [SY2559: $i,SY2560: $i,SY2561: $i] :
( ( ( c_List_Olist_OCons @ SV341 @ SV699 @ SY2559 )
!= ( c_List_Oappend @ SY2560 @ SY2561 @ SY2559 ) )
| ( SV699
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV341 @ SV699 @ SY2560 @ SY2561 @ SY2559 ) @ SY2561 @ SY2559 ) )
| ( SY2560
= ( c_List_Olist_ONil @ SY2559 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1689]) ).
thf(2061,plain,
! [SV700: $i,SV342: $i] :
( ( ! [SY2562: $i,SY2563: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV342 ) @ SV700 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY2562 ) @ SY2563 ) )
| ( SV700 = SY2563 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1690]) ).
thf(2062,plain,
! [SV701: $i,SV343: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV343 )
!= ( c_Lambda_OdB_OAbs @ SV701 ) )
| ( SV343 = SV701 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1691]) ).
thf(2063,plain,
! [SV702: $i,SV344: $i] :
( ( ! [SY2564: $i,SY2565: $i,SY2566: $i] :
( ( ( c_List_Oappend @ SV344 @ SV702 @ SY2564 )
!= ( c_List_Olist_OCons @ SY2565 @ SY2566 @ SY2564 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY2565 @ SY2566 @ SV344 @ SV702 @ SY2564 ) @ SV702 @ SY2564 )
= SY2566 )
| ( SV702
= ( c_List_Olist_OCons @ SY2565 @ SY2566 @ SY2564 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1692]) ).
thf(2064,plain,
! [SV703: $i,SV345: $i] :
( ( ( ( c_List_Orotate1 @ SV345 @ SV703 )
!= ( c_List_Olist_ONil @ SV703 ) )
| ( SV345
= ( c_List_Olist_ONil @ SV703 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1693]) ).
thf(2065,plain,
! [SV704: $i,SV346: $i] :
( ( ! [SY2567: $i,SY2568: $i,SY2569: $i] :
( ( ( c_List_Olist_OCons @ SV346 @ SV704 @ SY2567 )
!= ( c_List_Oappend @ SY2568 @ SY2569 @ SY2567 ) )
| ( ( c_List_Olist_OCons @ SV346 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV346 @ SV704 @ SY2568 @ SY2569 @ SY2567 ) @ SY2567 )
= SY2568 )
| ( SY2568
= ( c_List_Olist_ONil @ SY2567 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1694]) ).
thf(2066,plain,
! [SV705: $i,SV347: $i] :
( ( ! [SY2570: $i] :
( ( ( c_List_Olist_ONil @ SV347 )
!= ( c_List_Oreplicate @ SV705 @ SY2570 @ SV347 ) )
| ( SV705
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1695]) ).
thf(2067,plain,
! [SV706: $i,SV348: $i] :
( ( ! [SY2571: $i,SY2572: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV348 ) @ SV706 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2571 ) @ SY2572 ) )
| ( SV706 = SY2572 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1696]) ).
thf(2068,plain,
! [SV707: $i,SV349: $i] :
( ( ! [SY2573: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ SV349 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV707 @ SV349 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY2573 @ SV349 ) )
| ( SV707 = SY2573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1697]) ).
thf(2069,plain,
! [SV708: $i,SV350: $i] :
( ( ! [SY2574: $i,SY2575: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV350 ) @ SV708 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2574 @ SY2575 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV350
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2574 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV350 @ SV708 @ SY2574 @ SY2575 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2575
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1698]) ).
thf(2070,plain,
! [SV709: $i,SV351: $i] :
( ( ! [SY2576: $i,SY2577: $i,SY2578: $i] :
( ( ( c_List_Oappend @ SV351 @ ( c_List_Olist_OCons @ SV709 @ ( c_List_Olist_ONil @ SY2576 ) @ SY2576 ) @ SY2576 )
!= ( c_List_Oappend @ SY2577 @ ( c_List_Olist_OCons @ SY2578 @ ( c_List_Olist_ONil @ SY2576 ) @ SY2576 ) @ SY2576 ) )
| ( SV709 = SY2578 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1699]) ).
thf(2071,plain,
! [SV710: $i,SV352: $i] :
( ( ! [SY2579: $i,SY2580: $i,SY2581: $i] :
( ( ( c_List_Olist_OCons @ SV352 @ SV710 @ SY2579 )
!= ( c_List_Olist_OCons @ SY2580 @ SY2581 @ SY2579 ) )
| ( SV710 = SY2581 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1700]) ).
thf(2072,plain,
! [SV711: $i,SV353: $i] :
( ( ! [SY2582: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV353 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV711 @ SY2582 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2582
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1701]) ).
thf(2073,plain,
! [SV712: $i,SV354: $i] :
( ( ! [SY2583: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV354 @ SV712 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY2583 ) )
| ( SV712
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1702]) ).
thf(2074,plain,
! [SV713: $i,SV355: $i] :
( ( ! [SY2584: $i] :
( ( ( c_Lambda_OdB_OVar @ SV355 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV713 @ SY2584 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV355 )
= SV713 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1703]) ).
thf(2075,plain,
! [SV714: $i,SV356: $i] :
( ( ! [SY2585: $i] :
( ( ( c_List_Olist_OCons @ SV356 @ ( c_List_Olist_ONil @ SV714 ) @ SV714 )
!= ( c_List_Orev @ SY2585 @ SV714 ) )
| ( SY2585
= ( c_List_Olist_OCons @ SV356 @ ( c_List_Olist_ONil @ SV714 ) @ SV714 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1704]) ).
thf(2076,plain,
! [SV715: $i,SV357: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV357 ) @ SV715 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV357
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1705]) ).
thf(2077,plain,
! [SV716: $i,SV358: $i] :
( ( ! [SY2586: $i,SY2587: $i,SY2588: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV358 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV716 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SY2586 ) @ SY2587 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SY2586 ) @ SY2588 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV716 ) @ SY2587 )
= SY2588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1706]) ).
thf(2078,plain,
! [SV717: $i,SV359: $i] :
( ( ! [SY2589: $i,SY2590: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV359 ) @ SV717 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY2589 ) @ SY2590 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV359 = SY2589 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1707]) ).
thf(2079,plain,
! [SV718: $i,SV360: $i] :
( ( ( ( c_List_Olist_ONil @ SV360 )
!= ( c_List_Orev @ SV718 @ SV360 ) )
| ( SV718
= ( c_List_Olist_ONil @ SV360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1708]) ).
thf(2080,plain,
! [SV719: $i,SV361: $i] :
( ( ! [SY2591: $i,SY2592: $i,SY2593: $i] :
( ( ( c_List_Olist_OCons @ SV361 @ SV719 @ SY2591 )
!= ( c_List_Oappend @ SY2592 @ SY2593 @ SY2591 ) )
| ( ( c_List_Olist_OCons @ SV361 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV361 @ SV719 @ SY2592 @ SY2593 @ SY2591 ) @ SY2591 )
= SY2592 )
| ( ( c_List_Olist_OCons @ SV361 @ SV719 @ SY2591 )
= SY2593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1709]) ).
thf(2081,plain,
! [SV720: $i,SV362: $i] :
( ( ! [SY2594: $i,SY2595: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV362 ) @ SV720 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY2594 ) @ SY2595 ) )
| ( SV362 = SY2594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1710]) ).
thf(2082,plain,
! [SV721: $i,SV363: $i] :
( ( ! [SY2596: $i,SY2597: $i] :
( ( ( c_List_Orev @ SV363 @ SV721 )
!= ( c_List_Olist_OCons @ SY2596 @ SY2597 @ SV721 ) )
| ( SV363
= ( c_List_Oappend @ ( c_List_Orev @ SY2597 @ SV721 ) @ ( c_List_Olist_OCons @ SY2596 @ ( c_List_Olist_ONil @ SV721 ) @ SV721 ) @ SV721 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1711]) ).
thf(2083,plain,
! [SV722: $i,SV364: $i] :
( ( ! [SY2598: $i] :
( ( ( c_List_Oappend @ SV364 @ SV722 @ SY2598 )
!= SV722 )
| ( SV364
= ( c_List_Olist_ONil @ SY2598 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1712]) ).
thf(2084,plain,
! [SV723: $i,SV365: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV365 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV365 ) @ SV723 ) @ SV723 )
!= ( c_HOL_Ozero__class_Ozero @ SV365 ) )
| ( SV723
= ( c_HOL_Ozero__class_Ozero @ SV365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1713]) ).
thf(2085,plain,
! [SV724: $i,SV366: $i] :
( ( ! [SY2599: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV366 ) @ SV724 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2599 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV366 ) @ SV724 )
= SY2599 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1714]) ).
thf(2086,plain,
! [SV725: $i,SV367: $i] :
( ( ! [SY2600: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV367 ) @ SV725 )
!= ( c_Lambda_OdB_OAbs @ SY2600 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1715]) ).
thf(2087,plain,
! [SV726: $i,SV368: $i] :
( ( ! [SY2601: $i,SY2602: $i,SY2603: $i] :
( ( ( c_List_Oappend @ SV368 @ SV726 @ SY2601 )
!= ( c_List_Olist_OCons @ SY2602 @ SY2603 @ SY2601 ) )
| ( SV368
= ( c_List_Olist_OCons @ SY2602 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY2602 @ SY2603 @ SV368 @ SV726 @ SY2601 ) @ SY2601 ) )
| ( SV726
= ( c_List_Olist_OCons @ SY2602 @ SY2603 @ SY2601 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1716]) ).
thf(2088,plain,
! [SV727: $i,SV369: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV369 ) @ SV727 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV727
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1717]) ).
thf(2089,plain,
! [SV728: $i,SV370: $i] :
( ( ! [SY2604: $i,SY2605: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV370 ) @ SV728 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2604 ) @ SY2605 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV370 = SY2604 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1718]) ).
thf(2090,plain,
! [SV729: $i,SV371: $i] :
( ( ! [SY2606: $i] :
( ( ( c_Lambda_OdB_OVar @ SV371 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV729 @ SY2606 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2606
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1719]) ).
thf(2091,plain,
! [SV730: $i,SV372: $i] :
( ( ! [SY2607: $i] :
( ( ( c_List_Olist_ONil @ SV372 )
!= ( c_List_Oappend @ SV730 @ SY2607 @ SV372 ) )
| ( SV730
= ( c_List_Olist_ONil @ SV372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1720]) ).
thf(2092,plain,
! [SV731: $i,SV373: $i] :
( ( ! [SY2608: $i] :
( ( ( c_List_Oappend @ SV373 @ SV731 @ SY2608 )
!= SV373 )
| ( SV731
= ( c_List_Olist_ONil @ SY2608 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1721]) ).
thf(2093,plain,
! [SV732: $i,SV374: $i] :
( ( ! [SY2609: $i,SY2610: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV374 ) @ SV732 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY2609 ) @ SY2610 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1722]) ).
thf(2094,plain,
! [SV733: $i,SV375: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV375 )
!= ( c_Lambda_OdB_OVar @ SV733 ) )
| ( SV375 = SV733 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1723]) ).
thf(2095,plain,
! [SV734: $i,SV376: $i] :
( ( ! [SY2611: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV376 @ SV734 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2611 @ SV734 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV376 = SY2611 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1724]) ).
thf(2096,plain,
! [SV735: $i,SV377: $i] :
( ( ! [SY2612: $i,SY2613: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV377 ) @ SV735 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2612 ) @ SY2613 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV735 = SY2613 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1725]) ).
thf(2097,plain,
! [SV736: $i,SV378: $i] :
( ( ! [SY2614: $i,SY2615: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV378 )
| ~ ( class_Int_Onumber__ring @ SV378 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV378 ) @ SV736 ) @ SY2614 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV378 ) @ SV736 ) @ SY2615 ) )
| ( SY2614 = SY2615 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1726]) ).
thf(2098,plain,
! [SV737: $i,SV379: $i] :
( ( ! [SY2616: $i] :
( ( c_List_Olist_OCons @ SV379 @ SV737 @ SY2616 )
!= ( c_List_Olist_ONil @ SY2616 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1727]) ).
thf(2099,plain,
! [SV738: $i,SV380: $i] :
( ( ! [SY2617: $i,SY2618: $i,SY2619: $i,SY2620: $i,SY2621: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV380 ) @ SV738 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SY2617 @ SY2618 @ SY2619 ) ) )
| ~ ( c_Type_Otyping @ SY2620 @ SY2618 @ SV380 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY2618 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY2620 @ SY2619 @ SV380 @ tc_Type_Otype ) @ SY2617 @ SY2621 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY2617 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1728]) ).
thf(2100,plain,
! [SV739: $i,SV381: $i] :
( ( ! [SY2622: $i] :
( ( ( c_List_Olist_ONil @ SV381 )
!= ( c_List_Oappend @ SV739 @ SY2622 @ SV381 ) )
| ( SY2622
= ( c_List_Olist_ONil @ SV381 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1729]) ).
thf(2101,plain,
! [SV740: $i,SV382: $i] :
( ( ! [SY2623: $i,SY2624: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV382 ) @ SV740 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY2623 ) @ SY2624 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV740 = SY2624 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1730]) ).
thf(2102,plain,
! [SV741: $i,SV383: $i] :
( ( ! [SY2625: $i] :
( ( c_Lambda_OdB_OAbs @ SV383 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV741 ) @ SY2625 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1731]) ).
thf(2103,plain,
! [SV742: $i,SV384: $i] :
( ( ! [SY2626: $i,SY2627: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV384 ) ) @ SV742 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2626 ) @ SY2627 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1732]) ).
thf(2104,plain,
! [SV743: $i,SV385: $i] :
( ( ( ( c_Nat_Osize__class_Osize @ SV385 @ ( tc_List_Olist @ SV743 ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV385
= ( c_List_Olist_ONil @ SV743 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1733]) ).
thf(2105,plain,
! [SV744: $i,SV386: $i] :
( ( ! [SY2628: $i,SY2629: $i,SY2630: $i] :
( ( ( c_List_Oappend @ SV386 @ ( c_List_Olist_OCons @ SV744 @ ( c_List_Olist_ONil @ SY2628 ) @ SY2628 ) @ SY2628 )
!= ( c_List_Oappend @ SY2629 @ ( c_List_Olist_OCons @ SY2630 @ ( c_List_Olist_ONil @ SY2628 ) @ SY2628 ) @ SY2628 ) )
| ( SV386 = SY2629 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1734]) ).
thf(2106,plain,
! [SV745: $i,SV387: $i] :
( ( ! [SY2631: $i,SY2632: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV387 ) @ SV745 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2631 ) @ SY2632 ) )
| ( SV387 = SY2631 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1735]) ).
thf(2107,plain,
! [SV388: $i,SV1: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV1 ) )
= $true )
| ( ( ( c_List_Olistsum @ SV388 @ SV1 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV1 ) @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SV388 @ SV1 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1736]) ).
thf(2108,plain,
! [SV389: $i,SV2: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV2 @ ( tc_List_Olist @ SV389 ) ) @ tc_nat )
= $true )
| ( ( SV2
= ( c_List_Olist_ONil @ SV389 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1737]) ).
thf(2109,plain,
! [SV746: $i,SV390: $i,SV3: $i] :
( ( ! [SY2633: $i] :
( ( c_Type_Otyping @ SV3 @ SV390 @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ SV746 @ SV3 @ SV390 @ SY2633 ) )
| ~ ( c_Type_Otypings @ SV3 @ ( c_List_Oappend @ SY2633 @ ( c_List_Olist_OCons @ SV390 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SV746 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1738]) ).
thf(2110,plain,
! [SV747: $i,SV391: $i,SV4: $i] :
( ( ( c_List_Orev @ ( c_List_Oappend @ SV4 @ SV391 @ SV747 ) @ SV747 )
= ( c_List_Oappend @ ( c_List_Orev @ SV391 @ SV747 ) @ ( c_List_Orev @ SV4 @ SV747 ) @ SV747 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1739]) ).
thf(2111,plain,
! [SV748: $i,SV392: $i,SV9: $i] :
( ( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV9 @ SV392 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV748 @ SV392 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1740]) ).
thf(2112,plain,
! [SV749: $i,SV393: $i,SV10: $i] :
( ( ( ( c_List_Olast @ ( c_List_Oreplicate @ SV10 @ SV393 @ SV749 ) @ SV749 )
= SV393 )
| ( SV10
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1741]) ).
thf(2113,plain,
! [SV750: $i,SV394: $i,SV11: $i] :
( ( ! [SY2634: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV11 @ SV394 @ SV394 ) @ SV394 ) @ SV750 ) @ SY2634 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV11 @ SV394 ) @ SY2634 ) @ SV750 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1742]) ).
thf(2114,plain,
! [SV751: $i,SV395: $i,SV12: $i] :
( ( ! [SY2635: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV12 @ SV395 ) @ SV751 ) @ SY2635 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV12 @ SV395 @ SV395 ) @ SV395 ) @ SY2635 ) @ SV751 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1743]) ).
thf(2115,plain,
! [SV752: $i,SV396: $i,SV13: $i] :
( ( ! [SY2636: $i,SY2637: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV13 @ SV396 ) @ SV752 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV13 @ SY2636 @ SY2637 ) @ SV752 ) @ SV396 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1744]) ).
thf(2116,plain,
! [SV753: $i,SV397: $i,SV14: $i] :
( ( ! [SY2638: $i,SY2639: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV14 @ SV397 @ SV753 ) @ SY2638 ) @ SY2639 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV14 @ SY2639 ) @ SY2638 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1745]) ).
thf(2117,plain,
! [SV754: $i,SV398: $i,SV15: $i] :
( ( ! [SY2640: $i,SY2641: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV15 @ SV398 ) @ SV754 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV15 @ SY2640 @ SY2641 ) @ SV754 ) @ SV398 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1746]) ).
thf(2118,plain,
! [SV755: $i,SV399: $i,SV16: $i] :
( ( ! [SY2642: $i,SY2643: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV16 @ SV399 @ SV755 ) @ SY2642 ) @ SY2643 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV16 @ SY2643 ) @ SY2642 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1747]) ).
thf(2119,plain,
! [SV756: $i,SV400: $i,SV17: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV17 ) @ SV400 ) ) @ SV756 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV17 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV400 ) @ SV756 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1748]) ).
thf(2120,plain,
! [SV757: $i,SV401: $i,SV18: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV18 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV401 ) @ SV757 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV401 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV18 ) @ SV757 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1749]) ).
thf(2121,plain,
! [SV758: $i,SV402: $i,SV20: $i] :
( ( ! [SY2644: $i] :
( ( c_Wellfounded_Oaccp @ SV20 @ SV402 @ SV758 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV20 @ SV758 ) @ SV402 ) @ SY2644 ) )
| ~ ( c_Wellfounded_Oaccp @ SV20 @ SY2644 @ SV758 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1750]) ).
thf(2122,plain,
! [SV759: $i,SV403: $i,SV21: $i] :
( ( ! [SY2645: $i] :
( ( c_Wellfounded_Oaccp @ SV21 @ SV403 @ SV759 )
| ~ ( c_Wellfounded_Oaccp @ SV21 @ SY2645 @ SV759 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV21 @ SV759 ) @ SV403 ) @ SY2645 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1751]) ).
thf(2123,plain,
! [SV22: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV22 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV22 @ tc_Lambda_OdB )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1752]) ).
thf(2124,plain,
! [SV23: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV23 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1753]) ).
thf(2125,plain,
! [SV760: $i,SV407: $i,SV27: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV27 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV407 ) @ SV760 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV27 @ SV407 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1757]) ).
thf(2126,plain,
! [SV761: $i,SV408: $i,SV28: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV28 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV408 ) @ SV761 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV28 @ SV761 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1758]) ).
thf(2127,plain,
! [SV762: $i,SV409: $i,SV29: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV29 @ SV409 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV29 ) @ SV762 ) @ SV409 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1759]) ).
thf(2128,plain,
! [SV763: $i,SV410: $i,SV30: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV30 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV410 ) @ SV763 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV30 @ SV410 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1760]) ).
thf(2129,plain,
! [SV764: $i,SV411: $i,SV31: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV31 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV411 ) @ SV764 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV31 @ SV764 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1761]) ).
thf(2130,plain,
! [SV765: $i,SV413: $i,SV33: $i] :
( ( ( c_List_Orev @ ( c_List_Oreplicate @ SV33 @ SV413 @ SV765 ) @ SV765 )
= ( c_List_Oreplicate @ SV33 @ SV413 @ SV765 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1763]) ).
thf(2131,plain,
! [SV766: $i,SV415: $i,SV36: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Oappend @ SV36 @ SV415 @ SV766 ) @ ( tc_List_Olist @ SV766 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV36 @ ( tc_List_Olist @ SV766 ) ) ) @ ( c_Nat_Osize__class_Osize @ SV415 @ ( tc_List_Olist @ SV766 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1765]) ).
thf(2132,plain,
! [SV767: $i,SV416: $i,SV37: $i] :
( ( ! [SY2646: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV37 @ SV416 @ SV767 ) @ ( c_List_Oreplicate @ SY2646 @ SV416 @ SV767 ) @ SV767 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SY2646 @ SV416 @ SV767 ) @ ( c_List_Oreplicate @ SV37 @ SV416 @ SV767 ) @ SV767 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1766]) ).
thf(2133,plain,
! [SV768: $i,SV417: $i,SV38: $i] :
( ( ! [SY2647: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV38 ) @ SV417 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV768 ) @ SY2647 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV417 @ SY2647 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV38 @ SV768 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1767]) ).
thf(2134,plain,
! [SV769: $i,SV418: $i,SV39: $i] :
( ( ! [SY2648: $i] :
( ( c_List_Oreplicate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV39 ) @ SV418 ) @ SV769 @ SY2648 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SV39 @ SV769 @ SY2648 ) @ ( c_List_Oreplicate @ SV418 @ SV769 @ SY2648 ) @ SY2648 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1768]) ).
thf(2135,plain,
! [SV419: $i,SV40: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV40 ) )
= $true )
| ( ( ( c_List_Olistsum @ ( c_List_Orev @ SV419 @ SV40 ) @ SV40 )
= ( c_List_Olistsum @ SV419 @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1769]) ).
thf(2136,plain,
! [SV770: $i,SV420: $i,SV41: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ SV41 @ SV420 @ SV770 ) @ ( tc_List_Olist @ SV770 ) )
= SV41 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1770]) ).
thf(2137,plain,
! [SV771: $i,SV421: $i,SV42: $i] :
( ( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ SV42 @ SV421 @ SV771 ) @ SV771 @ SV421 )
= SV42 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1771]) ).
thf(2138,plain,
! [SV422: $i,SV43: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV43 ) @ SV422 ) @ SV43 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1772]) ).
thf(2139,plain,
! [SV423: $i,SV44: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV44 ) @ SV423 ) @ SV423 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1773]) ).
thf(2140,plain,
! [SV772: $i,SV424: $i,SV45: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV45 ) @ SV424 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV772 ) @ SV424 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV45 @ SV772 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1774]) ).
thf(2141,plain,
! [SV773: $i,SV425: $i,SV46: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV46 @ SV425 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV773 ) @ SV46 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV773 ) @ SV425 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1775]) ).
thf(2142,plain,
! [SV774: $i,SV426: $i,SV47: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV47 ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV47 ) @ SV774 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV426 @ SV774 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1776]) ).
thf(2143,plain,
! [SV775: $i,SV428: $i,SV51: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV51 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV428 ) @ SV775 ) @ SV51 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV51 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV428 @ SV51 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV775 @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1778]) ).
thf(2144,plain,
! [SV776: $i,SV429: $i,SV52: $i] :
( ( ! [SY2649: $i] :
( ( c_Wellfounded_Oaccp @ SV52 @ SV429 @ SV776 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV52 @ SV429 ) @ SY2649 ) )
| ~ ( c_Wellfounded_Oaccp @ SV52 @ SY2649 @ SV776 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1779]) ).
thf(2145,plain,
! [SV777: $i,SV430: $i,SV53: $i] :
( ( ! [SY2650: $i] :
( ( c_Wellfounded_Oaccp @ SV53 @ SV430 @ SV777 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV53 @ SV430 ) @ SY2650 ) )
| ~ ( c_Wellfounded_Oaccp @ SV53 @ SY2650 @ SV777 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1780]) ).
thf(2146,plain,
! [SV431: $i,SV54: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Obutlast @ SV54 @ SV431 ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ SV54 @ SV431 ) @ ( c_List_Olist_ONil @ SV431 ) @ SV431 ) @ SV431 )
= SV54 )
= $true )
| ( ( SV54
= ( c_List_Olist_ONil @ SV431 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1781]) ).
thf(2147,plain,
! [SV432: $i,SV55: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV55 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV432 @ SV55 ) @ ( c_HOL_Ozero__class_Ozero @ SV55 ) @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1782]) ).
thf(2148,plain,
! [SV56: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV56 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV56 )
= ( c_HOL_Ozero__class_Ozero @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1783]) ).
thf(2149,plain,
! [SV778: $i,SV433: $i,SV57: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV57 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV433 @ SV57 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV778 @ SV57 ) @ SV57 )
| ~ ( c_HOL_Oord__class_Oless @ SV433 @ SV778 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1784]) ).
thf(2150,plain,
! [SV779: $i,SV434: $i,SV58: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV58 )
| ( c_HOL_Oord__class_Oless @ SV434 @ SV779 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV434 @ SV58 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV779 @ SV58 ) @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1785]) ).
thf(2151,plain,
! [SV59: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV59 )
= $false )
| ( ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ SV59 ) @ SV59 )
= ( c_HOL_Ozero__class_Ozero @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1786]) ).
thf(2152,plain,
! [SV780: $i,SV435: $i,SV60: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV60 )
| ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ SV435 @ SV780 @ SV60 ) @ SV60 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV435 ) @ ( c_List_Olistsum @ SV780 @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1787]) ).
thf(2153,plain,
! [SV436: $i,SV61: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV61 ) @ SV436 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV61 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1788]) ).
thf(2154,plain,
! [SV437: $i,SV62: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV62 ) @ SV437 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV437 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1789]) ).
thf(2155,plain,
! [SV438: $i,SV63: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV63 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV438 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV438 ) @ SV63 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1790]) ).
thf(2156,plain,
! [SV781: $i,SV441: $i,SV67: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV67 )
| ( ( c_List_Olistsum @ ( c_List_Oappend @ SV441 @ SV781 @ SV67 ) @ SV67 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ ( c_List_Olistsum @ SV441 @ SV67 ) ) @ ( c_List_Olistsum @ SV781 @ SV67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1793]) ).
thf(2157,plain,
! [SV782: $i,SV443: $i,SV69: $i] :
( ( ( ( c_List_Olast @ ( c_List_Olist_OCons @ SV69 @ SV443 @ SV782 ) @ SV782 )
= ( c_List_Olast @ SV443 @ SV782 ) )
| ( SV443
= ( c_List_Olist_ONil @ SV782 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1795]) ).
thf(2158,plain,
! [SV783: $i,SV447: $i,SV73: $i] :
( ( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV73 @ SV447 @ SV783 ) @ SV783 )
= ( c_List_Olist_OCons @ SV73 @ ( c_List_Obutlast @ SV447 @ SV783 ) @ SV783 ) )
| ( SV447
= ( c_List_Olist_ONil @ SV783 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1799]) ).
thf(2159,plain,
! [SV784: $i,SV448: $i,SV74: $i] :
( ( ! [SY2651: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV74 @ SV448 @ SV784 ) @ ( c_List_Olist_OCons @ SV448 @ SY2651 @ SV784 ) @ SV784 )
= ( c_List_Olist_OCons @ SV448 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV74 @ SV448 @ SV784 ) @ SY2651 @ SV784 ) @ SV784 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1800]) ).
thf(2160,plain,
! [SV785: $i,SV450: $i,SV76: $i] :
( ( ( ( c_List_Olast @ ( c_List_Oappend @ SV76 @ SV450 @ SV785 ) @ SV785 )
= ( c_List_Olast @ SV450 @ SV785 ) )
| ( SV450
= ( c_List_Olist_ONil @ SV785 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1802]) ).
thf(2161,plain,
! [SV786: $i,SV452: $i,SV78: $i] :
( ( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV78 @ SV452 @ SV786 ) @ SV786 )
= ( c_List_Oappend @ SV78 @ ( c_List_Obutlast @ SV452 @ SV786 ) @ SV786 ) )
| ( SV452
= ( c_List_Olist_ONil @ SV786 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(2162,plain,
! [SV787: $i,SV453: $i,SV80: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ SV80 @ ( c_List_Olist_OCons @ SV453 @ ( c_List_Olist_ONil @ SV787 ) @ SV787 ) @ SV787 ) @ SV787 )
= SV453 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1806]) ).
thf(2163,plain,
! [SV788: $i,SV454: $i,SV81: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV81 @ ( c_List_Olist_OCons @ SV454 @ ( c_List_Olist_ONil @ SV788 ) @ SV788 ) @ SV788 ) @ SV788 )
= SV81 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1807]) ).
thf(2164,plain,
! [SV789: $i,SV455: $i,SV82: $i] :
( ( ( c_List_Orev @ ( c_List_Olist_OCons @ SV82 @ SV455 @ SV789 ) @ SV789 )
= ( c_List_Oappend @ ( c_List_Orev @ SV455 @ SV789 ) @ ( c_List_Olist_OCons @ SV82 @ ( c_List_Olist_ONil @ SV789 ) @ SV789 ) @ SV789 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1808]) ).
thf(2165,plain,
! [SV790: $i,SV456: $i,SV83: $i] :
( ( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ SV83 @ SV456 ) @ ( c_List_Olist_OCons @ SV790 @ ( c_List_Olist_ONil @ SV456 ) @ SV456 ) @ SV456 ) @ SV456 )
= ( c_List_Olist_OCons @ SV790 @ SV83 @ SV456 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1809]) ).
thf(2166,plain,
! [SV791: $i,SV457: $i,SV84: $i] :
( ( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ SV84 @ SV457 @ SV791 ) @ SV791 )
= ( c_List_Oappend @ SV457 @ ( c_List_Olist_OCons @ SV84 @ ( c_List_Olist_ONil @ SV791 ) @ SV791 ) @ SV791 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(2167,plain,
! [SV792: $i,SV458: $i,SV85: $i] :
( ( ( c_List_Oappend @ ( c_List_Oreplicate @ SV85 @ SV458 @ SV792 ) @ ( c_List_Olist_OCons @ SV458 @ ( c_List_Olist_ONil @ SV792 ) @ SV792 ) @ SV792 )
= ( c_List_Olist_OCons @ SV458 @ ( c_List_Oreplicate @ SV85 @ SV458 @ SV792 ) @ SV792 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1811]) ).
thf(2168,plain,
! [SV793: $i,SV459: $i,SV86: $i] :
( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV86 @ SV459 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV793 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV459 @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV86 ) ) @ SV459 ) @ SV793 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1812]) ).
thf(2169,plain,
! [SV460: $i,SV87: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV87 ) )
= $true )
| ( ( ( c_List_Olistsum @ SV460 @ SV87 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV87 ) @ SV460 @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1813]) ).
thf(2170,plain,
! [SV794: $i,SV461: $i,SV88: $i] :
( ( ( ( c_Lambda_Oliftn @ SV88 @ ( c_Lambda_OdB_OVar @ SV461 ) @ SV794 )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV461 ) @ SV88 ) ) )
| ( c_HOL_Oord__class_Oless @ SV461 @ SV794 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1814]) ).
thf(2171,plain,
! [SV462: $i,SV89: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV89 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV462 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV462 @ SV89 ) @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1815]) ).
thf(2172,plain,
! [SV463: $i,SV90: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV90 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV463 @ SV90 ) @ SV90 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV463 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1816]) ).
thf(2173,plain,
! [SV795: $i,SV464: $i,SV91: $i] :
( ( ( ( c_List_Oappend @ SV91 @ ( c_List_Olist_OCons @ SV464 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV795 @ SV91 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV464 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV795 @ ( c_List_Oappend @ SV91 @ ( c_List_Olist_OCons @ SV464 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1817]) ).
thf(2174,plain,
! [SV796: $i,SV465: $i,SV92: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV92 @ SV465 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV796 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV92 @ ( c_List_Oappend @ SV465 @ ( c_List_Olist_OCons @ SV796 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1818]) ).
thf(2175,plain,
! [SV466: $i,SV93: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV93 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV93 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__4 @ SV93 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV93 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV93 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV93 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ SV93 @ SV466 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1819]) ).
thf(2176,plain,
! [SV467: $i,SV94: $i] :
( ( ( hBOOL @ ( hAPP @ SV94 @ SV467 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV94 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV94 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4 @ SV94 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ SV94 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV94 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV94 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1820]) ).
thf(2177,plain,
! [SV797: $i,SV469: $i,SV96: $i] :
( ( ! [SY2652: $i,SY2653: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV96 @ SV469 ) @ SV797 ) )
| ( c_ListOrder_Ostep1 @ SV96 @ ( c_List_Olist_OCons @ SV469 @ SY2652 @ SY2653 ) @ ( c_List_Olist_OCons @ SV797 @ SY2652 @ SY2653 ) @ SY2653 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1822]) ).
thf(2178,plain,
! [SV798: $i,SV470: $i,SV97: $i] :
( ( ! [SY2654: $i,SY2655: $i,SY2656: $i] :
( ( SV97 = SV470 )
| ( SV798 = SY2654 )
| ~ ( c_ListOrder_Ostep1 @ SY2655 @ ( c_List_Olist_OCons @ SV470 @ SY2654 @ SY2656 ) @ ( c_List_Olist_OCons @ SV97 @ SV798 @ SY2656 ) @ SY2656 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1823]) ).
thf(2179,plain,
! [SV799: $i,SV471: $i,SV98: $i] :
( ( ! [SY2657: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV98 @ SV471 @ SV799 ) ) @ ( c_Lambda_Osubst @ SY2657 @ SV471 @ SV799 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV98 ) @ SY2657 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1824]) ).
thf(2180,plain,
! [SV800: $i,SV472: $i,SV99: $i] :
( ( ! [SY2658: $i,SY2659: $i] :
( ( c_Lambda_OdB_OdB__case @ SV99 @ SV472 @ SV800 @ ( c_Lambda_OdB_OAbs @ SY2658 ) @ SY2659 )
= ( hAPP @ SV800 @ SY2658 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1825]) ).
thf(2181,plain,
! [SV801: $i,SV473: $i,SV100: $i] :
( ( ! [SY2660: $i] :
( ( c_List_Olistsp @ SV100 @ SV473 @ SV801 )
| ~ ( c_List_Olistsp @ SV100 @ ( c_List_Oappend @ SY2660 @ SV473 @ SV801 ) @ SV801 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(2182,plain,
! [SV802: $i,SV474: $i,SV101: $i] :
( ( ! [SY2661: $i] :
( ( c_List_Olistsp @ SV101 @ SV474 @ SV802 )
| ~ ( c_List_Olistsp @ SV101 @ ( c_List_Oappend @ SV474 @ SY2661 @ SV802 ) @ SV802 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1827]) ).
thf(2183,plain,
! [SV803: $i,SV475: $i,SV102: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV102 ) @ SV475 @ SV803 )
= ( c_Lambda_OdB_OVar @ SV102 ) )
| ( SV102 = SV803 )
| ( c_HOL_Oord__class_Oless @ SV803 @ SV102 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1828]) ).
thf(2184,plain,
! [SV476: $i,SV103: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV103 ) ) @ ( c_Lambda_OdB_OAbs @ SV476 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV103 ) @ SV476 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1829]) ).
thf(2185,plain,
! [SV804: $i,SV477: $i,SV104: $i] :
( ( ! [SY2662: $i,SY2663: $i] :
( ( c_ListOrder_Ostep1 @ SV104 @ ( c_List_Oappend @ SV477 @ SV804 @ SY2662 ) @ ( c_List_Oappend @ SV477 @ SY2663 @ SY2662 ) @ SY2662 )
| ~ ( c_ListOrder_Ostep1 @ SV104 @ SV804 @ SY2663 @ SY2662 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1830]) ).
thf(2186,plain,
! [SV805: $i,SV478: $i,SV105: $i] :
( ( ! [SY2664: $i,SY2665: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV105 @ SV478 @ SV805 @ SY2664 )
| ( c_ListOrder_Ostep1 @ SV105 @ ( c_List_Oappend @ SV478 @ SY2665 @ SY2664 ) @ ( c_List_Oappend @ SV805 @ SY2665 @ SY2664 ) @ SY2664 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(2187,plain,
! [SV806: $i,SV479: $i,SV106: $i] :
( ( ( c_Lambda_Osubstn @ SV106 @ SV479 @ SV806 )
= ( c_Lambda_Osubst @ SV106 @ ( c_Lambda_Oliftn @ SV806 @ SV479 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV806 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1832]) ).
thf(2188,plain,
! [SV107: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV107 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Ozero__class_Ozero @ SV107 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV107 ) )
= ( c_HOL_Ozero__class_Ozero @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1833]) ).
thf(2189,plain,
! [SV807: $i,SV480: $i,SV108: $i] :
( ( ! [SY2666: $i] :
( ~ ( class_Orderings_Opreorder @ SV108 )
| ( c_HOL_Oord__class_Oless @ SV480 @ SV807 @ SV108 )
| ~ ( c_HOL_Oord__class_Oless @ SY2666 @ SV807 @ SV108 )
| ~ ( c_HOL_Oord__class_Oless @ SV480 @ SY2666 @ SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1834]) ).
thf(2190,plain,
! [SV808: $i,SV481: $i,SV109: $i] :
( ( ! [SY2667: $i] :
( ~ ( class_Orderings_Oorder @ SV109 )
| ( c_HOL_Oord__class_Oless @ SV481 @ SV808 @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ SV481 @ SY2667 @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ SY2667 @ SV808 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1835]) ).
thf(2191,plain,
! [SV809: $i,SV482: $i,SV110: $i] :
( ( ! [SY2668: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV110 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV482 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV809 ) @ SY2668 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV482 ) @ SV809 ) ) @ SY2668 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1836]) ).
thf(2192,plain,
! [SV810: $i,SV483: $i,SV111: $i] :
( ( ! [SY2669: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV111 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV483 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV810 ) @ SY2669 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV810 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV483 ) @ SY2669 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1837]) ).
thf(2193,plain,
! [SV811: $i,SV484: $i,SV112: $i] :
( ( ! [SY2670: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV112 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SV484 ) @ SV811 ) ) @ SY2670 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SV484 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SV811 ) @ SY2670 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1838]) ).
thf(2194,plain,
! [SV812: $i,SV485: $i,SV113: $i] :
( ( ! [SY2671: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV113 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV485 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV812 ) @ SY2671 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV812 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV485 ) @ SY2671 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1839]) ).
thf(2195,plain,
! [SV813: $i,SV486: $i,SV114: $i] :
( ( ! [SY2672: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV114 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SV486 ) @ SV813 ) ) @ SY2672 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SV486 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SV813 ) @ SY2672 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1840]) ).
thf(2196,plain,
! [SV814: $i,SV487: $i,SV115: $i] :
( ( ! [SY2673: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV115 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SV487 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SV814 ) @ SY2673 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SV487 ) @ SV814 ) ) @ SY2673 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1841]) ).
thf(2197,plain,
! [SV815: $i,SV488: $i,SV116: $i] :
( ( ! [SY2674: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV116 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV488 ) @ SV815 ) ) @ SY2674 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV488 ) @ SY2674 ) ) @ SV815 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1842]) ).
thf(2198,plain,
! [SV816: $i,SV489: $i,SV117: $i] :
( ( ! [SY2675: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV117 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV489 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV816 ) @ SY2675 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV816 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV489 ) @ SY2675 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1843]) ).
thf(2199,plain,
! [SV817: $i,SV490: $i,SV118: $i] :
( ( ! [SY2676: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV118 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV490 ) @ SV817 ) ) @ SY2676 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV490 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV817 ) @ SY2676 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1844]) ).
thf(2200,plain,
! [SV491: $i,SV121: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV121 @ SV121 @ tc_nat )
= $true )
| ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV121 ) @ SV491 @ SV121 )
= SV491 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1847]) ).
thf(2201,plain,
! [SV818: $i,SV492: $i,SV122: $i] :
( ( ! [SY2677: $i] :
( ( c_List_Ofoldr @ SV122 @ ( c_List_Olist_ONil @ SV492 ) @ SV818 @ SV492 @ SY2677 )
= SV818 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1848]) ).
thf(2202,plain,
! [SV819: $i,SV493: $i,SV123: $i] :
( ( ! [SY2678: $i,SY2679: $i,SY2680: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SV493 ) @ SV819 ) )
| ( c_ListOrder_Ostep1 @ SV123 @ SY2678 @ SY2679 @ SY2680 )
| ~ ( c_ListOrder_Ostep1 @ SV123 @ ( c_List_Oappend @ SY2678 @ ( c_List_Olist_OCons @ SV493 @ ( c_List_Olist_ONil @ SY2680 ) @ SY2680 ) @ SY2680 ) @ ( c_List_Oappend @ SY2679 @ ( c_List_Olist_OCons @ SV819 @ ( c_List_Olist_ONil @ SY2680 ) @ SY2680 ) @ SY2680 ) @ SY2680 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(2203,plain,
! [SV820: $i,SV494: $i,SV124: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV124 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV124 ) @ SV494 ) @ SV820 ) @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ SV124 )
| ~ ( c_HOL_Oord__class_Oless @ SV820 @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ SV124 )
| ~ ( c_HOL_Oord__class_Oless @ SV494 @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(2204,plain,
! [SV821: $i,SV495: $i,SV125: $i] :
( ( ! [SY2681: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV125 @ SV495 @ SV821 ) @ SY2681 @ SV821 )
= ( c_List_Olist_OCons @ SV125 @ ( c_List_Oappend @ SV495 @ SY2681 @ SV821 ) @ SV821 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1851]) ).
thf(2205,plain,
! [SV822: $i,SV496: $i,SV126: $i] :
( ( ! [SY2682: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV126 @ SV496 @ SV822 ) @ SY2682 @ SV822 )
= ( c_List_Olist_OCons @ SV126 @ ( c_List_Oappend @ SV496 @ SY2682 @ SV822 ) @ SV822 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1852]) ).
thf(2206,plain,
! [SV823: $i,SV497: $i,SV127: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV127 ) @ SV497 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV127 ) @ SV823 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV497 ) @ SV823 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1853]) ).
thf(2207,plain,
! [SV824: $i,SV498: $i,SV128: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV128 ) @ SV498 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV824 ) @ SV498 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV128 ) @ SV824 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1854]) ).
thf(2208,plain,
! [SV825: $i,SV499: $i,SV129: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV129 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV129 ) @ SV499 @ SV825 @ SV129 @ SV129 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV129 ) @ SV499 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV129 ) @ SV825 @ ( c_HOL_Ozero__class_Ozero @ SV129 ) @ SV129 @ SV129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1855]) ).
thf(2209,plain,
! [SV826: $i,SV500: $i,SV130: $i] :
( ( ! [SY2683: $i] :
( ( c_List_Olist_OCons @ SV130 @ ( c_List_Oappend @ SV500 @ SV826 @ SY2683 ) @ SY2683 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV130 @ SV500 @ SY2683 ) @ SV826 @ SY2683 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(2210,plain,
! [SV827: $i,SV501: $i,SV131: $i] :
( ( ! [SY2684: $i] :
( ( c_List_Olist_OCons @ SV131 @ ( c_List_Oappend @ SV501 @ SV827 @ SY2684 ) @ SY2684 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV131 @ SV501 @ SY2684 ) @ SV827 @ SY2684 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1857]) ).
thf(2211,plain,
! [SV828: $i,SV502: $i,SV132: $i] :
( ( ! [SY2685: $i,SY2686: $i,SY2687: $i] :
( ( SV132 = SV502 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV828 @ SV502 ) @ SV132 ) )
| ~ ( c_ListOrder_Ostep1 @ SV828 @ ( c_List_Olist_OCons @ SV502 @ SY2685 @ SY2686 ) @ ( c_List_Olist_OCons @ SV132 @ SY2687 @ SY2686 ) @ SY2686 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1858]) ).
thf(2212,plain,
! [SV133: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV133 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV133 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1859]) ).
thf(2213,plain,
! [SV829: $i,SV503: $i,SV134: $i] :
( ( ! [SY2688: $i,SY2689: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV134 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ SV503 ) @ SV829 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ SY2688 ) @ SY2689 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ SV503 ) @ SY2688 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ SV829 ) @ SY2689 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1860]) ).
thf(2214,plain,
! [SV830: $i,SV504: $i,SV135: $i] :
( ( ! [SY2690: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV135 ) @ SV504 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV830 ) @ SY2690 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV504 ) @ SY2690 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV135 ) @ SV830 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1861]) ).
thf(2215,plain,
! [SV831: $i,SV505: $i,SV136: $i] :
( ( ( ( c_Lambda_Oliftn @ SV136 @ ( c_Lambda_OdB_OVar @ SV505 ) @ SV831 )
= ( c_Lambda_OdB_OVar @ SV505 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV505 @ SV831 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(2216,plain,
! [SV832: $i,SV506: $i,SV137: $i] :
( ( ! [SY2691: $i] :
( ( c_Type_Otyping @ SV137 @ SV506 @ SV832 )
| ~ ( c_Type_Otyping @ SV137 @ SY2691 @ SV832 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY2691 ) @ SV506 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(2217,plain,
! [SV833: $i,SV507: $i,SV138: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV138 @ SV507 ) @ SV833 @ SV507 )
= SV138 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(2218,plain,
! [SV508: $i,SV139: $i] :
( ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV139 ) @ SV508 )
= ( c_Lambda_OdB_OVar @ SV139 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV139 @ SV508 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1865]) ).
thf(2219,plain,
! [SV834: $i,SV509: $i,SV140: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV140 @ SV509 ) ) @ ( c_Lambda_Olift @ SV834 @ SV509 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV140 ) @ SV834 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1866]) ).
thf(2220,plain,
! [SV510: $i,SV141: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV141 @ SV141 @ tc_nat )
= $true )
| ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV141 ) @ SV510 @ SV141 )
= ( c_Lambda_Oliftn @ SV141 @ SV510 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1867]) ).
thf(2221,plain,
! [SV835: $i,SV511: $i,SV142: $i] :
( ( ( c_List_Olist_OCons @ SV142 @ SV511 @ SV835 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV835 ) @ ( c_List_Olist_OCons @ SV142 @ SV511 @ SV835 ) @ SV835 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1868]) ).
thf(2222,plain,
! [SV836: $i,SV512: $i,SV143: $i] :
( ( ! [SY2692: $i,SY2693: $i,SY2694: $i] :
( ( SV143 = SV512 )
| ( c_ListOrder_Ostep1 @ SV836 @ SV143 @ SV512 @ SY2692 )
| ~ ( c_ListOrder_Ostep1 @ SV836 @ ( c_List_Oappend @ SV143 @ ( c_List_Olist_OCons @ SY2693 @ ( c_List_Olist_ONil @ SY2692 ) @ SY2692 ) @ SY2692 ) @ ( c_List_Oappend @ SV512 @ ( c_List_Olist_OCons @ SY2694 @ ( c_List_Olist_ONil @ SY2692 ) @ SY2692 ) @ SY2692 ) @ SY2692 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1869]) ).
thf(2223,plain,
! [SV514: $i,SV146: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV146 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ ( c_HOL_Ozero__class_Ozero @ SV146 ) ) @ SV514 )
= SV514 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1871]) ).
thf(2224,plain,
! [SV515: $i,SV147: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV147 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ ( c_HOL_Ozero__class_Ozero @ SV147 ) ) @ SV515 )
= SV515 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1872]) ).
thf(2225,plain,
! [SV516: $i,SV148: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV148 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV148 )
| ( SV516
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV516 ) @ ( c_HOL_Ozero__class_Ozero @ SV148 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1873]) ).
thf(2226,plain,
! [SV517: $i,SV149: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV149 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV517 ) @ ( c_HOL_Ozero__class_Ozero @ SV149 ) )
= SV517 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1874]) ).
thf(2227,plain,
! [SV518: $i,SV150: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV150 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV150 ) @ ( c_HOL_Ozero__class_Ozero @ SV150 ) ) @ SV518 )
= SV518 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1875]) ).
thf(2228,plain,
! [SV519: $i,SV151: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV151 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV519 ) @ ( c_HOL_Ozero__class_Ozero @ SV151 ) )
= SV519 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1876]) ).
thf(2229,plain,
! [SV520: $i,SV152: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV152 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV520 ) @ ( c_HOL_Ozero__class_Ozero @ SV152 ) )
= SV520 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1877]) ).
thf(2230,plain,
! [SV521: $i,SV153: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV153 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ ( c_HOL_Ozero__class_Ozero @ SV153 ) ) @ SV521 )
= SV521 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1878]) ).
thf(2231,plain,
! [SV522: $i,SV154: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV154 ) ) @ ( c_Lambda_OdB_OAbs @ SV522 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV154 ) @ SV522 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1879]) ).
thf(2232,plain,
! [SV837: $i,SV523: $i,SV155: $i] :
( ( ! [SY2695: $i] :
( ( ( hAPP @ ( hAPP @ SV155 @ SV523 ) @ SV837 )
= SV523 )
| ~ ( c_OrderedGroup_Omonoid__add @ SV837 @ SV155 @ SY2695 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1880]) ).
thf(2233,plain,
! [SV838: $i,SV524: $i,SV156: $i] :
( ( ! [SY2696: $i] :
( ( ( hAPP @ ( hAPP @ SV156 @ SV524 ) @ SV838 )
= SV838 )
| ~ ( c_OrderedGroup_Omonoid__add @ SV524 @ SV156 @ SY2696 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1881]) ).
thf(2234,plain,
! [SV525: $i,SV157: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV157 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV157 ) @ SV525 @ SV157 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV157 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV525 ) @ SV525 ) @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1882]) ).
thf(2235,plain,
! [SV526: $i,SV158: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV158 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV526 ) @ SV526 ) @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV526 @ SV158 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1883]) ).
thf(2236,plain,
! [SV839: $i,SV527: $i,SV159: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV159 @ SV527 ) @ SV839 ) @ SV839 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(2237,plain,
! [SV840: $i,SV528: $i,SV160: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV160 @ SV528 ) @ SV840 ) @ SV840 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(2238,plain,
! [SV841: $i,SV529: $i,SV161: $i] :
( ( ! [SY2697: $i,SY2698: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV161 @ SV529 ) @ SV841 ) @ SY2697 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV161 @ SV529 ) @ SY2698 ) @ SY2697 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV161 @ SV529 ) @ SV841 ) @ SY2698 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1886]) ).
thf(2239,plain,
! [SV842: $i,SV535: $i,SV167: $i] :
( ( ! [SY2699: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV167 @ SV535 @ SV842 ) ) @ ( c_Lambda_Osubst @ SV167 @ SY2699 @ SV842 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV535 ) @ SY2699 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1892]) ).
thf(2240,plain,
! [SV843: $i,SV536: $i,SV168: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV168 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV168 ) @ SV536 ) @ SV843 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV168 ) @ SV843 ) @ SV536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1893]) ).
thf(2241,plain,
! [SV844: $i,SV537: $i,SV169: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV169 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV169 ) @ SV537 ) @ SV844 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV169 ) @ SV844 ) @ SV537 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1894]) ).
thf(2242,plain,
! [SV845: $i,SV538: $i,SV170: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV170 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV170 ) @ SV538 ) @ SV845 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV170 ) @ SV845 ) @ SV538 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1895]) ).
thf(2243,plain,
! [SV846: $i,SV539: $i,SV171: $i] :
( ( ! [SY2700: $i,SY2701: $i,SY2702: $i] :
( ( c_List_Ofoldr @ SV171 @ ( c_List_Oappend @ SV539 @ SV846 @ SY2700 ) @ SY2701 @ SY2700 @ SY2702 )
= ( c_List_Ofoldr @ SV171 @ SV539 @ ( c_List_Ofoldr @ SV171 @ SV846 @ SY2701 @ SY2700 @ SY2702 ) @ SY2700 @ SY2702 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(2244,plain,
! [SV847: $i,SV540: $i,SV172: $i] :
( ( ! [SY2703: $i,SY2704: $i,SY2705: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV172 @ SV540 ) @ SV847 ) )
| ( SV540 = SV847 )
| ~ ( c_ListOrder_Ostep1 @ SV172 @ ( c_List_Oappend @ SY2703 @ ( c_List_Olist_OCons @ SV540 @ ( c_List_Olist_ONil @ SY2704 ) @ SY2704 ) @ SY2704 ) @ ( c_List_Oappend @ SY2705 @ ( c_List_Olist_OCons @ SV847 @ ( c_List_Olist_ONil @ SY2704 ) @ SY2704 ) @ SY2704 ) @ SY2704 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1897]) ).
thf(2245,plain,
! [SV848: $i,SV541: $i,SV173: $i] :
( ( ! [SY2706: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV173 @ SV541 @ SV848 ) ) @ ( c_Lambda_Osubst @ SY2706 @ SV541 @ SV848 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV173 ) @ SY2706 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(2246,plain,
! [SV849: $i,SV542: $i,SV174: $i] :
( ( ! [SY2707: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV174 @ SV542 @ SV849 ) ) @ ( c_Lambda_Osubst @ SV174 @ SY2707 @ SV849 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV542 ) @ SY2707 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1899]) ).
thf(2247,plain,
! [SV850: $i,SV543: $i,SV175: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV175 )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV175 ) @ SV543 @ SV850 @ SV175 @ SV175 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV175 ) @ SV850 @ SV543 @ SV175 @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1900]) ).
thf(2248,plain,
! [SV851: $i,SV544: $i,SV176: $i] :
( ( ! [SY2708: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV176 @ SV544 ) @ SV851 ) @ SY2708 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV176 @ SV851 ) @ SY2708 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1901]) ).
thf(2249,plain,
! [SV852: $i,SV545: $i,SV177: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV177 @ ( c_List_Olist_ONil @ SV545 ) @ SV852 @ SV545 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1902]) ).
thf(2250,plain,
! [SV853: $i,SV546: $i,SV178: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV178 @ SV546 @ ( c_List_Olist_ONil @ SV853 ) @ SV853 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1903]) ).
thf(2251,plain,
! [SV547: $i,SV179: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV179 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV179 ) @ SV547 ) @ SV547 ) @ ( c_HOL_Ozero__class_Ozero @ SV179 ) @ SV179 )
| ~ ( c_HOL_Oord__class_Oless @ SV547 @ ( c_HOL_Ozero__class_Ozero @ SV179 ) @ SV179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1904]) ).
thf(2252,plain,
! [SV548: $i,SV180: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV180 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV548 @ ( c_HOL_Ozero__class_Ozero @ SV180 ) @ SV180 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV180 ) @ SV548 ) @ SV548 ) @ ( c_HOL_Ozero__class_Ozero @ SV180 ) @ SV180 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1905]) ).
thf(2253,plain,
! [SV549: $i,SV181: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV181 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV549 @ ( c_HOL_Ozero__class_Ozero @ SV181 ) @ SV181 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV181 ) @ SV549 ) @ SV549 ) @ ( c_HOL_Ozero__class_Ozero @ SV181 ) @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1906]) ).
thf(2254,plain,
! [SV550: $i,SV182: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV182 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV182 ) @ SV550 ) @ SV550 ) @ ( c_HOL_Ozero__class_Ozero @ SV182 ) @ SV182 )
| ~ ( c_HOL_Oord__class_Oless @ SV550 @ ( c_HOL_Ozero__class_Ozero @ SV182 ) @ SV182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1907]) ).
thf(2255,plain,
! [SV854: $i,SV551: $i,SV183: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV183 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ SV551 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ ( c_HOL_Ozero__class_Ozero @ SV183 ) @ SV854 @ SV183 @ SV183 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ SV551 @ SV854 @ SV183 @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1908]) ).
thf(2256,plain,
! [SV855: $i,SV552: $i,SV184: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV184 ) ) @ SV552 ) @ SV855 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV552 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV184 @ SV552 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV855 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1909]) ).
thf(2257,plain,
! [SV856: $i,SV553: $i,SV185: $i] :
( ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV185 ) @ SV553 @ SV856 )
= ( c_Lambda_OdB_OVar @ SV185 ) )
| ( SV185 = SV856 )
| ( c_HOL_Oord__class_Oless @ SV856 @ SV185 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1910]) ).
thf(2258,plain,
! [SV554: $i,SV186: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV186 @ SV554 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV186 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1911]) ).
thf(2259,plain,
! [SV555: $i,SV189: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV189 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV555 @ SV555 @ SV189 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1914]) ).
thf(2260,plain,
! [SV556: $i,SV190: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV190 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV556 @ SV556 @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1915]) ).
thf(2261,plain,
! [SV557: $i,SV191: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV191 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV557 @ SV557 @ SV191 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1916]) ).
thf(2262,plain,
! [SV857: $i,SV559: $i,SV193: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV193 @ SV559 ) ) @ ( c_Lambda_Olift @ SV857 @ SV559 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV193 ) @ SV857 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(2263,plain,
! [SV858: $i,SV560: $i,SV194: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV194 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV194 ) @ SV560 ) @ SV858 ) @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV858 @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV560 @ SV194 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(2264,plain,
! [SV859: $i,SV561: $i,SV195: $i] :
( ( ! [SY2709: $i,SY2710: $i,SY2711: $i] :
( ( c_ListOrder_Ostep1 @ SV195 @ SV561 @ SV859 @ SY2709 )
| ( SV859 = SV561 )
| ~ ( c_ListOrder_Ostep1 @ SV195 @ ( c_List_Olist_OCons @ SY2710 @ SV561 @ SY2709 ) @ ( c_List_Olist_OCons @ SY2711 @ SV859 @ SY2709 ) @ SY2709 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1920]) ).
thf(2265,plain,
! [SV860: $i,SV562: $i,SV196: $i] :
( ( ! [SY2712: $i,SY2713: $i] :
( ( ( hAPP @ ( hAPP @ SV196 @ ( hAPP @ ( hAPP @ SV196 @ SV562 ) @ SV860 ) ) @ SY2712 )
= ( hAPP @ ( hAPP @ SV196 @ SV562 ) @ ( hAPP @ ( hAPP @ SV196 @ SV860 ) @ SY2712 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV196 @ SY2713 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(2266,plain,
! [SV861: $i,SV563: $i,SV197: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV197 )
| ( c_HOL_Oord__class_Oless @ SV563 @ SV861 @ SV197 )
| ( c_HOL_Oord__class_Oless @ SV861 @ SV563 @ SV197 )
| ( SV861 = SV563 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1922]) ).
thf(2267,plain,
! [SV862: $i,SV564: $i,SV198: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV198 )
| ( SV564 = SV862 )
| ( c_HOL_Oord__class_Oless @ SV862 @ SV564 @ SV198 )
| ( c_HOL_Oord__class_Oless @ SV564 @ SV862 @ SV198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1923]) ).
thf(2268,plain,
! [SV565: $i,SV199: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV199 @ SV565 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV565 @ SV199 @ tc_nat )
| ( SV565 = SV199 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1924]) ).
thf(2269,plain,
! [SV863: $i,SV566: $i,SV200: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV200 @ SV566 ) @ SV863 ) )
| ( c_HOL_Oord__class_Oless @ SV566 @ SV863 @ tc_nat )
| ( SV863 = SV566 )
| ( c_HOL_Oord__class_Oless @ SV863 @ SV566 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1925]) ).
thf(2270,plain,
! [SV567: $i,SV201: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV201 @ SV567 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV567 @ SV201 @ tc_nat )
| ( SV567 = SV201 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1926]) ).
thf(2271,plain,
! [SV864: $i,SV568: $i,SV202: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV202 )
| ( c_HOL_Oord__class_Oless @ SV568 @ SV864 @ SV202 )
| ( c_HOL_Oord__class_Oless @ SV864 @ SV568 @ SV202 )
| ( SV864 = SV568 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1927]) ).
thf(2272,plain,
! [SV865: $i,SV569: $i,SV203: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV203 )
| ( c_HOL_Oord__class_Oless @ SV569 @ SV865 @ SV203 )
| ( SV865 = SV569 )
| ( c_HOL_Oord__class_Oless @ SV865 @ SV569 @ SV203 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1928]) ).
thf(2273,plain,
! [SV866: $i,SV570: $i,SV204: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV204 )
| ( SV570 = SV866 )
| ( c_HOL_Oord__class_Oless @ SV570 @ SV866 @ SV204 )
| ( c_HOL_Oord__class_Oless @ SV866 @ SV570 @ SV204 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1929]) ).
thf(2274,plain,
! [SV867: $i,SV571: $i,SV205: $i] :
( ( ! [SY2714: $i,SY2715: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV205 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV205 ) @ SV571 ) @ SV867 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV205 ) @ SY2714 ) @ SY2715 ) @ SV205 )
| ~ ( c_HOL_Oord__class_Oless @ SV867 @ SY2715 @ SV205 )
| ~ ( c_HOL_Oord__class_Oless @ SV571 @ SY2714 @ SV205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(2275,plain,
! [SV572: $i,SV206: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV206 ) )
= $true )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV206 ) @ ( c_HOL_Ozero__class_Ozero @ SV206 ) @ SV572 @ SV206 @ SV206 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV206 ) @ SV572 @ ( c_HOL_Ozero__class_Ozero @ SV206 ) @ SV206 @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1931]) ).
thf(2276,plain,
! [SV868: $i,SV573: $i,SV207: $i] :
( ( ! [SY2716: $i,SY2717: $i,SY2718: $i] :
( ( SV207 = SV573 )
| ( SV868 = SY2716 )
| ~ ( c_ListOrder_Ostep1 @ SY2717 @ ( c_List_Oappend @ SV207 @ ( c_List_Olist_OCons @ SV868 @ ( c_List_Olist_ONil @ SY2718 ) @ SY2718 ) @ SY2718 ) @ ( c_List_Oappend @ SV573 @ ( c_List_Olist_OCons @ SY2716 @ ( c_List_Olist_ONil @ SY2718 ) @ SY2718 ) @ SY2718 ) @ SY2718 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2277,plain,
! [SV869: $i,SV574: $i,SV209: $i] :
( ( ! [SY2719: $i] :
( ( c_List_Olistsp @ SV209 @ ( c_List_Oappend @ SV574 @ SV869 @ SY2719 ) @ SY2719 )
| ~ ( c_List_Olistsp @ SV209 @ SV869 @ SY2719 )
| ~ ( c_List_Olistsp @ SV209 @ SV574 @ SY2719 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(2278,plain,
! [SV870: $i,SV575: $i,SV210: $i] :
( ( ! [SY2720: $i,SY2721: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV210 @ SV575 @ SV870 @ ( c_Lambda_OdB_OAbs @ SY2720 ) @ SY2721 )
= ( hAPP @ ( hAPP @ SV870 @ SY2720 ) @ ( c_Lambda_OdB_OdB__rec @ SV210 @ SV575 @ SV870 @ SY2720 @ SY2721 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2279,plain,
! [SV212: $i] :
( ( ( class_OrderedGroup_Osemigroup__add @ SV212 )
= $false )
| ( ( c_OrderedGroup_Osemigroup__add @ ( c_HOL_Oplus__class_Oplus @ SV212 ) @ SV212 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1937]) ).
thf(2280,plain,
! [SV871: $i,SV578: $i,SV214: $i] :
( ( ! [SY2722: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV214 )
| ( c_HOL_Oord__class_Oless @ SV578 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV214 ) @ SV871 ) @ SY2722 ) @ SV214 )
| ~ ( c_HOL_Oord__class_Oless @ SV578 @ SY2722 @ SV214 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV214 ) @ SV871 @ SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1939]) ).
thf(2281,plain,
! [SV872: $i,SV579: $i,SV215: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV215 ) @ SV579 @ SV872 )
= ( c_Lambda_OdB_OVar @ SV215 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV215 @ SV872 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2282,plain,
! [SV873: $i,SV580: $i,SV216: $i] :
( ( ! [SY2723: $i,SY2724: $i,SY2725: $i] :
( ( c_List_Ofoldr @ SV216 @ ( c_List_Olist_OCons @ SV580 @ SV873 @ SY2723 ) @ SY2724 @ SY2723 @ SY2725 )
= ( hAPP @ ( hAPP @ SV216 @ SV580 ) @ ( c_List_Ofoldr @ SV216 @ SV873 @ SY2724 @ SY2723 @ SY2725 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1941]) ).
thf(2283,plain,
! [SV874: $i,SV581: $i,SV217: $i] :
( ( ! [SY2726: $i,SY2727: $i] :
( ~ ( hBOOL @ ( hAPP @ SV217 @ ( c_Lambda_OdB_OdB__case @ SV581 @ SV874 @ SY2726 @ ( c_Lambda_OdB_OAbs @ SY2727 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV217 @ ( hAPP @ SY2726 @ SY2727 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1942]) ).
thf(2284,plain,
! [SV875: $i,SV582: $i,SV218: $i] :
( ( ! [SY2728: $i,SY2729: $i] :
( ~ ( hBOOL @ ( hAPP @ SV218 @ ( c_Lambda_OdB_OdB__case @ SV582 @ SV875 @ SY2728 @ ( c_Lambda_OdB_OAbs @ SY2729 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV218 @ ( hAPP @ SY2728 @ SY2729 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2285,plain,
! [SV876: $i,SV583: $i,SV219: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV219 @ ( c_Lambda_OdB_OVar @ SV583 ) @ SV876 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(2286,plain,
! [SV877: $i,SV584: $i,SV220: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV220 ) @ ( c_List_Olist_OCons @ SV584 @ SV877 @ SV220 ) @ SV220 )
= ( c_List_Olist_OCons @ SV584 @ SV877 @ SV220 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2287,plain,
! [SV878: $i,SV585: $i,SV221: $i] :
( ( ! [SY2730: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV221 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV221 ) @ SV585 ) @ SV878 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV221 ) @ SY2730 ) @ SV878 ) @ SV221 )
| ~ ( c_HOL_Oord__class_Oless @ SV585 @ SY2730 @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(2288,plain,
! [SV879: $i,SV586: $i,SV222: $i] :
( ( ! [SY2731: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV222 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV222 ) @ SV586 ) @ SV879 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV222 ) @ SY2731 ) @ SV879 ) @ SV222 )
| ~ ( c_HOL_Oord__class_Oless @ SV586 @ SY2731 @ SV222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1947]) ).
thf(2289,plain,
! [SV880: $i,SV587: $i,SV223: $i] :
( ( ! [SY2732: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV223 )
| ( c_HOL_Oord__class_Oless @ SV587 @ SV880 @ SV223 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV223 ) @ SV587 ) @ SY2732 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV223 ) @ SV880 ) @ SY2732 ) @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1948]) ).
thf(2290,plain,
! [SV881: $i,SV588: $i,SV224: $i] :
( ( ! [SY2733: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV224 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV224 ) @ SV588 ) @ SV881 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV224 ) @ SV588 ) @ SY2733 ) @ SV224 )
| ~ ( c_HOL_Oord__class_Oless @ SV881 @ SY2733 @ SV224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1949]) ).
thf(2291,plain,
! [SV882: $i,SV589: $i,SV225: $i] :
( ( ! [SY2734: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV225 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV225 ) @ SV589 ) @ SV882 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV225 ) @ SV589 ) @ SY2734 ) @ SV225 )
| ~ ( c_HOL_Oord__class_Oless @ SV882 @ SY2734 @ SV225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1950]) ).
thf(2292,plain,
! [SV883: $i,SV590: $i,SV226: $i] :
( ( ! [SY2735: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV226 )
| ( c_HOL_Oord__class_Oless @ SV590 @ SV883 @ SV226 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV226 ) @ SY2735 ) @ SV590 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV226 ) @ SY2735 ) @ SV883 ) @ SV226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1951]) ).
thf(2293,plain,
! [SV884: $i,SV591: $i,SV227: $i] :
( ( ! [SY2736: $i,SY2737: $i,SY2738: $i] :
( ( c_ListOrder_Ostep1 @ SV227 @ SV591 @ SV884 @ SY2736 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV227 @ SY2737 ) @ SY2738 ) )
| ~ ( c_ListOrder_Ostep1 @ SV227 @ ( c_List_Olist_OCons @ SY2737 @ SV591 @ SY2736 ) @ ( c_List_Olist_OCons @ SY2738 @ SV884 @ SY2736 ) @ SY2736 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1952]) ).
thf(2294,plain,
! [SV885: $i,SV592: $i,SV228: $i] :
( ( ! [SY2739: $i,SY2740: $i] :
( ( c_ListOrder_Ostep1 @ SV228 @ ( c_List_Olist_OCons @ SV592 @ SV885 @ SY2739 ) @ ( c_List_Olist_OCons @ SV592 @ SY2740 @ SY2739 ) @ SY2739 )
| ~ ( c_ListOrder_Ostep1 @ SV228 @ SV885 @ SY2740 @ SY2739 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1953]) ).
thf(2295,plain,
! [SV886: $i,SV593: $i,SV230: $i] :
( ( ! [SY2741: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV230 @ SV593 @ SV886 ) @ SY2741 @ SV886 )
= ( c_List_Oappend @ SV230 @ ( c_List_Oappend @ SV593 @ SY2741 @ SV886 ) @ SV886 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(2296,plain,
! [SV887: $i,SV594: $i,SV231: $i] :
( ( ! [SY2742: $i] :
( ( c_List_Oappend @ SV231 @ ( c_List_Oappend @ SV594 @ SV887 @ SY2742 ) @ SY2742 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV231 @ SV594 @ SY2742 ) @ SV887 @ SY2742 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1955]) ).
thf(2297,plain,
! [SV888: $i,SV595: $i,SV232: $i] :
( ( ! [SY2743: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV232 @ SV595 @ SV888 ) @ SY2743 @ SV888 )
= ( c_List_Oappend @ SV232 @ ( c_List_Oappend @ SV595 @ SY2743 @ SV888 ) @ SV888 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(2298,plain,
! [SV889: $i,SV596: $i,SV233: $i] :
( ( ! [SY2744: $i] :
( ( c_List_Oappend @ SV233 @ ( c_List_Oappend @ SV596 @ SV889 @ SY2744 ) @ SY2744 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV233 @ SV596 @ SY2744 ) @ SV889 @ SY2744 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2299,plain,
! [SV890: $i,SV597: $i,SV234: $i] :
( ( ~ ( class_Orderings_Oorder @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SV597 @ SV890 @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SV890 @ SV597 @ SV234 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1958]) ).
thf(2300,plain,
! [SV891: $i,SV598: $i,SV235: $i] :
( ( ! [SY2745: $i,SY2746: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV235 @ SV598 ) @ SV891 ) @ SY2745 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV235 @ SV598 ) @ SY2746 ) @ SY2745 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV891 ) @ SY2746 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1959]) ).
thf(2301,plain,
! [SV892: $i,SV599: $i,SV236: $i] :
( ( ! [SY2747: $i,SY2748: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV236 @ SV599 ) @ SV892 ) @ SY2747 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV236 @ SY2748 ) @ SY2747 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV236 @ SV599 ) @ SV892 ) @ SY2748 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1960]) ).
thf(2302,plain,
! [SV893: $i,SV600: $i,SV237: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV237 )
| ~ ( c_HOL_Oord__class_Oless @ SV600 @ SV893 @ SV237 )
| ~ ( c_HOL_Oord__class_Oless @ SV893 @ SV600 @ SV237 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1961]) ).
thf(2303,plain,
! [SV894: $i,SV601: $i,SV238: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV238 )
| ~ ( c_HOL_Oord__class_Oless @ SV601 @ SV894 @ SV238 )
| ~ ( c_HOL_Oord__class_Oless @ SV894 @ SV601 @ SV238 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(2304,plain,
! [SV895: $i,SV602: $i,SV239: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV239 )
| ~ ( c_HOL_Oord__class_Oless @ SV602 @ SV895 @ SV239 )
| ~ ( c_HOL_Oord__class_Oless @ SV895 @ SV602 @ SV239 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1963]) ).
thf(2305,plain,
! [SV896: $i,SV603: $i,SV240: $i] :
( ( ! [SY2749: $i,SY2750: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV240 @ SV603 @ SV896 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SY2749 @ SV603 ) @ SY2750 )
| ~ ( c_Type_Otyping @ SV240 @ SY2749 @ SY2750 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1964]) ).
thf(2306,plain,
! [SV604: $i,SV241: $i] :
( ( ( hBOOL @ ( hAPP @ SV241 @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV241 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV241 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV241 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV241 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ SV241 @ SV604 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1965]) ).
thf(2307,plain,
! [SV897: $i,SV605: $i,SV242: $i] :
( ( ! [SY2751: $i,SY2752: $i] :
( ( ( c_List_Ofoldl @ SV242 @ ( hAPP @ ( hAPP @ SV242 @ SV605 ) @ SV897 ) @ SY2751 @ SY2752 @ SY2752 )
= ( hAPP @ ( hAPP @ SV242 @ SV605 ) @ ( c_List_Ofoldl @ SV242 @ SV897 @ SY2751 @ SY2752 @ SY2752 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV242 @ SY2752 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1966]) ).
thf(2308,plain,
! [SV898: $i,SV607: $i,SV244: $i] :
( ( ! [SY2753: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV244 ) @ SV607 ) @ SV898 @ SY2753 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV244 @ SV898 @ SY2753 ) ) @ ( c_Lambda_Osubst @ SV607 @ SV898 @ SY2753 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(2309,plain,
! [SV899: $i,SV608: $i,SV245: $i] :
( ( ! [SY2754: $i] :
( ( c_Type_Otypings @ SV245 @ SV608 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV899 @ SV245 @ SY2754 @ SV608 ) )
| ~ ( c_Type_Otyping @ SV245 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2754 ) @ SV608 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV899 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1969]) ).
thf(2310,plain,
! [SV900: $i,SV609: $i,SV246: $i] :
( ( ! [SY2755: $i,SY2756: $i] :
( ~ ( hBOOL @ ( hAPP @ SV246 @ ( c_Lambda_OdB_OdB__case @ SV609 @ SV900 @ SY2755 @ ( c_Lambda_OdB_OVar @ SY2756 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV246 @ ( hAPP @ SV609 @ SY2756 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2311,plain,
! [SV901: $i,SV610: $i,SV247: $i] :
( ( ! [SY2757: $i,SY2758: $i] :
( ~ ( hBOOL @ ( hAPP @ SV247 @ ( c_Lambda_OdB_OdB__case @ SV610 @ SV901 @ SY2757 @ ( c_Lambda_OdB_OVar @ SY2758 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV247 @ ( hAPP @ SV610 @ SY2758 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(2312,plain,
! [SV902: $i,SV611: $i,SV248: $i] :
( ( ! [SY2759: $i] :
( ( c_Type_Otyping @ SV248 @ SV611 @ SV902 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY2759 ) @ SV611 ) )
| ~ ( c_Type_Otyping @ SV248 @ SY2759 @ SV902 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1972]) ).
thf(2313,plain,
! [SV903: $i,SV613: $i,SV250: $i] :
( ( ! [SY2760: $i,SY2761: $i,SY2762: $i] :
( ~ ( hBOOL @ ( hAPP @ SV250 @ ( c_Lambda_OdB_OdB__case @ SV613 @ SV903 @ SY2760 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2761 ) @ SY2762 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV250 @ ( hAPP @ ( hAPP @ SV903 @ SY2761 ) @ SY2762 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1974]) ).
thf(2314,plain,
! [SV904: $i,SV614: $i,SV251: $i] :
( ( ! [SY2763: $i,SY2764: $i,SY2765: $i] :
( ~ ( hBOOL @ ( hAPP @ SV251 @ ( c_Lambda_OdB_OdB__case @ SV614 @ SV904 @ SY2763 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2764 ) @ SY2765 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV251 @ ( hAPP @ ( hAPP @ SV904 @ SY2764 ) @ SY2765 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(2315,plain,
! [SV905: $i,SV615: $i,SV252: $i] :
( ( ! [SY2766: $i] :
( ( c_Type_Otypings @ SV252 @ SV615 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV905 @ SV252 @ SY2766 @ SV615 ) )
| ~ ( c_Type_Otyping @ SV252 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2766 @ SV615 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV905 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1976]) ).
thf(2316,plain,
! [SV906: $i,SV616: $i,SV253: $i] :
( ( ! [SY2767: $i,SY2768: $i,SY2769: $i,SY2770: $i] :
( ( SV253
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV616 @ SV253 @ SV906 @ SY2767 ) @ SV616 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV906 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2768 ) @ SY2769 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV253 )
| ~ ( c_Type_Otypings @ SV906 @ SY2769 @ SY2770 )
| ~ ( c_Type_Otyping @ SV906 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2768 ) @ SY2769 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2767 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV616 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1977]) ).
thf(2317,plain,
! [SV907: $i,SV617: $i,SV254: $i] :
( ( ! [SY2771: $i,SY2772: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV254 @ SV617 @ SV907 @ SY2771 ) @ SY2772 )
= ( hAPP @ SV254 @ SY2772 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2772 @ SV617 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1978]) ).
thf(2318,plain,
! [SV908: $i,SV618: $i,SV255: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV255 @ SV618 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV908 @ SV618 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV255 ) @ SV908 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1979]) ).
thf(2319,plain,
! [SV619: $i,SV256: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV256 ) ) @ SV619 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1980]) ).
thf(2320,plain,
! [SV909: $i,SV620: $i,SV257: $i] :
( ( ! [SY2773: $i,SY2774: $i] :
( ( c_Type_Otyping @ SV257 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV620 ) @ SV909 ) @ SY2773 )
| ~ ( c_Type_Otyping @ SV257 @ SV909 @ SY2774 )
| ~ ( c_Type_Otyping @ SV257 @ SV620 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY2774 ) @ SY2773 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1981]) ).
thf(2321,plain,
! [SV621: $i,SV258: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV258 ) @ SV621 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV621 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1982]) ).
thf(2322,plain,
! [SV910: $i,SV622: $i,SV259: $i] :
( ( ! [SY2775: $i,SY2776: $i] :
( ( SV259 = SV622 )
| ~ ( c_Type_Otyping @ SV910 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2775 ) @ SY2776 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV622 )
| ~ ( c_Type_Otyping @ SV910 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2775 ) @ SY2776 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2323,plain,
! [SV911: $i,SV623: $i,SV260: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV260 @ SV623 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV260 @ SV911 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV623 @ SV911 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1984]) ).
thf(2324,plain,
! [SV624: $i,SV261: $i] :
( ( ( hBOOL @ ( hAPP @ SV261 @ SV624 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV261 @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV261 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV261 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV261 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV261 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1985]) ).
thf(2325,plain,
! [SV912: $i,SV625: $i,SV262: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV262 @ SV625 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV912 @ SV625 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV262 ) @ SV912 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1986]) ).
thf(2326,plain,
! [SV913: $i,SV626: $i,SV263: $i] :
( ( ! [SY2777: $i,SY2778: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV263 @ SV626 @ SV913 @ ( c_Lambda_OdB_OVar @ SY2777 ) @ SY2778 )
= ( hAPP @ SV263 @ SY2777 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2327,plain,
! [SV914: $i,SV627: $i,SV264: $i] :
( ( ! [SY2779: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV264 @ SV627 @ SV914 @ SY2779 ) @ SV627 )
= SV914 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1988]) ).
thf(2328,plain,
! [SV915: $i,SV628: $i,SV265: $i] :
( ( ! [SY2780: $i] :
( ( c_List_Ofoldl @ SV265 @ SV628 @ ( c_List_Olist_ONil @ SV915 ) @ SY2780 @ SV915 )
= SV628 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1989]) ).
thf(2329,plain,
! [SV916: $i,SV629: $i,SV266: $i] :
( ( ! [SY2781: $i] :
( ( c_Type_Otyping @ SV266 @ ( c_Lambda_OdB_OAbs @ SV629 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV916 ) @ SY2781 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV266 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV916 @ tc_Type_Otype ) @ SV629 @ SY2781 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1990]) ).
thf(2330,plain,
! [SV917: $i,SV630: $i,SV268: $i] :
( ( ( ( hAPP @ SV268 @ SV630 )
= SV917 )
| ~ ( c_Type_Otyping @ SV268 @ ( c_Lambda_OdB_OVar @ SV630 ) @ SV917 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1991]) ).
thf(2331,plain,
! [SV918: $i,SV631: $i,SV269: $i] :
( ( ! [SY2782: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ SV269 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV269 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV269 ) @ SV631 ) @ SV918 ) @ SY2782 @ SV269 @ SV269 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV269 ) @ SV631 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV269 ) @ SV918 @ SY2782 @ SV269 @ SV269 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(2332,plain,
! [SV919: $i,SV632: $i,SV270: $i] :
( ( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV270 ) @ SV632 ) @ SV919 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV270 @ SV919 ) ) @ ( c_Lambda_Olift @ SV632 @ SV919 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1993]) ).
thf(2333,plain,
! [SV920: $i,SV633: $i,SV271: $i] :
( ( ! [SY2783: $i] :
( ( c_Type_Otyping @ SV271 @ SV633 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV920 @ SV271 @ SV633 @ SY2783 ) @ SV920 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV271 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV633 @ SY2783 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV920 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1994]) ).
thf(2334,plain,
! [SV921: $i,SV634: $i,SV272: $i] :
( ( ! [SY2784: $i] :
( ( c_Type_Otyping @ SV272 @ ( c_Lambda_OdB_OVar @ SV634 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV921 @ SV272 @ SV634 @ SY2784 ) @ SV921 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV272 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV634 ) @ SY2784 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV921 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1995]) ).
thf(2335,plain,
! [SV922: $i,SV635: $i,SV273: $i] :
( ( ! [SY2785: $i,SY2786: $i] :
( ( c_Type_Otyping @ SV273 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV635 @ SV922 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2785 )
| ~ ( c_Type_Otypings @ SV273 @ SV922 @ SY2786 )
| ~ ( c_Type_Otyping @ SV273 @ SV635 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY2786 @ SY2785 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2336,plain,
! [SV923: $i,SV636: $i,SV274: $i] :
( ( ( SV274
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV636 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV636 @ SV923 @ SV274 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV636 ) @ SV923 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1997]) ).
thf(2337,plain,
! [SV924: $i,SV637: $i,SV275: $i] :
( ( ! [SY2787: $i,SY2788: $i,SY2789: $i] :
( ( c_Lambda_OdB_OdB__case @ SV275 @ SV637 @ SV924 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2787 ) @ SY2788 ) @ SY2789 )
= ( hAPP @ ( hAPP @ SV637 @ SY2787 ) @ SY2788 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1998]) ).
thf(2338,plain,
! [SV925: $i,SV638: $i,SV276: $i] :
( ( ! [SY2790: $i,SY2791: $i] :
( ( ( hAPP @ ( hAPP @ SV276 @ SV638 ) @ ( c_List_Ofoldl @ SV276 @ SV925 @ SY2790 @ SY2791 @ SY2791 ) )
= ( c_List_Ofoldl @ SV276 @ SV638 @ SY2790 @ SY2791 @ SY2791 ) )
| ~ ( c_OrderedGroup_Omonoid__add @ SV925 @ SV276 @ SY2791 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1999]) ).
thf(2339,plain,
! [SV926: $i,SV639: $i,SV277: $i] :
( ( ! [SY2792: $i] :
( ( c_Type_Otyping @ SV277 @ SV639 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV926 @ SV277 @ SY2792 @ SV639 ) )
| ~ ( c_Type_Otyping @ SV277 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2792 ) @ SV639 ) @ SV926 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2000]) ).
thf(2340,plain,
! [SV927: $i,SV640: $i,SV279: $i] :
( ( ! [SY2793: $i,SY2794: $i] :
( ( c_Lambda_OdB_OdB__case @ SV279 @ SV640 @ SV927 @ ( c_Lambda_OdB_OVar @ SY2793 ) @ SY2794 )
= ( hAPP @ SV279 @ SY2793 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2001]) ).
thf(2341,plain,
! [SV928: $i,SV641: $i,SV280: $i] :
( ( ! [SY2795: $i] :
( ( c_Type_Otypings @ SV280 @ SV641 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV928 @ SV280 @ SY2795 @ SV641 ) )
| ~ ( c_Type_Otyping @ SV280 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2795 @ SV641 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV928 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2002]) ).
thf(2342,plain,
! [SV929: $i,SV642: $i,SV281: $i] :
( ( ! [SY2796: $i,SY2797: $i,SY2798: $i] :
( ( c_List_Ofoldl @ SV281 @ SV642 @ ( c_List_Olist_OCons @ SV929 @ SY2796 @ SY2797 ) @ SY2798 @ SY2797 )
= ( c_List_Ofoldl @ SV281 @ ( hAPP @ ( hAPP @ SV281 @ SV642 ) @ SV929 ) @ SY2796 @ SY2798 @ SY2797 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(2343,plain,
! [SV930: $i,SV644: $i,SV284: $i] :
( ( ! [SY2799: $i,SY2800: $i,SY2801: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV284 @ SV644 @ SV930 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2799 ) @ SY2800 ) @ SY2801 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV644 @ SY2799 ) @ SY2800 ) @ ( c_Lambda_OdB_OdB__rec @ SV284 @ SV644 @ SV930 @ SY2799 @ SY2801 ) ) @ ( c_Lambda_OdB_OdB__rec @ SV284 @ SV644 @ SV930 @ SY2800 @ SY2801 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2005]) ).
thf(2344,plain,
! [SV931: $i,SV645: $i,SV286: $i] :
( ( ! [SY2802: $i,SY2803: $i,SY2804: $i,SY2805: $i] :
( ( c_Type_Otypings @ SV286 @ SV645 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV931 @ SY2802 @ SV286 @ SV645 ) )
| ~ ( c_Type_Otyping @ SV286 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2803 ) @ SY2804 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2802 )
| ~ ( c_Type_Otypings @ SV286 @ SY2804 @ SY2805 )
| ~ ( c_Type_Otyping @ SV286 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2803 ) @ SY2804 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV645 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV931 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2006]) ).
thf(2345,plain,
! [SV932: $i,SV646: $i,SV287: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV287 ) @ SV646 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV287 ) @ SV932 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV646 ) @ SV932 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2007]) ).
thf(2346,plain,
! [SV933: $i,SV647: $i,SV288: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV288 ) @ SV647 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV933 ) @ SV647 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV288 ) @ SV933 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2347,plain,
! [SV934: $i,SV648: $i,SV289: $i] :
( ( ! [SY2806: $i] :
( ( c_Lambda_Oliftn @ SV289 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV648 ) @ SV934 ) @ SY2806 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ SV289 @ SV648 @ SY2806 ) ) @ ( c_Lambda_Oliftn @ SV289 @ SV934 @ SY2806 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2009]) ).
thf(2348,plain,
! [SV935: $i,SV649: $i,SV291: $i] :
( ( ! [SY2807: $i] :
( ( c_Type_Otyping @ SV291 @ SV649 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV935 @ SV291 @ SV649 @ SY2807 ) @ SV935 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV291 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV649 @ SY2807 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV935 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2010]) ).
thf(2349,plain,
! [SV650: $i,SV292: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV292 ) @ ( c_Lambda_OdB_OVar @ SV650 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV292 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2011]) ).
thf(2350,plain,
! [SV936: $i,SV651: $i,SV293: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV293 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV651 @ SV293 @ SV936 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV651 ) @ SV293 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV936 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2012]) ).
thf(2351,plain,
! [SV937: $i,SV652: $i,SV294: $i] :
( ( ! [SY2808: $i,SY2809: $i,SY2810: $i] :
( ~ ( c_Type_Otyping @ SV294 @ SV652 @ SV937 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV294 @ SY2808 @ SV937 @ tc_Type_Otype ) @ SY2809 @ SY2810 )
| ( c_Type_Otyping @ SV294 @ ( c_Lambda_Osubst @ SY2809 @ SV652 @ SY2808 ) @ SY2810 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2013]) ).
thf(2352,plain,
! [SV938: $i,SV653: $i,SV295: $i] :
( ( ! [SY2811: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV295 ) @ SV653 ) @ SV938 @ SY2811 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ SV295 @ SV938 @ SY2811 ) ) @ ( c_Lambda_Osubstn @ SV653 @ SV938 @ SY2811 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2353,plain,
! [SV939: $i,SV654: $i,SV296: $i] :
( ( ! [SY2812: $i,SY2813: $i,SY2814: $i] :
( ( c_List_Ofoldl @ SV296 @ SV654 @ ( c_List_Oappend @ SV939 @ SY2812 @ SY2813 ) @ SY2814 @ SY2813 )
= ( c_List_Ofoldl @ SV296 @ ( c_List_Ofoldl @ SV296 @ SV654 @ SV939 @ SY2814 @ SY2813 ) @ SY2812 @ SY2814 @ SY2813 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2015]) ).
thf(2354,plain,
! [SV940: $i,SV655: $i,SV297: $i] :
( ( ! [SY2815: $i] :
( ( c_Type_Otyping @ SV297 @ SV655 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV940 @ SV297 @ SV655 @ SY2815 ) ) @ SV940 ) )
| ~ ( c_Type_Otyping @ SV297 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV655 ) @ SY2815 ) @ SV940 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2016]) ).
thf(2355,plain,
! [SV656: $i,SV298: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV298 @ SV656 ) )
= $true )
| ( ( ~ ( class_Orderings_Opreorder @ SV656 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2017]) ).
thf(2356,plain,
! [SV657: $i,SV299: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV299 @ SV657 ) )
= $true )
| ( ( ~ ( class_Orderings_Oorder @ SV657 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2018]) ).
thf(2357,plain,
! [SV941: $i,SV659: $i,SV301: $i] :
( ( ( SV301 = SV659 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV941 ) @ SV301 ) @ SV659 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2020]) ).
thf(2358,plain,
! [SV942: $i,SV660: $i,SV302: $i] :
( ( ( ( c_List_Orev @ SV302 @ SV660 )
!= ( c_List_Orev @ SV942 @ SV660 ) )
| ( SV302 = SV942 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2021]) ).
thf(2359,plain,
! [SV943: $i,SV661: $i,SV303: $i] :
( ( ( ( c_List_Oappend @ SV303 @ SV661 @ SV943 )
!= ( c_List_Olist_ONil @ SV943 ) )
| ( SV303
= ( c_List_Olist_ONil @ SV943 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2022]) ).
thf(2360,plain,
! [SV944: $i,SV662: $i,SV304: $i] :
( ( ! [SY2816: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV304 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV304 ) @ SV662 ) @ SV944 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV304 ) @ SV662 ) @ SY2816 ) )
| ( SV944 = SY2816 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2361,plain,
! [SV945: $i,SV663: $i,SV305: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV305 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV663 @ SV945 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV305 )
= SV663 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(2362,plain,
! [SV664: $i,SV306: $i] :
( ( ( SV306
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV306 ) @ SV664 ) )
= $true )
| ( ( SV664
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2025]) ).
thf(2363,plain,
! [SV946: $i,SV665: $i,SV307: $i] :
( ( ( ( c_List_Oreplicate @ SV307 @ SV665 @ SV946 )
!= ( c_List_Olist_ONil @ SV946 ) )
| ( SV307
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2026]) ).
thf(2364,plain,
! [SV947: $i,SV666: $i,SV308: $i] :
( ( ! [SY2817: $i,SY2818: $i] :
( ( ( c_List_Oreplicate @ SV308 @ SV666 @ SV947 )
!= ( c_List_Oreplicate @ SY2817 @ SY2818 @ SV947 ) )
| ( SV666 = SY2818 )
| ( SV308
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2027]) ).
thf(2365,plain,
! [SV948: $i,SV667: $i,SV309: $i] :
( ( ! [SY2819: $i,SY2820: $i] :
( ( ( c_List_Oappend @ SV309 @ SV667 @ SV948 )
!= ( c_List_Olist_OCons @ SY2819 @ SY2820 @ SV948 ) )
| ( SV309
= ( c_List_Olist_OCons @ SY2819 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY2819 @ SY2820 @ SV309 @ SV667 @ SV948 ) @ SV948 ) )
| ( SV309
= ( c_List_Olist_ONil @ SV948 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2366,plain,
! [SV949: $i,SV668: $i,SV310: $i] :
( ( ! [SY2821: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV310 ) @ SV668 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV949 ) @ SY2821 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV949 @ SV668 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV310 @ SY2821 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2367,plain,
! [SV950: $i,SV669: $i,SV311: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV311 ) @ SV669 )
!= ( c_Lambda_OdB_OVar @ SV950 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2030]) ).
thf(2368,plain,
! [SV951: $i,SV670: $i,SV312: $i] :
( ( ( ( c_List_Oappend @ SV312 @ SV670 @ SV951 )
!= ( c_List_Olist_ONil @ SV951 ) )
| ( SV670
= ( c_List_Olist_ONil @ SV951 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2031]) ).
thf(2369,plain,
! [SV952: $i,SV671: $i,SV313: $i] :
( ( ( c_List_Olist_ONil @ SV313 )
!= ( c_List_Olist_OCons @ SV671 @ SV952 @ SV313 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2032]) ).
thf(2370,plain,
! [SV953: $i,SV672: $i,SV314: $i] :
( ( ! [SY2822: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV314 ) @ SV672 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV953 @ SY2822 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2822
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV314 @ SV672 @ SV953 @ SY2822 ) @ ( c_List_Olist_OCons @ SV672 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( SY2822
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2033]) ).
thf(2371,plain,
! [SV954: $i,SV673: $i,SV315: $i] :
( ( ( SV315
!= ( c_List_Oappend @ SV673 @ SV315 @ SV954 ) )
| ( SV673
= ( c_List_Olist_ONil @ SV954 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2034]) ).
thf(2372,plain,
! [SV955: $i,SV674: $i,SV316: $i] :
( ( ! [SY2823: $i,SY2824: $i] :
( ( ( c_List_Olist_OCons @ SV316 @ SV674 @ SV955 )
!= ( c_List_Oappend @ SY2823 @ SY2824 @ SV955 ) )
| ( SV674
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV316 @ SV674 @ SY2823 @ SY2824 @ SV955 ) @ SY2824 @ SV955 ) )
| ( ( c_List_Olist_OCons @ SV316 @ SV674 @ SV955 )
= SY2824 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2373,plain,
! [SV675: $i,SV317: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV317 ) @ SV675 )
!= SV317 )
= $true )
| ( ( SV675
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2036]) ).
thf(2374,plain,
! [SV956: $i,SV676: $i,SV318: $i] :
( ( ( c_List_Olist_OCons @ SV318 @ SV676 @ SV956 )
!= SV676 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2037]) ).
thf(2375,plain,
! [SV957: $i,SV677: $i,SV319: $i] :
( ( ( SV319
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV319 ) @ SV677 ) @ SV957 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV319 ) @ SV677 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV319 ) @ SV677 ) @ ( c_List_Oappend @ SV957 @ ( c_List_Olist_OCons @ SV677 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2038]) ).
thf(2376,plain,
! [SV958: $i,SV678: $i,SV320: $i] :
( ( ! [SY2825: $i,SY2826: $i] :
( ( ( c_List_Olist_OCons @ SV320 @ SV678 @ SV958 )
!= ( c_List_Olist_OCons @ SY2825 @ SY2826 @ SV958 ) )
| ( SV320 = SY2825 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2039]) ).
thf(2377,plain,
! [SV959: $i,SV679: $i,SV321: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV321 ) @ SV679 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV321 ) @ SV959 ) )
| ( SV679 = SV959 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2040]) ).
thf(2378,plain,
! [SV960: $i,SV680: $i,SV322: $i] :
( ( ! [SY2827: $i] :
( ( ( c_List_Oappend @ SV322 @ SV680 @ SV960 )
!= ( c_List_Oappend @ SY2827 @ SV680 @ SV960 ) )
| ( SV322 = SY2827 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(2379,plain,
! [SV961: $i,SV681: $i,SV323: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV323 ) @ SV681 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV323 ) @ SV961 ) )
| ( SV681 = SV961 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2042]) ).
thf(2380,plain,
! [SV962: $i,SV682: $i,SV324: $i] :
( ( ( c_List_Olist_OCons @ SV324 @ SV682 @ SV962 )
!= ( c_List_Olist_ONil @ SV962 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2043]) ).
thf(2381,plain,
! [SV963: $i,SV683: $i,SV325: $i] :
( ( ! [SY2828: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV325 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV325 ) @ SV683 ) @ SV963 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV325 ) @ SY2828 ) @ SV963 ) )
| ( SV683 = SY2828 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2382,plain,
! [SV964: $i,SV684: $i,SV326: $i] :
( ( ( SV326
!= ( c_List_Oappend @ SV326 @ SV684 @ SV964 ) )
| ( SV684
= ( c_List_Olist_ONil @ SV964 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2045]) ).
thf(2383,plain,
! [SV965: $i,SV685: $i,SV327: $i] :
( ( ! [SY2829: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV327 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SV685 ) @ SV965 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SV685 ) @ SY2829 ) )
| ( SV965 = SY2829 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2046]) ).
thf(2384,plain,
! [SV966: $i,SV686: $i,SV328: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV328 ) @ SV686 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV966 ) @ SV686 ) )
| ( SV328 = SV966 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2047]) ).
thf(2385,plain,
! [SV967: $i,SV687: $i,SV329: $i] :
( ( ! [SY2830: $i,SY2831: $i,SY2832: $i,SY2833: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV329 ) @ SV687 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV967 @ SY2830 @ SY2831 ) ) )
| ~ ( c_Type_Otyping @ SY2832 @ SY2830 @ SV687 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY2830 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY2832 @ SY2831 @ SV687 @ tc_Type_Otype ) @ SV967 @ SY2833 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV967 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2048]) ).
thf(2386,plain,
! [SV688: $i,SV330: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV330 )
= ( c_Lambda_OdB_OVar @ SV688 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2049]) ).
thf(2387,plain,
! [SV689: $i,SV331: $i] :
( ( ( ( c_List_Orev @ SV331 @ SV689 )
!= ( c_List_Olist_ONil @ SV689 ) )
= $true )
| ( ( SV331
= ( c_List_Olist_ONil @ SV689 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2050]) ).
thf(2388,plain,
! [SV968: $i,SV690: $i,SV332: $i] :
( ( ! [SY2834: $i,SY2835: $i] :
( ( ( c_List_Oreplicate @ SV332 @ SV690 @ SV968 )
!= ( c_List_Oreplicate @ SY2834 @ SY2835 @ SV968 ) )
| ( SV332 = SY2834 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2051]) ).
thf(2389,plain,
! [SV691: $i,SV333: $i] :
( ( ( c_Lambda_OdB_OVar @ SV333 )
= ( c_Lambda_OdB_OAbs @ SV691 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2052]) ).
thf(2390,plain,
! [SV969: $i,SV692: $i,SV334: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV334 @ SV692 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV969 ) )
| ( SV334
= ( c_Lambda_OdB_OAbs @ SV969 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2053]) ).
thf(2391,plain,
! [SV970: $i,SV693: $i,SV335: $i] :
( ( ( c_Lambda_OdB_OVar @ SV335 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV693 ) @ SV970 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2054]) ).
thf(2392,plain,
! [SV971: $i,SV694: $i,SV336: $i] :
( ( ( ( c_List_Orev @ SV336 @ SV694 )
!= ( c_List_Olist_OCons @ SV971 @ ( c_List_Olist_ONil @ SV694 ) @ SV694 ) )
| ( SV336
= ( c_List_Olist_OCons @ SV971 @ ( c_List_Olist_ONil @ SV694 ) @ SV694 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2055]) ).
thf(2393,plain,
! [SV972: $i,SV695: $i,SV337: $i] :
( ( SV337
!= ( c_List_Olist_OCons @ SV695 @ SV337 @ SV972 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2056]) ).
thf(2394,plain,
! [SV973: $i,SV696: $i,SV338: $i] :
( ( ! [SY2836: $i,SY2837: $i] :
( ( ( c_List_Oappend @ SV338 @ SV696 @ SV973 )
!= ( c_List_Olist_OCons @ SY2836 @ SY2837 @ SV973 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY2836 @ SY2837 @ SV338 @ SV696 @ SV973 ) @ SV696 @ SV973 )
= SY2837 )
| ( SV338
= ( c_List_Olist_ONil @ SV973 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2057]) ).
thf(2395,plain,
! [SV974: $i,SV697: $i,SV339: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV339 )
| ~ ( class_Int_Onumber__ring @ SV339 )
| ( SV697
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV339 ) @ SV697 ) @ SV974 ) )
| ( SV974
= ( c_HOL_Ozero__class_Ozero @ SV339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2058]) ).
thf(2396,plain,
! [SV975: $i,SV698: $i,SV340: $i] :
( ( ! [SY2838: $i] :
( ( ( c_List_Oappend @ SV340 @ SV698 @ SV975 )
!= ( c_List_Oappend @ SV340 @ SY2838 @ SV975 ) )
| ( SV698 = SY2838 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2059]) ).
thf(2397,plain,
! [SV976: $i,SV699: $i,SV341: $i] :
( ( ! [SY2839: $i,SY2840: $i] :
( ( ( c_List_Olist_OCons @ SV341 @ SV699 @ SV976 )
!= ( c_List_Oappend @ SY2839 @ SY2840 @ SV976 ) )
| ( SV699
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV341 @ SV699 @ SY2839 @ SY2840 @ SV976 ) @ SY2840 @ SV976 ) )
| ( SY2839
= ( c_List_Olist_ONil @ SV976 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2398,plain,
! [SV977: $i,SV700: $i,SV342: $i] :
( ( ! [SY2841: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV342 ) @ SV700 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV977 ) @ SY2841 ) )
| ( SV700 = SY2841 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2399,plain,
! [SV701: $i,SV343: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV343 )
!= ( c_Lambda_OdB_OAbs @ SV701 ) )
= $true )
| ( ( SV343 = SV701 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2062]) ).
thf(2400,plain,
! [SV978: $i,SV702: $i,SV344: $i] :
( ( ! [SY2842: $i,SY2843: $i] :
( ( ( c_List_Oappend @ SV344 @ SV702 @ SV978 )
!= ( c_List_Olist_OCons @ SY2842 @ SY2843 @ SV978 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY2842 @ SY2843 @ SV344 @ SV702 @ SV978 ) @ SV702 @ SV978 )
= SY2843 )
| ( SV702
= ( c_List_Olist_OCons @ SY2842 @ SY2843 @ SV978 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2063]) ).
thf(2401,plain,
! [SV703: $i,SV345: $i] :
( ( ( ( c_List_Orotate1 @ SV345 @ SV703 )
!= ( c_List_Olist_ONil @ SV703 ) )
= $true )
| ( ( SV345
= ( c_List_Olist_ONil @ SV703 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2064]) ).
thf(2402,plain,
! [SV979: $i,SV704: $i,SV346: $i] :
( ( ! [SY2844: $i,SY2845: $i] :
( ( ( c_List_Olist_OCons @ SV346 @ SV704 @ SV979 )
!= ( c_List_Oappend @ SY2844 @ SY2845 @ SV979 ) )
| ( ( c_List_Olist_OCons @ SV346 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV346 @ SV704 @ SY2844 @ SY2845 @ SV979 ) @ SV979 )
= SY2844 )
| ( SY2844
= ( c_List_Olist_ONil @ SV979 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2065]) ).
thf(2403,plain,
! [SV980: $i,SV705: $i,SV347: $i] :
( ( ( ( c_List_Olist_ONil @ SV347 )
!= ( c_List_Oreplicate @ SV705 @ SV980 @ SV347 ) )
| ( SV705
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(2404,plain,
! [SV981: $i,SV706: $i,SV348: $i] :
( ( ! [SY2846: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV348 ) @ SV706 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV981 ) @ SY2846 ) )
| ( SV706 = SY2846 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2067]) ).
thf(2405,plain,
! [SV982: $i,SV707: $i,SV349: $i] :
( ( ~ ( class_Nat_Osemiring__char__0 @ SV349 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV707 @ SV349 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV982 @ SV349 ) )
| ( SV707 = SV982 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2068]) ).
thf(2406,plain,
! [SV983: $i,SV708: $i,SV350: $i] :
( ( ! [SY2847: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV350 ) @ SV708 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV983 @ SY2847 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV350
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV983 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV350 @ SV708 @ SV983 @ SY2847 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2847
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(2407,plain,
! [SV984: $i,SV709: $i,SV351: $i] :
( ( ! [SY2848: $i,SY2849: $i] :
( ( ( c_List_Oappend @ SV351 @ ( c_List_Olist_OCons @ SV709 @ ( c_List_Olist_ONil @ SV984 ) @ SV984 ) @ SV984 )
!= ( c_List_Oappend @ SY2848 @ ( c_List_Olist_OCons @ SY2849 @ ( c_List_Olist_ONil @ SV984 ) @ SV984 ) @ SV984 ) )
| ( SV709 = SY2849 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2070]) ).
thf(2408,plain,
! [SV985: $i,SV710: $i,SV352: $i] :
( ( ! [SY2850: $i,SY2851: $i] :
( ( ( c_List_Olist_OCons @ SV352 @ SV710 @ SV985 )
!= ( c_List_Olist_OCons @ SY2850 @ SY2851 @ SV985 ) )
| ( SV710 = SY2851 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2071]) ).
thf(2409,plain,
! [SV986: $i,SV711: $i,SV353: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV353 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV711 @ SV986 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV986
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2072]) ).
thf(2410,plain,
! [SV987: $i,SV712: $i,SV354: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV354 @ SV712 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV987 ) )
| ( SV712
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2073]) ).
thf(2411,plain,
! [SV988: $i,SV713: $i,SV355: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV355 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV713 @ SV988 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV355 )
= SV713 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2074]) ).
thf(2412,plain,
! [SV989: $i,SV714: $i,SV356: $i] :
( ( ( ( c_List_Olist_OCons @ SV356 @ ( c_List_Olist_ONil @ SV714 ) @ SV714 )
!= ( c_List_Orev @ SV989 @ SV714 ) )
| ( SV989
= ( c_List_Olist_OCons @ SV356 @ ( c_List_Olist_ONil @ SV714 ) @ SV714 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2413,plain,
! [SV715: $i,SV357: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV357 ) @ SV715 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV357
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2076]) ).
thf(2414,plain,
! [SV990: $i,SV716: $i,SV358: $i] :
( ( ! [SY2852: $i,SY2853: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV358 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV716 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV990 ) @ SY2852 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV990 ) @ SY2853 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV716 ) @ SY2852 )
= SY2853 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2077]) ).
thf(2415,plain,
! [SV991: $i,SV717: $i,SV359: $i] :
( ( ! [SY2854: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV359 ) @ SV717 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV991 ) @ SY2854 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV359 = SV991 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2078]) ).
thf(2416,plain,
! [SV718: $i,SV360: $i] :
( ( ( ( c_List_Olist_ONil @ SV360 )
!= ( c_List_Orev @ SV718 @ SV360 ) )
= $true )
| ( ( SV718
= ( c_List_Olist_ONil @ SV360 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2079]) ).
thf(2417,plain,
! [SV992: $i,SV719: $i,SV361: $i] :
( ( ! [SY2855: $i,SY2856: $i] :
( ( ( c_List_Olist_OCons @ SV361 @ SV719 @ SV992 )
!= ( c_List_Oappend @ SY2855 @ SY2856 @ SV992 ) )
| ( ( c_List_Olist_OCons @ SV361 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV361 @ SV719 @ SY2855 @ SY2856 @ SV992 ) @ SV992 )
= SY2855 )
| ( ( c_List_Olist_OCons @ SV361 @ SV719 @ SV992 )
= SY2856 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2080]) ).
thf(2418,plain,
! [SV993: $i,SV720: $i,SV362: $i] :
( ( ! [SY2857: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV362 ) @ SV720 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV993 ) @ SY2857 ) )
| ( SV362 = SV993 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2081]) ).
thf(2419,plain,
! [SV994: $i,SV721: $i,SV363: $i] :
( ( ! [SY2858: $i] :
( ( ( c_List_Orev @ SV363 @ SV721 )
!= ( c_List_Olist_OCons @ SV994 @ SY2858 @ SV721 ) )
| ( SV363
= ( c_List_Oappend @ ( c_List_Orev @ SY2858 @ SV721 ) @ ( c_List_Olist_OCons @ SV994 @ ( c_List_Olist_ONil @ SV721 ) @ SV721 ) @ SV721 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2082]) ).
thf(2420,plain,
! [SV995: $i,SV722: $i,SV364: $i] :
( ( ( ( c_List_Oappend @ SV364 @ SV722 @ SV995 )
!= SV722 )
| ( SV364
= ( c_List_Olist_ONil @ SV995 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2083]) ).
thf(2421,plain,
! [SV723: $i,SV365: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV365 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV365 ) @ SV723 ) @ SV723 )
!= ( c_HOL_Ozero__class_Ozero @ SV365 ) )
| ( SV723
= ( c_HOL_Ozero__class_Ozero @ SV365 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2084]) ).
thf(2422,plain,
! [SV996: $i,SV724: $i,SV366: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV366 ) @ SV724 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV996 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV366 ) @ SV724 )
= SV996 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2085]) ).
thf(2423,plain,
! [SV997: $i,SV725: $i,SV367: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV367 ) @ SV725 )
!= ( c_Lambda_OdB_OAbs @ SV997 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2086]) ).
thf(2424,plain,
! [SV998: $i,SV726: $i,SV368: $i] :
( ( ! [SY2859: $i,SY2860: $i] :
( ( ( c_List_Oappend @ SV368 @ SV726 @ SV998 )
!= ( c_List_Olist_OCons @ SY2859 @ SY2860 @ SV998 ) )
| ( SV368
= ( c_List_Olist_OCons @ SY2859 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY2859 @ SY2860 @ SV368 @ SV726 @ SV998 ) @ SV998 ) )
| ( SV726
= ( c_List_Olist_OCons @ SY2859 @ SY2860 @ SV998 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2087]) ).
thf(2425,plain,
! [SV727: $i,SV369: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV369 ) @ SV727 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV727
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2088]) ).
thf(2426,plain,
! [SV999: $i,SV728: $i,SV370: $i] :
( ( ! [SY2861: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV370 ) @ SV728 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV999 ) @ SY2861 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV370 = SV999 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2089]) ).
thf(2427,plain,
! [SV1000: $i,SV729: $i,SV371: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV371 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV729 @ SV1000 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1000
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2090]) ).
thf(2428,plain,
! [SV1001: $i,SV730: $i,SV372: $i] :
( ( ( ( c_List_Olist_ONil @ SV372 )
!= ( c_List_Oappend @ SV730 @ SV1001 @ SV372 ) )
| ( SV730
= ( c_List_Olist_ONil @ SV372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2091]) ).
thf(2429,plain,
! [SV1002: $i,SV731: $i,SV373: $i] :
( ( ( ( c_List_Oappend @ SV373 @ SV731 @ SV1002 )
!= SV373 )
| ( SV731
= ( c_List_Olist_ONil @ SV1002 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2092]) ).
thf(2430,plain,
! [SV1003: $i,SV732: $i,SV374: $i] :
( ( ! [SY2862: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV374 ) @ SV732 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1003 ) @ SY2862 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2093]) ).
thf(2431,plain,
! [SV733: $i,SV375: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV375 )
!= ( c_Lambda_OdB_OVar @ SV733 ) )
= $true )
| ( ( SV375 = SV733 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2094]) ).
thf(2432,plain,
! [SV1004: $i,SV734: $i,SV376: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV376 @ SV734 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1004 @ SV734 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV376 = SV1004 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2095]) ).
thf(2433,plain,
! [SV1005: $i,SV735: $i,SV377: $i] :
( ( ! [SY2863: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV377 ) @ SV735 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1005 ) @ SY2863 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV735 = SY2863 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2096]) ).
thf(2434,plain,
! [SV1006: $i,SV736: $i,SV378: $i] :
( ( ! [SY2864: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV378 )
| ~ ( class_Int_Onumber__ring @ SV378 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV378 ) @ SV736 ) @ SV1006 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV378 ) @ SV736 ) @ SY2864 ) )
| ( SV1006 = SY2864 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2097]) ).
thf(2435,plain,
! [SV1007: $i,SV737: $i,SV379: $i] :
( ( ( c_List_Olist_OCons @ SV379 @ SV737 @ SV1007 )
!= ( c_List_Olist_ONil @ SV1007 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2098]) ).
thf(2436,plain,
! [SV1008: $i,SV738: $i,SV380: $i] :
( ( ! [SY2865: $i,SY2866: $i,SY2867: $i,SY2868: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV380 ) @ SV738 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV1008 @ SY2865 @ SY2866 ) ) )
| ~ ( c_Type_Otyping @ SY2867 @ SY2865 @ SV380 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY2865 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY2867 @ SY2866 @ SV380 @ tc_Type_Otype ) @ SV1008 @ SY2868 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1008 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2099]) ).
thf(2437,plain,
! [SV1009: $i,SV739: $i,SV381: $i] :
( ( ( ( c_List_Olist_ONil @ SV381 )
!= ( c_List_Oappend @ SV739 @ SV1009 @ SV381 ) )
| ( SV1009
= ( c_List_Olist_ONil @ SV381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2100]) ).
thf(2438,plain,
! [SV1010: $i,SV740: $i,SV382: $i] :
( ( ! [SY2869: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV382 ) @ SV740 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1010 ) @ SY2869 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV740 = SY2869 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2101]) ).
thf(2439,plain,
! [SV1011: $i,SV741: $i,SV383: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV383 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV741 ) @ SV1011 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2102]) ).
thf(2440,plain,
! [SV1012: $i,SV742: $i,SV384: $i] :
( ( ! [SY2870: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV384 ) ) @ SV742 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1012 ) @ SY2870 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2103]) ).
thf(2441,plain,
! [SV743: $i,SV385: $i] :
( ( ( ( c_Nat_Osize__class_Osize @ SV385 @ ( tc_List_Olist @ SV743 ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV385
= ( c_List_Olist_ONil @ SV743 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2104]) ).
thf(2442,plain,
! [SV1013: $i,SV744: $i,SV386: $i] :
( ( ! [SY2871: $i,SY2872: $i] :
( ( ( c_List_Oappend @ SV386 @ ( c_List_Olist_OCons @ SV744 @ ( c_List_Olist_ONil @ SV1013 ) @ SV1013 ) @ SV1013 )
!= ( c_List_Oappend @ SY2871 @ ( c_List_Olist_OCons @ SY2872 @ ( c_List_Olist_ONil @ SV1013 ) @ SV1013 ) @ SV1013 ) )
| ( SV386 = SY2871 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2105]) ).
thf(2443,plain,
! [SV1014: $i,SV745: $i,SV387: $i] :
( ( ! [SY2873: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV387 ) @ SV745 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1014 ) @ SY2873 ) )
| ( SV387 = SV1014 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2106]) ).
thf(2444,plain,
! [SV388: $i,SV1: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV1 )
= $false )
| ( ( ( c_List_Olistsum @ SV388 @ SV1 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV1 ) @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SV388 @ SV1 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2107]) ).
thf(2445,plain,
! [SV1015: $i,SV746: $i,SV390: $i,SV3: $i] :
( ( ( c_Type_Otyping @ SV3 @ SV390 @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ SV746 @ SV3 @ SV390 @ SV1015 ) )
| ~ ( c_Type_Otypings @ SV3 @ ( c_List_Oappend @ SV1015 @ ( c_List_Olist_OCons @ SV390 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SV746 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2109]) ).
thf(2446,plain,
! [SV749: $i,SV393: $i,SV10: $i] :
( ( ( ( c_List_Olast @ ( c_List_Oreplicate @ SV10 @ SV393 @ SV749 ) @ SV749 )
= SV393 )
= $true )
| ( ( SV10
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2112]) ).
thf(2447,plain,
! [SV1016: $i,SV750: $i,SV394: $i,SV11: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV11 @ SV394 @ SV394 ) @ SV394 ) @ SV750 ) @ SV1016 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV11 @ SV394 ) @ SV1016 ) @ SV750 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2113]) ).
thf(2448,plain,
! [SV1017: $i,SV751: $i,SV395: $i,SV12: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV12 @ SV395 ) @ SV751 ) @ SV1017 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV12 @ SV395 @ SV395 ) @ SV395 ) @ SV1017 ) @ SV751 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2114]) ).
thf(2449,plain,
! [SV1018: $i,SV752: $i,SV396: $i,SV13: $i] :
( ( ! [SY2874: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV13 @ SV396 ) @ SV752 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV13 @ SV1018 @ SY2874 ) @ SV752 ) @ SV396 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2115]) ).
thf(2450,plain,
! [SV1019: $i,SV753: $i,SV397: $i,SV14: $i] :
( ( ! [SY2875: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV14 @ SV397 @ SV753 ) @ SV1019 ) @ SY2875 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV14 @ SY2875 ) @ SV1019 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2116]) ).
thf(2451,plain,
! [SV1020: $i,SV754: $i,SV398: $i,SV15: $i] :
( ( ! [SY2876: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV15 @ SV398 ) @ SV754 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV15 @ SV1020 @ SY2876 ) @ SV754 ) @ SV398 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2117]) ).
thf(2452,plain,
! [SV1021: $i,SV755: $i,SV399: $i,SV16: $i] :
( ( ! [SY2877: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV16 @ SV399 @ SV755 ) @ SV1021 ) @ SY2877 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV16 @ SY2877 ) @ SV1021 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2118]) ).
thf(2453,plain,
! [SV1022: $i,SV758: $i,SV402: $i,SV20: $i] :
( ( ( c_Wellfounded_Oaccp @ SV20 @ SV402 @ SV758 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV20 @ SV758 ) @ SV402 ) @ SV1022 ) )
| ~ ( c_Wellfounded_Oaccp @ SV20 @ SV1022 @ SV758 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2121]) ).
thf(2454,plain,
! [SV1023: $i,SV759: $i,SV403: $i,SV21: $i] :
( ( ( c_Wellfounded_Oaccp @ SV21 @ SV403 @ SV759 )
| ~ ( c_Wellfounded_Oaccp @ SV21 @ SV1023 @ SV759 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV21 @ SV759 ) @ SV403 ) @ SV1023 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2122]) ).
thf(2455,plain,
! [SV760: $i,SV407: $i,SV27: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV27 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV407 ) @ SV760 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV27 @ SV407 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2125]) ).
thf(2456,plain,
! [SV761: $i,SV408: $i,SV28: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV28 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV408 ) @ SV761 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV28 @ SV761 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2126]) ).
thf(2457,plain,
! [SV762: $i,SV409: $i,SV29: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV29 @ SV409 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV29 ) @ SV762 ) @ SV409 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2127]) ).
thf(2458,plain,
! [SV763: $i,SV410: $i,SV30: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV30 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV410 ) @ SV763 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV30 @ SV410 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2128]) ).
thf(2459,plain,
! [SV764: $i,SV411: $i,SV31: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV31 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV411 ) @ SV764 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV31 @ SV764 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2129]) ).
thf(2460,plain,
! [SV1024: $i,SV767: $i,SV416: $i,SV37: $i] :
( ( ( c_List_Oappend @ ( c_List_Oreplicate @ SV37 @ SV416 @ SV767 ) @ ( c_List_Oreplicate @ SV1024 @ SV416 @ SV767 ) @ SV767 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SV1024 @ SV416 @ SV767 ) @ ( c_List_Oreplicate @ SV37 @ SV416 @ SV767 ) @ SV767 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2132]) ).
thf(2461,plain,
! [SV1025: $i,SV768: $i,SV417: $i,SV38: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV38 ) @ SV417 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV768 ) @ SV1025 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV417 @ SV1025 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV38 @ SV768 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2133]) ).
thf(2462,plain,
! [SV1026: $i,SV769: $i,SV418: $i,SV39: $i] :
( ( ( c_List_Oreplicate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV39 ) @ SV418 ) @ SV769 @ SV1026 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SV39 @ SV769 @ SV1026 ) @ ( c_List_Oreplicate @ SV418 @ SV769 @ SV1026 ) @ SV1026 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2134]) ).
thf(2463,plain,
! [SV419: $i,SV40: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV40 )
= $false )
| ( ( ( c_List_Olistsum @ ( c_List_Orev @ SV419 @ SV40 ) @ SV40 )
= ( c_List_Olistsum @ SV419 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2135]) ).
thf(2464,plain,
! [SV772: $i,SV424: $i,SV45: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV45 ) @ SV424 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV772 ) @ SV424 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV45 @ SV772 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2140]) ).
thf(2465,plain,
! [SV773: $i,SV425: $i,SV46: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV46 @ SV425 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV773 ) @ SV46 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV773 ) @ SV425 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2141]) ).
thf(2466,plain,
! [SV774: $i,SV426: $i,SV47: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV47 ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV47 ) @ SV774 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV426 @ SV774 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2142]) ).
thf(2467,plain,
! [SV775: $i,SV428: $i,SV51: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV51 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV428 ) @ SV775 ) @ SV51 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV51 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV428 @ SV51 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV775 @ SV51 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2143]) ).
thf(2468,plain,
! [SV1027: $i,SV776: $i,SV429: $i,SV52: $i] :
( ( ( c_Wellfounded_Oaccp @ SV52 @ SV429 @ SV776 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV52 @ SV429 ) @ SV1027 ) )
| ~ ( c_Wellfounded_Oaccp @ SV52 @ SV1027 @ SV776 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2144]) ).
thf(2469,plain,
! [SV1028: $i,SV777: $i,SV430: $i,SV53: $i] :
( ( ( c_Wellfounded_Oaccp @ SV53 @ SV430 @ SV777 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV53 @ SV430 ) @ SV1028 ) )
| ~ ( c_Wellfounded_Oaccp @ SV53 @ SV1028 @ SV777 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2145]) ).
thf(2470,plain,
! [SV432: $i,SV55: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV55 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV432 @ SV55 ) @ ( c_HOL_Ozero__class_Ozero @ SV55 ) @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2147]) ).
thf(2471,plain,
! [SV778: $i,SV433: $i,SV57: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV57 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV433 @ SV57 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV778 @ SV57 ) @ SV57 )
| ~ ( c_HOL_Oord__class_Oless @ SV433 @ SV778 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2149]) ).
thf(2472,plain,
! [SV779: $i,SV434: $i,SV58: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV58 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV434 @ SV779 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV434 @ SV58 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV779 @ SV58 ) @ SV58 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2150]) ).
thf(2473,plain,
! [SV780: $i,SV435: $i,SV60: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV60 ) )
= $true )
| ( ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ SV435 @ SV780 @ SV60 ) @ SV60 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV435 ) @ ( c_List_Olistsum @ SV780 @ SV60 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2152]) ).
thf(2474,plain,
! [SV436: $i,SV61: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV61 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV61 ) @ SV436 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2153]) ).
thf(2475,plain,
! [SV62: $i,SV437: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV437 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV62 ) @ SV437 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2154]) ).
thf(2476,plain,
! [SV63: $i,SV438: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV438 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV438 ) @ SV63 ) @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV63 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2155]) ).
thf(2477,plain,
! [SV781: $i,SV441: $i,SV67: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV67 ) )
= $true )
| ( ( ( c_List_Olistsum @ ( c_List_Oappend @ SV441 @ SV781 @ SV67 ) @ SV67 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ ( c_List_Olistsum @ SV441 @ SV67 ) ) @ ( c_List_Olistsum @ SV781 @ SV67 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2156]) ).
thf(2478,plain,
! [SV782: $i,SV443: $i,SV69: $i] :
( ( ( ( c_List_Olast @ ( c_List_Olist_OCons @ SV69 @ SV443 @ SV782 ) @ SV782 )
= ( c_List_Olast @ SV443 @ SV782 ) )
= $true )
| ( ( SV443
= ( c_List_Olist_ONil @ SV782 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2157]) ).
thf(2479,plain,
! [SV783: $i,SV447: $i,SV73: $i] :
( ( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV73 @ SV447 @ SV783 ) @ SV783 )
= ( c_List_Olist_OCons @ SV73 @ ( c_List_Obutlast @ SV447 @ SV783 ) @ SV783 ) )
= $true )
| ( ( SV447
= ( c_List_Olist_ONil @ SV783 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2158]) ).
thf(2480,plain,
! [SV1029: $i,SV784: $i,SV448: $i,SV74: $i] :
( ( ( c_List_Oappend @ ( c_List_Oreplicate @ SV74 @ SV448 @ SV784 ) @ ( c_List_Olist_OCons @ SV448 @ SV1029 @ SV784 ) @ SV784 )
= ( c_List_Olist_OCons @ SV448 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV74 @ SV448 @ SV784 ) @ SV1029 @ SV784 ) @ SV784 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2159]) ).
thf(2481,plain,
! [SV785: $i,SV450: $i,SV76: $i] :
( ( ( ( c_List_Olast @ ( c_List_Oappend @ SV76 @ SV450 @ SV785 ) @ SV785 )
= ( c_List_Olast @ SV450 @ SV785 ) )
= $true )
| ( ( SV450
= ( c_List_Olist_ONil @ SV785 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2160]) ).
thf(2482,plain,
! [SV786: $i,SV452: $i,SV78: $i] :
( ( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV78 @ SV452 @ SV786 ) @ SV786 )
= ( c_List_Oappend @ SV78 @ ( c_List_Obutlast @ SV452 @ SV786 ) @ SV786 ) )
= $true )
| ( ( SV452
= ( c_List_Olist_ONil @ SV786 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2161]) ).
thf(2483,plain,
! [SV793: $i,SV459: $i,SV86: $i] :
( ( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV86 @ SV459 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV793 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV459 @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV86 ) ) @ SV459 ) @ SV793 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2168]) ).
thf(2484,plain,
! [SV460: $i,SV87: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV87 )
= $false )
| ( ( ( c_List_Olistsum @ SV460 @ SV87 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV87 ) @ SV460 @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2169]) ).
thf(2485,plain,
! [SV794: $i,SV461: $i,SV88: $i] :
( ( ( ( c_Lambda_Oliftn @ SV88 @ ( c_Lambda_OdB_OVar @ SV461 ) @ SV794 )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV461 ) @ SV88 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV461 @ SV794 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2170]) ).
thf(2486,plain,
! [SV462: $i,SV89: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV89 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV462 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV462 @ SV89 ) @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2171]) ).
thf(2487,plain,
! [SV463: $i,SV90: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV90 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV463 @ SV90 ) @ SV90 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV463 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2172]) ).
thf(2488,plain,
! [SV795: $i,SV464: $i,SV91: $i] :
( ( ( ( c_List_Oappend @ SV91 @ ( c_List_Olist_OCons @ SV464 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV795 @ SV91 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV464 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV795 @ ( c_List_Oappend @ SV91 @ ( c_List_Olist_OCons @ SV464 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2173]) ).
thf(2489,plain,
! [SV466: $i,SV93: $i] :
( ( ( hBOOL @ ( hAPP @ SV93 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV93 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__4 @ SV93 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV93 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV93 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV93 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ SV93 @ SV466 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2175]) ).
thf(2490,plain,
! [SV467: $i,SV94: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV94 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV94 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4 @ SV94 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV94 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV94 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV94 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV94 @ SV467 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2176]) ).
thf(2491,plain,
! [SV1030: $i,SV797: $i,SV469: $i,SV96: $i] :
( ( ! [SY2878: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV96 @ SV469 ) @ SV797 ) )
| ( c_ListOrder_Ostep1 @ SV96 @ ( c_List_Olist_OCons @ SV469 @ SV1030 @ SY2878 ) @ ( c_List_Olist_OCons @ SV797 @ SV1030 @ SY2878 ) @ SY2878 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2177]) ).
thf(2492,plain,
! [SV1031: $i,SV798: $i,SV470: $i,SV97: $i] :
( ( ! [SY2879: $i,SY2880: $i] :
( ( SV97 = SV470 )
| ( SV798 = SV1031 )
| ~ ( c_ListOrder_Ostep1 @ SY2879 @ ( c_List_Olist_OCons @ SV470 @ SV1031 @ SY2880 ) @ ( c_List_Olist_OCons @ SV97 @ SV798 @ SY2880 ) @ SY2880 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2178]) ).
thf(2493,plain,
! [SV1032: $i,SV799: $i,SV471: $i,SV98: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV98 @ SV471 @ SV799 ) ) @ ( c_Lambda_Osubst @ SV1032 @ SV471 @ SV799 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV98 ) @ SV1032 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2179]) ).
thf(2494,plain,
! [SV1033: $i,SV800: $i,SV472: $i,SV99: $i] :
( ( ! [SY2881: $i] :
( ( c_Lambda_OdB_OdB__case @ SV99 @ SV472 @ SV800 @ ( c_Lambda_OdB_OAbs @ SV1033 ) @ SY2881 )
= ( hAPP @ SV800 @ SV1033 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2180]) ).
thf(2495,plain,
! [SV1034: $i,SV801: $i,SV473: $i,SV100: $i] :
( ( ( c_List_Olistsp @ SV100 @ SV473 @ SV801 )
| ~ ( c_List_Olistsp @ SV100 @ ( c_List_Oappend @ SV1034 @ SV473 @ SV801 ) @ SV801 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2181]) ).
thf(2496,plain,
! [SV1035: $i,SV802: $i,SV474: $i,SV101: $i] :
( ( ( c_List_Olistsp @ SV101 @ SV474 @ SV802 )
| ~ ( c_List_Olistsp @ SV101 @ ( c_List_Oappend @ SV474 @ SV1035 @ SV802 ) @ SV802 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2182]) ).
thf(2497,plain,
! [SV803: $i,SV475: $i,SV102: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV102 ) @ SV475 @ SV803 )
= ( c_Lambda_OdB_OVar @ SV102 ) )
= $true )
| ( ( ( SV102 = SV803 )
| ( c_HOL_Oord__class_Oless @ SV803 @ SV102 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2183]) ).
thf(2498,plain,
! [SV476: $i,SV103: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV103 ) @ SV476 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV103 ) ) @ ( c_Lambda_OdB_OAbs @ SV476 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2184]) ).
thf(2499,plain,
! [SV1036: $i,SV804: $i,SV477: $i,SV104: $i] :
( ( ! [SY2882: $i] :
( ( c_ListOrder_Ostep1 @ SV104 @ ( c_List_Oappend @ SV477 @ SV804 @ SV1036 ) @ ( c_List_Oappend @ SV477 @ SY2882 @ SV1036 ) @ SV1036 )
| ~ ( c_ListOrder_Ostep1 @ SV104 @ SV804 @ SY2882 @ SV1036 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2185]) ).
thf(2500,plain,
! [SV1037: $i,SV805: $i,SV478: $i,SV105: $i] :
( ( ! [SY2883: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV105 @ SV478 @ SV805 @ SV1037 )
| ( c_ListOrder_Ostep1 @ SV105 @ ( c_List_Oappend @ SV478 @ SY2883 @ SV1037 ) @ ( c_List_Oappend @ SV805 @ SY2883 @ SV1037 ) @ SV1037 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2186]) ).
thf(2501,plain,
! [SV1038: $i,SV807: $i,SV480: $i,SV108: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV108 )
| ( c_HOL_Oord__class_Oless @ SV480 @ SV807 @ SV108 )
| ~ ( c_HOL_Oord__class_Oless @ SV1038 @ SV807 @ SV108 )
| ~ ( c_HOL_Oord__class_Oless @ SV480 @ SV1038 @ SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2189]) ).
thf(2502,plain,
! [SV1039: $i,SV808: $i,SV481: $i,SV109: $i] :
( ( ~ ( class_Orderings_Oorder @ SV109 )
| ( c_HOL_Oord__class_Oless @ SV481 @ SV808 @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ SV481 @ SV1039 @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ SV1039 @ SV808 @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2190]) ).
thf(2503,plain,
! [SV1040: $i,SV809: $i,SV482: $i,SV110: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV110 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV482 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV809 ) @ SV1040 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV482 ) @ SV809 ) ) @ SV1040 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2191]) ).
thf(2504,plain,
! [SV1041: $i,SV810: $i,SV483: $i,SV111: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV111 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV483 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV810 ) @ SV1041 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV810 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV483 ) @ SV1041 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2192]) ).
thf(2505,plain,
! [SV1042: $i,SV811: $i,SV484: $i,SV112: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV112 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SV484 ) @ SV811 ) ) @ SV1042 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SV484 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SV811 ) @ SV1042 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2193]) ).
thf(2506,plain,
! [SV1043: $i,SV812: $i,SV485: $i,SV113: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV113 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV485 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV812 ) @ SV1043 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV812 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV485 ) @ SV1043 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2194]) ).
thf(2507,plain,
! [SV1044: $i,SV813: $i,SV486: $i,SV114: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV114 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SV486 ) @ SV813 ) ) @ SV1044 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SV486 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SV813 ) @ SV1044 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2195]) ).
thf(2508,plain,
! [SV1045: $i,SV814: $i,SV487: $i,SV115: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV115 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SV487 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SV814 ) @ SV1045 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SV487 ) @ SV814 ) ) @ SV1045 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2196]) ).
thf(2509,plain,
! [SV1046: $i,SV815: $i,SV488: $i,SV116: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV116 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV488 ) @ SV815 ) ) @ SV1046 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV488 ) @ SV1046 ) ) @ SV815 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2197]) ).
thf(2510,plain,
! [SV1047: $i,SV816: $i,SV489: $i,SV117: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV117 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV489 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV816 ) @ SV1047 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV816 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV489 ) @ SV1047 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2198]) ).
thf(2511,plain,
! [SV1048: $i,SV817: $i,SV490: $i,SV118: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV118 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV490 ) @ SV817 ) ) @ SV1048 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV490 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV817 ) @ SV1048 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2199]) ).
thf(2512,plain,
! [SV1049: $i,SV818: $i,SV492: $i,SV122: $i] :
( ( ( c_List_Ofoldr @ SV122 @ ( c_List_Olist_ONil @ SV492 ) @ SV818 @ SV492 @ SV1049 )
= SV818 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2201]) ).
thf(2513,plain,
! [SV1050: $i,SV819: $i,SV493: $i,SV123: $i] :
( ( ! [SY2884: $i,SY2885: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SV493 ) @ SV819 ) )
| ( c_ListOrder_Ostep1 @ SV123 @ SV1050 @ SY2884 @ SY2885 )
| ~ ( c_ListOrder_Ostep1 @ SV123 @ ( c_List_Oappend @ SV1050 @ ( c_List_Olist_OCons @ SV493 @ ( c_List_Olist_ONil @ SY2885 ) @ SY2885 ) @ SY2885 ) @ ( c_List_Oappend @ SY2884 @ ( c_List_Olist_OCons @ SV819 @ ( c_List_Olist_ONil @ SY2885 ) @ SY2885 ) @ SY2885 ) @ SY2885 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2202]) ).
thf(2514,plain,
! [SV820: $i,SV494: $i,SV124: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV124 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV124 ) @ SV494 ) @ SV820 ) @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ SV124 )
| ~ ( c_HOL_Oord__class_Oless @ SV820 @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ SV124 )
| ~ ( c_HOL_Oord__class_Oless @ SV494 @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2203]) ).
thf(2515,plain,
! [SV1051: $i,SV821: $i,SV495: $i,SV125: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV125 @ SV495 @ SV821 ) @ SV1051 @ SV821 )
= ( c_List_Olist_OCons @ SV125 @ ( c_List_Oappend @ SV495 @ SV1051 @ SV821 ) @ SV821 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2204]) ).
thf(2516,plain,
! [SV1052: $i,SV822: $i,SV496: $i,SV126: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV126 @ SV496 @ SV822 ) @ SV1052 @ SV822 )
= ( c_List_Olist_OCons @ SV126 @ ( c_List_Oappend @ SV496 @ SV1052 @ SV822 ) @ SV822 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2205]) ).
thf(2517,plain,
! [SV823: $i,SV497: $i,SV127: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV127 ) @ SV497 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV127 ) @ SV823 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV497 ) @ SV823 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2206]) ).
thf(2518,plain,
! [SV824: $i,SV498: $i,SV128: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV128 ) @ SV498 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV824 ) @ SV498 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV128 ) @ SV824 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2207]) ).
thf(2519,plain,
! [SV825: $i,SV499: $i,SV129: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV129 ) )
= $true )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV129 ) @ SV499 @ SV825 @ SV129 @ SV129 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV129 ) @ SV499 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV129 ) @ SV825 @ ( c_HOL_Ozero__class_Ozero @ SV129 ) @ SV129 @ SV129 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2208]) ).
thf(2520,plain,
! [SV1053: $i,SV826: $i,SV500: $i,SV130: $i] :
( ( ( c_List_Olist_OCons @ SV130 @ ( c_List_Oappend @ SV500 @ SV826 @ SV1053 ) @ SV1053 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV130 @ SV500 @ SV1053 ) @ SV826 @ SV1053 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2209]) ).
thf(2521,plain,
! [SV1054: $i,SV827: $i,SV501: $i,SV131: $i] :
( ( ( c_List_Olist_OCons @ SV131 @ ( c_List_Oappend @ SV501 @ SV827 @ SV1054 ) @ SV1054 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV131 @ SV501 @ SV1054 ) @ SV827 @ SV1054 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2210]) ).
thf(2522,plain,
! [SV1055: $i,SV828: $i,SV502: $i,SV132: $i] :
( ( ! [SY2886: $i,SY2887: $i] :
( ( SV132 = SV502 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV828 @ SV502 ) @ SV132 ) )
| ~ ( c_ListOrder_Ostep1 @ SV828 @ ( c_List_Olist_OCons @ SV502 @ SV1055 @ SY2886 ) @ ( c_List_Olist_OCons @ SV132 @ SY2887 @ SY2886 ) @ SY2886 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2211]) ).
thf(2523,plain,
! [SV1056: $i,SV829: $i,SV503: $i,SV134: $i] :
( ( ! [SY2888: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV134 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ SV503 ) @ SV829 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ SV1056 ) @ SY2888 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ SV503 ) @ SV1056 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ SV829 ) @ SY2888 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2213]) ).
thf(2524,plain,
! [SV1057: $i,SV830: $i,SV504: $i,SV135: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV135 ) @ SV504 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV830 ) @ SV1057 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV504 ) @ SV1057 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV135 ) @ SV830 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2214]) ).
thf(2525,plain,
! [SV831: $i,SV505: $i,SV136: $i] :
( ( ( ( c_Lambda_Oliftn @ SV136 @ ( c_Lambda_OdB_OVar @ SV505 ) @ SV831 )
= ( c_Lambda_OdB_OVar @ SV505 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV505 @ SV831 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2215]) ).
thf(2526,plain,
! [SV1058: $i,SV832: $i,SV506: $i,SV137: $i] :
( ( ( c_Type_Otyping @ SV137 @ SV506 @ SV832 )
| ~ ( c_Type_Otyping @ SV137 @ SV1058 @ SV832 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV1058 ) @ SV506 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2216]) ).
thf(2527,plain,
! [SV508: $i,SV139: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV139 @ SV508 @ tc_nat )
= $false )
| ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV139 ) @ SV508 )
= ( c_Lambda_OdB_OVar @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2218]) ).
thf(2528,plain,
! [SV834: $i,SV509: $i,SV140: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV140 @ SV509 ) ) @ ( c_Lambda_Olift @ SV834 @ SV509 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV140 ) @ SV834 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2219]) ).
thf(2529,plain,
! [SV1059: $i,SV836: $i,SV512: $i,SV143: $i] :
( ( ! [SY2889: $i,SY2890: $i] :
( ( SV143 = SV512 )
| ( c_ListOrder_Ostep1 @ SV836 @ SV143 @ SV512 @ SV1059 )
| ~ ( c_ListOrder_Ostep1 @ SV836 @ ( c_List_Oappend @ SV143 @ ( c_List_Olist_OCons @ SY2889 @ ( c_List_Olist_ONil @ SV1059 ) @ SV1059 ) @ SV1059 ) @ ( c_List_Oappend @ SV512 @ ( c_List_Olist_OCons @ SY2890 @ ( c_List_Olist_ONil @ SV1059 ) @ SV1059 ) @ SV1059 ) @ SV1059 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2222]) ).
thf(2530,plain,
! [SV514: $i,SV146: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV146 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ ( c_HOL_Ozero__class_Ozero @ SV146 ) ) @ SV514 )
= SV514 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2223]) ).
thf(2531,plain,
! [SV515: $i,SV147: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV147 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ ( c_HOL_Ozero__class_Ozero @ SV147 ) ) @ SV515 )
= SV515 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2224]) ).
thf(2532,plain,
! [SV516: $i,SV148: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV148 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV148 )
| ( SV516
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV516 ) @ ( c_HOL_Ozero__class_Ozero @ SV148 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2225]) ).
thf(2533,plain,
! [SV517: $i,SV149: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV149 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV517 ) @ ( c_HOL_Ozero__class_Ozero @ SV149 ) )
= SV517 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2226]) ).
thf(2534,plain,
! [SV518: $i,SV150: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV150 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV150 ) @ ( c_HOL_Ozero__class_Ozero @ SV150 ) ) @ SV518 )
= SV518 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2227]) ).
thf(2535,plain,
! [SV519: $i,SV151: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV151 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV519 ) @ ( c_HOL_Ozero__class_Ozero @ SV151 ) )
= SV519 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2228]) ).
thf(2536,plain,
! [SV520: $i,SV152: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV152 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV520 ) @ ( c_HOL_Ozero__class_Ozero @ SV152 ) )
= SV520 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2229]) ).
thf(2537,plain,
! [SV521: $i,SV153: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV153 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ ( c_HOL_Ozero__class_Ozero @ SV153 ) ) @ SV521 )
= SV521 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2230]) ).
thf(2538,plain,
! [SV522: $i,SV154: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV154 ) @ SV522 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV154 ) ) @ ( c_Lambda_OdB_OAbs @ SV522 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2231]) ).
thf(2539,plain,
! [SV1060: $i,SV837: $i,SV523: $i,SV155: $i] :
( ( ( ( hAPP @ ( hAPP @ SV155 @ SV523 ) @ SV837 )
= SV523 )
| ~ ( c_OrderedGroup_Omonoid__add @ SV837 @ SV155 @ SV1060 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2232]) ).
thf(2540,plain,
! [SV1061: $i,SV838: $i,SV524: $i,SV156: $i] :
( ( ( ( hAPP @ ( hAPP @ SV156 @ SV524 ) @ SV838 )
= SV838 )
| ~ ( c_OrderedGroup_Omonoid__add @ SV524 @ SV156 @ SV1061 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2233]) ).
thf(2541,plain,
! [SV525: $i,SV157: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV157 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV157 ) @ SV525 @ SV157 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV157 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV525 ) @ SV525 ) @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2234]) ).
thf(2542,plain,
! [SV526: $i,SV158: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV158 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV526 ) @ SV526 ) @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV526 @ SV158 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2235]) ).
thf(2543,plain,
! [SV1062: $i,SV841: $i,SV529: $i,SV161: $i] :
( ( ! [SY2891: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV161 @ SV529 ) @ SV841 ) @ SV1062 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV161 @ SV529 ) @ SY2891 ) @ SV1062 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV161 @ SV529 ) @ SV841 ) @ SY2891 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2238]) ).
thf(2544,plain,
! [SV1063: $i,SV842: $i,SV535: $i,SV167: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV167 @ SV535 @ SV842 ) ) @ ( c_Lambda_Osubst @ SV167 @ SV1063 @ SV842 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV535 ) @ SV1063 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2239]) ).
thf(2545,plain,
! [SV843: $i,SV536: $i,SV168: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV168 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV168 ) @ SV536 ) @ SV843 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV168 ) @ SV843 ) @ SV536 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2240]) ).
thf(2546,plain,
! [SV844: $i,SV537: $i,SV169: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV169 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV169 ) @ SV537 ) @ SV844 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV169 ) @ SV844 ) @ SV537 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2241]) ).
thf(2547,plain,
! [SV845: $i,SV538: $i,SV170: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV170 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV170 ) @ SV538 ) @ SV845 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV170 ) @ SV845 ) @ SV538 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2242]) ).
thf(2548,plain,
! [SV1064: $i,SV846: $i,SV539: $i,SV171: $i] :
( ( ! [SY2892: $i,SY2893: $i] :
( ( c_List_Ofoldr @ SV171 @ ( c_List_Oappend @ SV539 @ SV846 @ SV1064 ) @ SY2892 @ SV1064 @ SY2893 )
= ( c_List_Ofoldr @ SV171 @ SV539 @ ( c_List_Ofoldr @ SV171 @ SV846 @ SY2892 @ SV1064 @ SY2893 ) @ SV1064 @ SY2893 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2243]) ).
thf(2549,plain,
! [SV1065: $i,SV847: $i,SV540: $i,SV172: $i] :
( ( ! [SY2894: $i,SY2895: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV172 @ SV540 ) @ SV847 ) )
| ( SV540 = SV847 )
| ~ ( c_ListOrder_Ostep1 @ SV172 @ ( c_List_Oappend @ SV1065 @ ( c_List_Olist_OCons @ SV540 @ ( c_List_Olist_ONil @ SY2894 ) @ SY2894 ) @ SY2894 ) @ ( c_List_Oappend @ SY2895 @ ( c_List_Olist_OCons @ SV847 @ ( c_List_Olist_ONil @ SY2894 ) @ SY2894 ) @ SY2894 ) @ SY2894 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2244]) ).
thf(2550,plain,
! [SV1066: $i,SV848: $i,SV541: $i,SV173: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV173 @ SV541 @ SV848 ) ) @ ( c_Lambda_Osubst @ SV1066 @ SV541 @ SV848 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV173 ) @ SV1066 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2245]) ).
thf(2551,plain,
! [SV1067: $i,SV849: $i,SV542: $i,SV174: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV174 @ SV542 @ SV849 ) ) @ ( c_Lambda_Osubst @ SV174 @ SV1067 @ SV849 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV542 ) @ SV1067 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2246]) ).
thf(2552,plain,
! [SV850: $i,SV543: $i,SV175: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV175 ) )
= $true )
| ( ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV175 ) @ SV543 @ SV850 @ SV175 @ SV175 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV175 ) @ SV850 @ SV543 @ SV175 @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2247]) ).
thf(2553,plain,
! [SV1068: $i,SV851: $i,SV544: $i,SV176: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV176 @ SV544 ) @ SV851 ) @ SV1068 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV176 @ SV851 ) @ SV1068 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2248]) ).
thf(2554,plain,
! [SV852: $i,SV545: $i,SV177: $i] :
( ( c_ListOrder_Ostep1 @ SV177 @ ( c_List_Olist_ONil @ SV545 ) @ SV852 @ SV545 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2249]) ).
thf(2555,plain,
! [SV853: $i,SV546: $i,SV178: $i] :
( ( c_ListOrder_Ostep1 @ SV178 @ SV546 @ ( c_List_Olist_ONil @ SV853 ) @ SV853 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2250]) ).
thf(2556,plain,
! [SV547: $i,SV179: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV179 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV179 ) @ SV547 ) @ SV547 ) @ ( c_HOL_Ozero__class_Ozero @ SV179 ) @ SV179 )
| ~ ( c_HOL_Oord__class_Oless @ SV547 @ ( c_HOL_Ozero__class_Ozero @ SV179 ) @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2251]) ).
thf(2557,plain,
! [SV548: $i,SV180: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV180 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV548 @ ( c_HOL_Ozero__class_Ozero @ SV180 ) @ SV180 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV180 ) @ SV548 ) @ SV548 ) @ ( c_HOL_Ozero__class_Ozero @ SV180 ) @ SV180 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2252]) ).
thf(2558,plain,
! [SV549: $i,SV181: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV181 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV549 @ ( c_HOL_Ozero__class_Ozero @ SV181 ) @ SV181 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV181 ) @ SV549 ) @ SV549 ) @ ( c_HOL_Ozero__class_Ozero @ SV181 ) @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2253]) ).
thf(2559,plain,
! [SV550: $i,SV182: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV182 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV182 ) @ SV550 ) @ SV550 ) @ ( c_HOL_Ozero__class_Ozero @ SV182 ) @ SV182 )
| ~ ( c_HOL_Oord__class_Oless @ SV550 @ ( c_HOL_Ozero__class_Ozero @ SV182 ) @ SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2254]) ).
thf(2560,plain,
! [SV854: $i,SV551: $i,SV183: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV183 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ SV551 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ ( c_HOL_Ozero__class_Ozero @ SV183 ) @ SV854 @ SV183 @ SV183 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ SV551 @ SV854 @ SV183 @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2255]) ).
thf(2561,plain,
! [SV855: $i,SV552: $i,SV184: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV184 ) ) @ SV552 ) @ SV855 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV552 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV184 @ SV552 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV855 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2256]) ).
thf(2562,plain,
! [SV856: $i,SV553: $i,SV185: $i] :
( ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV185 ) @ SV553 @ SV856 )
= ( c_Lambda_OdB_OVar @ SV185 ) )
= $true )
| ( ( ( SV185 = SV856 )
| ( c_HOL_Oord__class_Oless @ SV856 @ SV185 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2257]) ).
thf(2563,plain,
! [SV554: $i,SV186: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV186 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV186 @ SV554 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2258]) ).
thf(2564,plain,
! [SV555: $i,SV189: $i] :
( ( ( class_Orderings_Oorder @ SV189 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV555 @ SV555 @ SV189 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2259]) ).
thf(2565,plain,
! [SV556: $i,SV190: $i] :
( ( ( class_Orderings_Olinorder @ SV190 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV556 @ SV556 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2260]) ).
thf(2566,plain,
! [SV557: $i,SV191: $i] :
( ( ( class_Orderings_Opreorder @ SV191 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV557 @ SV557 @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2261]) ).
thf(2567,plain,
! [SV857: $i,SV559: $i,SV193: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV193 @ SV559 ) ) @ ( c_Lambda_Olift @ SV857 @ SV559 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV193 ) @ SV857 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2262]) ).
thf(2568,plain,
! [SV858: $i,SV560: $i,SV194: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV194 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV194 ) @ SV560 ) @ SV858 ) @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV858 @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV560 @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2263]) ).
thf(2569,plain,
! [SV1069: $i,SV859: $i,SV561: $i,SV195: $i] :
( ( ! [SY2896: $i,SY2897: $i] :
( ( c_ListOrder_Ostep1 @ SV195 @ SV561 @ SV859 @ SV1069 )
| ( SV859 = SV561 )
| ~ ( c_ListOrder_Ostep1 @ SV195 @ ( c_List_Olist_OCons @ SY2896 @ SV561 @ SV1069 ) @ ( c_List_Olist_OCons @ SY2897 @ SV859 @ SV1069 ) @ SV1069 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2264]) ).
thf(2570,plain,
! [SV1070: $i,SV860: $i,SV562: $i,SV196: $i] :
( ( ! [SY2898: $i] :
( ( ( hAPP @ ( hAPP @ SV196 @ ( hAPP @ ( hAPP @ SV196 @ SV562 ) @ SV860 ) ) @ SV1070 )
= ( hAPP @ ( hAPP @ SV196 @ SV562 ) @ ( hAPP @ ( hAPP @ SV196 @ SV860 ) @ SV1070 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV196 @ SY2898 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2265]) ).
thf(2571,plain,
! [SV861: $i,SV563: $i,SV197: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV197 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV563 @ SV861 @ SV197 )
| ( c_HOL_Oord__class_Oless @ SV861 @ SV563 @ SV197 )
| ( SV861 = SV563 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2266]) ).
thf(2572,plain,
! [SV862: $i,SV564: $i,SV198: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV198 ) )
= $true )
| ( ( ( SV564 = SV862 )
| ( c_HOL_Oord__class_Oless @ SV862 @ SV564 @ SV198 )
| ( c_HOL_Oord__class_Oless @ SV564 @ SV862 @ SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2267]) ).
thf(2573,plain,
! [SV199: $i,SV565: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV565 @ SV199 @ tc_nat )
= $true )
| ( ( SV565 = SV199 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV199 @ SV565 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2268]) ).
thf(2574,plain,
! [SV863: $i,SV566: $i,SV200: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV200 @ SV566 ) @ SV863 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV566 @ SV863 @ tc_nat )
| ( SV863 = SV566 )
| ( c_HOL_Oord__class_Oless @ SV863 @ SV566 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2269]) ).
thf(2575,plain,
! [SV201: $i,SV567: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV567 @ SV201 @ tc_nat )
= $true )
| ( ( SV567 = SV201 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV201 @ SV567 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2270]) ).
thf(2576,plain,
! [SV864: $i,SV568: $i,SV202: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV202 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV568 @ SV864 @ SV202 )
| ( c_HOL_Oord__class_Oless @ SV864 @ SV568 @ SV202 )
| ( SV864 = SV568 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2271]) ).
thf(2577,plain,
! [SV865: $i,SV569: $i,SV203: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV203 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV569 @ SV865 @ SV203 )
| ( SV865 = SV569 )
| ( c_HOL_Oord__class_Oless @ SV865 @ SV569 @ SV203 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2272]) ).
thf(2578,plain,
! [SV866: $i,SV570: $i,SV204: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV204 ) )
= $true )
| ( ( ( SV570 = SV866 )
| ( c_HOL_Oord__class_Oless @ SV570 @ SV866 @ SV204 )
| ( c_HOL_Oord__class_Oless @ SV866 @ SV570 @ SV204 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2273]) ).
thf(2579,plain,
! [SV1071: $i,SV867: $i,SV571: $i,SV205: $i] :
( ( ! [SY2899: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV205 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV205 ) @ SV571 ) @ SV867 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV205 ) @ SV1071 ) @ SY2899 ) @ SV205 )
| ~ ( c_HOL_Oord__class_Oless @ SV867 @ SY2899 @ SV205 )
| ~ ( c_HOL_Oord__class_Oless @ SV571 @ SV1071 @ SV205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2274]) ).
thf(2580,plain,
! [SV572: $i,SV206: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV206 )
= $false )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV206 ) @ ( c_HOL_Ozero__class_Ozero @ SV206 ) @ SV572 @ SV206 @ SV206 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV206 ) @ SV572 @ ( c_HOL_Ozero__class_Ozero @ SV206 ) @ SV206 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2275]) ).
thf(2581,plain,
! [SV1072: $i,SV868: $i,SV573: $i,SV207: $i] :
( ( ! [SY2900: $i,SY2901: $i] :
( ( SV207 = SV573 )
| ( SV868 = SV1072 )
| ~ ( c_ListOrder_Ostep1 @ SY2900 @ ( c_List_Oappend @ SV207 @ ( c_List_Olist_OCons @ SV868 @ ( c_List_Olist_ONil @ SY2901 ) @ SY2901 ) @ SY2901 ) @ ( c_List_Oappend @ SV573 @ ( c_List_Olist_OCons @ SV1072 @ ( c_List_Olist_ONil @ SY2901 ) @ SY2901 ) @ SY2901 ) @ SY2901 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2276]) ).
thf(2582,plain,
! [SV1073: $i,SV869: $i,SV574: $i,SV209: $i] :
( ( ( c_List_Olistsp @ SV209 @ ( c_List_Oappend @ SV574 @ SV869 @ SV1073 ) @ SV1073 )
| ~ ( c_List_Olistsp @ SV209 @ SV869 @ SV1073 )
| ~ ( c_List_Olistsp @ SV209 @ SV574 @ SV1073 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2277]) ).
thf(2583,plain,
! [SV1074: $i,SV870: $i,SV575: $i,SV210: $i] :
( ( ! [SY2902: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV210 @ SV575 @ SV870 @ ( c_Lambda_OdB_OAbs @ SV1074 ) @ SY2902 )
= ( hAPP @ ( hAPP @ SV870 @ SV1074 ) @ ( c_Lambda_OdB_OdB__rec @ SV210 @ SV575 @ SV870 @ SV1074 @ SY2902 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2278]) ).
thf(2584,plain,
! [SV1075: $i,SV871: $i,SV578: $i,SV214: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV214 )
| ( c_HOL_Oord__class_Oless @ SV578 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV214 ) @ SV871 ) @ SV1075 ) @ SV214 )
| ~ ( c_HOL_Oord__class_Oless @ SV578 @ SV1075 @ SV214 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV214 ) @ SV871 @ SV214 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2280]) ).
thf(2585,plain,
! [SV872: $i,SV579: $i,SV215: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV215 ) @ SV579 @ SV872 )
= ( c_Lambda_OdB_OVar @ SV215 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV215 @ SV872 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2281]) ).
thf(2586,plain,
! [SV1076: $i,SV873: $i,SV580: $i,SV216: $i] :
( ( ! [SY2903: $i,SY2904: $i] :
( ( c_List_Ofoldr @ SV216 @ ( c_List_Olist_OCons @ SV580 @ SV873 @ SV1076 ) @ SY2903 @ SV1076 @ SY2904 )
= ( hAPP @ ( hAPP @ SV216 @ SV580 ) @ ( c_List_Ofoldr @ SV216 @ SV873 @ SY2903 @ SV1076 @ SY2904 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2282]) ).
thf(2587,plain,
! [SV1077: $i,SV874: $i,SV581: $i,SV217: $i] :
( ( ! [SY2905: $i] :
( ~ ( hBOOL @ ( hAPP @ SV217 @ ( c_Lambda_OdB_OdB__case @ SV581 @ SV874 @ SV1077 @ ( c_Lambda_OdB_OAbs @ SY2905 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV217 @ ( hAPP @ SV1077 @ SY2905 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2283]) ).
thf(2588,plain,
! [SV1078: $i,SV875: $i,SV582: $i,SV218: $i] :
( ( ! [SY2906: $i] :
( ~ ( hBOOL @ ( hAPP @ SV218 @ ( c_Lambda_OdB_OdB__case @ SV582 @ SV875 @ SV1078 @ ( c_Lambda_OdB_OAbs @ SY2906 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV218 @ ( hAPP @ SV1078 @ SY2906 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2284]) ).
thf(2589,plain,
! [SV876: $i,SV583: $i,SV219: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV219 @ ( c_Lambda_OdB_OVar @ SV583 ) @ SV876 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV219 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2285]) ).
thf(2590,plain,
! [SV1079: $i,SV878: $i,SV585: $i,SV221: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV221 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV221 ) @ SV585 ) @ SV878 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV221 ) @ SV1079 ) @ SV878 ) @ SV221 )
| ~ ( c_HOL_Oord__class_Oless @ SV585 @ SV1079 @ SV221 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2287]) ).
thf(2591,plain,
! [SV1080: $i,SV879: $i,SV586: $i,SV222: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV222 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV222 ) @ SV586 ) @ SV879 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV222 ) @ SV1080 ) @ SV879 ) @ SV222 )
| ~ ( c_HOL_Oord__class_Oless @ SV586 @ SV1080 @ SV222 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2288]) ).
thf(2592,plain,
! [SV1081: $i,SV880: $i,SV587: $i,SV223: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV223 )
| ( c_HOL_Oord__class_Oless @ SV587 @ SV880 @ SV223 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV223 ) @ SV587 ) @ SV1081 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV223 ) @ SV880 ) @ SV1081 ) @ SV223 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2289]) ).
thf(2593,plain,
! [SV1082: $i,SV881: $i,SV588: $i,SV224: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV224 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV224 ) @ SV588 ) @ SV881 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV224 ) @ SV588 ) @ SV1082 ) @ SV224 )
| ~ ( c_HOL_Oord__class_Oless @ SV881 @ SV1082 @ SV224 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2290]) ).
thf(2594,plain,
! [SV1083: $i,SV882: $i,SV589: $i,SV225: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV225 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV225 ) @ SV589 ) @ SV882 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV225 ) @ SV589 ) @ SV1083 ) @ SV225 )
| ~ ( c_HOL_Oord__class_Oless @ SV882 @ SV1083 @ SV225 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2291]) ).
thf(2595,plain,
! [SV1084: $i,SV883: $i,SV590: $i,SV226: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV226 )
| ( c_HOL_Oord__class_Oless @ SV590 @ SV883 @ SV226 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV226 ) @ SV1084 ) @ SV590 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV226 ) @ SV1084 ) @ SV883 ) @ SV226 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2292]) ).
thf(2596,plain,
! [SV1085: $i,SV884: $i,SV591: $i,SV227: $i] :
( ( ! [SY2907: $i,SY2908: $i] :
( ( c_ListOrder_Ostep1 @ SV227 @ SV591 @ SV884 @ SV1085 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV227 @ SY2907 ) @ SY2908 ) )
| ~ ( c_ListOrder_Ostep1 @ SV227 @ ( c_List_Olist_OCons @ SY2907 @ SV591 @ SV1085 ) @ ( c_List_Olist_OCons @ SY2908 @ SV884 @ SV1085 ) @ SV1085 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2293]) ).
thf(2597,plain,
! [SV1086: $i,SV885: $i,SV592: $i,SV228: $i] :
( ( ! [SY2909: $i] :
( ( c_ListOrder_Ostep1 @ SV228 @ ( c_List_Olist_OCons @ SV592 @ SV885 @ SV1086 ) @ ( c_List_Olist_OCons @ SV592 @ SY2909 @ SV1086 ) @ SV1086 )
| ~ ( c_ListOrder_Ostep1 @ SV228 @ SV885 @ SY2909 @ SV1086 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2294]) ).
thf(2598,plain,
! [SV1087: $i,SV886: $i,SV593: $i,SV230: $i] :
( ( ( c_List_Oappend @ ( c_List_Oappend @ SV230 @ SV593 @ SV886 ) @ SV1087 @ SV886 )
= ( c_List_Oappend @ SV230 @ ( c_List_Oappend @ SV593 @ SV1087 @ SV886 ) @ SV886 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2295]) ).
thf(2599,plain,
! [SV1088: $i,SV887: $i,SV594: $i,SV231: $i] :
( ( ( c_List_Oappend @ SV231 @ ( c_List_Oappend @ SV594 @ SV887 @ SV1088 ) @ SV1088 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV231 @ SV594 @ SV1088 ) @ SV887 @ SV1088 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2296]) ).
thf(2600,plain,
! [SV1089: $i,SV888: $i,SV595: $i,SV232: $i] :
( ( ( c_List_Oappend @ ( c_List_Oappend @ SV232 @ SV595 @ SV888 ) @ SV1089 @ SV888 )
= ( c_List_Oappend @ SV232 @ ( c_List_Oappend @ SV595 @ SV1089 @ SV888 ) @ SV888 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2297]) ).
thf(2601,plain,
! [SV1090: $i,SV889: $i,SV596: $i,SV233: $i] :
( ( ( c_List_Oappend @ SV233 @ ( c_List_Oappend @ SV596 @ SV889 @ SV1090 ) @ SV1090 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV233 @ SV596 @ SV1090 ) @ SV889 @ SV1090 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2298]) ).
thf(2602,plain,
! [SV890: $i,SV597: $i,SV234: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV234 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV597 @ SV890 @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SV890 @ SV597 @ SV234 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2299]) ).
thf(2603,plain,
! [SV1091: $i,SV891: $i,SV598: $i,SV235: $i] :
( ( ! [SY2910: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV235 @ SV598 ) @ SV891 ) @ SV1091 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV235 @ SV598 ) @ SY2910 ) @ SV1091 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV891 ) @ SY2910 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2300]) ).
thf(2604,plain,
! [SV1092: $i,SV892: $i,SV599: $i,SV236: $i] :
( ( ! [SY2911: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV236 @ SV599 ) @ SV892 ) @ SV1092 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV236 @ SY2911 ) @ SV1092 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV236 @ SV599 ) @ SV892 ) @ SY2911 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2301]) ).
thf(2605,plain,
! [SV893: $i,SV600: $i,SV237: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV237 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV600 @ SV893 @ SV237 )
| ~ ( c_HOL_Oord__class_Oless @ SV893 @ SV600 @ SV237 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2302]) ).
thf(2606,plain,
! [SV894: $i,SV601: $i,SV238: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV238 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV601 @ SV894 @ SV238 )
| ~ ( c_HOL_Oord__class_Oless @ SV894 @ SV601 @ SV238 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2303]) ).
thf(2607,plain,
! [SV895: $i,SV602: $i,SV239: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV239 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV602 @ SV895 @ SV239 )
| ~ ( c_HOL_Oord__class_Oless @ SV895 @ SV602 @ SV239 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2304]) ).
thf(2608,plain,
! [SV1093: $i,SV896: $i,SV603: $i,SV240: $i] :
( ( ! [SY2912: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV240 @ SV603 @ SV896 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SV1093 @ SV603 ) @ SY2912 )
| ~ ( c_Type_Otyping @ SV240 @ SV1093 @ SY2912 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2305]) ).
thf(2609,plain,
! [SV604: $i,SV241: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV241 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV241 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV241 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV241 @ SV604 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV241 @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV241 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2306]) ).
thf(2610,plain,
! [SV1094: $i,SV897: $i,SV605: $i,SV242: $i] :
( ( ! [SY2913: $i] :
( ( ( c_List_Ofoldl @ SV242 @ ( hAPP @ ( hAPP @ SV242 @ SV605 ) @ SV897 ) @ SV1094 @ SY2913 @ SY2913 )
= ( hAPP @ ( hAPP @ SV242 @ SV605 ) @ ( c_List_Ofoldl @ SV242 @ SV897 @ SV1094 @ SY2913 @ SY2913 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV242 @ SY2913 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2307]) ).
thf(2611,plain,
! [SV1095: $i,SV898: $i,SV607: $i,SV244: $i] :
( ( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV244 ) @ SV607 ) @ SV898 @ SV1095 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV244 @ SV898 @ SV1095 ) ) @ ( c_Lambda_Osubst @ SV607 @ SV898 @ SV1095 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2308]) ).
thf(2612,plain,
! [SV1096: $i,SV899: $i,SV608: $i,SV245: $i] :
( ( ( c_Type_Otypings @ SV245 @ SV608 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV899 @ SV245 @ SV1096 @ SV608 ) )
| ~ ( c_Type_Otyping @ SV245 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1096 ) @ SV608 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV899 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2309]) ).
thf(2613,plain,
! [SV1097: $i,SV900: $i,SV609: $i,SV246: $i] :
( ( ! [SY2914: $i] :
( ~ ( hBOOL @ ( hAPP @ SV246 @ ( c_Lambda_OdB_OdB__case @ SV609 @ SV900 @ SV1097 @ ( c_Lambda_OdB_OVar @ SY2914 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV246 @ ( hAPP @ SV609 @ SY2914 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2310]) ).
thf(2614,plain,
! [SV1098: $i,SV901: $i,SV610: $i,SV247: $i] :
( ( ! [SY2915: $i] :
( ~ ( hBOOL @ ( hAPP @ SV247 @ ( c_Lambda_OdB_OdB__case @ SV610 @ SV901 @ SV1098 @ ( c_Lambda_OdB_OVar @ SY2915 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV247 @ ( hAPP @ SV610 @ SY2915 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2311]) ).
thf(2615,plain,
! [SV1099: $i,SV902: $i,SV611: $i,SV248: $i] :
( ( ( c_Type_Otyping @ SV248 @ SV611 @ SV902 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV1099 ) @ SV611 ) )
| ~ ( c_Type_Otyping @ SV248 @ SV1099 @ SV902 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2312]) ).
thf(2616,plain,
! [SV1100: $i,SV903: $i,SV613: $i,SV250: $i] :
( ( ! [SY2916: $i,SY2917: $i] :
( ~ ( hBOOL @ ( hAPP @ SV250 @ ( c_Lambda_OdB_OdB__case @ SV613 @ SV903 @ SV1100 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2916 ) @ SY2917 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV250 @ ( hAPP @ ( hAPP @ SV903 @ SY2916 ) @ SY2917 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2313]) ).
thf(2617,plain,
! [SV1101: $i,SV904: $i,SV614: $i,SV251: $i] :
( ( ! [SY2918: $i,SY2919: $i] :
( ~ ( hBOOL @ ( hAPP @ SV251 @ ( c_Lambda_OdB_OdB__case @ SV614 @ SV904 @ SV1101 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2918 ) @ SY2919 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV251 @ ( hAPP @ ( hAPP @ SV904 @ SY2918 ) @ SY2919 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2314]) ).
thf(2618,plain,
! [SV1102: $i,SV905: $i,SV615: $i,SV252: $i] :
( ( ( c_Type_Otypings @ SV252 @ SV615 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV905 @ SV252 @ SV1102 @ SV615 ) )
| ~ ( c_Type_Otyping @ SV252 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1102 @ SV615 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV905 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2315]) ).
thf(2619,plain,
! [SV1103: $i,SV906: $i,SV616: $i,SV253: $i] :
( ( ! [SY2920: $i,SY2921: $i,SY2922: $i] :
( ( SV253
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV616 @ SV253 @ SV906 @ SV1103 ) @ SV616 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV906 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2920 ) @ SY2921 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV253 )
| ~ ( c_Type_Otypings @ SV906 @ SY2921 @ SY2922 )
| ~ ( c_Type_Otyping @ SV906 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2920 ) @ SY2921 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1103 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV616 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2316]) ).
thf(2620,plain,
! [SV1104: $i,SV907: $i,SV617: $i,SV254: $i] :
( ( ! [SY2923: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV254 @ SV617 @ SV907 @ SV1104 ) @ SY2923 )
= ( hAPP @ SV254 @ SY2923 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2923 @ SV617 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2317]) ).
thf(2621,plain,
! [SV908: $i,SV618: $i,SV255: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV255 @ SV618 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV908 @ SV618 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV255 ) @ SV908 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2318]) ).
thf(2622,plain,
! [SV1105: $i,SV909: $i,SV620: $i,SV257: $i] :
( ( ! [SY2924: $i] :
( ( c_Type_Otyping @ SV257 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV620 ) @ SV909 ) @ SV1105 )
| ~ ( c_Type_Otyping @ SV257 @ SV909 @ SY2924 )
| ~ ( c_Type_Otyping @ SV257 @ SV620 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY2924 ) @ SV1105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2320]) ).
thf(2623,plain,
! [SV258: $i,SV621: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ SV621 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV258 ) @ SV621 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2321]) ).
thf(2624,plain,
! [SV1106: $i,SV910: $i,SV622: $i,SV259: $i] :
( ( ! [SY2925: $i] :
( ( SV259 = SV622 )
| ~ ( c_Type_Otyping @ SV910 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1106 ) @ SY2925 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV622 )
| ~ ( c_Type_Otyping @ SV910 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1106 ) @ SY2925 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2322]) ).
thf(2625,plain,
! [SV911: $i,SV623: $i,SV260: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV260 @ SV623 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV260 @ SV911 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV623 @ SV911 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2323]) ).
thf(2626,plain,
! [SV624: $i,SV261: $i] :
( ( ( hBOOL @ ( hAPP @ SV261 @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV261 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV261 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV261 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV261 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV261 @ SV624 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2324]) ).
thf(2627,plain,
! [SV912: $i,SV625: $i,SV262: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV262 @ SV625 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV912 @ SV625 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV262 ) @ SV912 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2325]) ).
thf(2628,plain,
! [SV1107: $i,SV913: $i,SV626: $i,SV263: $i] :
( ( ! [SY2926: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV263 @ SV626 @ SV913 @ ( c_Lambda_OdB_OVar @ SV1107 ) @ SY2926 )
= ( hAPP @ SV263 @ SV1107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2326]) ).
thf(2629,plain,
! [SV1108: $i,SV914: $i,SV627: $i,SV264: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV264 @ SV627 @ SV914 @ SV1108 ) @ SV627 )
= SV914 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2327]) ).
thf(2630,plain,
! [SV1109: $i,SV915: $i,SV628: $i,SV265: $i] :
( ( ( c_List_Ofoldl @ SV265 @ SV628 @ ( c_List_Olist_ONil @ SV915 ) @ SV1109 @ SV915 )
= SV628 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2328]) ).
thf(2631,plain,
! [SV1110: $i,SV916: $i,SV629: $i,SV266: $i] :
( ( ( c_Type_Otyping @ SV266 @ ( c_Lambda_OdB_OAbs @ SV629 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV916 ) @ SV1110 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV266 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV916 @ tc_Type_Otype ) @ SV629 @ SV1110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2329]) ).
thf(2632,plain,
! [SV917: $i,SV630: $i,SV268: $i] :
( ( ( ( hAPP @ SV268 @ SV630 )
= SV917 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV268 @ ( c_Lambda_OdB_OVar @ SV630 ) @ SV917 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2330]) ).
thf(2633,plain,
! [SV1111: $i,SV918: $i,SV631: $i,SV269: $i] :
( ( ~ ( class_OrderedGroup_Osemigroup__add @ SV269 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV269 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV269 ) @ SV631 ) @ SV918 ) @ SV1111 @ SV269 @ SV269 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV269 ) @ SV631 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV269 ) @ SV918 @ SV1111 @ SV269 @ SV269 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2331]) ).
thf(2634,plain,
! [SV1112: $i,SV920: $i,SV633: $i,SV271: $i] :
( ( ( c_Type_Otyping @ SV271 @ SV633 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV920 @ SV271 @ SV633 @ SV1112 ) @ SV920 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV271 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV633 @ SV1112 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV920 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2333]) ).
thf(2635,plain,
! [SV1113: $i,SV921: $i,SV634: $i,SV272: $i] :
( ( ( c_Type_Otyping @ SV272 @ ( c_Lambda_OdB_OVar @ SV634 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV921 @ SV272 @ SV634 @ SV1113 ) @ SV921 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV272 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV634 ) @ SV1113 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV921 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2334]) ).
thf(2636,plain,
! [SV1114: $i,SV922: $i,SV635: $i,SV273: $i] :
( ( ! [SY2927: $i] :
( ( c_Type_Otyping @ SV273 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV635 @ SV922 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1114 )
| ~ ( c_Type_Otypings @ SV273 @ SV922 @ SY2927 )
| ~ ( c_Type_Otyping @ SV273 @ SV635 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY2927 @ SV1114 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2335]) ).
thf(2637,plain,
! [SV923: $i,SV636: $i,SV274: $i] :
( ( ( SV274
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV636 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV636 @ SV923 @ SV274 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV636 ) @ SV923 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV274 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2336]) ).
thf(2638,plain,
! [SV1115: $i,SV924: $i,SV637: $i,SV275: $i] :
( ( ! [SY2928: $i,SY2929: $i] :
( ( c_Lambda_OdB_OdB__case @ SV275 @ SV637 @ SV924 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1115 ) @ SY2928 ) @ SY2929 )
= ( hAPP @ ( hAPP @ SV637 @ SV1115 ) @ SY2928 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2337]) ).
thf(2639,plain,
! [SV1116: $i,SV925: $i,SV638: $i,SV276: $i] :
( ( ! [SY2930: $i] :
( ( ( hAPP @ ( hAPP @ SV276 @ SV638 ) @ ( c_List_Ofoldl @ SV276 @ SV925 @ SV1116 @ SY2930 @ SY2930 ) )
= ( c_List_Ofoldl @ SV276 @ SV638 @ SV1116 @ SY2930 @ SY2930 ) )
| ~ ( c_OrderedGroup_Omonoid__add @ SV925 @ SV276 @ SY2930 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2338]) ).
thf(2640,plain,
! [SV1117: $i,SV926: $i,SV639: $i,SV277: $i] :
( ( ( c_Type_Otyping @ SV277 @ SV639 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV926 @ SV277 @ SV1117 @ SV639 ) )
| ~ ( c_Type_Otyping @ SV277 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1117 ) @ SV639 ) @ SV926 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2339]) ).
thf(2641,plain,
! [SV1118: $i,SV927: $i,SV640: $i,SV279: $i] :
( ( ! [SY2931: $i] :
( ( c_Lambda_OdB_OdB__case @ SV279 @ SV640 @ SV927 @ ( c_Lambda_OdB_OVar @ SV1118 ) @ SY2931 )
= ( hAPP @ SV279 @ SV1118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2340]) ).
thf(2642,plain,
! [SV1119: $i,SV928: $i,SV641: $i,SV280: $i] :
( ( ( c_Type_Otypings @ SV280 @ SV641 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV928 @ SV280 @ SV1119 @ SV641 ) )
| ~ ( c_Type_Otyping @ SV280 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1119 @ SV641 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV928 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2341]) ).
thf(2643,plain,
! [SV1120: $i,SV929: $i,SV642: $i,SV281: $i] :
( ( ! [SY2932: $i,SY2933: $i] :
( ( c_List_Ofoldl @ SV281 @ SV642 @ ( c_List_Olist_OCons @ SV929 @ SV1120 @ SY2932 ) @ SY2933 @ SY2932 )
= ( c_List_Ofoldl @ SV281 @ ( hAPP @ ( hAPP @ SV281 @ SV642 ) @ SV929 ) @ SV1120 @ SY2933 @ SY2932 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2342]) ).
thf(2644,plain,
! [SV1121: $i,SV930: $i,SV644: $i,SV284: $i] :
( ( ! [SY2934: $i,SY2935: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV284 @ SV644 @ SV930 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1121 ) @ SY2934 ) @ SY2935 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV644 @ SV1121 ) @ SY2934 ) @ ( c_Lambda_OdB_OdB__rec @ SV284 @ SV644 @ SV930 @ SV1121 @ SY2935 ) ) @ ( c_Lambda_OdB_OdB__rec @ SV284 @ SV644 @ SV930 @ SY2934 @ SY2935 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2343]) ).
thf(2645,plain,
! [SV1122: $i,SV931: $i,SV645: $i,SV286: $i] :
( ( ! [SY2936: $i,SY2937: $i,SY2938: $i] :
( ( c_Type_Otypings @ SV286 @ SV645 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV931 @ SV1122 @ SV286 @ SV645 ) )
| ~ ( c_Type_Otyping @ SV286 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2936 ) @ SY2937 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1122 )
| ~ ( c_Type_Otypings @ SV286 @ SY2937 @ SY2938 )
| ~ ( c_Type_Otyping @ SV286 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2936 ) @ SY2937 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV645 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV931 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2344]) ).
thf(2646,plain,
! [SV932: $i,SV646: $i,SV287: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV287 ) @ SV646 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV287 ) @ SV932 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV646 ) @ SV932 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2345]) ).
thf(2647,plain,
! [SV933: $i,SV647: $i,SV288: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV288 ) @ SV647 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV933 ) @ SV647 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV288 ) @ SV933 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2346]) ).
thf(2648,plain,
! [SV1123: $i,SV934: $i,SV648: $i,SV289: $i] :
( ( ( c_Lambda_Oliftn @ SV289 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV648 ) @ SV934 ) @ SV1123 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ SV289 @ SV648 @ SV1123 ) ) @ ( c_Lambda_Oliftn @ SV289 @ SV934 @ SV1123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2347]) ).
thf(2649,plain,
! [SV1124: $i,SV935: $i,SV649: $i,SV291: $i] :
( ( ( c_Type_Otyping @ SV291 @ SV649 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV935 @ SV291 @ SV649 @ SV1124 ) @ SV935 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV291 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV649 @ SV1124 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV935 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2348]) ).
thf(2650,plain,
! [SV650: $i,SV292: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV292 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV292 ) @ ( c_Lambda_OdB_OVar @ SV650 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2349]) ).
thf(2651,plain,
! [SV936: $i,SV651: $i,SV293: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV293 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV651 @ SV293 @ SV936 ) @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV651 ) @ SV293 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV936 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2350]) ).
thf(2652,plain,
! [SV1125: $i,SV937: $i,SV652: $i,SV294: $i] :
( ( ! [SY2939: $i,SY2940: $i] :
( ~ ( c_Type_Otyping @ SV294 @ SV652 @ SV937 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV294 @ SV1125 @ SV937 @ tc_Type_Otype ) @ SY2939 @ SY2940 )
| ( c_Type_Otyping @ SV294 @ ( c_Lambda_Osubst @ SY2939 @ SV652 @ SV1125 ) @ SY2940 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2351]) ).
thf(2653,plain,
! [SV1126: $i,SV938: $i,SV653: $i,SV295: $i] :
( ( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV295 ) @ SV653 ) @ SV938 @ SV1126 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ SV295 @ SV938 @ SV1126 ) ) @ ( c_Lambda_Osubstn @ SV653 @ SV938 @ SV1126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2352]) ).
thf(2654,plain,
! [SV1127: $i,SV939: $i,SV654: $i,SV296: $i] :
( ( ! [SY2941: $i,SY2942: $i] :
( ( c_List_Ofoldl @ SV296 @ SV654 @ ( c_List_Oappend @ SV939 @ SV1127 @ SY2941 ) @ SY2942 @ SY2941 )
= ( c_List_Ofoldl @ SV296 @ ( c_List_Ofoldl @ SV296 @ SV654 @ SV939 @ SY2942 @ SY2941 ) @ SV1127 @ SY2942 @ SY2941 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2353]) ).
thf(2655,plain,
! [SV1128: $i,SV940: $i,SV655: $i,SV297: $i] :
( ( ( c_Type_Otyping @ SV297 @ SV655 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV940 @ SV297 @ SV655 @ SV1128 ) ) @ SV940 ) )
| ~ ( c_Type_Otyping @ SV297 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV655 ) @ SV1128 ) @ SV940 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2354]) ).
thf(2656,plain,
! [SV298: $i,SV656: $i] :
( ( ( class_Orderings_Opreorder @ SV656 )
= $false )
| ( ( class_Orderings_Opreorder @ ( tc_fun @ SV298 @ SV656 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2355]) ).
thf(2657,plain,
! [SV299: $i,SV657: $i] :
( ( ( class_Orderings_Oorder @ SV657 )
= $false )
| ( ( class_Orderings_Oorder @ ( tc_fun @ SV299 @ SV657 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2356]) ).
thf(2658,plain,
! [SV941: $i,SV659: $i,SV301: $i] :
( ( ( SV301 = SV659 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV941 ) @ SV301 ) @ SV659 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2357]) ).
thf(2659,plain,
! [SV942: $i,SV660: $i,SV302: $i] :
( ( ( ( c_List_Orev @ SV302 @ SV660 )
!= ( c_List_Orev @ SV942 @ SV660 ) )
= $true )
| ( ( SV302 = SV942 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2358]) ).
thf(2660,plain,
! [SV943: $i,SV661: $i,SV303: $i] :
( ( ( ( c_List_Oappend @ SV303 @ SV661 @ SV943 )
!= ( c_List_Olist_ONil @ SV943 ) )
= $true )
| ( ( SV303
= ( c_List_Olist_ONil @ SV943 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2359]) ).
thf(2661,plain,
! [SV1129: $i,SV944: $i,SV662: $i,SV304: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV304 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV304 ) @ SV662 ) @ SV944 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV304 ) @ SV662 ) @ SV1129 ) )
| ( SV944 = SV1129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2360]) ).
thf(2662,plain,
! [SV945: $i,SV663: $i,SV305: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV305 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV663 @ SV945 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_Lambda_OdB_OAbs @ SV305 )
= SV663 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2361]) ).
thf(2663,plain,
! [SV664: $i,SV306: $i] :
( ( ( SV306
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV306 ) @ SV664 ) )
= $false )
| ( ( SV664
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2362]) ).
thf(2664,plain,
! [SV946: $i,SV665: $i,SV307: $i] :
( ( ( ( c_List_Oreplicate @ SV307 @ SV665 @ SV946 )
!= ( c_List_Olist_ONil @ SV946 ) )
= $true )
| ( ( SV307
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2363]) ).
thf(2665,plain,
! [SV1130: $i,SV947: $i,SV666: $i,SV308: $i] :
( ( ! [SY2943: $i] :
( ( ( c_List_Oreplicate @ SV308 @ SV666 @ SV947 )
!= ( c_List_Oreplicate @ SV1130 @ SY2943 @ SV947 ) )
| ( SV666 = SY2943 )
| ( SV308
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2364]) ).
thf(2666,plain,
! [SV1131: $i,SV948: $i,SV667: $i,SV309: $i] :
( ( ! [SY2944: $i] :
( ( ( c_List_Oappend @ SV309 @ SV667 @ SV948 )
!= ( c_List_Olist_OCons @ SV1131 @ SY2944 @ SV948 ) )
| ( SV309
= ( c_List_Olist_OCons @ SV1131 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1131 @ SY2944 @ SV309 @ SV667 @ SV948 ) @ SV948 ) )
| ( SV309
= ( c_List_Olist_ONil @ SV948 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2365]) ).
thf(2667,plain,
! [SV1132: $i,SV949: $i,SV668: $i,SV310: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV310 ) @ SV668 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV949 ) @ SV1132 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV949 @ SV668 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV310 @ SV1132 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2366]) ).
thf(2668,plain,
! [SV950: $i,SV669: $i,SV311: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV311 ) @ SV669 )
= ( c_Lambda_OdB_OVar @ SV950 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2367]) ).
thf(2669,plain,
! [SV951: $i,SV670: $i,SV312: $i] :
( ( ( ( c_List_Oappend @ SV312 @ SV670 @ SV951 )
!= ( c_List_Olist_ONil @ SV951 ) )
= $true )
| ( ( SV670
= ( c_List_Olist_ONil @ SV951 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2368]) ).
thf(2670,plain,
! [SV952: $i,SV671: $i,SV313: $i] :
( ( ( c_List_Olist_ONil @ SV313 )
= ( c_List_Olist_OCons @ SV671 @ SV952 @ SV313 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2369]) ).
thf(2671,plain,
! [SV1133: $i,SV953: $i,SV672: $i,SV314: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV314 ) @ SV672 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV953 @ SV1133 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1133
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV314 @ SV672 @ SV953 @ SV1133 ) @ ( c_List_Olist_OCons @ SV672 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( SV1133
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2370]) ).
thf(2672,plain,
! [SV954: $i,SV673: $i,SV315: $i] :
( ( ( SV315
!= ( c_List_Oappend @ SV673 @ SV315 @ SV954 ) )
= $true )
| ( ( SV673
= ( c_List_Olist_ONil @ SV954 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2371]) ).
thf(2673,plain,
! [SV1134: $i,SV955: $i,SV674: $i,SV316: $i] :
( ( ! [SY2945: $i] :
( ( ( c_List_Olist_OCons @ SV316 @ SV674 @ SV955 )
!= ( c_List_Oappend @ SV1134 @ SY2945 @ SV955 ) )
| ( SV674
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV316 @ SV674 @ SV1134 @ SY2945 @ SV955 ) @ SY2945 @ SV955 ) )
| ( ( c_List_Olist_OCons @ SV316 @ SV674 @ SV955 )
= SY2945 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2372]) ).
thf(2674,plain,
! [SV675: $i,SV317: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV317 ) @ SV675 )
= SV317 )
= $false )
| ( ( SV675
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2373]) ).
thf(2675,plain,
! [SV956: $i,SV676: $i,SV318: $i] :
( ( ( c_List_Olist_OCons @ SV318 @ SV676 @ SV956 )
= SV676 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2374]) ).
thf(2676,plain,
! [SV957: $i,SV677: $i,SV319: $i] :
( ( ( SV319
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV319 ) @ SV677 ) @ SV957 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV319 ) @ SV677 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV319 ) @ SV677 ) @ ( c_List_Oappend @ SV957 @ ( c_List_Olist_OCons @ SV677 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2375]) ).
thf(2677,plain,
! [SV1135: $i,SV958: $i,SV678: $i,SV320: $i] :
( ( ! [SY2946: $i] :
( ( ( c_List_Olist_OCons @ SV320 @ SV678 @ SV958 )
!= ( c_List_Olist_OCons @ SV1135 @ SY2946 @ SV958 ) )
| ( SV320 = SV1135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2376]) ).
thf(2678,plain,
! [SV959: $i,SV679: $i,SV321: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV321 ) @ SV679 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV321 ) @ SV959 ) )
= $true )
| ( ( SV679 = SV959 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2377]) ).
thf(2679,plain,
! [SV1136: $i,SV960: $i,SV680: $i,SV322: $i] :
( ( ( ( c_List_Oappend @ SV322 @ SV680 @ SV960 )
!= ( c_List_Oappend @ SV1136 @ SV680 @ SV960 ) )
| ( SV322 = SV1136 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2378]) ).
thf(2680,plain,
! [SV961: $i,SV681: $i,SV323: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV323 ) @ SV681 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV323 ) @ SV961 ) )
= $true )
| ( ( SV681 = SV961 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2379]) ).
thf(2681,plain,
! [SV962: $i,SV682: $i,SV324: $i] :
( ( ( c_List_Olist_OCons @ SV324 @ SV682 @ SV962 )
= ( c_List_Olist_ONil @ SV962 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2380]) ).
thf(2682,plain,
! [SV1137: $i,SV963: $i,SV683: $i,SV325: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV325 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV325 ) @ SV683 ) @ SV963 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV325 ) @ SV1137 ) @ SV963 ) )
| ( SV683 = SV1137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2381]) ).
thf(2683,plain,
! [SV964: $i,SV684: $i,SV326: $i] :
( ( ( SV326
!= ( c_List_Oappend @ SV326 @ SV684 @ SV964 ) )
= $true )
| ( ( SV684
= ( c_List_Olist_ONil @ SV964 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2382]) ).
thf(2684,plain,
! [SV1138: $i,SV965: $i,SV685: $i,SV327: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV327 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SV685 ) @ SV965 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SV685 ) @ SV1138 ) )
| ( SV965 = SV1138 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2383]) ).
thf(2685,plain,
! [SV966: $i,SV686: $i,SV328: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV328 ) @ SV686 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV966 ) @ SV686 ) )
= $true )
| ( ( SV328 = SV966 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2384]) ).
thf(2686,plain,
! [SV1139: $i,SV967: $i,SV687: $i,SV329: $i] :
( ( ! [SY2947: $i,SY2948: $i,SY2949: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV329 ) @ SV687 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV967 @ SV1139 @ SY2947 ) ) )
| ~ ( c_Type_Otyping @ SY2948 @ SV1139 @ SV687 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1139 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY2948 @ SY2947 @ SV687 @ tc_Type_Otype ) @ SV967 @ SY2949 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV967 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2385]) ).
thf(2687,plain,
! [SV689: $i,SV331: $i] :
( ( ( ( c_List_Orev @ SV331 @ SV689 )
= ( c_List_Olist_ONil @ SV689 ) )
= $false )
| ( ( SV331
= ( c_List_Olist_ONil @ SV689 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2387]) ).
thf(2688,plain,
! [SV1140: $i,SV968: $i,SV690: $i,SV332: $i] :
( ( ! [SY2950: $i] :
( ( ( c_List_Oreplicate @ SV332 @ SV690 @ SV968 )
!= ( c_List_Oreplicate @ SV1140 @ SY2950 @ SV968 ) )
| ( SV332 = SV1140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2388]) ).
thf(2689,plain,
! [SV969: $i,SV692: $i,SV334: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV334 @ SV692 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV969 ) )
= $true )
| ( ( SV334
= ( c_Lambda_OdB_OAbs @ SV969 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2390]) ).
thf(2690,plain,
! [SV970: $i,SV693: $i,SV335: $i] :
( ( ( c_Lambda_OdB_OVar @ SV335 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV693 ) @ SV970 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2391]) ).
thf(2691,plain,
! [SV971: $i,SV694: $i,SV336: $i] :
( ( ( ( c_List_Orev @ SV336 @ SV694 )
!= ( c_List_Olist_OCons @ SV971 @ ( c_List_Olist_ONil @ SV694 ) @ SV694 ) )
= $true )
| ( ( SV336
= ( c_List_Olist_OCons @ SV971 @ ( c_List_Olist_ONil @ SV694 ) @ SV694 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2392]) ).
thf(2692,plain,
! [SV972: $i,SV695: $i,SV337: $i] :
( ( SV337
= ( c_List_Olist_OCons @ SV695 @ SV337 @ SV972 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2393]) ).
thf(2693,plain,
! [SV1141: $i,SV973: $i,SV696: $i,SV338: $i] :
( ( ! [SY2951: $i] :
( ( ( c_List_Oappend @ SV338 @ SV696 @ SV973 )
!= ( c_List_Olist_OCons @ SV1141 @ SY2951 @ SV973 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1141 @ SY2951 @ SV338 @ SV696 @ SV973 ) @ SV696 @ SV973 )
= SY2951 )
| ( SV338
= ( c_List_Olist_ONil @ SV973 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2394]) ).
thf(2694,plain,
! [SV974: $i,SV697: $i,SV339: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV339 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV339 )
| ( SV697
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV339 ) @ SV697 ) @ SV974 ) )
| ( SV974
= ( c_HOL_Ozero__class_Ozero @ SV339 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2395]) ).
thf(2695,plain,
! [SV1142: $i,SV975: $i,SV698: $i,SV340: $i] :
( ( ( ( c_List_Oappend @ SV340 @ SV698 @ SV975 )
!= ( c_List_Oappend @ SV340 @ SV1142 @ SV975 ) )
| ( SV698 = SV1142 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2396]) ).
thf(2696,plain,
! [SV1143: $i,SV976: $i,SV699: $i,SV341: $i] :
( ( ! [SY2952: $i] :
( ( ( c_List_Olist_OCons @ SV341 @ SV699 @ SV976 )
!= ( c_List_Oappend @ SV1143 @ SY2952 @ SV976 ) )
| ( SV699
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV341 @ SV699 @ SV1143 @ SY2952 @ SV976 ) @ SY2952 @ SV976 ) )
| ( SV1143
= ( c_List_Olist_ONil @ SV976 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2397]) ).
thf(2697,plain,
! [SV1144: $i,SV977: $i,SV700: $i,SV342: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV342 ) @ SV700 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV977 ) @ SV1144 ) )
| ( SV700 = SV1144 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2398]) ).
thf(2698,plain,
! [SV701: $i,SV343: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV343 )
= ( c_Lambda_OdB_OAbs @ SV701 ) )
= $false )
| ( ( SV343 = SV701 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2399]) ).
thf(2699,plain,
! [SV1145: $i,SV978: $i,SV702: $i,SV344: $i] :
( ( ! [SY2953: $i] :
( ( ( c_List_Oappend @ SV344 @ SV702 @ SV978 )
!= ( c_List_Olist_OCons @ SV1145 @ SY2953 @ SV978 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1145 @ SY2953 @ SV344 @ SV702 @ SV978 ) @ SV702 @ SV978 )
= SY2953 )
| ( SV702
= ( c_List_Olist_OCons @ SV1145 @ SY2953 @ SV978 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2400]) ).
thf(2700,plain,
! [SV703: $i,SV345: $i] :
( ( ( ( c_List_Orotate1 @ SV345 @ SV703 )
= ( c_List_Olist_ONil @ SV703 ) )
= $false )
| ( ( SV345
= ( c_List_Olist_ONil @ SV703 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2401]) ).
thf(2701,plain,
! [SV1146: $i,SV979: $i,SV704: $i,SV346: $i] :
( ( ! [SY2954: $i] :
( ( ( c_List_Olist_OCons @ SV346 @ SV704 @ SV979 )
!= ( c_List_Oappend @ SV1146 @ SY2954 @ SV979 ) )
| ( ( c_List_Olist_OCons @ SV346 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV346 @ SV704 @ SV1146 @ SY2954 @ SV979 ) @ SV979 )
= SV1146 )
| ( SV1146
= ( c_List_Olist_ONil @ SV979 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2402]) ).
thf(2702,plain,
! [SV980: $i,SV705: $i,SV347: $i] :
( ( ( ( c_List_Olist_ONil @ SV347 )
!= ( c_List_Oreplicate @ SV705 @ SV980 @ SV347 ) )
= $true )
| ( ( SV705
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2403]) ).
thf(2703,plain,
! [SV1147: $i,SV981: $i,SV706: $i,SV348: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV348 ) @ SV706 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV981 ) @ SV1147 ) )
| ( SV706 = SV1147 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2404]) ).
thf(2704,plain,
! [SV982: $i,SV707: $i,SV349: $i] :
( ( ( ~ ( class_Nat_Osemiring__char__0 @ SV349 ) )
= $true )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV707 @ SV349 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV982 @ SV349 ) )
| ( SV707 = SV982 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2405]) ).
thf(2705,plain,
! [SV1148: $i,SV983: $i,SV708: $i,SV350: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV350 ) @ SV708 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV983 @ SV1148 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV350
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV983 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV350 @ SV708 @ SV983 @ SV1148 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1148
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2406]) ).
thf(2706,plain,
! [SV1149: $i,SV984: $i,SV709: $i,SV351: $i] :
( ( ! [SY2955: $i] :
( ( ( c_List_Oappend @ SV351 @ ( c_List_Olist_OCons @ SV709 @ ( c_List_Olist_ONil @ SV984 ) @ SV984 ) @ SV984 )
!= ( c_List_Oappend @ SV1149 @ ( c_List_Olist_OCons @ SY2955 @ ( c_List_Olist_ONil @ SV984 ) @ SV984 ) @ SV984 ) )
| ( SV709 = SY2955 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2407]) ).
thf(2707,plain,
! [SV1150: $i,SV985: $i,SV710: $i,SV352: $i] :
( ( ! [SY2956: $i] :
( ( ( c_List_Olist_OCons @ SV352 @ SV710 @ SV985 )
!= ( c_List_Olist_OCons @ SV1150 @ SY2956 @ SV985 ) )
| ( SV710 = SY2956 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2408]) ).
thf(2708,plain,
! [SV986: $i,SV711: $i,SV353: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV353 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV711 @ SV986 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV986
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2409]) ).
thf(2709,plain,
! [SV987: $i,SV712: $i,SV354: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV354 @ SV712 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV987 ) )
= $true )
| ( ( SV712
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2410]) ).
thf(2710,plain,
! [SV988: $i,SV713: $i,SV355: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV355 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV713 @ SV988 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_Lambda_OdB_OVar @ SV355 )
= SV713 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2411]) ).
thf(2711,plain,
! [SV989: $i,SV714: $i,SV356: $i] :
( ( ( ( c_List_Olist_OCons @ SV356 @ ( c_List_Olist_ONil @ SV714 ) @ SV714 )
!= ( c_List_Orev @ SV989 @ SV714 ) )
= $true )
| ( ( SV989
= ( c_List_Olist_OCons @ SV356 @ ( c_List_Olist_ONil @ SV714 ) @ SV714 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2412]) ).
thf(2712,plain,
! [SV715: $i,SV357: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV357 ) @ SV715 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV357
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2413]) ).
thf(2713,plain,
! [SV1151: $i,SV990: $i,SV716: $i,SV358: $i] :
( ( ! [SY2957: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV358 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV716 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV990 ) @ SV1151 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV990 ) @ SY2957 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV716 ) @ SV1151 )
= SY2957 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2414]) ).
thf(2714,plain,
! [SV1152: $i,SV991: $i,SV717: $i,SV359: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV359 ) @ SV717 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV991 ) @ SV1152 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV359 = SV991 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2415]) ).
thf(2715,plain,
! [SV718: $i,SV360: $i] :
( ( ( ( c_List_Olist_ONil @ SV360 )
= ( c_List_Orev @ SV718 @ SV360 ) )
= $false )
| ( ( SV718
= ( c_List_Olist_ONil @ SV360 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2416]) ).
thf(2716,plain,
! [SV1153: $i,SV992: $i,SV719: $i,SV361: $i] :
( ( ! [SY2958: $i] :
( ( ( c_List_Olist_OCons @ SV361 @ SV719 @ SV992 )
!= ( c_List_Oappend @ SV1153 @ SY2958 @ SV992 ) )
| ( ( c_List_Olist_OCons @ SV361 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV361 @ SV719 @ SV1153 @ SY2958 @ SV992 ) @ SV992 )
= SV1153 )
| ( ( c_List_Olist_OCons @ SV361 @ SV719 @ SV992 )
= SY2958 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2417]) ).
thf(2717,plain,
! [SV1154: $i,SV993: $i,SV720: $i,SV362: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV362 ) @ SV720 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV993 ) @ SV1154 ) )
| ( SV362 = SV993 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2418]) ).
thf(2718,plain,
! [SV1155: $i,SV994: $i,SV721: $i,SV363: $i] :
( ( ( ( c_List_Orev @ SV363 @ SV721 )
!= ( c_List_Olist_OCons @ SV994 @ SV1155 @ SV721 ) )
| ( SV363
= ( c_List_Oappend @ ( c_List_Orev @ SV1155 @ SV721 ) @ ( c_List_Olist_OCons @ SV994 @ ( c_List_Olist_ONil @ SV721 ) @ SV721 ) @ SV721 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2419]) ).
thf(2719,plain,
! [SV995: $i,SV722: $i,SV364: $i] :
( ( ( ( c_List_Oappend @ SV364 @ SV722 @ SV995 )
!= SV722 )
= $true )
| ( ( SV364
= ( c_List_Olist_ONil @ SV995 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2420]) ).
thf(2720,plain,
! [SV723: $i,SV365: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV365 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV365 ) @ SV723 ) @ SV723 )
!= ( c_HOL_Ozero__class_Ozero @ SV365 ) )
| ( SV723
= ( c_HOL_Ozero__class_Ozero @ SV365 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2421]) ).
thf(2721,plain,
! [SV996: $i,SV724: $i,SV366: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV366 ) @ SV724 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV996 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV366 ) @ SV724 )
= SV996 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2422]) ).
thf(2722,plain,
! [SV997: $i,SV725: $i,SV367: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV367 ) @ SV725 )
= ( c_Lambda_OdB_OAbs @ SV997 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2423]) ).
thf(2723,plain,
! [SV1156: $i,SV998: $i,SV726: $i,SV368: $i] :
( ( ! [SY2959: $i] :
( ( ( c_List_Oappend @ SV368 @ SV726 @ SV998 )
!= ( c_List_Olist_OCons @ SV1156 @ SY2959 @ SV998 ) )
| ( SV368
= ( c_List_Olist_OCons @ SV1156 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1156 @ SY2959 @ SV368 @ SV726 @ SV998 ) @ SV998 ) )
| ( SV726
= ( c_List_Olist_OCons @ SV1156 @ SY2959 @ SV998 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2424]) ).
thf(2724,plain,
! [SV727: $i,SV369: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV369 ) @ SV727 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV727
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2425]) ).
thf(2725,plain,
! [SV1157: $i,SV999: $i,SV728: $i,SV370: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV370 ) @ SV728 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV999 ) @ SV1157 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV370 = SV999 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2426]) ).
thf(2726,plain,
! [SV1000: $i,SV729: $i,SV371: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV371 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV729 @ SV1000 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV1000
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2427]) ).
thf(2727,plain,
! [SV1001: $i,SV730: $i,SV372: $i] :
( ( ( ( c_List_Olist_ONil @ SV372 )
!= ( c_List_Oappend @ SV730 @ SV1001 @ SV372 ) )
= $true )
| ( ( SV730
= ( c_List_Olist_ONil @ SV372 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2428]) ).
thf(2728,plain,
! [SV1002: $i,SV731: $i,SV373: $i] :
( ( ( ( c_List_Oappend @ SV373 @ SV731 @ SV1002 )
!= SV373 )
= $true )
| ( ( SV731
= ( c_List_Olist_ONil @ SV1002 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2429]) ).
thf(2729,plain,
! [SV1158: $i,SV1003: $i,SV732: $i,SV374: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV374 ) @ SV732 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1003 ) @ SV1158 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2430]) ).
thf(2730,plain,
! [SV733: $i,SV375: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV375 )
= ( c_Lambda_OdB_OVar @ SV733 ) )
= $false )
| ( ( SV375 = SV733 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2431]) ).
thf(2731,plain,
! [SV1004: $i,SV734: $i,SV376: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV376 @ SV734 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1004 @ SV734 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV376 = SV1004 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2432]) ).
thf(2732,plain,
! [SV1159: $i,SV1005: $i,SV735: $i,SV377: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV377 ) @ SV735 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1005 ) @ SV1159 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV735 = SV1159 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2433]) ).
thf(2733,plain,
! [SV1160: $i,SV1006: $i,SV736: $i,SV378: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV378 )
| ~ ( class_Int_Onumber__ring @ SV378 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV378 ) @ SV736 ) @ SV1006 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV378 ) @ SV736 ) @ SV1160 ) )
| ( SV1006 = SV1160 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2434]) ).
thf(2734,plain,
! [SV1007: $i,SV737: $i,SV379: $i] :
( ( ( c_List_Olist_OCons @ SV379 @ SV737 @ SV1007 )
= ( c_List_Olist_ONil @ SV1007 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2435]) ).
thf(2735,plain,
! [SV1161: $i,SV1008: $i,SV738: $i,SV380: $i] :
( ( ! [SY2960: $i,SY2961: $i,SY2962: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV380 ) @ SV738 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV1008 @ SV1161 @ SY2960 ) ) )
| ~ ( c_Type_Otyping @ SY2961 @ SV1161 @ SV380 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1161 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY2961 @ SY2960 @ SV380 @ tc_Type_Otype ) @ SV1008 @ SY2962 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1008 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2436]) ).
thf(2736,plain,
! [SV1009: $i,SV739: $i,SV381: $i] :
( ( ( ( c_List_Olist_ONil @ SV381 )
!= ( c_List_Oappend @ SV739 @ SV1009 @ SV381 ) )
= $true )
| ( ( SV1009
= ( c_List_Olist_ONil @ SV381 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2437]) ).
thf(2737,plain,
! [SV1162: $i,SV1010: $i,SV740: $i,SV382: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV382 ) @ SV740 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1010 ) @ SV1162 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV740 = SV1162 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2438]) ).
thf(2738,plain,
! [SV1011: $i,SV741: $i,SV383: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV383 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV741 ) @ SV1011 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2439]) ).
thf(2739,plain,
! [SV1163: $i,SV1012: $i,SV742: $i,SV384: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV384 ) ) @ SV742 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1012 ) @ SV1163 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2440]) ).
thf(2740,plain,
! [SV743: $i,SV385: $i] :
( ( ( ( c_Nat_Osize__class_Osize @ SV385 @ ( tc_List_Olist @ SV743 ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV385
= ( c_List_Olist_ONil @ SV743 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2441]) ).
thf(2741,plain,
! [SV1164: $i,SV1013: $i,SV744: $i,SV386: $i] :
( ( ! [SY2963: $i] :
( ( ( c_List_Oappend @ SV386 @ ( c_List_Olist_OCons @ SV744 @ ( c_List_Olist_ONil @ SV1013 ) @ SV1013 ) @ SV1013 )
!= ( c_List_Oappend @ SV1164 @ ( c_List_Olist_OCons @ SY2963 @ ( c_List_Olist_ONil @ SV1013 ) @ SV1013 ) @ SV1013 ) )
| ( SV386 = SV1164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2442]) ).
thf(2742,plain,
! [SV1165: $i,SV1014: $i,SV745: $i,SV387: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV387 ) @ SV745 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1014 ) @ SV1165 ) )
| ( SV387 = SV1014 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2443]) ).
thf(2743,plain,
! [SV1015: $i,SV746: $i,SV390: $i,SV3: $i] :
( ( ( c_Type_Otyping @ SV3 @ SV390 @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ SV746 @ SV3 @ SV390 @ SV1015 ) )
= $true )
| ( ( ~ ( c_Type_Otypings @ SV3 @ ( c_List_Oappend @ SV1015 @ ( c_List_Olist_OCons @ SV390 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SV746 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2445]) ).
thf(2744,plain,
! [SV1016: $i,SV750: $i,SV394: $i,SV11: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV11 @ SV394 @ SV394 ) @ SV394 ) @ SV750 ) @ SV1016 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV11 @ SV394 ) @ SV1016 ) @ SV750 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2447]) ).
thf(2745,plain,
! [SV1017: $i,SV751: $i,SV395: $i,SV12: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV12 @ SV395 ) @ SV751 ) @ SV1017 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV12 @ SV395 @ SV395 ) @ SV395 ) @ SV1017 ) @ SV751 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2448]) ).
thf(2746,plain,
! [SV1166: $i,SV1018: $i,SV752: $i,SV396: $i,SV13: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV13 @ SV396 ) @ SV752 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV13 @ SV1018 @ SV1166 ) @ SV752 ) @ SV396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2449]) ).
thf(2747,plain,
! [SV1167: $i,SV1019: $i,SV753: $i,SV397: $i,SV14: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV14 @ SV397 @ SV753 ) @ SV1019 ) @ SV1167 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV14 @ SV1167 ) @ SV1019 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2450]) ).
thf(2748,plain,
! [SV1168: $i,SV1020: $i,SV754: $i,SV398: $i,SV15: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV15 @ SV398 ) @ SV754 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV15 @ SV1020 @ SV1168 ) @ SV754 ) @ SV398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2451]) ).
thf(2749,plain,
! [SV1169: $i,SV1021: $i,SV755: $i,SV399: $i,SV16: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV16 @ SV399 @ SV755 ) @ SV1021 ) @ SV1169 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV16 @ SV1169 ) @ SV1021 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2452]) ).
thf(2750,plain,
! [SV1022: $i,SV758: $i,SV402: $i,SV20: $i] :
( ( ( c_Wellfounded_Oaccp @ SV20 @ SV402 @ SV758 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV20 @ SV758 ) @ SV402 ) @ SV1022 ) )
| ~ ( c_Wellfounded_Oaccp @ SV20 @ SV1022 @ SV758 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2453]) ).
thf(2751,plain,
! [SV1023: $i,SV759: $i,SV403: $i,SV21: $i] :
( ( ( c_Wellfounded_Oaccp @ SV21 @ SV403 @ SV759 )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV21 @ SV1023 @ SV759 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV21 @ SV759 ) @ SV403 ) @ SV1023 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2454]) ).
thf(2752,plain,
! [SV760: $i,SV407: $i,SV27: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV27 @ SV407 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV27 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV407 ) @ SV760 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2455]) ).
thf(2753,plain,
! [SV408: $i,SV761: $i,SV28: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV28 @ SV761 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV28 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV408 ) @ SV761 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2456]) ).
thf(2754,plain,
! [SV409: $i,SV762: $i,SV29: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV29 ) @ SV762 ) @ SV409 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV29 @ SV409 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2457]) ).
thf(2755,plain,
! [SV763: $i,SV410: $i,SV30: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV30 @ SV410 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV30 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV410 ) @ SV763 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2458]) ).
thf(2756,plain,
! [SV411: $i,SV764: $i,SV31: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV31 @ SV764 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV31 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV411 ) @ SV764 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2459]) ).
thf(2757,plain,
! [SV1025: $i,SV768: $i,SV417: $i,SV38: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV38 ) @ SV417 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV768 ) @ SV1025 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV417 @ SV1025 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV38 @ SV768 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2461]) ).
thf(2758,plain,
! [SV424: $i,SV772: $i,SV45: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV45 @ SV772 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV45 ) @ SV424 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV772 ) @ SV424 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2464]) ).
thf(2759,plain,
! [SV425: $i,SV46: $i,SV773: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV773 ) @ SV46 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV773 ) @ SV425 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV46 @ SV425 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2465]) ).
thf(2760,plain,
! [SV47: $i,SV774: $i,SV426: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV426 @ SV774 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV47 ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV47 ) @ SV774 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2466]) ).
thf(2761,plain,
! [SV775: $i,SV428: $i,SV51: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV51 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV428 ) @ SV775 ) @ SV51 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV51 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV428 @ SV51 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV775 @ SV51 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2467]) ).
thf(2762,plain,
! [SV1027: $i,SV776: $i,SV429: $i,SV52: $i] :
( ( ( c_Wellfounded_Oaccp @ SV52 @ SV429 @ SV776 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV52 @ SV429 ) @ SV1027 ) )
| ~ ( c_Wellfounded_Oaccp @ SV52 @ SV1027 @ SV776 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2468]) ).
thf(2763,plain,
! [SV1028: $i,SV777: $i,SV430: $i,SV53: $i] :
( ( ( c_Wellfounded_Oaccp @ SV53 @ SV430 @ SV777 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV53 @ SV430 ) @ SV1028 ) )
| ~ ( c_Wellfounded_Oaccp @ SV53 @ SV1028 @ SV777 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2469]) ).
thf(2764,plain,
! [SV55: $i,SV432: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV432 @ SV55 ) @ ( c_HOL_Ozero__class_Ozero @ SV55 ) @ SV55 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2470]) ).
thf(2765,plain,
! [SV778: $i,SV433: $i,SV57: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV57 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV433 @ SV57 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV778 @ SV57 ) @ SV57 )
| ~ ( c_HOL_Oord__class_Oless @ SV433 @ SV778 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2471]) ).
thf(2766,plain,
! [SV779: $i,SV434: $i,SV58: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV58 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV434 @ SV779 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV434 @ SV58 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV779 @ SV58 ) @ SV58 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2472]) ).
thf(2767,plain,
! [SV780: $i,SV435: $i,SV60: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV60 )
= $false )
| ( ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ SV435 @ SV780 @ SV60 ) @ SV60 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV435 ) @ ( c_List_Olistsum @ SV780 @ SV60 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2473]) ).
thf(2768,plain,
! [SV63: $i,SV438: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV438 ) @ SV63 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV438 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV63 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2476]) ).
thf(2769,plain,
! [SV781: $i,SV441: $i,SV67: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV67 )
= $false )
| ( ( ( c_List_Olistsum @ ( c_List_Oappend @ SV441 @ SV781 @ SV67 ) @ SV67 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV67 ) @ ( c_List_Olistsum @ SV441 @ SV67 ) ) @ ( c_List_Olistsum @ SV781 @ SV67 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2477]) ).
thf(2770,plain,
! [SV793: $i,SV459: $i,SV86: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV86 @ SV459 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV793 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV459 @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV86 ) ) @ SV459 ) @ SV793 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2483]) ).
thf(2771,plain,
! [SV89: $i,SV462: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV462 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV462 @ SV89 ) @ SV89 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2486]) ).
thf(2772,plain,
! [SV463: $i,SV90: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV463 @ SV90 ) @ SV90 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV463 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2487]) ).
thf(2773,plain,
! [SV466: $i,SV93: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV93 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV93 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV93 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV93 @ SV466 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV93 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV93 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__4 @ SV93 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2489]) ).
thf(2774,plain,
! [SV467: $i,SV94: $i] :
( ( ( hBOOL @ ( hAPP @ SV94 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV94 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4 @ SV94 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV94 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV94 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV94 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV94 @ SV467 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2490]) ).
thf(2775,plain,
! [SV1170: $i,SV1030: $i,SV797: $i,SV469: $i,SV96: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV96 @ SV469 ) @ SV797 ) )
| ( c_ListOrder_Ostep1 @ SV96 @ ( c_List_Olist_OCons @ SV469 @ SV1030 @ SV1170 ) @ ( c_List_Olist_OCons @ SV797 @ SV1030 @ SV1170 ) @ SV1170 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2491]) ).
thf(2776,plain,
! [SV1171: $i,SV1031: $i,SV798: $i,SV470: $i,SV97: $i] :
( ( ! [SY2964: $i] :
( ( SV97 = SV470 )
| ( SV798 = SV1031 )
| ~ ( c_ListOrder_Ostep1 @ SV1171 @ ( c_List_Olist_OCons @ SV470 @ SV1031 @ SY2964 ) @ ( c_List_Olist_OCons @ SV97 @ SV798 @ SY2964 ) @ SY2964 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2492]) ).
thf(2777,plain,
! [SV1032: $i,SV799: $i,SV471: $i,SV98: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV98 @ SV471 @ SV799 ) ) @ ( c_Lambda_Osubst @ SV1032 @ SV471 @ SV799 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV98 ) @ SV1032 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2493]) ).
thf(2778,plain,
! [SV1172: $i,SV1033: $i,SV800: $i,SV472: $i,SV99: $i] :
( ( ( c_Lambda_OdB_OdB__case @ SV99 @ SV472 @ SV800 @ ( c_Lambda_OdB_OAbs @ SV1033 ) @ SV1172 )
= ( hAPP @ SV800 @ SV1033 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2494]) ).
thf(2779,plain,
! [SV1034: $i,SV801: $i,SV473: $i,SV100: $i] :
( ( ( c_List_Olistsp @ SV100 @ SV473 @ SV801 )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV100 @ ( c_List_Oappend @ SV1034 @ SV473 @ SV801 ) @ SV801 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2495]) ).
thf(2780,plain,
! [SV1035: $i,SV802: $i,SV474: $i,SV101: $i] :
( ( ( c_List_Olistsp @ SV101 @ SV474 @ SV802 )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV101 @ ( c_List_Oappend @ SV474 @ SV1035 @ SV802 ) @ SV802 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2496]) ).
thf(2781,plain,
! [SV475: $i,SV803: $i,SV102: $i] :
( ( ( SV102 = SV803 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV803 @ SV102 @ tc_nat )
= $true )
| ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV102 ) @ SV475 @ SV803 )
= ( c_Lambda_OdB_OVar @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2497]) ).
thf(2782,plain,
! [SV1173: $i,SV1036: $i,SV804: $i,SV477: $i,SV104: $i] :
( ( ( c_ListOrder_Ostep1 @ SV104 @ ( c_List_Oappend @ SV477 @ SV804 @ SV1036 ) @ ( c_List_Oappend @ SV477 @ SV1173 @ SV1036 ) @ SV1036 )
| ~ ( c_ListOrder_Ostep1 @ SV104 @ SV804 @ SV1173 @ SV1036 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2499]) ).
thf(2783,plain,
! [SV1174: $i,SV1037: $i,SV805: $i,SV478: $i,SV105: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV105 @ SV478 @ SV805 @ SV1037 )
| ( c_ListOrder_Ostep1 @ SV105 @ ( c_List_Oappend @ SV478 @ SV1174 @ SV1037 ) @ ( c_List_Oappend @ SV805 @ SV1174 @ SV1037 ) @ SV1037 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2500]) ).
thf(2784,plain,
! [SV1038: $i,SV807: $i,SV480: $i,SV108: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV108 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV480 @ SV807 @ SV108 )
| ~ ( c_HOL_Oord__class_Oless @ SV1038 @ SV807 @ SV108 )
| ~ ( c_HOL_Oord__class_Oless @ SV480 @ SV1038 @ SV108 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2501]) ).
thf(2785,plain,
! [SV1039: $i,SV808: $i,SV481: $i,SV109: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV109 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV481 @ SV808 @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ SV481 @ SV1039 @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ SV1039 @ SV808 @ SV109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2502]) ).
thf(2786,plain,
! [SV1040: $i,SV809: $i,SV482: $i,SV110: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV110 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV482 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV809 ) @ SV1040 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV482 ) @ SV809 ) ) @ SV1040 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2503]) ).
thf(2787,plain,
! [SV1041: $i,SV810: $i,SV483: $i,SV111: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV111 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV483 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV810 ) @ SV1041 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV810 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV483 ) @ SV1041 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2504]) ).
thf(2788,plain,
! [SV1042: $i,SV811: $i,SV484: $i,SV112: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV112 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SV484 ) @ SV811 ) ) @ SV1042 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SV484 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SV811 ) @ SV1042 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2505]) ).
thf(2789,plain,
! [SV1043: $i,SV812: $i,SV485: $i,SV113: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV113 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV485 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV812 ) @ SV1043 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV812 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV485 ) @ SV1043 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2506]) ).
thf(2790,plain,
! [SV1044: $i,SV813: $i,SV486: $i,SV114: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV114 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SV486 ) @ SV813 ) ) @ SV1044 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SV486 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SV813 ) @ SV1044 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2507]) ).
thf(2791,plain,
! [SV1045: $i,SV814: $i,SV487: $i,SV115: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV115 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SV487 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SV814 ) @ SV1045 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SV487 ) @ SV814 ) ) @ SV1045 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2508]) ).
thf(2792,plain,
! [SV1046: $i,SV815: $i,SV488: $i,SV116: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV116 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV488 ) @ SV815 ) ) @ SV1046 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV488 ) @ SV1046 ) ) @ SV815 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2509]) ).
thf(2793,plain,
! [SV1047: $i,SV816: $i,SV489: $i,SV117: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV117 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV489 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV816 ) @ SV1047 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV816 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV489 ) @ SV1047 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2510]) ).
thf(2794,plain,
! [SV1048: $i,SV817: $i,SV490: $i,SV118: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV118 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV490 ) @ SV817 ) ) @ SV1048 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV490 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV817 ) @ SV1048 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2511]) ).
thf(2795,plain,
! [SV1175: $i,SV1050: $i,SV819: $i,SV493: $i,SV123: $i] :
( ( ! [SY2965: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SV493 ) @ SV819 ) )
| ( c_ListOrder_Ostep1 @ SV123 @ SV1050 @ SV1175 @ SY2965 )
| ~ ( c_ListOrder_Ostep1 @ SV123 @ ( c_List_Oappend @ SV1050 @ ( c_List_Olist_OCons @ SV493 @ ( c_List_Olist_ONil @ SY2965 ) @ SY2965 ) @ SY2965 ) @ ( c_List_Oappend @ SV1175 @ ( c_List_Olist_OCons @ SV819 @ ( c_List_Olist_ONil @ SY2965 ) @ SY2965 ) @ SY2965 ) @ SY2965 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2513]) ).
thf(2796,plain,
! [SV820: $i,SV494: $i,SV124: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV124 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV124 ) @ SV494 ) @ SV820 ) @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ SV124 )
| ~ ( c_HOL_Oord__class_Oless @ SV820 @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ SV124 )
| ~ ( c_HOL_Oord__class_Oless @ SV494 @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2514]) ).
thf(2797,plain,
! [SV127: $i,SV823: $i,SV497: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV497 ) @ SV823 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV127 ) @ SV497 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV127 ) @ SV823 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2517]) ).
thf(2798,plain,
! [SV498: $i,SV824: $i,SV128: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV128 ) @ SV824 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV128 ) @ SV498 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV824 ) @ SV498 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2518]) ).
thf(2799,plain,
! [SV825: $i,SV499: $i,SV129: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV129 )
= $false )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV129 ) @ SV499 @ SV825 @ SV129 @ SV129 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV129 ) @ SV499 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV129 ) @ SV825 @ ( c_HOL_Ozero__class_Ozero @ SV129 ) @ SV129 @ SV129 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2519]) ).
thf(2800,plain,
! [SV1176: $i,SV1055: $i,SV828: $i,SV502: $i,SV132: $i] :
( ( ! [SY2966: $i] :
( ( SV132 = SV502 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV828 @ SV502 ) @ SV132 ) )
| ~ ( c_ListOrder_Ostep1 @ SV828 @ ( c_List_Olist_OCons @ SV502 @ SV1055 @ SV1176 ) @ ( c_List_Olist_OCons @ SV132 @ SY2966 @ SV1176 ) @ SV1176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2522]) ).
thf(2801,plain,
! [SV1177: $i,SV1056: $i,SV829: $i,SV503: $i,SV134: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV134 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ SV503 ) @ SV829 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ SV1056 ) @ SV1177 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ SV503 ) @ SV1056 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ SV829 ) @ SV1177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2523]) ).
thf(2802,plain,
! [SV1057: $i,SV830: $i,SV504: $i,SV135: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV135 ) @ SV504 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV830 ) @ SV1057 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV504 ) @ SV1057 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV135 ) @ SV830 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2524]) ).
thf(2803,plain,
! [SV136: $i,SV831: $i,SV505: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV505 @ SV831 @ tc_nat )
= $false )
| ( ( ( c_Lambda_Oliftn @ SV136 @ ( c_Lambda_OdB_OVar @ SV505 ) @ SV831 )
= ( c_Lambda_OdB_OVar @ SV505 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2525]) ).
thf(2804,plain,
! [SV1058: $i,SV832: $i,SV506: $i,SV137: $i] :
( ( ( c_Type_Otyping @ SV137 @ SV506 @ SV832 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV137 @ SV1058 @ SV832 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV1058 ) @ SV506 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2526]) ).
thf(2805,plain,
! [SV509: $i,SV834: $i,SV140: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV140 ) @ SV834 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV140 @ SV509 ) ) @ ( c_Lambda_Olift @ SV834 @ SV509 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2528]) ).
thf(2806,plain,
! [SV1178: $i,SV1059: $i,SV836: $i,SV512: $i,SV143: $i] :
( ( ! [SY2967: $i] :
( ( SV143 = SV512 )
| ( c_ListOrder_Ostep1 @ SV836 @ SV143 @ SV512 @ SV1059 )
| ~ ( c_ListOrder_Ostep1 @ SV836 @ ( c_List_Oappend @ SV143 @ ( c_List_Olist_OCons @ SV1178 @ ( c_List_Olist_ONil @ SV1059 ) @ SV1059 ) @ SV1059 ) @ ( c_List_Oappend @ SV512 @ ( c_List_Olist_OCons @ SY2967 @ ( c_List_Olist_ONil @ SV1059 ) @ SV1059 ) @ SV1059 ) @ SV1059 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2529]) ).
thf(2807,plain,
! [SV516: $i,SV148: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV148 ) )
= $true )
| ( ( SV516
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV516 ) @ ( c_HOL_Ozero__class_Ozero @ SV148 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2532]) ).
thf(2808,plain,
! [SV1060: $i,SV837: $i,SV523: $i,SV155: $i] :
( ( ( ( hAPP @ ( hAPP @ SV155 @ SV523 ) @ SV837 )
= SV523 )
= $true )
| ( ( ~ ( c_OrderedGroup_Omonoid__add @ SV837 @ SV155 @ SV1060 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2539]) ).
thf(2809,plain,
! [SV1061: $i,SV838: $i,SV524: $i,SV156: $i] :
( ( ( ( hAPP @ ( hAPP @ SV156 @ SV524 ) @ SV838 )
= SV838 )
= $true )
| ( ( ~ ( c_OrderedGroup_Omonoid__add @ SV524 @ SV156 @ SV1061 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2540]) ).
thf(2810,plain,
! [SV525: $i,SV157: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV157 ) @ SV525 @ SV157 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV157 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV525 ) @ SV525 ) @ SV157 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2541]) ).
thf(2811,plain,
! [SV526: $i,SV158: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV526 ) @ SV526 ) @ SV158 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV526 @ SV158 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2542]) ).
thf(2812,plain,
! [SV1179: $i,SV1062: $i,SV841: $i,SV529: $i,SV161: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV161 @ SV529 ) @ SV841 ) @ SV1062 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV161 @ SV529 ) @ SV1179 ) @ SV1062 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV161 @ SV529 ) @ SV841 ) @ SV1179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2543]) ).
thf(2813,plain,
! [SV1063: $i,SV842: $i,SV535: $i,SV167: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV167 @ SV535 @ SV842 ) ) @ ( c_Lambda_Osubst @ SV167 @ SV1063 @ SV842 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV535 ) @ SV1063 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2544]) ).
thf(2814,plain,
! [SV843: $i,SV536: $i,SV168: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV168 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV168 ) @ SV536 ) @ SV843 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV168 ) @ SV843 ) @ SV536 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2545]) ).
thf(2815,plain,
! [SV844: $i,SV537: $i,SV169: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV169 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV169 ) @ SV537 ) @ SV844 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV169 ) @ SV844 ) @ SV537 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2546]) ).
thf(2816,plain,
! [SV845: $i,SV538: $i,SV170: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV170 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV170 ) @ SV538 ) @ SV845 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV170 ) @ SV845 ) @ SV538 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2547]) ).
thf(2817,plain,
! [SV1180: $i,SV1064: $i,SV846: $i,SV539: $i,SV171: $i] :
( ( ! [SY2968: $i] :
( ( c_List_Ofoldr @ SV171 @ ( c_List_Oappend @ SV539 @ SV846 @ SV1064 ) @ SV1180 @ SV1064 @ SY2968 )
= ( c_List_Ofoldr @ SV171 @ SV539 @ ( c_List_Ofoldr @ SV171 @ SV846 @ SV1180 @ SV1064 @ SY2968 ) @ SV1064 @ SY2968 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2548]) ).
thf(2818,plain,
! [SV1181: $i,SV1065: $i,SV847: $i,SV540: $i,SV172: $i] :
( ( ! [SY2969: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV172 @ SV540 ) @ SV847 ) )
| ( SV540 = SV847 )
| ~ ( c_ListOrder_Ostep1 @ SV172 @ ( c_List_Oappend @ SV1065 @ ( c_List_Olist_OCons @ SV540 @ ( c_List_Olist_ONil @ SV1181 ) @ SV1181 ) @ SV1181 ) @ ( c_List_Oappend @ SY2969 @ ( c_List_Olist_OCons @ SV847 @ ( c_List_Olist_ONil @ SV1181 ) @ SV1181 ) @ SV1181 ) @ SV1181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2549]) ).
thf(2819,plain,
! [SV1066: $i,SV848: $i,SV541: $i,SV173: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV173 @ SV541 @ SV848 ) ) @ ( c_Lambda_Osubst @ SV1066 @ SV541 @ SV848 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV173 ) @ SV1066 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2550]) ).
thf(2820,plain,
! [SV1067: $i,SV849: $i,SV542: $i,SV174: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV174 @ SV542 @ SV849 ) ) @ ( c_Lambda_Osubst @ SV174 @ SV1067 @ SV849 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV542 ) @ SV1067 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2551]) ).
thf(2821,plain,
! [SV850: $i,SV543: $i,SV175: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__add @ SV175 )
= $false )
| ( ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV175 ) @ SV543 @ SV850 @ SV175 @ SV175 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV175 ) @ SV850 @ SV543 @ SV175 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2552]) ).
thf(2822,plain,
! [SV1068: $i,SV851: $i,SV544: $i,SV176: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV176 @ SV544 ) @ SV851 ) @ SV1068 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV176 @ SV851 ) @ SV1068 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2553]) ).
thf(2823,plain,
! [SV547: $i,SV179: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV179 ) @ SV547 ) @ SV547 ) @ ( c_HOL_Ozero__class_Ozero @ SV179 ) @ SV179 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV547 @ ( c_HOL_Ozero__class_Ozero @ SV179 ) @ SV179 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2556]) ).
thf(2824,plain,
! [SV180: $i,SV548: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV548 @ ( c_HOL_Ozero__class_Ozero @ SV180 ) @ SV180 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV180 ) @ SV548 ) @ SV548 ) @ ( c_HOL_Ozero__class_Ozero @ SV180 ) @ SV180 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV180 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2557]) ).
thf(2825,plain,
! [SV181: $i,SV549: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV549 @ ( c_HOL_Ozero__class_Ozero @ SV181 ) @ SV181 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV181 ) @ SV549 ) @ SV549 ) @ ( c_HOL_Ozero__class_Ozero @ SV181 ) @ SV181 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2558]) ).
thf(2826,plain,
! [SV550: $i,SV182: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV182 ) @ SV550 ) @ SV550 ) @ ( c_HOL_Ozero__class_Ozero @ SV182 ) @ SV182 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV550 @ ( c_HOL_Ozero__class_Ozero @ SV182 ) @ SV182 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2559]) ).
thf(2827,plain,
! [SV854: $i,SV551: $i,SV183: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV183 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ SV551 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ ( c_HOL_Ozero__class_Ozero @ SV183 ) @ SV854 @ SV183 @ SV183 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ SV551 @ SV854 @ SV183 @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2560]) ).
thf(2828,plain,
! [SV855: $i,SV184: $i,SV552: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV552 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV184 @ SV552 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV855 @ 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 @ SV184 ) ) @ SV552 ) @ SV855 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2561]) ).
thf(2829,plain,
! [SV553: $i,SV856: $i,SV185: $i] :
( ( ( SV185 = SV856 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV856 @ SV185 @ tc_nat )
= $true )
| ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV185 ) @ SV553 @ SV856 )
= ( c_Lambda_OdB_OVar @ SV185 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2562]) ).
thf(2830,plain,
! [SV189: $i,SV555: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV555 @ SV555 @ SV189 )
= $false )
| ( ( class_Orderings_Oorder @ SV189 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2564]) ).
thf(2831,plain,
! [SV190: $i,SV556: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV556 @ SV556 @ SV190 )
= $false )
| ( ( class_Orderings_Olinorder @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2565]) ).
thf(2832,plain,
! [SV191: $i,SV557: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV557 @ SV557 @ SV191 )
= $false )
| ( ( class_Orderings_Opreorder @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2566]) ).
thf(2833,plain,
! [SV559: $i,SV857: $i,SV193: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV193 ) @ SV857 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV193 @ SV559 ) ) @ ( c_Lambda_Olift @ SV857 @ SV559 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2567]) ).
thf(2834,plain,
! [SV858: $i,SV560: $i,SV194: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV194 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV194 ) @ SV560 ) @ SV858 ) @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV858 @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV560 @ SV194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2568]) ).
thf(2835,plain,
! [SV1182: $i,SV1069: $i,SV859: $i,SV561: $i,SV195: $i] :
( ( ! [SY2970: $i] :
( ( c_ListOrder_Ostep1 @ SV195 @ SV561 @ SV859 @ SV1069 )
| ( SV859 = SV561 )
| ~ ( c_ListOrder_Ostep1 @ SV195 @ ( c_List_Olist_OCons @ SV1182 @ SV561 @ SV1069 ) @ ( c_List_Olist_OCons @ SY2970 @ SV859 @ SV1069 ) @ SV1069 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2569]) ).
thf(2836,plain,
! [SV1183: $i,SV1070: $i,SV860: $i,SV562: $i,SV196: $i] :
( ( ( ( hAPP @ ( hAPP @ SV196 @ ( hAPP @ ( hAPP @ SV196 @ SV562 ) @ SV860 ) ) @ SV1070 )
= ( hAPP @ ( hAPP @ SV196 @ SV562 ) @ ( hAPP @ ( hAPP @ SV196 @ SV860 ) @ SV1070 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV196 @ SV1183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2570]) ).
thf(2837,plain,
! [SV861: $i,SV563: $i,SV197: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV197 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV563 @ SV861 @ SV197 )
| ( c_HOL_Oord__class_Oless @ SV861 @ SV563 @ SV197 )
| ( SV861 = SV563 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2571]) ).
thf(2838,plain,
! [SV862: $i,SV564: $i,SV198: $i] :
( ( ( class_Orderings_Olinorder @ SV198 )
= $false )
| ( ( ( SV564 = SV862 )
| ( c_HOL_Oord__class_Oless @ SV862 @ SV564 @ SV198 )
| ( c_HOL_Oord__class_Oless @ SV564 @ SV862 @ SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2572]) ).
thf(2839,plain,
! [SV200: $i,SV863: $i,SV566: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV566 @ SV863 @ tc_nat )
= $true )
| ( ( ( SV863 = SV566 )
| ( c_HOL_Oord__class_Oless @ SV863 @ SV566 @ tc_nat ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV200 @ SV566 ) @ SV863 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2574]) ).
thf(2840,plain,
! [SV864: $i,SV568: $i,SV202: $i] :
( ( ( class_Orderings_Olinorder @ SV202 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV568 @ SV864 @ SV202 )
| ( c_HOL_Oord__class_Oless @ SV864 @ SV568 @ SV202 )
| ( SV864 = SV568 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2576]) ).
thf(2841,plain,
! [SV865: $i,SV569: $i,SV203: $i] :
( ( ( class_Orderings_Olinorder @ SV203 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV569 @ SV865 @ SV203 )
| ( SV865 = SV569 )
| ( c_HOL_Oord__class_Oless @ SV865 @ SV569 @ SV203 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2577]) ).
thf(2842,plain,
! [SV866: $i,SV570: $i,SV204: $i] :
( ( ( class_Orderings_Olinorder @ SV204 )
= $false )
| ( ( ( SV570 = SV866 )
| ( c_HOL_Oord__class_Oless @ SV570 @ SV866 @ SV204 )
| ( c_HOL_Oord__class_Oless @ SV866 @ SV570 @ SV204 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2578]) ).
thf(2843,plain,
! [SV1184: $i,SV1071: $i,SV867: $i,SV571: $i,SV205: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV205 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV205 ) @ SV571 ) @ SV867 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV205 ) @ SV1071 ) @ SV1184 ) @ SV205 )
| ~ ( c_HOL_Oord__class_Oless @ SV867 @ SV1184 @ SV205 )
| ~ ( c_HOL_Oord__class_Oless @ SV571 @ SV1071 @ SV205 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2579]) ).
thf(2844,plain,
! [SV1185: $i,SV1072: $i,SV868: $i,SV573: $i,SV207: $i] :
( ( ! [SY2971: $i] :
( ( SV207 = SV573 )
| ( SV868 = SV1072 )
| ~ ( c_ListOrder_Ostep1 @ SV1185 @ ( c_List_Oappend @ SV207 @ ( c_List_Olist_OCons @ SV868 @ ( c_List_Olist_ONil @ SY2971 ) @ SY2971 ) @ SY2971 ) @ ( c_List_Oappend @ SV573 @ ( c_List_Olist_OCons @ SV1072 @ ( c_List_Olist_ONil @ SY2971 ) @ SY2971 ) @ SY2971 ) @ SY2971 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2581]) ).
thf(2845,plain,
! [SV1073: $i,SV869: $i,SV574: $i,SV209: $i] :
( ( ( c_List_Olistsp @ SV209 @ ( c_List_Oappend @ SV574 @ SV869 @ SV1073 ) @ SV1073 )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV209 @ SV869 @ SV1073 )
| ~ ( c_List_Olistsp @ SV209 @ SV574 @ SV1073 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2582]) ).
thf(2846,plain,
! [SV1186: $i,SV1074: $i,SV870: $i,SV575: $i,SV210: $i] :
( ( ( c_Lambda_OdB_OdB__rec @ SV210 @ SV575 @ SV870 @ ( c_Lambda_OdB_OAbs @ SV1074 ) @ SV1186 )
= ( hAPP @ ( hAPP @ SV870 @ SV1074 ) @ ( c_Lambda_OdB_OdB__rec @ SV210 @ SV575 @ SV870 @ SV1074 @ SV1186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2583]) ).
thf(2847,plain,
! [SV1075: $i,SV871: $i,SV578: $i,SV214: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV214 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV578 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV214 ) @ SV871 ) @ SV1075 ) @ SV214 )
| ~ ( c_HOL_Oord__class_Oless @ SV578 @ SV1075 @ SV214 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV214 ) @ SV871 @ SV214 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2584]) ).
thf(2848,plain,
! [SV579: $i,SV872: $i,SV215: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV215 @ SV872 @ tc_nat )
= $false )
| ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV215 ) @ SV579 @ SV872 )
= ( c_Lambda_OdB_OVar @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2585]) ).
thf(2849,plain,
! [SV1187: $i,SV1076: $i,SV873: $i,SV580: $i,SV216: $i] :
( ( ! [SY2972: $i] :
( ( c_List_Ofoldr @ SV216 @ ( c_List_Olist_OCons @ SV580 @ SV873 @ SV1076 ) @ SV1187 @ SV1076 @ SY2972 )
= ( hAPP @ ( hAPP @ SV216 @ SV580 ) @ ( c_List_Ofoldr @ SV216 @ SV873 @ SV1187 @ SV1076 @ SY2972 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2586]) ).
thf(2850,plain,
! [SV1188: $i,SV1077: $i,SV874: $i,SV581: $i,SV217: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV217 @ ( c_Lambda_OdB_OdB__case @ SV581 @ SV874 @ SV1077 @ ( c_Lambda_OdB_OAbs @ SV1188 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV217 @ ( hAPP @ SV1077 @ SV1188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2587]) ).
thf(2851,plain,
! [SV1189: $i,SV1078: $i,SV875: $i,SV582: $i,SV218: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV218 @ ( c_Lambda_OdB_OdB__case @ SV582 @ SV875 @ SV1078 @ ( c_Lambda_OdB_OAbs @ SV1189 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV218 @ ( hAPP @ SV1078 @ SV1189 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2588]) ).
thf(2852,plain,
! [SV876: $i,SV583: $i,SV219: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV219 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV219 @ ( c_Lambda_OdB_OVar @ SV583 ) @ SV876 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2589]) ).
thf(2853,plain,
! [SV1079: $i,SV878: $i,SV585: $i,SV221: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV221 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV221 ) @ SV585 ) @ SV878 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV221 ) @ SV1079 ) @ SV878 ) @ SV221 )
| ~ ( c_HOL_Oord__class_Oless @ SV585 @ SV1079 @ SV221 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2590]) ).
thf(2854,plain,
! [SV1080: $i,SV879: $i,SV586: $i,SV222: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV222 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV222 ) @ SV586 ) @ SV879 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV222 ) @ SV1080 ) @ SV879 ) @ SV222 )
| ~ ( c_HOL_Oord__class_Oless @ SV586 @ SV1080 @ SV222 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2591]) ).
thf(2855,plain,
! [SV1081: $i,SV880: $i,SV587: $i,SV223: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV223 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV587 @ SV880 @ SV223 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV223 ) @ SV587 ) @ SV1081 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV223 ) @ SV880 ) @ SV1081 ) @ SV223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2592]) ).
thf(2856,plain,
! [SV1082: $i,SV881: $i,SV588: $i,SV224: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV224 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV224 ) @ SV588 ) @ SV881 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV224 ) @ SV588 ) @ SV1082 ) @ SV224 )
| ~ ( c_HOL_Oord__class_Oless @ SV881 @ SV1082 @ SV224 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2593]) ).
thf(2857,plain,
! [SV1083: $i,SV882: $i,SV589: $i,SV225: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV225 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV225 ) @ SV589 ) @ SV882 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV225 ) @ SV589 ) @ SV1083 ) @ SV225 )
| ~ ( c_HOL_Oord__class_Oless @ SV882 @ SV1083 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2594]) ).
thf(2858,plain,
! [SV1084: $i,SV883: $i,SV590: $i,SV226: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV226 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV590 @ SV883 @ SV226 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV226 ) @ SV1084 ) @ SV590 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV226 ) @ SV1084 ) @ SV883 ) @ SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2595]) ).
thf(2859,plain,
! [SV1190: $i,SV1085: $i,SV884: $i,SV591: $i,SV227: $i] :
( ( ! [SY2973: $i] :
( ( c_ListOrder_Ostep1 @ SV227 @ SV591 @ SV884 @ SV1085 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV227 @ SV1190 ) @ SY2973 ) )
| ~ ( c_ListOrder_Ostep1 @ SV227 @ ( c_List_Olist_OCons @ SV1190 @ SV591 @ SV1085 ) @ ( c_List_Olist_OCons @ SY2973 @ SV884 @ SV1085 ) @ SV1085 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2596]) ).
thf(2860,plain,
! [SV1191: $i,SV1086: $i,SV885: $i,SV592: $i,SV228: $i] :
( ( ( c_ListOrder_Ostep1 @ SV228 @ ( c_List_Olist_OCons @ SV592 @ SV885 @ SV1086 ) @ ( c_List_Olist_OCons @ SV592 @ SV1191 @ SV1086 ) @ SV1086 )
| ~ ( c_ListOrder_Ostep1 @ SV228 @ SV885 @ SV1191 @ SV1086 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2597]) ).
thf(2861,plain,
! [SV890: $i,SV597: $i,SV234: $i] :
( ( ( class_Orderings_Oorder @ SV234 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV597 @ SV890 @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SV890 @ SV597 @ SV234 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2602]) ).
thf(2862,plain,
! [SV1192: $i,SV1091: $i,SV891: $i,SV598: $i,SV235: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV235 @ SV598 ) @ SV891 ) @ SV1091 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV235 @ SV598 ) @ SV1192 ) @ SV1091 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV891 ) @ SV1192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2603]) ).
thf(2863,plain,
! [SV1193: $i,SV1092: $i,SV892: $i,SV599: $i,SV236: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV236 @ SV599 ) @ SV892 ) @ SV1092 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV236 @ SV1193 ) @ SV1092 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV236 @ SV599 ) @ SV892 ) @ SV1193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2604]) ).
thf(2864,plain,
! [SV893: $i,SV600: $i,SV237: $i] :
( ( ( class_Orderings_Olinorder @ SV237 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV600 @ SV893 @ SV237 )
| ~ ( c_HOL_Oord__class_Oless @ SV893 @ SV600 @ SV237 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2605]) ).
thf(2865,plain,
! [SV894: $i,SV601: $i,SV238: $i] :
( ( ( class_Orderings_Opreorder @ SV238 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV601 @ SV894 @ SV238 )
| ~ ( c_HOL_Oord__class_Oless @ SV894 @ SV601 @ SV238 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2606]) ).
thf(2866,plain,
! [SV895: $i,SV602: $i,SV239: $i] :
( ( ( class_Orderings_Opreorder @ SV239 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV602 @ SV895 @ SV239 )
| ~ ( c_HOL_Oord__class_Oless @ SV895 @ SV602 @ SV239 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2607]) ).
thf(2867,plain,
! [SV1194: $i,SV1093: $i,SV896: $i,SV603: $i,SV240: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV240 @ SV603 @ SV896 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SV1093 @ SV603 ) @ SV1194 )
| ~ ( c_Type_Otyping @ SV240 @ SV1093 @ SV1194 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2608]) ).
thf(2868,plain,
! [SV604: $i,SV241: $i] :
( ( ( hBOOL @ ( hAPP @ SV241 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV241 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV241 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV241 @ SV604 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV241 @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV241 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2609]) ).
thf(2869,plain,
! [SV1195: $i,SV1094: $i,SV897: $i,SV605: $i,SV242: $i] :
( ( ( ( c_List_Ofoldl @ SV242 @ ( hAPP @ ( hAPP @ SV242 @ SV605 ) @ SV897 ) @ SV1094 @ SV1195 @ SV1195 )
= ( hAPP @ ( hAPP @ SV242 @ SV605 ) @ ( c_List_Ofoldl @ SV242 @ SV897 @ SV1094 @ SV1195 @ SV1195 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV242 @ SV1195 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2610]) ).
thf(2870,plain,
! [SV1096: $i,SV899: $i,SV608: $i,SV245: $i] :
( ( ( c_Type_Otypings @ SV245 @ SV608 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV899 @ SV245 @ SV1096 @ SV608 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV245 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1096 ) @ SV608 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV899 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2612]) ).
thf(2871,plain,
! [SV1196: $i,SV1097: $i,SV900: $i,SV609: $i,SV246: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV246 @ ( c_Lambda_OdB_OdB__case @ SV609 @ SV900 @ SV1097 @ ( c_Lambda_OdB_OVar @ SV1196 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV246 @ ( hAPP @ SV609 @ SV1196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2613]) ).
thf(2872,plain,
! [SV1197: $i,SV1098: $i,SV901: $i,SV610: $i,SV247: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV247 @ ( c_Lambda_OdB_OdB__case @ SV610 @ SV901 @ SV1098 @ ( c_Lambda_OdB_OVar @ SV1197 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV247 @ ( hAPP @ SV610 @ SV1197 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2614]) ).
thf(2873,plain,
! [SV1099: $i,SV902: $i,SV611: $i,SV248: $i] :
( ( ( c_Type_Otyping @ SV248 @ SV611 @ SV902 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV1099 ) @ SV611 ) )
| ~ ( c_Type_Otyping @ SV248 @ SV1099 @ SV902 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2615]) ).
thf(2874,plain,
! [SV1198: $i,SV1100: $i,SV903: $i,SV613: $i,SV250: $i] :
( ( ! [SY2974: $i] :
( ~ ( hBOOL @ ( hAPP @ SV250 @ ( c_Lambda_OdB_OdB__case @ SV613 @ SV903 @ SV1100 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1198 ) @ SY2974 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV250 @ ( hAPP @ ( hAPP @ SV903 @ SV1198 ) @ SY2974 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2616]) ).
thf(2875,plain,
! [SV1199: $i,SV1101: $i,SV904: $i,SV614: $i,SV251: $i] :
( ( ! [SY2975: $i] :
( ~ ( hBOOL @ ( hAPP @ SV251 @ ( c_Lambda_OdB_OdB__case @ SV614 @ SV904 @ SV1101 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1199 ) @ SY2975 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV251 @ ( hAPP @ ( hAPP @ SV904 @ SV1199 ) @ SY2975 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2617]) ).
thf(2876,plain,
! [SV1102: $i,SV905: $i,SV615: $i,SV252: $i] :
( ( ( c_Type_Otypings @ SV252 @ SV615 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV905 @ SV252 @ SV1102 @ SV615 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV252 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1102 @ SV615 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV905 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2618]) ).
thf(2877,plain,
! [SV1200: $i,SV1103: $i,SV906: $i,SV616: $i,SV253: $i] :
( ( ! [SY2976: $i,SY2977: $i] :
( ( SV253
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV616 @ SV253 @ SV906 @ SV1103 ) @ SV616 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV906 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1200 ) @ SY2976 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV253 )
| ~ ( c_Type_Otypings @ SV906 @ SY2976 @ SY2977 )
| ~ ( c_Type_Otyping @ SV906 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1200 ) @ SY2976 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1103 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV616 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2619]) ).
thf(2878,plain,
! [SV1201: $i,SV1104: $i,SV907: $i,SV617: $i,SV254: $i] :
( ( ( ( hAPP @ ( c_Type_Oshift @ SV254 @ SV617 @ SV907 @ SV1104 ) @ SV1201 )
= ( hAPP @ SV254 @ SV1201 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1201 @ SV617 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2620]) ).
thf(2879,plain,
! [SV618: $i,SV908: $i,SV255: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV255 ) @ SV908 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV255 @ SV618 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV908 @ SV618 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2621]) ).
thf(2880,plain,
! [SV1202: $i,SV1105: $i,SV909: $i,SV620: $i,SV257: $i] :
( ( ( c_Type_Otyping @ SV257 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV620 ) @ SV909 ) @ SV1105 )
| ~ ( c_Type_Otyping @ SV257 @ SV909 @ SV1202 )
| ~ ( c_Type_Otyping @ SV257 @ SV620 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1202 ) @ SV1105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2622]) ).
thf(2881,plain,
! [SV1203: $i,SV1106: $i,SV910: $i,SV622: $i,SV259: $i] :
( ( ( SV259 = SV622 )
| ~ ( c_Type_Otyping @ SV910 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1106 ) @ SV1203 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV622 )
| ~ ( c_Type_Otyping @ SV910 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1106 ) @ SV1203 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV259 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2624]) ).
thf(2882,plain,
! [SV260: $i,SV911: $i,SV623: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV623 @ SV911 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV260 @ SV623 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV260 @ SV911 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2625]) ).
thf(2883,plain,
! [SV624: $i,SV261: $i] :
( ( ( hBOOL @ ( hAPP @ SV261 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV261 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV261 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV261 @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV261 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV261 @ SV624 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2626]) ).
thf(2884,plain,
! [SV625: $i,SV912: $i,SV262: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV262 ) @ SV912 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV262 @ SV625 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV912 @ SV625 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2627]) ).
thf(2885,plain,
! [SV1204: $i,SV1107: $i,SV913: $i,SV626: $i,SV263: $i] :
( ( ( c_Lambda_OdB_OdB__rec @ SV263 @ SV626 @ SV913 @ ( c_Lambda_OdB_OVar @ SV1107 ) @ SV1204 )
= ( hAPP @ SV263 @ SV1107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2628]) ).
thf(2886,plain,
! [SV1110: $i,SV916: $i,SV629: $i,SV266: $i] :
( ( ( c_Type_Otyping @ SV266 @ ( c_Lambda_OdB_OAbs @ SV629 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV916 ) @ SV1110 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV266 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV916 @ tc_Type_Otype ) @ SV629 @ SV1110 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2631]) ).
thf(2887,plain,
! [SV917: $i,SV630: $i,SV268: $i] :
( ( ( c_Type_Otyping @ SV268 @ ( c_Lambda_OdB_OVar @ SV630 ) @ SV917 )
= $false )
| ( ( ( hAPP @ SV268 @ SV630 )
= SV917 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2632]) ).
thf(2888,plain,
! [SV1111: $i,SV918: $i,SV631: $i,SV269: $i] :
( ( ( ~ ( class_OrderedGroup_Osemigroup__add @ SV269 ) )
= $true )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV269 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV269 ) @ SV631 ) @ SV918 ) @ SV1111 @ SV269 @ SV269 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV269 ) @ SV631 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV269 ) @ SV918 @ SV1111 @ SV269 @ SV269 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2633]) ).
thf(2889,plain,
! [SV1112: $i,SV920: $i,SV633: $i,SV271: $i] :
( ( ( c_Type_Otyping @ SV271 @ SV633 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV920 @ SV271 @ SV633 @ SV1112 ) @ SV920 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV271 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV633 @ SV1112 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV920 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2634]) ).
thf(2890,plain,
! [SV1113: $i,SV921: $i,SV634: $i,SV272: $i] :
( ( ( c_Type_Otyping @ SV272 @ ( c_Lambda_OdB_OVar @ SV634 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV921 @ SV272 @ SV634 @ SV1113 ) @ SV921 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV272 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV634 ) @ SV1113 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV921 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2635]) ).
thf(2891,plain,
! [SV1205: $i,SV1114: $i,SV922: $i,SV635: $i,SV273: $i] :
( ( ( c_Type_Otyping @ SV273 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV635 @ SV922 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1114 )
| ~ ( c_Type_Otypings @ SV273 @ SV922 @ SV1205 )
| ~ ( c_Type_Otyping @ SV273 @ SV635 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV1205 @ SV1114 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2636]) ).
thf(2892,plain,
! [SV274: $i,SV923: $i,SV636: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV636 ) @ SV923 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV274 ) )
= $false )
| ( ( SV274
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV636 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV636 @ SV923 @ SV274 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2637]) ).
thf(2893,plain,
! [SV1206: $i,SV1115: $i,SV924: $i,SV637: $i,SV275: $i] :
( ( ! [SY2978: $i] :
( ( c_Lambda_OdB_OdB__case @ SV275 @ SV637 @ SV924 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1115 ) @ SV1206 ) @ SY2978 )
= ( hAPP @ ( hAPP @ SV637 @ SV1115 ) @ SV1206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2638]) ).
thf(2894,plain,
! [SV1207: $i,SV1116: $i,SV925: $i,SV638: $i,SV276: $i] :
( ( ( ( hAPP @ ( hAPP @ SV276 @ SV638 ) @ ( c_List_Ofoldl @ SV276 @ SV925 @ SV1116 @ SV1207 @ SV1207 ) )
= ( c_List_Ofoldl @ SV276 @ SV638 @ SV1116 @ SV1207 @ SV1207 ) )
| ~ ( c_OrderedGroup_Omonoid__add @ SV925 @ SV276 @ SV1207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2639]) ).
thf(2895,plain,
! [SV1117: $i,SV926: $i,SV639: $i,SV277: $i] :
( ( ( c_Type_Otyping @ SV277 @ SV639 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV926 @ SV277 @ SV1117 @ SV639 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV277 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1117 ) @ SV639 ) @ SV926 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2640]) ).
thf(2896,plain,
! [SV1208: $i,SV1118: $i,SV927: $i,SV640: $i,SV279: $i] :
( ( ( c_Lambda_OdB_OdB__case @ SV279 @ SV640 @ SV927 @ ( c_Lambda_OdB_OVar @ SV1118 ) @ SV1208 )
= ( hAPP @ SV279 @ SV1118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2641]) ).
thf(2897,plain,
! [SV1119: $i,SV928: $i,SV641: $i,SV280: $i] :
( ( ( c_Type_Otypings @ SV280 @ SV641 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV928 @ SV280 @ SV1119 @ SV641 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV280 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1119 @ SV641 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV928 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2642]) ).
thf(2898,plain,
! [SV1209: $i,SV1120: $i,SV929: $i,SV642: $i,SV281: $i] :
( ( ! [SY2979: $i] :
( ( c_List_Ofoldl @ SV281 @ SV642 @ ( c_List_Olist_OCons @ SV929 @ SV1120 @ SV1209 ) @ SY2979 @ SV1209 )
= ( c_List_Ofoldl @ SV281 @ ( hAPP @ ( hAPP @ SV281 @ SV642 ) @ SV929 ) @ SV1120 @ SY2979 @ SV1209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2643]) ).
thf(2899,plain,
! [SV1210: $i,SV1121: $i,SV930: $i,SV644: $i,SV284: $i] :
( ( ! [SY2980: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV284 @ SV644 @ SV930 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1121 ) @ SV1210 ) @ SY2980 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV644 @ SV1121 ) @ SV1210 ) @ ( c_Lambda_OdB_OdB__rec @ SV284 @ SV644 @ SV930 @ SV1121 @ SY2980 ) ) @ ( c_Lambda_OdB_OdB__rec @ SV284 @ SV644 @ SV930 @ SV1210 @ SY2980 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2644]) ).
thf(2900,plain,
! [SV1211: $i,SV1122: $i,SV931: $i,SV645: $i,SV286: $i] :
( ( ! [SY2981: $i,SY2982: $i] :
( ( c_Type_Otypings @ SV286 @ SV645 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV931 @ SV1122 @ SV286 @ SV645 ) )
| ~ ( c_Type_Otyping @ SV286 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1211 ) @ SY2981 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1122 )
| ~ ( c_Type_Otypings @ SV286 @ SY2981 @ SY2982 )
| ~ ( c_Type_Otyping @ SV286 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1211 ) @ SY2981 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV645 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV931 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2645]) ).
thf(2901,plain,
! [SV287: $i,SV932: $i,SV646: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV646 ) @ SV932 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV287 ) @ SV646 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV287 ) @ SV932 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2646]) ).
thf(2902,plain,
! [SV647: $i,SV933: $i,SV288: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV288 ) @ SV933 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV288 ) @ SV647 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV933 ) @ SV647 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2647]) ).
thf(2903,plain,
! [SV1124: $i,SV935: $i,SV649: $i,SV291: $i] :
( ( ( c_Type_Otyping @ SV291 @ SV649 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV935 @ SV291 @ SV649 @ SV1124 ) @ SV935 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV291 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV649 @ SV1124 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV935 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2649]) ).
thf(2904,plain,
! [SV936: $i,SV293: $i,SV651: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV651 ) @ SV293 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV936 ) )
= $false )
| ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV293 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV651 @ SV293 @ SV936 ) @ tc_Lambda_OdB )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2651]) ).
thf(2905,plain,
! [SV1212: $i,SV1125: $i,SV937: $i,SV652: $i,SV294: $i] :
( ( ! [SY2983: $i] :
( ~ ( c_Type_Otyping @ SV294 @ SV652 @ SV937 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV294 @ SV1125 @ SV937 @ tc_Type_Otype ) @ SV1212 @ SY2983 )
| ( c_Type_Otyping @ SV294 @ ( c_Lambda_Osubst @ SV1212 @ SV652 @ SV1125 ) @ SY2983 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2652]) ).
thf(2906,plain,
! [SV1213: $i,SV1127: $i,SV939: $i,SV654: $i,SV296: $i] :
( ( ! [SY2984: $i] :
( ( c_List_Ofoldl @ SV296 @ SV654 @ ( c_List_Oappend @ SV939 @ SV1127 @ SV1213 ) @ SY2984 @ SV1213 )
= ( c_List_Ofoldl @ SV296 @ ( c_List_Ofoldl @ SV296 @ SV654 @ SV939 @ SY2984 @ SV1213 ) @ SV1127 @ SY2984 @ SV1213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2654]) ).
thf(2907,plain,
! [SV1128: $i,SV940: $i,SV655: $i,SV297: $i] :
( ( ( c_Type_Otyping @ SV297 @ SV655 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV940 @ SV297 @ SV655 @ SV1128 ) ) @ SV940 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV297 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV655 ) @ SV1128 ) @ SV940 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2655]) ).
thf(2908,plain,
! [SV659: $i,SV301: $i,SV941: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV941 ) @ SV301 ) @ SV659 ) )
= $false )
| ( ( SV301 = SV659 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2658]) ).
thf(2909,plain,
! [SV942: $i,SV660: $i,SV302: $i] :
( ( ( ( c_List_Orev @ SV302 @ SV660 )
= ( c_List_Orev @ SV942 @ SV660 ) )
= $false )
| ( ( SV302 = SV942 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2659]) ).
thf(2910,plain,
! [SV943: $i,SV661: $i,SV303: $i] :
( ( ( ( c_List_Oappend @ SV303 @ SV661 @ SV943 )
= ( c_List_Olist_ONil @ SV943 ) )
= $false )
| ( ( SV303
= ( c_List_Olist_ONil @ SV943 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2660]) ).
thf(2911,plain,
! [SV1129: $i,SV944: $i,SV662: $i,SV304: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV304 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV304 ) @ SV662 ) @ SV944 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV304 ) @ SV662 ) @ SV1129 ) )
| ( SV944 = SV1129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2661]) ).
thf(2912,plain,
! [SV945: $i,SV663: $i,SV305: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV305 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV663 @ SV945 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( c_Lambda_OdB_OAbs @ SV305 )
= SV663 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2662]) ).
thf(2913,plain,
! [SV946: $i,SV665: $i,SV307: $i] :
( ( ( ( c_List_Oreplicate @ SV307 @ SV665 @ SV946 )
= ( c_List_Olist_ONil @ SV946 ) )
= $false )
| ( ( SV307
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2664]) ).
thf(2914,plain,
! [SV1214: $i,SV1130: $i,SV947: $i,SV666: $i,SV308: $i] :
( ( ( ( c_List_Oreplicate @ SV308 @ SV666 @ SV947 )
!= ( c_List_Oreplicate @ SV1130 @ SV1214 @ SV947 ) )
| ( SV666 = SV1214 )
| ( SV308
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2665]) ).
thf(2915,plain,
! [SV1215: $i,SV1131: $i,SV948: $i,SV667: $i,SV309: $i] :
( ( ( ( c_List_Oappend @ SV309 @ SV667 @ SV948 )
!= ( c_List_Olist_OCons @ SV1131 @ SV1215 @ SV948 ) )
| ( SV309
= ( c_List_Olist_OCons @ SV1131 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1131 @ SV1215 @ SV309 @ SV667 @ SV948 ) @ SV948 ) )
| ( SV309
= ( c_List_Olist_ONil @ SV948 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2666]) ).
thf(2916,plain,
! [SV1132: $i,SV949: $i,SV668: $i,SV310: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV310 ) @ SV668 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV949 ) @ SV1132 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV949 @ SV668 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV310 @ SV1132 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2667]) ).
thf(2917,plain,
! [SV951: $i,SV670: $i,SV312: $i] :
( ( ( ( c_List_Oappend @ SV312 @ SV670 @ SV951 )
= ( c_List_Olist_ONil @ SV951 ) )
= $false )
| ( ( SV670
= ( c_List_Olist_ONil @ SV951 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2669]) ).
thf(2918,plain,
! [SV1133: $i,SV953: $i,SV672: $i,SV314: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV314 ) @ SV672 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV953 @ SV1133 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( SV1133
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV314 @ SV672 @ SV953 @ SV1133 ) @ ( c_List_Olist_OCons @ SV672 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( SV1133
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2671]) ).
thf(2919,plain,
! [SV954: $i,SV673: $i,SV315: $i] :
( ( ( SV315
= ( c_List_Oappend @ SV673 @ SV315 @ SV954 ) )
= $false )
| ( ( SV673
= ( c_List_Olist_ONil @ SV954 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2672]) ).
thf(2920,plain,
! [SV1216: $i,SV1134: $i,SV955: $i,SV674: $i,SV316: $i] :
( ( ( ( c_List_Olist_OCons @ SV316 @ SV674 @ SV955 )
!= ( c_List_Oappend @ SV1134 @ SV1216 @ SV955 ) )
| ( SV674
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV316 @ SV674 @ SV1134 @ SV1216 @ SV955 ) @ SV1216 @ SV955 ) )
| ( ( c_List_Olist_OCons @ SV316 @ SV674 @ SV955 )
= SV1216 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2673]) ).
thf(2921,plain,
! [SV957: $i,SV677: $i,SV319: $i] :
( ( ( SV319
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV319 ) @ SV677 ) @ SV957 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV319 ) @ SV677 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV319 ) @ SV677 ) @ ( c_List_Oappend @ SV957 @ ( c_List_Olist_OCons @ SV677 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2676]) ).
thf(2922,plain,
! [SV1217: $i,SV1135: $i,SV958: $i,SV678: $i,SV320: $i] :
( ( ( ( c_List_Olist_OCons @ SV320 @ SV678 @ SV958 )
!= ( c_List_Olist_OCons @ SV1135 @ SV1217 @ SV958 ) )
| ( SV320 = SV1135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2677]) ).
thf(2923,plain,
! [SV959: $i,SV679: $i,SV321: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV321 ) @ SV679 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV321 ) @ SV959 ) )
= $false )
| ( ( SV679 = SV959 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2678]) ).
thf(2924,plain,
! [SV1136: $i,SV960: $i,SV680: $i,SV322: $i] :
( ( ( ( c_List_Oappend @ SV322 @ SV680 @ SV960 )
!= ( c_List_Oappend @ SV1136 @ SV680 @ SV960 ) )
= $true )
| ( ( SV322 = SV1136 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2679]) ).
thf(2925,plain,
! [SV961: $i,SV681: $i,SV323: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV323 ) @ SV681 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV323 ) @ SV961 ) )
= $false )
| ( ( SV681 = SV961 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2680]) ).
thf(2926,plain,
! [SV1137: $i,SV963: $i,SV683: $i,SV325: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV325 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV325 ) @ SV683 ) @ SV963 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV325 ) @ SV1137 ) @ SV963 ) )
| ( SV683 = SV1137 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2682]) ).
thf(2927,plain,
! [SV964: $i,SV684: $i,SV326: $i] :
( ( ( SV326
= ( c_List_Oappend @ SV326 @ SV684 @ SV964 ) )
= $false )
| ( ( SV684
= ( c_List_Olist_ONil @ SV964 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2683]) ).
thf(2928,plain,
! [SV1138: $i,SV965: $i,SV685: $i,SV327: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV327 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SV685 ) @ SV965 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SV685 ) @ SV1138 ) )
| ( SV965 = SV1138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2684]) ).
thf(2929,plain,
! [SV966: $i,SV686: $i,SV328: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV328 ) @ SV686 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV966 ) @ SV686 ) )
= $false )
| ( ( SV328 = SV966 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2685]) ).
thf(2930,plain,
! [SV1218: $i,SV1139: $i,SV967: $i,SV687: $i,SV329: $i] :
( ( ! [SY2985: $i,SY2986: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV329 ) @ SV687 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV967 @ SV1139 @ SV1218 ) ) )
| ~ ( c_Type_Otyping @ SY2985 @ SV1139 @ SV687 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1139 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY2985 @ SV1218 @ SV687 @ tc_Type_Otype ) @ SV967 @ SY2986 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV967 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2686]) ).
thf(2931,plain,
! [SV1219: $i,SV1140: $i,SV968: $i,SV690: $i,SV332: $i] :
( ( ( ( c_List_Oreplicate @ SV332 @ SV690 @ SV968 )
!= ( c_List_Oreplicate @ SV1140 @ SV1219 @ SV968 ) )
| ( SV332 = SV1140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2688]) ).
thf(2932,plain,
! [SV969: $i,SV692: $i,SV334: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV334 @ SV692 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV969 ) )
= $false )
| ( ( SV334
= ( c_Lambda_OdB_OAbs @ SV969 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2689]) ).
thf(2933,plain,
! [SV971: $i,SV694: $i,SV336: $i] :
( ( ( ( c_List_Orev @ SV336 @ SV694 )
= ( c_List_Olist_OCons @ SV971 @ ( c_List_Olist_ONil @ SV694 ) @ SV694 ) )
= $false )
| ( ( SV336
= ( c_List_Olist_OCons @ SV971 @ ( c_List_Olist_ONil @ SV694 ) @ SV694 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2691]) ).
thf(2934,plain,
! [SV1220: $i,SV1141: $i,SV973: $i,SV696: $i,SV338: $i] :
( ( ( ( c_List_Oappend @ SV338 @ SV696 @ SV973 )
!= ( c_List_Olist_OCons @ SV1141 @ SV1220 @ SV973 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1141 @ SV1220 @ SV338 @ SV696 @ SV973 ) @ SV696 @ SV973 )
= SV1220 )
| ( SV338
= ( c_List_Olist_ONil @ SV973 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2693]) ).
thf(2935,plain,
! [SV974: $i,SV697: $i,SV339: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV339 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV339 )
| ( SV697
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV339 ) @ SV697 ) @ SV974 ) )
| ( SV974
= ( c_HOL_Ozero__class_Ozero @ SV339 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2694]) ).
thf(2936,plain,
! [SV1142: $i,SV975: $i,SV698: $i,SV340: $i] :
( ( ( ( c_List_Oappend @ SV340 @ SV698 @ SV975 )
!= ( c_List_Oappend @ SV340 @ SV1142 @ SV975 ) )
= $true )
| ( ( SV698 = SV1142 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2695]) ).
thf(2937,plain,
! [SV1221: $i,SV1143: $i,SV976: $i,SV699: $i,SV341: $i] :
( ( ( ( c_List_Olist_OCons @ SV341 @ SV699 @ SV976 )
!= ( c_List_Oappend @ SV1143 @ SV1221 @ SV976 ) )
| ( SV699
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV341 @ SV699 @ SV1143 @ SV1221 @ SV976 ) @ SV1221 @ SV976 ) )
| ( SV1143
= ( c_List_Olist_ONil @ SV976 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2696]) ).
thf(2938,plain,
! [SV1144: $i,SV977: $i,SV700: $i,SV342: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV342 ) @ SV700 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV977 ) @ SV1144 ) )
= $true )
| ( ( SV700 = SV1144 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2697]) ).
thf(2939,plain,
! [SV1222: $i,SV1145: $i,SV978: $i,SV702: $i,SV344: $i] :
( ( ( ( c_List_Oappend @ SV344 @ SV702 @ SV978 )
!= ( c_List_Olist_OCons @ SV1145 @ SV1222 @ SV978 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1145 @ SV1222 @ SV344 @ SV702 @ SV978 ) @ SV702 @ SV978 )
= SV1222 )
| ( SV702
= ( c_List_Olist_OCons @ SV1145 @ SV1222 @ SV978 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2699]) ).
thf(2940,plain,
! [SV1223: $i,SV1146: $i,SV979: $i,SV704: $i,SV346: $i] :
( ( ( ( c_List_Olist_OCons @ SV346 @ SV704 @ SV979 )
!= ( c_List_Oappend @ SV1146 @ SV1223 @ SV979 ) )
| ( ( c_List_Olist_OCons @ SV346 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV346 @ SV704 @ SV1146 @ SV1223 @ SV979 ) @ SV979 )
= SV1146 )
| ( SV1146
= ( c_List_Olist_ONil @ SV979 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2701]) ).
thf(2941,plain,
! [SV980: $i,SV705: $i,SV347: $i] :
( ( ( ( c_List_Olist_ONil @ SV347 )
= ( c_List_Oreplicate @ SV705 @ SV980 @ SV347 ) )
= $false )
| ( ( SV705
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2702]) ).
thf(2942,plain,
! [SV1147: $i,SV981: $i,SV706: $i,SV348: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV348 ) @ SV706 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV981 ) @ SV1147 ) )
= $true )
| ( ( SV706 = SV1147 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2703]) ).
thf(2943,plain,
! [SV982: $i,SV707: $i,SV349: $i] :
( ( ( class_Nat_Osemiring__char__0 @ SV349 )
= $false )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV707 @ SV349 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV982 @ SV349 ) )
| ( SV707 = SV982 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2704]) ).
thf(2944,plain,
! [SV1148: $i,SV983: $i,SV708: $i,SV350: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV350 ) @ SV708 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV983 @ SV1148 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( SV350
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV983 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV350 @ SV708 @ SV983 @ SV1148 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1148
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2705]) ).
thf(2945,plain,
! [SV1224: $i,SV1149: $i,SV984: $i,SV709: $i,SV351: $i] :
( ( ( ( c_List_Oappend @ SV351 @ ( c_List_Olist_OCons @ SV709 @ ( c_List_Olist_ONil @ SV984 ) @ SV984 ) @ SV984 )
!= ( c_List_Oappend @ SV1149 @ ( c_List_Olist_OCons @ SV1224 @ ( c_List_Olist_ONil @ SV984 ) @ SV984 ) @ SV984 ) )
| ( SV709 = SV1224 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2706]) ).
thf(2946,plain,
! [SV1225: $i,SV1150: $i,SV985: $i,SV710: $i,SV352: $i] :
( ( ( ( c_List_Olist_OCons @ SV352 @ SV710 @ SV985 )
!= ( c_List_Olist_OCons @ SV1150 @ SV1225 @ SV985 ) )
| ( SV710 = SV1225 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2707]) ).
thf(2947,plain,
! [SV986: $i,SV711: $i,SV353: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV353 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV711 @ SV986 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV986
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2708]) ).
thf(2948,plain,
! [SV987: $i,SV712: $i,SV354: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV354 @ SV712 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV987 ) )
= $false )
| ( ( SV712
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2709]) ).
thf(2949,plain,
! [SV988: $i,SV713: $i,SV355: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV355 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV713 @ SV988 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( c_Lambda_OdB_OVar @ SV355 )
= SV713 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2710]) ).
thf(2950,plain,
! [SV989: $i,SV714: $i,SV356: $i] :
( ( ( ( c_List_Olist_OCons @ SV356 @ ( c_List_Olist_ONil @ SV714 ) @ SV714 )
= ( c_List_Orev @ SV989 @ SV714 ) )
= $false )
| ( ( SV989
= ( c_List_Olist_OCons @ SV356 @ ( c_List_Olist_ONil @ SV714 ) @ SV714 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2711]) ).
thf(2951,plain,
! [SV1226: $i,SV1151: $i,SV990: $i,SV716: $i,SV358: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV358 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV716 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV990 ) @ SV1151 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV990 ) @ SV1226 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV716 ) @ SV1151 )
= SV1226 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2713]) ).
thf(2952,plain,
! [SV1152: $i,SV991: $i,SV717: $i,SV359: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV359 ) @ SV717 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV991 ) @ SV1152 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV359 = SV991 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2714]) ).
thf(2953,plain,
! [SV1227: $i,SV1153: $i,SV992: $i,SV719: $i,SV361: $i] :
( ( ( ( c_List_Olist_OCons @ SV361 @ SV719 @ SV992 )
!= ( c_List_Oappend @ SV1153 @ SV1227 @ SV992 ) )
| ( ( c_List_Olist_OCons @ SV361 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV361 @ SV719 @ SV1153 @ SV1227 @ SV992 ) @ SV992 )
= SV1153 )
| ( ( c_List_Olist_OCons @ SV361 @ SV719 @ SV992 )
= SV1227 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2716]) ).
thf(2954,plain,
! [SV1154: $i,SV993: $i,SV720: $i,SV362: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV362 ) @ SV720 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV993 ) @ SV1154 ) )
= $true )
| ( ( SV362 = SV993 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2717]) ).
thf(2955,plain,
! [SV1155: $i,SV994: $i,SV721: $i,SV363: $i] :
( ( ( ( c_List_Orev @ SV363 @ SV721 )
!= ( c_List_Olist_OCons @ SV994 @ SV1155 @ SV721 ) )
= $true )
| ( ( SV363
= ( c_List_Oappend @ ( c_List_Orev @ SV1155 @ SV721 ) @ ( c_List_Olist_OCons @ SV994 @ ( c_List_Olist_ONil @ SV721 ) @ SV721 ) @ SV721 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2718]) ).
thf(2956,plain,
! [SV995: $i,SV722: $i,SV364: $i] :
( ( ( ( c_List_Oappend @ SV364 @ SV722 @ SV995 )
= SV722 )
= $false )
| ( ( SV364
= ( c_List_Olist_ONil @ SV995 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2719]) ).
thf(2957,plain,
! [SV723: $i,SV365: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV365 ) @ SV723 ) @ SV723 )
!= ( c_HOL_Ozero__class_Ozero @ SV365 ) )
= $true )
| ( ( SV723
= ( c_HOL_Ozero__class_Ozero @ SV365 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV365 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2720]) ).
thf(2958,plain,
! [SV996: $i,SV724: $i,SV366: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV366 ) @ SV724 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV996 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV366 ) @ SV724 )
= SV996 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2721]) ).
thf(2959,plain,
! [SV1228: $i,SV1156: $i,SV998: $i,SV726: $i,SV368: $i] :
( ( ( ( c_List_Oappend @ SV368 @ SV726 @ SV998 )
!= ( c_List_Olist_OCons @ SV1156 @ SV1228 @ SV998 ) )
| ( SV368
= ( c_List_Olist_OCons @ SV1156 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1156 @ SV1228 @ SV368 @ SV726 @ SV998 ) @ SV998 ) )
| ( SV726
= ( c_List_Olist_OCons @ SV1156 @ SV1228 @ SV998 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2723]) ).
thf(2960,plain,
! [SV1157: $i,SV999: $i,SV728: $i,SV370: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV370 ) @ SV728 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV999 ) @ SV1157 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV370 = SV999 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2725]) ).
thf(2961,plain,
! [SV1000: $i,SV729: $i,SV371: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV371 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV729 @ SV1000 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV1000
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2726]) ).
thf(2962,plain,
! [SV1001: $i,SV730: $i,SV372: $i] :
( ( ( ( c_List_Olist_ONil @ SV372 )
= ( c_List_Oappend @ SV730 @ SV1001 @ SV372 ) )
= $false )
| ( ( SV730
= ( c_List_Olist_ONil @ SV372 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2727]) ).
thf(2963,plain,
! [SV1002: $i,SV731: $i,SV373: $i] :
( ( ( ( c_List_Oappend @ SV373 @ SV731 @ SV1002 )
= SV373 )
= $false )
| ( ( SV731
= ( c_List_Olist_ONil @ SV1002 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2728]) ).
thf(2964,plain,
! [SV1158: $i,SV1003: $i,SV732: $i,SV374: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV374 ) @ SV732 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1003 ) @ SV1158 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2729]) ).
thf(2965,plain,
! [SV1004: $i,SV734: $i,SV376: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV376 @ SV734 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1004 @ SV734 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV376 = SV1004 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2731]) ).
thf(2966,plain,
! [SV1159: $i,SV1005: $i,SV735: $i,SV377: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV377 ) @ SV735 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1005 ) @ SV1159 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV735 = SV1159 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2732]) ).
thf(2967,plain,
! [SV1160: $i,SV1006: $i,SV736: $i,SV378: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV378 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV378 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV378 ) @ SV736 ) @ SV1006 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV378 ) @ SV736 ) @ SV1160 ) )
| ( SV1006 = SV1160 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2733]) ).
thf(2968,plain,
! [SV1229: $i,SV1161: $i,SV1008: $i,SV738: $i,SV380: $i] :
( ( ! [SY2987: $i,SY2988: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV380 ) @ SV738 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV1008 @ SV1161 @ SV1229 ) ) )
| ~ ( c_Type_Otyping @ SY2987 @ SV1161 @ SV380 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1161 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY2987 @ SV1229 @ SV380 @ tc_Type_Otype ) @ SV1008 @ SY2988 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1008 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2735]) ).
thf(2969,plain,
! [SV1009: $i,SV739: $i,SV381: $i] :
( ( ( ( c_List_Olist_ONil @ SV381 )
= ( c_List_Oappend @ SV739 @ SV1009 @ SV381 ) )
= $false )
| ( ( SV1009
= ( c_List_Olist_ONil @ SV381 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2736]) ).
thf(2970,plain,
! [SV1162: $i,SV1010: $i,SV740: $i,SV382: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV382 ) @ SV740 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1010 ) @ SV1162 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV740 = SV1162 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2737]) ).
thf(2971,plain,
! [SV1163: $i,SV1012: $i,SV742: $i,SV384: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV384 ) ) @ SV742 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1012 ) @ SV1163 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2739]) ).
thf(2972,plain,
! [SV1230: $i,SV1164: $i,SV1013: $i,SV744: $i,SV386: $i] :
( ( ( ( c_List_Oappend @ SV386 @ ( c_List_Olist_OCons @ SV744 @ ( c_List_Olist_ONil @ SV1013 ) @ SV1013 ) @ SV1013 )
!= ( c_List_Oappend @ SV1164 @ ( c_List_Olist_OCons @ SV1230 @ ( c_List_Olist_ONil @ SV1013 ) @ SV1013 ) @ SV1013 ) )
| ( SV386 = SV1164 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2741]) ).
thf(2973,plain,
! [SV1165: $i,SV1014: $i,SV745: $i,SV387: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV387 ) @ SV745 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1014 ) @ SV1165 ) )
= $true )
| ( ( SV387 = SV1014 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2742]) ).
thf(2974,plain,
! [SV746: $i,SV390: $i,SV1015: $i,SV3: $i] :
( ( ( c_Type_Otypings @ SV3 @ ( c_List_Oappend @ SV1015 @ ( c_List_Olist_OCons @ SV390 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SV746 )
= $false )
| ( ( c_Type_Otyping @ SV3 @ SV390 @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ SV746 @ SV3 @ SV390 @ SV1015 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2743]) ).
thf(2975,plain,
! [SV750: $i,SV1016: $i,SV394: $i,SV11: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV11 @ SV394 ) @ SV1016 ) @ SV750 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV11 @ SV394 @ SV394 ) @ SV394 ) @ SV750 ) @ SV1016 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2744]) ).
thf(2976,plain,
! [SV751: $i,SV1017: $i,SV395: $i,SV12: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV12 @ SV395 @ SV395 ) @ SV395 ) @ SV1017 ) @ SV751 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV12 @ SV395 ) @ SV751 ) @ SV1017 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2745]) ).
thf(2977,plain,
! [SV1166: $i,SV1018: $i,SV752: $i,SV396: $i,SV13: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV13 @ SV396 ) @ SV752 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV13 @ SV1018 @ SV1166 ) @ SV752 ) @ SV396 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2746]) ).
thf(2978,plain,
! [SV1167: $i,SV1019: $i,SV753: $i,SV397: $i,SV14: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV14 @ SV397 @ SV753 ) @ SV1019 ) @ SV1167 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV14 @ SV1167 ) @ SV1019 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2747]) ).
thf(2979,plain,
! [SV1168: $i,SV1020: $i,SV754: $i,SV398: $i,SV15: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV15 @ SV398 ) @ SV754 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV15 @ SV1020 @ SV1168 ) @ SV754 ) @ SV398 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2748]) ).
thf(2980,plain,
! [SV1169: $i,SV1021: $i,SV755: $i,SV399: $i,SV16: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV16 @ SV399 @ SV755 ) @ SV1021 ) @ SV1169 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV16 @ SV1169 ) @ SV1021 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2749]) ).
thf(2981,plain,
! [SV1022: $i,SV402: $i,SV758: $i,SV20: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV20 @ SV758 ) @ SV402 ) @ SV1022 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV20 @ SV1022 @ SV758 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV20 @ SV402 @ SV758 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2750]) ).
thf(2982,plain,
! [SV403: $i,SV759: $i,SV1023: $i,SV21: $i] :
( ( ( ~ ( c_Wellfounded_Oaccp @ SV21 @ SV1023 @ SV759 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV21 @ SV759 ) @ SV403 ) @ SV1023 ) ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV21 @ SV403 @ SV759 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2751]) ).
thf(2983,plain,
! [SV768: $i,SV38: $i,SV1025: $i,SV417: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV417 @ SV1025 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV38 @ SV768 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV38 ) @ SV417 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV768 ) @ SV1025 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2757]) ).
thf(2984,plain,
! [SV776: $i,SV1027: $i,SV429: $i,SV52: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV52 @ SV429 ) @ SV1027 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV52 @ SV1027 @ SV776 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV52 @ SV429 @ SV776 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2762]) ).
thf(2985,plain,
! [SV777: $i,SV1028: $i,SV430: $i,SV53: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV53 @ SV430 ) @ SV1028 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV53 @ SV1028 @ SV777 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV53 @ SV430 @ SV777 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2763]) ).
thf(2986,plain,
! [SV778: $i,SV57: $i,SV433: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV433 @ SV57 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV778 @ SV57 ) @ SV57 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV433 @ SV778 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2765]) ).
thf(2987,plain,
! [SV58: $i,SV779: $i,SV434: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV434 @ SV779 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV434 @ SV58 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV779 @ SV58 ) @ SV58 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2766]) ).
thf(2988,plain,
! [SV793: $i,SV86: $i,SV459: $i] :
( ( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV459 @ tc_Lambda_OdB ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV86 ) ) @ SV459 ) @ SV793 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $true )
| ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV86 @ SV459 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV793 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2770]) ).
thf(2989,plain,
! [SV462: $i,SV89: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV462 @ SV89 ) @ SV89 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV462 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2771]) ).
thf(2990,plain,
! [SV90: $i,SV463: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV463 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV463 @ SV90 ) @ SV90 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2772]) ).
thf(2991,plain,
! [SV466: $i,SV93: $i] :
( ( ( hBOOL @ ( hAPP @ SV93 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV93 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV93 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV93 @ SV466 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV93 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV93 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__4 @ SV93 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2773]) ).
thf(2992,plain,
! [SV467: $i,SV94: $i] :
( ( ( hBOOL @ ( hAPP @ SV94 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV94 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV94 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV94 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV94 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4 @ SV94 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV94 @ SV467 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2774]) ).
thf(2993,plain,
! [SV1170: $i,SV1030: $i,SV797: $i,SV469: $i,SV96: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV96 @ SV469 ) @ SV797 ) ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV96 @ ( c_List_Olist_OCons @ SV469 @ SV1030 @ SV1170 ) @ ( c_List_Olist_OCons @ SV797 @ SV1030 @ SV1170 ) @ SV1170 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2775]) ).
thf(2994,plain,
! [SV1231: $i,SV1171: $i,SV1031: $i,SV798: $i,SV470: $i,SV97: $i] :
( ( ( SV97 = SV470 )
| ( SV798 = SV1031 )
| ~ ( c_ListOrder_Ostep1 @ SV1171 @ ( c_List_Olist_OCons @ SV470 @ SV1031 @ SV1231 ) @ ( c_List_Olist_OCons @ SV97 @ SV798 @ SV1231 ) @ SV1231 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2776]) ).
thf(2995,plain,
! [SV799: $i,SV471: $i,SV1032: $i,SV98: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV98 ) @ SV1032 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV98 @ SV471 @ SV799 ) ) @ ( c_Lambda_Osubst @ SV1032 @ SV471 @ SV799 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2777]) ).
thf(2996,plain,
! [SV801: $i,SV473: $i,SV1034: $i,SV100: $i] :
( ( ( c_List_Olistsp @ SV100 @ ( c_List_Oappend @ SV1034 @ SV473 @ SV801 ) @ SV801 )
= $false )
| ( ( c_List_Olistsp @ SV100 @ SV473 @ SV801 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2779]) ).
thf(2997,plain,
! [SV802: $i,SV1035: $i,SV474: $i,SV101: $i] :
( ( ( c_List_Olistsp @ SV101 @ ( c_List_Oappend @ SV474 @ SV1035 @ SV802 ) @ SV802 )
= $false )
| ( ( c_List_Olistsp @ SV101 @ SV474 @ SV802 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2780]) ).
thf(2998,plain,
! [SV1173: $i,SV1036: $i,SV804: $i,SV477: $i,SV104: $i] :
( ( ( c_ListOrder_Ostep1 @ SV104 @ ( c_List_Oappend @ SV477 @ SV804 @ SV1036 ) @ ( c_List_Oappend @ SV477 @ SV1173 @ SV1036 ) @ SV1036 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV104 @ SV804 @ SV1173 @ SV1036 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2782]) ).
thf(2999,plain,
! [SV1174: $i,SV1037: $i,SV805: $i,SV478: $i,SV105: $i] :
( ( ( ~ ( c_ListOrder_Ostep1 @ SV105 @ SV478 @ SV805 @ SV1037 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV105 @ ( c_List_Oappend @ SV478 @ SV1174 @ SV1037 ) @ ( c_List_Oappend @ SV805 @ SV1174 @ SV1037 ) @ SV1037 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2783]) ).
thf(3000,plain,
! [SV1038: $i,SV807: $i,SV480: $i,SV108: $i] :
( ( ( class_Orderings_Opreorder @ SV108 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV480 @ SV807 @ SV108 )
| ~ ( c_HOL_Oord__class_Oless @ SV1038 @ SV807 @ SV108 )
| ~ ( c_HOL_Oord__class_Oless @ SV480 @ SV1038 @ SV108 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2784]) ).
thf(3001,plain,
! [SV1039: $i,SV808: $i,SV481: $i,SV109: $i] :
( ( ( class_Orderings_Oorder @ SV109 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV481 @ SV808 @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ SV481 @ SV1039 @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ SV1039 @ SV808 @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2785]) ).
thf(3002,plain,
! [SV1040: $i,SV809: $i,SV482: $i,SV110: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV110 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV482 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV809 ) @ SV1040 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV482 ) @ SV809 ) ) @ SV1040 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2786]) ).
thf(3003,plain,
! [SV1041: $i,SV810: $i,SV483: $i,SV111: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV111 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV483 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV810 ) @ SV1041 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV810 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV483 ) @ SV1041 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2787]) ).
thf(3004,plain,
! [SV1042: $i,SV811: $i,SV484: $i,SV112: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV112 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SV484 ) @ SV811 ) ) @ SV1042 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SV484 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SV811 ) @ SV1042 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2788]) ).
thf(3005,plain,
! [SV1043: $i,SV812: $i,SV485: $i,SV113: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV113 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV485 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV812 ) @ SV1043 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV812 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV485 ) @ SV1043 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2789]) ).
thf(3006,plain,
! [SV1044: $i,SV813: $i,SV486: $i,SV114: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__add @ SV114 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SV486 ) @ SV813 ) ) @ SV1044 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SV486 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SV813 ) @ SV1044 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2790]) ).
thf(3007,plain,
! [SV1045: $i,SV814: $i,SV487: $i,SV115: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV115 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SV487 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SV814 ) @ SV1045 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SV487 ) @ SV814 ) ) @ SV1045 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2791]) ).
thf(3008,plain,
! [SV1046: $i,SV815: $i,SV488: $i,SV116: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV116 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV488 ) @ SV815 ) ) @ SV1046 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV488 ) @ SV1046 ) ) @ SV815 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2792]) ).
thf(3009,plain,
! [SV1047: $i,SV816: $i,SV489: $i,SV117: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV117 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV489 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV816 ) @ SV1047 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV816 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV489 ) @ SV1047 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2793]) ).
thf(3010,plain,
! [SV1048: $i,SV817: $i,SV490: $i,SV118: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV118 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV490 ) @ SV817 ) ) @ SV1048 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV490 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV817 ) @ SV1048 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2794]) ).
thf(3011,plain,
! [SV1232: $i,SV1175: $i,SV1050: $i,SV819: $i,SV493: $i,SV123: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SV493 ) @ SV819 ) )
| ( c_ListOrder_Ostep1 @ SV123 @ SV1050 @ SV1175 @ SV1232 )
| ~ ( c_ListOrder_Ostep1 @ SV123 @ ( c_List_Oappend @ SV1050 @ ( c_List_Olist_OCons @ SV493 @ ( c_List_Olist_ONil @ SV1232 ) @ SV1232 ) @ SV1232 ) @ ( c_List_Oappend @ SV1175 @ ( c_List_Olist_OCons @ SV819 @ ( c_List_Olist_ONil @ SV1232 ) @ SV1232 ) @ SV1232 ) @ SV1232 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2795]) ).
thf(3012,plain,
! [SV820: $i,SV494: $i,SV124: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV124 ) @ SV494 ) @ SV820 ) @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ SV124 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV820 @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ SV124 )
| ~ ( c_HOL_Oord__class_Oless @ SV494 @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ SV124 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2796]) ).
thf(3013,plain,
! [SV1233: $i,SV1176: $i,SV1055: $i,SV828: $i,SV502: $i,SV132: $i] :
( ( ( SV132 = SV502 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV828 @ SV502 ) @ SV132 ) )
| ~ ( c_ListOrder_Ostep1 @ SV828 @ ( c_List_Olist_OCons @ SV502 @ SV1055 @ SV1176 ) @ ( c_List_Olist_OCons @ SV132 @ SV1233 @ SV1176 ) @ SV1176 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2800]) ).
thf(3014,plain,
! [SV1177: $i,SV1056: $i,SV829: $i,SV503: $i,SV134: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV134 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ SV503 ) @ SV829 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ SV1056 ) @ SV1177 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ SV503 ) @ SV1056 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ SV829 ) @ SV1177 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2801]) ).
thf(3015,plain,
! [SV830: $i,SV135: $i,SV1057: $i,SV504: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV504 ) @ SV1057 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV135 ) @ SV830 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV135 ) @ SV504 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV830 ) @ SV1057 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2802]) ).
thf(3016,plain,
! [SV506: $i,SV832: $i,SV1058: $i,SV137: $i] :
( ( ( ~ ( c_Type_Otyping @ SV137 @ SV1058 @ SV832 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV1058 ) @ SV506 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV137 @ SV506 @ SV832 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2804]) ).
thf(3017,plain,
! [SV1234: $i,SV1178: $i,SV1059: $i,SV836: $i,SV512: $i,SV143: $i] :
( ( ( SV143 = SV512 )
| ( c_ListOrder_Ostep1 @ SV836 @ SV143 @ SV512 @ SV1059 )
| ~ ( c_ListOrder_Ostep1 @ SV836 @ ( c_List_Oappend @ SV143 @ ( c_List_Olist_OCons @ SV1178 @ ( c_List_Olist_ONil @ SV1059 ) @ SV1059 ) @ SV1059 ) @ ( c_List_Oappend @ SV512 @ ( c_List_Olist_OCons @ SV1234 @ ( c_List_Olist_ONil @ SV1059 ) @ SV1059 ) @ SV1059 ) @ SV1059 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2806]) ).
thf(3018,plain,
! [SV516: $i,SV148: $i] :
( ( ( class_Int_Onumber__ring @ SV148 )
= $false )
| ( ( SV516
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV516 ) @ ( c_HOL_Ozero__class_Ozero @ SV148 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2807]) ).
thf(3019,plain,
! [SV523: $i,SV1060: $i,SV155: $i,SV837: $i] :
( ( ( c_OrderedGroup_Omonoid__add @ SV837 @ SV155 @ SV1060 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV155 @ SV523 ) @ SV837 )
= SV523 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2808]) ).
thf(3020,plain,
! [SV838: $i,SV1061: $i,SV156: $i,SV524: $i] :
( ( ( c_OrderedGroup_Omonoid__add @ SV524 @ SV156 @ SV1061 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV156 @ SV524 ) @ SV838 )
= SV838 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2809]) ).
thf(3021,plain,
! [SV525: $i,SV157: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV157 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV525 ) @ SV525 ) @ SV157 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV157 ) @ SV525 @ SV157 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2810]) ).
thf(3022,plain,
! [SV526: $i,SV158: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV526 @ SV158 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV526 ) @ SV526 ) @ SV158 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2811]) ).
thf(3023,plain,
! [SV1179: $i,SV1062: $i,SV841: $i,SV529: $i,SV161: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV161 @ SV529 ) @ SV841 ) @ SV1062 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV161 @ SV529 ) @ SV1179 ) @ SV1062 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV161 @ SV529 ) @ SV841 ) @ SV1179 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2812]) ).
thf(3024,plain,
! [SV842: $i,SV167: $i,SV1063: $i,SV535: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV535 ) @ SV1063 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV167 @ SV535 @ SV842 ) ) @ ( c_Lambda_Osubst @ SV167 @ SV1063 @ SV842 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2813]) ).
thf(3025,plain,
! [SV1235: $i,SV1180: $i,SV1064: $i,SV846: $i,SV539: $i,SV171: $i] :
( ( ( c_List_Ofoldr @ SV171 @ ( c_List_Oappend @ SV539 @ SV846 @ SV1064 ) @ SV1180 @ SV1064 @ SV1235 )
= ( c_List_Ofoldr @ SV171 @ SV539 @ ( c_List_Ofoldr @ SV171 @ SV846 @ SV1180 @ SV1064 @ SV1235 ) @ SV1064 @ SV1235 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2817]) ).
thf(3026,plain,
! [SV1236: $i,SV1181: $i,SV1065: $i,SV847: $i,SV540: $i,SV172: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV172 @ SV540 ) @ SV847 ) )
| ( SV540 = SV847 )
| ~ ( c_ListOrder_Ostep1 @ SV172 @ ( c_List_Oappend @ SV1065 @ ( c_List_Olist_OCons @ SV540 @ ( c_List_Olist_ONil @ SV1181 ) @ SV1181 ) @ SV1181 ) @ ( c_List_Oappend @ SV1236 @ ( c_List_Olist_OCons @ SV847 @ ( c_List_Olist_ONil @ SV1181 ) @ SV1181 ) @ SV1181 ) @ SV1181 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2818]) ).
thf(3027,plain,
! [SV848: $i,SV541: $i,SV1066: $i,SV173: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV173 ) @ SV1066 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV173 @ SV541 @ SV848 ) ) @ ( c_Lambda_Osubst @ SV1066 @ SV541 @ SV848 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2819]) ).
thf(3028,plain,
! [SV849: $i,SV174: $i,SV1067: $i,SV542: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV542 ) @ SV1067 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV174 @ SV542 @ SV849 ) ) @ ( c_Lambda_Osubst @ SV174 @ SV1067 @ SV849 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2820]) ).
thf(3029,plain,
! [SV544: $i,SV1068: $i,SV851: $i,SV176: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV176 @ SV851 ) @ SV1068 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV176 @ SV544 ) @ SV851 ) @ SV1068 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2822]) ).
thf(3030,plain,
! [SV179: $i,SV547: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV547 @ ( c_HOL_Ozero__class_Ozero @ SV179 ) @ SV179 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV179 ) @ SV547 ) @ SV547 ) @ ( c_HOL_Ozero__class_Ozero @ SV179 ) @ SV179 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2823]) ).
thf(3031,plain,
! [SV548: $i,SV180: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV180 ) @ SV548 ) @ SV548 ) @ ( c_HOL_Ozero__class_Ozero @ SV180 ) @ SV180 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV548 @ ( c_HOL_Ozero__class_Ozero @ SV180 ) @ SV180 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2824]) ).
thf(3032,plain,
! [SV549: $i,SV181: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV181 ) @ SV549 ) @ SV549 ) @ ( c_HOL_Ozero__class_Ozero @ SV181 ) @ SV181 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV549 @ ( c_HOL_Ozero__class_Ozero @ SV181 ) @ SV181 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2825]) ).
thf(3033,plain,
! [SV182: $i,SV550: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV550 @ ( c_HOL_Ozero__class_Ozero @ SV182 ) @ SV182 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV182 ) @ SV550 ) @ SV550 ) @ ( c_HOL_Ozero__class_Ozero @ SV182 ) @ SV182 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2826]) ).
thf(3034,plain,
! [SV855: $i,SV184: $i,SV552: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV552 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV184 @ SV552 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV855 @ 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 @ SV184 ) ) @ SV552 ) @ SV855 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2828]) ).
thf(3035,plain,
! [SV858: $i,SV560: $i,SV194: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV194 ) @ SV560 ) @ SV858 ) @ SV194 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV858 @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV560 @ SV194 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2834]) ).
thf(3036,plain,
! [SV1237: $i,SV1182: $i,SV1069: $i,SV859: $i,SV561: $i,SV195: $i] :
( ( ( c_ListOrder_Ostep1 @ SV195 @ SV561 @ SV859 @ SV1069 )
| ( SV859 = SV561 )
| ~ ( c_ListOrder_Ostep1 @ SV195 @ ( c_List_Olist_OCons @ SV1182 @ SV561 @ SV1069 ) @ ( c_List_Olist_OCons @ SV1237 @ SV859 @ SV1069 ) @ SV1069 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2835]) ).
thf(3037,plain,
! [SV1183: $i,SV1070: $i,SV860: $i,SV562: $i,SV196: $i] :
( ( ( ( hAPP @ ( hAPP @ SV196 @ ( hAPP @ ( hAPP @ SV196 @ SV562 ) @ SV860 ) ) @ SV1070 )
= ( hAPP @ ( hAPP @ SV196 @ SV562 ) @ ( hAPP @ ( hAPP @ SV196 @ SV860 ) @ SV1070 ) ) )
= $true )
| ( ( ~ ( c_OrderedGroup_Osemigroup__add @ SV196 @ SV1183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2836]) ).
thf(3038,plain,
! [SV197: $i,SV861: $i,SV563: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV563 @ SV861 @ SV197 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV861 @ SV563 @ SV197 )
| ( SV861 = SV563 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2837]) ).
thf(3039,plain,
! [SV198: $i,SV862: $i,SV564: $i] :
( ( ( SV564 = SV862 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV862 @ SV564 @ SV198 )
| ( c_HOL_Oord__class_Oless @ SV564 @ SV862 @ SV198 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV198 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2838]) ).
thf(3040,plain,
! [SV200: $i,SV566: $i,SV863: $i] :
( ( ( SV863 = SV566 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV863 @ SV566 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV566 @ SV863 @ tc_nat )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV200 @ SV566 ) @ SV863 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2839]) ).
thf(3041,plain,
! [SV202: $i,SV864: $i,SV568: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV568 @ SV864 @ SV202 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV864 @ SV568 @ SV202 )
| ( SV864 = SV568 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV202 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2840]) ).
thf(3042,plain,
! [SV203: $i,SV865: $i,SV569: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV569 @ SV865 @ SV203 )
= $true )
| ( ( ( SV865 = SV569 )
| ( c_HOL_Oord__class_Oless @ SV865 @ SV569 @ SV203 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV203 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2841]) ).
thf(3043,plain,
! [SV204: $i,SV866: $i,SV570: $i] :
( ( ( SV570 = SV866 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV570 @ SV866 @ SV204 )
| ( c_HOL_Oord__class_Oless @ SV866 @ SV570 @ SV204 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2842]) ).
thf(3044,plain,
! [SV1184: $i,SV1071: $i,SV867: $i,SV571: $i,SV205: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV205 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV205 ) @ SV571 ) @ SV867 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV205 ) @ SV1071 ) @ SV1184 ) @ SV205 )
| ~ ( c_HOL_Oord__class_Oless @ SV867 @ SV1184 @ SV205 )
| ~ ( c_HOL_Oord__class_Oless @ SV571 @ SV1071 @ SV205 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2843]) ).
thf(3045,plain,
! [SV1238: $i,SV1185: $i,SV1072: $i,SV868: $i,SV573: $i,SV207: $i] :
( ( ( SV207 = SV573 )
| ( SV868 = SV1072 )
| ~ ( c_ListOrder_Ostep1 @ SV1185 @ ( c_List_Oappend @ SV207 @ ( c_List_Olist_OCons @ SV868 @ ( c_List_Olist_ONil @ SV1238 ) @ SV1238 ) @ SV1238 ) @ ( c_List_Oappend @ SV573 @ ( c_List_Olist_OCons @ SV1072 @ ( c_List_Olist_ONil @ SV1238 ) @ SV1238 ) @ SV1238 ) @ SV1238 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2844]) ).
thf(3046,plain,
! [SV574: $i,SV1073: $i,SV869: $i,SV209: $i] :
( ( ( ~ ( c_List_Olistsp @ SV209 @ SV869 @ SV1073 ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV209 @ SV574 @ SV1073 ) )
= $true )
| ( ( c_List_Olistsp @ SV209 @ ( c_List_Oappend @ SV574 @ SV869 @ SV1073 ) @ SV1073 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2845]) ).
thf(3047,plain,
! [SV1075: $i,SV871: $i,SV578: $i,SV214: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV214 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV578 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV214 ) @ SV871 ) @ SV1075 ) @ SV214 )
| ~ ( c_HOL_Oord__class_Oless @ SV578 @ SV1075 @ SV214 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV214 ) @ SV871 @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2847]) ).
thf(3048,plain,
! [SV1239: $i,SV1187: $i,SV1076: $i,SV873: $i,SV580: $i,SV216: $i] :
( ( ( c_List_Ofoldr @ SV216 @ ( c_List_Olist_OCons @ SV580 @ SV873 @ SV1076 ) @ SV1187 @ SV1076 @ SV1239 )
= ( hAPP @ ( hAPP @ SV216 @ SV580 ) @ ( c_List_Ofoldr @ SV216 @ SV873 @ SV1187 @ SV1076 @ SV1239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2849]) ).
thf(3049,plain,
! [SV1188: $i,SV1077: $i,SV874: $i,SV581: $i,SV217: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV217 @ ( c_Lambda_OdB_OdB__case @ SV581 @ SV874 @ SV1077 @ ( c_Lambda_OdB_OAbs @ SV1188 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV217 @ ( hAPP @ SV1077 @ SV1188 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2850]) ).
thf(3050,plain,
! [SV1189: $i,SV1078: $i,SV875: $i,SV582: $i,SV218: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV218 @ ( c_Lambda_OdB_OdB__case @ SV582 @ SV875 @ SV1078 @ ( c_Lambda_OdB_OAbs @ SV1189 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV218 @ ( hAPP @ SV1078 @ SV1189 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2851]) ).
thf(3051,plain,
! [SV1079: $i,SV878: $i,SV585: $i,SV221: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV221 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV221 ) @ SV585 ) @ SV878 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV221 ) @ SV1079 ) @ SV878 ) @ SV221 )
| ~ ( c_HOL_Oord__class_Oless @ SV585 @ SV1079 @ SV221 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2853]) ).
thf(3052,plain,
! [SV1080: $i,SV879: $i,SV586: $i,SV222: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV222 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV222 ) @ SV586 ) @ SV879 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV222 ) @ SV1080 ) @ SV879 ) @ SV222 )
| ~ ( c_HOL_Oord__class_Oless @ SV586 @ SV1080 @ SV222 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2854]) ).
thf(3053,plain,
! [SV1081: $i,SV880: $i,SV587: $i,SV223: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV223 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV587 @ SV880 @ SV223 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV223 ) @ SV587 ) @ SV1081 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV223 ) @ SV880 ) @ SV1081 ) @ SV223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2855]) ).
thf(3054,plain,
! [SV1082: $i,SV881: $i,SV588: $i,SV224: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV224 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV224 ) @ SV588 ) @ SV881 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV224 ) @ SV588 ) @ SV1082 ) @ SV224 )
| ~ ( c_HOL_Oord__class_Oless @ SV881 @ SV1082 @ SV224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2856]) ).
thf(3055,plain,
! [SV1083: $i,SV882: $i,SV589: $i,SV225: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV225 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV225 ) @ SV589 ) @ SV882 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV225 ) @ SV589 ) @ SV1083 ) @ SV225 )
| ~ ( c_HOL_Oord__class_Oless @ SV882 @ SV1083 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2857]) ).
thf(3056,plain,
! [SV1084: $i,SV883: $i,SV590: $i,SV226: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV226 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV590 @ SV883 @ SV226 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV226 ) @ SV1084 ) @ SV590 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV226 ) @ SV1084 ) @ SV883 ) @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2858]) ).
thf(3057,plain,
! [SV1240: $i,SV1190: $i,SV1085: $i,SV884: $i,SV591: $i,SV227: $i] :
( ( ( c_ListOrder_Ostep1 @ SV227 @ SV591 @ SV884 @ SV1085 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV227 @ SV1190 ) @ SV1240 ) )
| ~ ( c_ListOrder_Ostep1 @ SV227 @ ( c_List_Olist_OCons @ SV1190 @ SV591 @ SV1085 ) @ ( c_List_Olist_OCons @ SV1240 @ SV884 @ SV1085 ) @ SV1085 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2859]) ).
thf(3058,plain,
! [SV1191: $i,SV1086: $i,SV885: $i,SV592: $i,SV228: $i] :
( ( ( c_ListOrder_Ostep1 @ SV228 @ ( c_List_Olist_OCons @ SV592 @ SV885 @ SV1086 ) @ ( c_List_Olist_OCons @ SV592 @ SV1191 @ SV1086 ) @ SV1086 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV228 @ SV885 @ SV1191 @ SV1086 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2860]) ).
thf(3059,plain,
! [SV234: $i,SV890: $i,SV597: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV597 @ SV890 @ SV234 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV890 @ SV597 @ SV234 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV234 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2861]) ).
thf(3060,plain,
! [SV1192: $i,SV1091: $i,SV891: $i,SV598: $i,SV235: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV235 @ SV598 ) @ SV891 ) @ SV1091 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV235 @ SV598 ) @ SV1192 ) @ SV1091 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV891 ) @ SV1192 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2862]) ).
thf(3061,plain,
! [SV1193: $i,SV1092: $i,SV892: $i,SV599: $i,SV236: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV236 @ SV599 ) @ SV892 ) @ SV1092 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV236 @ SV1193 ) @ SV1092 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV236 @ SV599 ) @ SV892 ) @ SV1193 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2863]) ).
thf(3062,plain,
! [SV237: $i,SV893: $i,SV600: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV600 @ SV893 @ SV237 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV893 @ SV600 @ SV237 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV237 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2864]) ).
thf(3063,plain,
! [SV238: $i,SV894: $i,SV601: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV601 @ SV894 @ SV238 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV894 @ SV601 @ SV238 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV238 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2865]) ).
thf(3064,plain,
! [SV239: $i,SV895: $i,SV602: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV602 @ SV895 @ SV239 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV895 @ SV602 @ SV239 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV239 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2866]) ).
thf(3065,plain,
! [SV1194: $i,SV1093: $i,SV896: $i,SV603: $i,SV240: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV240 @ SV603 @ SV896 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SV1093 @ SV603 ) @ SV1194 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV240 @ SV1093 @ SV1194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2867]) ).
thf(3066,plain,
! [SV1195: $i,SV1094: $i,SV897: $i,SV605: $i,SV242: $i] :
( ( ( ( c_List_Ofoldl @ SV242 @ ( hAPP @ ( hAPP @ SV242 @ SV605 ) @ SV897 ) @ SV1094 @ SV1195 @ SV1195 )
= ( hAPP @ ( hAPP @ SV242 @ SV605 ) @ ( c_List_Ofoldl @ SV242 @ SV897 @ SV1094 @ SV1195 @ SV1195 ) ) )
= $true )
| ( ( ~ ( c_OrderedGroup_Osemigroup__add @ SV242 @ SV1195 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2869]) ).
thf(3067,plain,
! [SV899: $i,SV608: $i,SV1096: $i,SV245: $i] :
( ( ( c_Type_Otyping @ SV245 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1096 ) @ SV608 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV899 )
= $false )
| ( ( c_Type_Otypings @ SV245 @ SV608 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV899 @ SV245 @ SV1096 @ SV608 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2870]) ).
thf(3068,plain,
! [SV1196: $i,SV1097: $i,SV900: $i,SV609: $i,SV246: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV246 @ ( c_Lambda_OdB_OdB__case @ SV609 @ SV900 @ SV1097 @ ( c_Lambda_OdB_OVar @ SV1196 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV246 @ ( hAPP @ SV609 @ SV1196 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2871]) ).
thf(3069,plain,
! [SV1197: $i,SV1098: $i,SV901: $i,SV610: $i,SV247: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV247 @ ( c_Lambda_OdB_OdB__case @ SV610 @ SV901 @ SV1098 @ ( c_Lambda_OdB_OVar @ SV1197 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV247 @ ( hAPP @ SV610 @ SV1197 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2872]) ).
thf(3070,plain,
! [SV902: $i,SV248: $i,SV611: $i,SV1099: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV1099 ) @ SV611 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV248 @ SV1099 @ SV902 ) )
= $true )
| ( ( c_Type_Otyping @ SV248 @ SV611 @ SV902 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2873]) ).
thf(3071,plain,
! [SV1241: $i,SV1198: $i,SV1100: $i,SV903: $i,SV613: $i,SV250: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV250 @ ( c_Lambda_OdB_OdB__case @ SV613 @ SV903 @ SV1100 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1198 ) @ SV1241 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV250 @ ( hAPP @ ( hAPP @ SV903 @ SV1198 ) @ SV1241 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2874]) ).
thf(3072,plain,
! [SV1242: $i,SV1199: $i,SV1101: $i,SV904: $i,SV614: $i,SV251: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV251 @ ( c_Lambda_OdB_OdB__case @ SV614 @ SV904 @ SV1101 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1199 ) @ SV1242 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV251 @ ( hAPP @ ( hAPP @ SV904 @ SV1199 ) @ SV1242 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2875]) ).
thf(3073,plain,
! [SV905: $i,SV615: $i,SV1102: $i,SV252: $i] :
( ( ( c_Type_Otyping @ SV252 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1102 @ SV615 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV905 )
= $false )
| ( ( c_Type_Otypings @ SV252 @ SV615 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV905 @ SV252 @ SV1102 @ SV615 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2876]) ).
thf(3074,plain,
! [SV1243: $i,SV1200: $i,SV1103: $i,SV906: $i,SV616: $i,SV253: $i] :
( ( ! [SY2989: $i] :
( ( SV253
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV616 @ SV253 @ SV906 @ SV1103 ) @ SV616 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV906 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1200 ) @ SV1243 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV253 )
| ~ ( c_Type_Otypings @ SV906 @ SV1243 @ SY2989 )
| ~ ( c_Type_Otyping @ SV906 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1200 ) @ SV1243 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1103 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV616 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2877]) ).
thf(3075,plain,
! [SV1201: $i,SV1104: $i,SV907: $i,SV617: $i,SV254: $i] :
( ( ( ( hAPP @ ( c_Type_Oshift @ SV254 @ SV617 @ SV907 @ SV1104 ) @ SV1201 )
= ( hAPP @ SV254 @ SV1201 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1201 @ SV617 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2878]) ).
thf(3076,plain,
! [SV1202: $i,SV1105: $i,SV909: $i,SV620: $i,SV257: $i] :
( ( ( c_Type_Otyping @ SV257 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV620 ) @ SV909 ) @ SV1105 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV257 @ SV909 @ SV1202 )
| ~ ( c_Type_Otyping @ SV257 @ SV620 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1202 ) @ SV1105 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2880]) ).
thf(3077,plain,
! [SV1203: $i,SV1106: $i,SV910: $i,SV622: $i,SV259: $i] :
( ( ( SV259 = SV622 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV910 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1106 ) @ SV1203 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV622 )
| ~ ( c_Type_Otyping @ SV910 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1106 ) @ SV1203 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV259 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2881]) ).
thf(3078,plain,
! [SV1110: $i,SV629: $i,SV916: $i,SV266: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV266 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV916 @ tc_Type_Otype ) @ SV629 @ SV1110 )
= $false )
| ( ( c_Type_Otyping @ SV266 @ ( c_Lambda_OdB_OAbs @ SV629 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV916 ) @ SV1110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2886]) ).
thf(3079,plain,
! [SV1111: $i,SV918: $i,SV631: $i,SV269: $i] :
( ( ( class_OrderedGroup_Osemigroup__add @ SV269 )
= $false )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV269 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV269 ) @ SV631 ) @ SV918 ) @ SV1111 @ SV269 @ SV269 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV269 ) @ SV631 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV269 ) @ SV918 @ SV1111 @ SV269 @ SV269 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2888]) ).
thf(3080,plain,
! [SV920: $i,SV1112: $i,SV633: $i,SV271: $i] :
( ( ( c_Type_Otyping @ SV271 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV633 @ SV1112 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV920 )
= $false )
| ( ( c_Type_Otyping @ SV271 @ SV633 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV920 @ SV271 @ SV633 @ SV1112 ) @ SV920 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2889]) ).
thf(3081,plain,
! [SV921: $i,SV1113: $i,SV634: $i,SV272: $i] :
( ( ( c_Type_Otyping @ SV272 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV634 ) @ SV1113 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV921 )
= $false )
| ( ( c_Type_Otyping @ SV272 @ ( c_Lambda_OdB_OVar @ SV634 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV921 @ SV272 @ SV634 @ SV1113 ) @ SV921 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2890]) ).
thf(3082,plain,
! [SV1205: $i,SV1114: $i,SV922: $i,SV635: $i,SV273: $i] :
( ( ( c_Type_Otyping @ SV273 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV635 @ SV922 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1114 )
= $true )
| ( ( ~ ( c_Type_Otypings @ SV273 @ SV922 @ SV1205 )
| ~ ( c_Type_Otyping @ SV273 @ SV635 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV1205 @ SV1114 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2891]) ).
thf(3083,plain,
! [SV1244: $i,SV1206: $i,SV1115: $i,SV924: $i,SV637: $i,SV275: $i] :
( ( ( c_Lambda_OdB_OdB__case @ SV275 @ SV637 @ SV924 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1115 ) @ SV1206 ) @ SV1244 )
= ( hAPP @ ( hAPP @ SV637 @ SV1115 ) @ SV1206 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2893]) ).
thf(3084,plain,
! [SV1207: $i,SV1116: $i,SV925: $i,SV638: $i,SV276: $i] :
( ( ( ( hAPP @ ( hAPP @ SV276 @ SV638 ) @ ( c_List_Ofoldl @ SV276 @ SV925 @ SV1116 @ SV1207 @ SV1207 ) )
= ( c_List_Ofoldl @ SV276 @ SV638 @ SV1116 @ SV1207 @ SV1207 ) )
= $true )
| ( ( ~ ( c_OrderedGroup_Omonoid__add @ SV925 @ SV276 @ SV1207 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2894]) ).
thf(3085,plain,
! [SV926: $i,SV639: $i,SV1117: $i,SV277: $i] :
( ( ( c_Type_Otyping @ SV277 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1117 ) @ SV639 ) @ SV926 )
= $false )
| ( ( c_Type_Otyping @ SV277 @ SV639 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV926 @ SV277 @ SV1117 @ SV639 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2895]) ).
thf(3086,plain,
! [SV928: $i,SV641: $i,SV1119: $i,SV280: $i] :
( ( ( c_Type_Otyping @ SV280 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1119 @ SV641 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV928 )
= $false )
| ( ( c_Type_Otypings @ SV280 @ SV641 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV928 @ SV280 @ SV1119 @ SV641 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2897]) ).
thf(3087,plain,
! [SV1245: $i,SV1209: $i,SV1120: $i,SV929: $i,SV642: $i,SV281: $i] :
( ( ( c_List_Ofoldl @ SV281 @ SV642 @ ( c_List_Olist_OCons @ SV929 @ SV1120 @ SV1209 ) @ SV1245 @ SV1209 )
= ( c_List_Ofoldl @ SV281 @ ( hAPP @ ( hAPP @ SV281 @ SV642 ) @ SV929 ) @ SV1120 @ SV1245 @ SV1209 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2898]) ).
thf(3088,plain,
! [SV1246: $i,SV1210: $i,SV1121: $i,SV930: $i,SV644: $i,SV284: $i] :
( ( ( c_Lambda_OdB_OdB__rec @ SV284 @ SV644 @ SV930 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1121 ) @ SV1210 ) @ SV1246 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV644 @ SV1121 ) @ SV1210 ) @ ( c_Lambda_OdB_OdB__rec @ SV284 @ SV644 @ SV930 @ SV1121 @ SV1246 ) ) @ ( c_Lambda_OdB_OdB__rec @ SV284 @ SV644 @ SV930 @ SV1210 @ SV1246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2899]) ).
thf(3089,plain,
! [SV1247: $i,SV1211: $i,SV1122: $i,SV931: $i,SV645: $i,SV286: $i] :
( ( ! [SY2990: $i] :
( ( c_Type_Otypings @ SV286 @ SV645 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV931 @ SV1122 @ SV286 @ SV645 ) )
| ~ ( c_Type_Otyping @ SV286 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1211 ) @ SV1247 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1122 )
| ~ ( c_Type_Otypings @ SV286 @ SV1247 @ SY2990 )
| ~ ( c_Type_Otyping @ SV286 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1211 ) @ SV1247 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV645 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV931 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2900]) ).
thf(3090,plain,
! [SV935: $i,SV1124: $i,SV649: $i,SV291: $i] :
( ( ( c_Type_Otyping @ SV291 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV649 @ SV1124 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV935 )
= $false )
| ( ( c_Type_Otyping @ SV291 @ SV649 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV935 @ SV291 @ SV649 @ SV1124 ) @ SV935 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2903]) ).
thf(3091,plain,
! [SV1248: $i,SV1212: $i,SV1125: $i,SV937: $i,SV652: $i,SV294: $i] :
( ( ~ ( c_Type_Otyping @ SV294 @ SV652 @ SV937 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV294 @ SV1125 @ SV937 @ tc_Type_Otype ) @ SV1212 @ SV1248 )
| ( c_Type_Otyping @ SV294 @ ( c_Lambda_Osubst @ SV1212 @ SV652 @ SV1125 ) @ SV1248 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2905]) ).
thf(3092,plain,
! [SV1249: $i,SV1213: $i,SV1127: $i,SV939: $i,SV654: $i,SV296: $i] :
( ( ( c_List_Ofoldl @ SV296 @ SV654 @ ( c_List_Oappend @ SV939 @ SV1127 @ SV1213 ) @ SV1249 @ SV1213 )
= ( c_List_Ofoldl @ SV296 @ ( c_List_Ofoldl @ SV296 @ SV654 @ SV939 @ SV1249 @ SV1213 ) @ SV1127 @ SV1249 @ SV1213 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2906]) ).
thf(3093,plain,
! [SV940: $i,SV1128: $i,SV655: $i,SV297: $i] :
( ( ( c_Type_Otyping @ SV297 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV655 ) @ SV1128 ) @ SV940 )
= $false )
| ( ( c_Type_Otyping @ SV297 @ SV655 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV940 @ SV297 @ SV655 @ SV1128 ) ) @ SV940 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2907]) ).
thf(3094,plain,
! [SV1129: $i,SV944: $i,SV662: $i,SV304: $i] :
( ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV304 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV304 ) @ SV662 ) @ SV944 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV304 ) @ SV662 ) @ SV1129 ) )
| ( SV944 = SV1129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2911]) ).
thf(3095,plain,
! [SV1214: $i,SV1130: $i,SV947: $i,SV666: $i,SV308: $i] :
( ( ( ( c_List_Oreplicate @ SV308 @ SV666 @ SV947 )
!= ( c_List_Oreplicate @ SV1130 @ SV1214 @ SV947 ) )
= $true )
| ( ( ( SV666 = SV1214 )
| ( SV308
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2914]) ).
thf(3096,plain,
! [SV1215: $i,SV1131: $i,SV948: $i,SV667: $i,SV309: $i] :
( ( ( ( c_List_Oappend @ SV309 @ SV667 @ SV948 )
!= ( c_List_Olist_OCons @ SV1131 @ SV1215 @ SV948 ) )
= $true )
| ( ( ( SV309
= ( c_List_Olist_OCons @ SV1131 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1131 @ SV1215 @ SV309 @ SV667 @ SV948 ) @ SV948 ) )
| ( SV309
= ( c_List_Olist_ONil @ SV948 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2915]) ).
thf(3097,plain,
! [SV1132: $i,SV949: $i,SV668: $i,SV310: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV310 ) @ SV668 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV949 ) @ SV1132 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV949 @ SV668 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV310 @ SV1132 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2916]) ).
thf(3098,plain,
! [SV1133: $i,SV953: $i,SV672: $i,SV314: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV314 ) @ SV672 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV953 @ SV1133 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( SV1133
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV314 @ SV672 @ SV953 @ SV1133 ) @ ( c_List_Olist_OCons @ SV672 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( SV1133
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2918]) ).
thf(3099,plain,
! [SV1216: $i,SV1134: $i,SV955: $i,SV674: $i,SV316: $i] :
( ( ( ( c_List_Olist_OCons @ SV316 @ SV674 @ SV955 )
!= ( c_List_Oappend @ SV1134 @ SV1216 @ SV955 ) )
= $true )
| ( ( ( SV674
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV316 @ SV674 @ SV1134 @ SV1216 @ SV955 ) @ SV1216 @ SV955 ) )
| ( ( c_List_Olist_OCons @ SV316 @ SV674 @ SV955 )
= SV1216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2920]) ).
thf(3100,plain,
! [SV1217: $i,SV1135: $i,SV958: $i,SV678: $i,SV320: $i] :
( ( ( ( c_List_Olist_OCons @ SV320 @ SV678 @ SV958 )
!= ( c_List_Olist_OCons @ SV1135 @ SV1217 @ SV958 ) )
= $true )
| ( ( SV320 = SV1135 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2922]) ).
thf(3101,plain,
! [SV1136: $i,SV960: $i,SV680: $i,SV322: $i] :
( ( ( ( c_List_Oappend @ SV322 @ SV680 @ SV960 )
= ( c_List_Oappend @ SV1136 @ SV680 @ SV960 ) )
= $false )
| ( ( SV322 = SV1136 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2924]) ).
thf(3102,plain,
! [SV1137: $i,SV963: $i,SV683: $i,SV325: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV325 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV325 ) @ SV683 ) @ SV963 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV325 ) @ SV1137 ) @ SV963 ) )
| ( SV683 = SV1137 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2926]) ).
thf(3103,plain,
! [SV1138: $i,SV965: $i,SV685: $i,SV327: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV327 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SV685 ) @ SV965 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SV685 ) @ SV1138 ) )
| ( SV965 = SV1138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2928]) ).
thf(3104,plain,
! [SV1250: $i,SV1218: $i,SV1139: $i,SV967: $i,SV687: $i,SV329: $i] :
( ( ! [SY2991: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV329 ) @ SV687 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV967 @ SV1139 @ SV1218 ) ) )
| ~ ( c_Type_Otyping @ SV1250 @ SV1139 @ SV687 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1139 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV1250 @ SV1218 @ SV687 @ tc_Type_Otype ) @ SV967 @ SY2991 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV967 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2930]) ).
thf(3105,plain,
! [SV1219: $i,SV1140: $i,SV968: $i,SV690: $i,SV332: $i] :
( ( ( ( c_List_Oreplicate @ SV332 @ SV690 @ SV968 )
!= ( c_List_Oreplicate @ SV1140 @ SV1219 @ SV968 ) )
= $true )
| ( ( SV332 = SV1140 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2931]) ).
thf(3106,plain,
! [SV1220: $i,SV1141: $i,SV973: $i,SV696: $i,SV338: $i] :
( ( ( ( c_List_Oappend @ SV338 @ SV696 @ SV973 )
!= ( c_List_Olist_OCons @ SV1141 @ SV1220 @ SV973 ) )
= $true )
| ( ( ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1141 @ SV1220 @ SV338 @ SV696 @ SV973 ) @ SV696 @ SV973 )
= SV1220 )
| ( SV338
= ( c_List_Olist_ONil @ SV973 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2934]) ).
thf(3107,plain,
! [SV974: $i,SV697: $i,SV339: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV339 ) )
= $true )
| ( ( ( SV697
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV339 ) @ SV697 ) @ SV974 ) )
| ( SV974
= ( c_HOL_Ozero__class_Ozero @ SV339 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV339 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2935]) ).
thf(3108,plain,
! [SV1142: $i,SV975: $i,SV698: $i,SV340: $i] :
( ( ( ( c_List_Oappend @ SV340 @ SV698 @ SV975 )
= ( c_List_Oappend @ SV340 @ SV1142 @ SV975 ) )
= $false )
| ( ( SV698 = SV1142 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2936]) ).
thf(3109,plain,
! [SV1221: $i,SV1143: $i,SV976: $i,SV699: $i,SV341: $i] :
( ( ( ( c_List_Olist_OCons @ SV341 @ SV699 @ SV976 )
!= ( c_List_Oappend @ SV1143 @ SV1221 @ SV976 ) )
= $true )
| ( ( ( SV699
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV341 @ SV699 @ SV1143 @ SV1221 @ SV976 ) @ SV1221 @ SV976 ) )
| ( SV1143
= ( c_List_Olist_ONil @ SV976 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2937]) ).
thf(3110,plain,
! [SV1144: $i,SV977: $i,SV700: $i,SV342: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV342 ) @ SV700 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV977 ) @ SV1144 ) )
= $false )
| ( ( SV700 = SV1144 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2938]) ).
thf(3111,plain,
! [SV1222: $i,SV1145: $i,SV978: $i,SV702: $i,SV344: $i] :
( ( ( ( c_List_Oappend @ SV344 @ SV702 @ SV978 )
!= ( c_List_Olist_OCons @ SV1145 @ SV1222 @ SV978 ) )
= $true )
| ( ( ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1145 @ SV1222 @ SV344 @ SV702 @ SV978 ) @ SV702 @ SV978 )
= SV1222 )
| ( SV702
= ( c_List_Olist_OCons @ SV1145 @ SV1222 @ SV978 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2939]) ).
thf(3112,plain,
! [SV1223: $i,SV1146: $i,SV979: $i,SV704: $i,SV346: $i] :
( ( ( ( c_List_Olist_OCons @ SV346 @ SV704 @ SV979 )
!= ( c_List_Oappend @ SV1146 @ SV1223 @ SV979 ) )
= $true )
| ( ( ( ( c_List_Olist_OCons @ SV346 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV346 @ SV704 @ SV1146 @ SV1223 @ SV979 ) @ SV979 )
= SV1146 )
| ( SV1146
= ( c_List_Olist_ONil @ SV979 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2940]) ).
thf(3113,plain,
! [SV1147: $i,SV981: $i,SV706: $i,SV348: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV348 ) @ SV706 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV981 ) @ SV1147 ) )
= $false )
| ( ( SV706 = SV1147 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2942]) ).
thf(3114,plain,
! [SV982: $i,SV349: $i,SV707: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV707 @ SV349 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV982 @ SV349 ) )
= $true )
| ( ( SV707 = SV982 )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV349 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2943]) ).
thf(3115,plain,
! [SV1148: $i,SV983: $i,SV708: $i,SV350: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV350 ) @ SV708 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV983 @ SV1148 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( SV350
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV983 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV350 @ SV708 @ SV983 @ SV1148 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1148
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2944]) ).
thf(3116,plain,
! [SV1224: $i,SV1149: $i,SV984: $i,SV709: $i,SV351: $i] :
( ( ( ( c_List_Oappend @ SV351 @ ( c_List_Olist_OCons @ SV709 @ ( c_List_Olist_ONil @ SV984 ) @ SV984 ) @ SV984 )
!= ( c_List_Oappend @ SV1149 @ ( c_List_Olist_OCons @ SV1224 @ ( c_List_Olist_ONil @ SV984 ) @ SV984 ) @ SV984 ) )
= $true )
| ( ( SV709 = SV1224 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2945]) ).
thf(3117,plain,
! [SV1225: $i,SV1150: $i,SV985: $i,SV710: $i,SV352: $i] :
( ( ( ( c_List_Olist_OCons @ SV352 @ SV710 @ SV985 )
!= ( c_List_Olist_OCons @ SV1150 @ SV1225 @ SV985 ) )
= $true )
| ( ( SV710 = SV1225 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2946]) ).
thf(3118,plain,
! [SV1226: $i,SV1151: $i,SV990: $i,SV716: $i,SV358: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV358 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV716 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV990 ) @ SV1151 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV990 ) @ SV1226 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV716 ) @ SV1151 )
= SV1226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2951]) ).
thf(3119,plain,
! [SV1152: $i,SV991: $i,SV717: $i,SV359: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV359 ) @ SV717 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV991 ) @ SV1152 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV359 = SV991 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2952]) ).
thf(3120,plain,
! [SV1227: $i,SV1153: $i,SV992: $i,SV719: $i,SV361: $i] :
( ( ( ( c_List_Olist_OCons @ SV361 @ SV719 @ SV992 )
!= ( c_List_Oappend @ SV1153 @ SV1227 @ SV992 ) )
= $true )
| ( ( ( ( c_List_Olist_OCons @ SV361 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV361 @ SV719 @ SV1153 @ SV1227 @ SV992 ) @ SV992 )
= SV1153 )
| ( ( c_List_Olist_OCons @ SV361 @ SV719 @ SV992 )
= SV1227 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2953]) ).
thf(3121,plain,
! [SV1154: $i,SV993: $i,SV720: $i,SV362: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV362 ) @ SV720 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV993 ) @ SV1154 ) )
= $false )
| ( ( SV362 = SV993 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2954]) ).
thf(3122,plain,
! [SV1155: $i,SV994: $i,SV721: $i,SV363: $i] :
( ( ( ( c_List_Orev @ SV363 @ SV721 )
= ( c_List_Olist_OCons @ SV994 @ SV1155 @ SV721 ) )
= $false )
| ( ( SV363
= ( c_List_Oappend @ ( c_List_Orev @ SV1155 @ SV721 ) @ ( c_List_Olist_OCons @ SV994 @ ( c_List_Olist_ONil @ SV721 ) @ SV721 ) @ SV721 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2955]) ).
thf(3123,plain,
! [SV723: $i,SV365: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV365 ) @ SV723 ) @ SV723 )
= ( c_HOL_Ozero__class_Ozero @ SV365 ) )
= $false )
| ( ( SV723
= ( c_HOL_Ozero__class_Ozero @ SV365 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV365 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2957]) ).
thf(3124,plain,
! [SV1228: $i,SV1156: $i,SV998: $i,SV726: $i,SV368: $i] :
( ( ( ( c_List_Oappend @ SV368 @ SV726 @ SV998 )
!= ( c_List_Olist_OCons @ SV1156 @ SV1228 @ SV998 ) )
= $true )
| ( ( ( SV368
= ( c_List_Olist_OCons @ SV1156 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1156 @ SV1228 @ SV368 @ SV726 @ SV998 ) @ SV998 ) )
| ( SV726
= ( c_List_Olist_OCons @ SV1156 @ SV1228 @ SV998 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2959]) ).
thf(3125,plain,
! [SV1157: $i,SV999: $i,SV728: $i,SV370: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV370 ) @ SV728 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV999 ) @ SV1157 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV370 = SV999 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2960]) ).
thf(3126,plain,
! [SV1159: $i,SV1005: $i,SV735: $i,SV377: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV377 ) @ SV735 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1005 ) @ SV1159 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV735 = SV1159 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2966]) ).
thf(3127,plain,
! [SV1160: $i,SV1006: $i,SV736: $i,SV378: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV378 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV378 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV378 ) @ SV736 ) @ SV1006 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV378 ) @ SV736 ) @ SV1160 ) )
| ( SV1006 = SV1160 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2967]) ).
thf(3128,plain,
! [SV1251: $i,SV1229: $i,SV1161: $i,SV1008: $i,SV738: $i,SV380: $i] :
( ( ! [SY2992: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV380 ) @ SV738 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV1008 @ SV1161 @ SV1229 ) ) )
| ~ ( c_Type_Otyping @ SV1251 @ SV1161 @ SV380 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1161 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV1251 @ SV1229 @ SV380 @ tc_Type_Otype ) @ SV1008 @ SY2992 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1008 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2968]) ).
thf(3129,plain,
! [SV1162: $i,SV1010: $i,SV740: $i,SV382: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV382 ) @ SV740 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1010 ) @ SV1162 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV740 = SV1162 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2970]) ).
thf(3130,plain,
! [SV1230: $i,SV1164: $i,SV1013: $i,SV744: $i,SV386: $i] :
( ( ( ( c_List_Oappend @ SV386 @ ( c_List_Olist_OCons @ SV744 @ ( c_List_Olist_ONil @ SV1013 ) @ SV1013 ) @ SV1013 )
!= ( c_List_Oappend @ SV1164 @ ( c_List_Olist_OCons @ SV1230 @ ( c_List_Olist_ONil @ SV1013 ) @ SV1013 ) @ SV1013 ) )
= $true )
| ( ( SV386 = SV1164 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2972]) ).
thf(3131,plain,
! [SV1165: $i,SV1014: $i,SV745: $i,SV387: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV387 ) @ SV745 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1014 ) @ SV1165 ) )
= $false )
| ( ( SV387 = SV1014 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2973]) ).
thf(3132,plain,
! [SV396: $i,SV752: $i,SV1166: $i,SV1018: $i,SV13: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV13 @ SV1018 @ SV1166 ) @ SV752 ) @ SV396 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV13 @ SV396 ) @ SV752 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2977]) ).
thf(3133,plain,
! [SV753: $i,SV397: $i,SV1019: $i,SV1167: $i,SV14: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV14 @ SV1167 ) @ SV1019 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV14 @ SV397 @ SV753 ) @ SV1019 ) @ SV1167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2978]) ).
thf(3134,plain,
! [SV398: $i,SV754: $i,SV1168: $i,SV1020: $i,SV15: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV15 @ SV1020 @ SV1168 ) @ SV754 ) @ SV398 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV15 @ SV398 ) @ SV754 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2979]) ).
thf(3135,plain,
! [SV755: $i,SV399: $i,SV1021: $i,SV1169: $i,SV16: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV16 @ SV1169 ) @ SV1021 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV16 @ SV399 @ SV755 ) @ SV1021 ) @ SV1169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2980]) ).
thf(3136,plain,
! [SV1022: $i,SV402: $i,SV758: $i,SV20: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV20 @ SV758 ) @ SV402 ) @ SV1022 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV20 @ SV1022 @ SV758 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV20 @ SV402 @ SV758 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2981]) ).
thf(3137,plain,
! [SV403: $i,SV759: $i,SV1023: $i,SV21: $i] :
( ( ( c_Wellfounded_Oaccp @ SV21 @ SV1023 @ SV759 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV21 @ SV759 ) @ SV403 ) @ SV1023 ) ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV21 @ SV403 @ SV759 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2982]) ).
thf(3138,plain,
! [SV768: $i,SV38: $i,SV1025: $i,SV417: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV417 @ SV1025 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV38 @ SV768 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV38 ) @ SV417 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV768 ) @ SV1025 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2983]) ).
thf(3139,plain,
! [SV776: $i,SV1027: $i,SV429: $i,SV52: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV52 @ SV429 ) @ SV1027 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV52 @ SV1027 @ SV776 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV52 @ SV429 @ SV776 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2984]) ).
thf(3140,plain,
! [SV777: $i,SV1028: $i,SV430: $i,SV53: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV53 @ SV430 ) @ SV1028 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV53 @ SV1028 @ SV777 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV53 @ SV430 @ SV777 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2985]) ).
thf(3141,plain,
! [SV57: $i,SV778: $i,SV433: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV433 @ SV778 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV433 @ SV57 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV778 @ SV57 ) @ SV57 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2986]) ).
thf(3142,plain,
! [SV779: $i,SV58: $i,SV434: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV434 @ SV58 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV779 @ SV58 ) @ SV58 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV434 @ SV779 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2987]) ).
thf(3143,plain,
! [SV793: $i,SV86: $i,SV459: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV459 @ tc_Lambda_OdB )
= $false )
| ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV86 ) ) @ SV459 ) @ SV793 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $true )
| ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV86 @ SV459 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV793 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2988]) ).
thf(3144,plain,
! [SV1170: $i,SV1030: $i,SV797: $i,SV469: $i,SV96: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV96 @ SV469 ) @ SV797 ) )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV96 @ ( c_List_Olist_OCons @ SV469 @ SV1030 @ SV1170 ) @ ( c_List_Olist_OCons @ SV797 @ SV1030 @ SV1170 ) @ SV1170 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2993]) ).
thf(3145,plain,
! [SV1231: $i,SV1171: $i,SV1031: $i,SV798: $i,SV470: $i,SV97: $i] :
( ( ( SV97 = SV470 )
= $true )
| ( ( ( SV798 = SV1031 )
| ~ ( c_ListOrder_Ostep1 @ SV1171 @ ( c_List_Olist_OCons @ SV470 @ SV1031 @ SV1231 ) @ ( c_List_Olist_OCons @ SV97 @ SV798 @ SV1231 ) @ SV1231 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2994]) ).
thf(3146,plain,
! [SV477: $i,SV1036: $i,SV1173: $i,SV804: $i,SV104: $i] :
( ( ( c_ListOrder_Ostep1 @ SV104 @ SV804 @ SV1173 @ SV1036 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV104 @ ( c_List_Oappend @ SV477 @ SV804 @ SV1036 ) @ ( c_List_Oappend @ SV477 @ SV1173 @ SV1036 ) @ SV1036 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2998]) ).
thf(3147,plain,
! [SV1174: $i,SV1037: $i,SV805: $i,SV478: $i,SV105: $i] :
( ( ( c_ListOrder_Ostep1 @ SV105 @ SV478 @ SV805 @ SV1037 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV105 @ ( c_List_Oappend @ SV478 @ SV1174 @ SV1037 ) @ ( c_List_Oappend @ SV805 @ SV1174 @ SV1037 ) @ SV1037 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2999]) ).
thf(3148,plain,
! [SV1038: $i,SV108: $i,SV807: $i,SV480: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV480 @ SV807 @ SV108 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1038 @ SV807 @ SV108 )
| ~ ( c_HOL_Oord__class_Oless @ SV480 @ SV1038 @ SV108 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV108 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3000]) ).
thf(3149,plain,
! [SV1039: $i,SV109: $i,SV808: $i,SV481: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV481 @ SV808 @ SV109 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV481 @ SV1039 @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ SV1039 @ SV808 @ SV109 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3001]) ).
thf(3150,plain,
! [SV1232: $i,SV1175: $i,SV1050: $i,SV819: $i,SV493: $i,SV123: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SV493 ) @ SV819 ) )
= $true )
| ( ( ( c_ListOrder_Ostep1 @ SV123 @ SV1050 @ SV1175 @ SV1232 )
| ~ ( c_ListOrder_Ostep1 @ SV123 @ ( c_List_Oappend @ SV1050 @ ( c_List_Olist_OCons @ SV493 @ ( c_List_Olist_ONil @ SV1232 ) @ SV1232 ) @ SV1232 ) @ ( c_List_Oappend @ SV1175 @ ( c_List_Olist_OCons @ SV819 @ ( c_List_Olist_ONil @ SV1232 ) @ SV1232 ) @ SV1232 ) @ SV1232 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3011]) ).
thf(3151,plain,
! [SV494: $i,SV124: $i,SV820: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV820 @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ SV124 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV494 @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ SV124 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV124 ) @ SV494 ) @ SV820 ) @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ SV124 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3012]) ).
thf(3152,plain,
! [SV1233: $i,SV1176: $i,SV1055: $i,SV828: $i,SV502: $i,SV132: $i] :
( ( ( SV132 = SV502 )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV828 @ SV502 ) @ SV132 ) )
| ~ ( c_ListOrder_Ostep1 @ SV828 @ ( c_List_Olist_OCons @ SV502 @ SV1055 @ SV1176 ) @ ( c_List_Olist_OCons @ SV132 @ SV1233 @ SV1176 ) @ SV1176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3013]) ).
thf(3153,plain,
! [SV1177: $i,SV1056: $i,SV829: $i,SV503: $i,SV134: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV134 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ SV503 ) @ SV829 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ SV1056 ) @ SV1177 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ SV503 ) @ SV1056 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ SV829 ) @ SV1177 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3014]) ).
thf(3154,plain,
! [SV830: $i,SV135: $i,SV1057: $i,SV504: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV504 ) @ SV1057 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV135 ) @ SV830 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV135 ) @ SV504 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV830 ) @ SV1057 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3015]) ).
thf(3155,plain,
! [SV506: $i,SV832: $i,SV1058: $i,SV137: $i] :
( ( ( c_Type_Otyping @ SV137 @ SV1058 @ SV832 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV1058 ) @ SV506 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV137 @ SV506 @ SV832 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3016]) ).
thf(3156,plain,
! [SV1234: $i,SV1178: $i,SV1059: $i,SV836: $i,SV512: $i,SV143: $i] :
( ( ( SV143 = SV512 )
= $true )
| ( ( ( c_ListOrder_Ostep1 @ SV836 @ SV143 @ SV512 @ SV1059 )
| ~ ( c_ListOrder_Ostep1 @ SV836 @ ( c_List_Oappend @ SV143 @ ( c_List_Olist_OCons @ SV1178 @ ( c_List_Olist_ONil @ SV1059 ) @ SV1059 ) @ SV1059 ) @ ( c_List_Oappend @ SV512 @ ( c_List_Olist_OCons @ SV1234 @ ( c_List_Olist_ONil @ SV1059 ) @ SV1059 ) @ SV1059 ) @ SV1059 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3017]) ).
thf(3157,plain,
! [SV841: $i,SV1062: $i,SV1179: $i,SV529: $i,SV161: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV161 @ SV529 ) @ SV1179 ) @ SV1062 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV161 @ SV529 ) @ SV841 ) @ SV1179 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV161 @ SV529 ) @ SV841 ) @ SV1062 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3023]) ).
thf(3158,plain,
! [SV1236: $i,SV1181: $i,SV1065: $i,SV847: $i,SV540: $i,SV172: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV172 @ SV540 ) @ SV847 ) )
= $true )
| ( ( ( SV540 = SV847 )
| ~ ( c_ListOrder_Ostep1 @ SV172 @ ( c_List_Oappend @ SV1065 @ ( c_List_Olist_OCons @ SV540 @ ( c_List_Olist_ONil @ SV1181 ) @ SV1181 ) @ SV1181 ) @ ( c_List_Oappend @ SV1236 @ ( c_List_Olist_OCons @ SV847 @ ( c_List_Olist_ONil @ SV1181 ) @ SV1181 ) @ SV1181 ) @ SV1181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3026]) ).
thf(3159,plain,
! [SV855: $i,SV552: $i,SV184: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV184 @ SV552 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV855 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV552 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV184 ) ) @ SV552 ) @ SV855 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3034]) ).
thf(3160,plain,
! [SV560: $i,SV858: $i,SV194: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV858 @ SV194 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV560 @ SV194 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV194 ) @ SV560 ) @ SV858 ) @ SV194 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3035]) ).
thf(3161,plain,
! [SV1237: $i,SV1182: $i,SV1069: $i,SV859: $i,SV561: $i,SV195: $i] :
( ( ( c_ListOrder_Ostep1 @ SV195 @ SV561 @ SV859 @ SV1069 )
= $true )
| ( ( ( SV859 = SV561 )
| ~ ( c_ListOrder_Ostep1 @ SV195 @ ( c_List_Olist_OCons @ SV1182 @ SV561 @ SV1069 ) @ ( c_List_Olist_OCons @ SV1237 @ SV859 @ SV1069 ) @ SV1069 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3036]) ).
thf(3162,plain,
! [SV1070: $i,SV860: $i,SV562: $i,SV1183: $i,SV196: $i] :
( ( ( c_OrderedGroup_Osemigroup__add @ SV196 @ SV1183 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV196 @ ( hAPP @ ( hAPP @ SV196 @ SV562 ) @ SV860 ) ) @ SV1070 )
= ( hAPP @ ( hAPP @ SV196 @ SV562 ) @ ( hAPP @ ( hAPP @ SV196 @ SV860 ) @ SV1070 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3037]) ).
thf(3163,plain,
! [SV197: $i,SV563: $i,SV861: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV861 @ SV563 @ SV197 )
= $true )
| ( ( SV861 = SV563 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV563 @ SV861 @ SV197 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3038]) ).
thf(3164,plain,
! [SV198: $i,SV564: $i,SV862: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV862 @ SV564 @ SV198 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV564 @ SV862 @ SV198 )
= $true )
| ( ( SV564 = SV862 )
= $true )
| ( ( class_Orderings_Olinorder @ SV198 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3039]) ).
thf(3165,plain,
! [SV202: $i,SV568: $i,SV864: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV864 @ SV568 @ SV202 )
= $true )
| ( ( SV864 = SV568 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV568 @ SV864 @ SV202 )
= $true )
| ( ( class_Orderings_Olinorder @ SV202 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3041]) ).
thf(3166,plain,
! [SV203: $i,SV569: $i,SV865: $i] :
( ( ( SV865 = SV569 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV865 @ SV569 @ SV203 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV569 @ SV865 @ SV203 )
= $true )
| ( ( class_Orderings_Olinorder @ SV203 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3042]) ).
thf(3167,plain,
! [SV204: $i,SV866: $i,SV570: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV570 @ SV866 @ SV204 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV866 @ SV570 @ SV204 )
= $true )
| ( ( SV570 = SV866 )
= $true )
| ( ( class_Orderings_Olinorder @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3043]) ).
thf(3168,plain,
! [SV1184: $i,SV1071: $i,SV867: $i,SV571: $i,SV205: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV205 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV205 ) @ SV571 ) @ SV867 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV205 ) @ SV1071 ) @ SV1184 ) @ SV205 )
| ~ ( c_HOL_Oord__class_Oless @ SV867 @ SV1184 @ SV205 )
| ~ ( c_HOL_Oord__class_Oless @ SV571 @ SV1071 @ SV205 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3044]) ).
thf(3169,plain,
! [SV1238: $i,SV1185: $i,SV1072: $i,SV868: $i,SV573: $i,SV207: $i] :
( ( ( SV207 = SV573 )
= $true )
| ( ( ( SV868 = SV1072 )
| ~ ( c_ListOrder_Ostep1 @ SV1185 @ ( c_List_Oappend @ SV207 @ ( c_List_Olist_OCons @ SV868 @ ( c_List_Olist_ONil @ SV1238 ) @ SV1238 ) @ SV1238 ) @ ( c_List_Oappend @ SV573 @ ( c_List_Olist_OCons @ SV1072 @ ( c_List_Olist_ONil @ SV1238 ) @ SV1238 ) @ SV1238 ) @ SV1238 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3045]) ).
thf(3170,plain,
! [SV574: $i,SV1073: $i,SV869: $i,SV209: $i] :
( ( ( c_List_Olistsp @ SV209 @ SV869 @ SV1073 )
= $false )
| ( ( ~ ( c_List_Olistsp @ SV209 @ SV574 @ SV1073 ) )
= $true )
| ( ( c_List_Olistsp @ SV209 @ ( c_List_Oappend @ SV574 @ SV869 @ SV1073 ) @ SV1073 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3046]) ).
thf(3171,plain,
! [SV1075: $i,SV871: $i,SV214: $i,SV578: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV578 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV214 ) @ SV871 ) @ SV1075 ) @ SV214 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV578 @ SV1075 @ SV214 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV214 ) @ SV871 @ SV214 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV214 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3047]) ).
thf(3172,plain,
! [SV1188: $i,SV1077: $i,SV874: $i,SV581: $i,SV217: $i] :
( ( ( hBOOL @ ( hAPP @ SV217 @ ( c_Lambda_OdB_OdB__case @ SV581 @ SV874 @ SV1077 @ ( c_Lambda_OdB_OAbs @ SV1188 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV217 @ ( hAPP @ SV1077 @ SV1188 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3049]) ).
thf(3173,plain,
! [SV1189: $i,SV1078: $i,SV875: $i,SV582: $i,SV218: $i] :
( ( ( hBOOL @ ( hAPP @ SV218 @ ( c_Lambda_OdB_OdB__case @ SV582 @ SV875 @ SV1078 @ ( c_Lambda_OdB_OAbs @ SV1189 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV218 @ ( hAPP @ SV1078 @ SV1189 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3050]) ).
thf(3174,plain,
! [SV1079: $i,SV878: $i,SV585: $i,SV221: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV221 ) @ SV585 ) @ SV878 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV221 ) @ SV1079 ) @ SV878 ) @ SV221 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV585 @ SV1079 @ SV221 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV221 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3051]) ).
thf(3175,plain,
! [SV1080: $i,SV879: $i,SV586: $i,SV222: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV222 ) @ SV586 ) @ SV879 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV222 ) @ SV1080 ) @ SV879 ) @ SV222 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV586 @ SV1080 @ SV222 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV222 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3052]) ).
thf(3176,plain,
! [SV1081: $i,SV223: $i,SV880: $i,SV587: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV587 @ SV880 @ SV223 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV223 ) @ SV587 ) @ SV1081 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV223 ) @ SV880 ) @ SV1081 ) @ SV223 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV223 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3053]) ).
thf(3177,plain,
! [SV1082: $i,SV881: $i,SV588: $i,SV224: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV224 ) @ SV588 ) @ SV881 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV224 ) @ SV588 ) @ SV1082 ) @ SV224 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV881 @ SV1082 @ SV224 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV224 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3054]) ).
thf(3178,plain,
! [SV1083: $i,SV882: $i,SV589: $i,SV225: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV225 ) @ SV589 ) @ SV882 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV225 ) @ SV589 ) @ SV1083 ) @ SV225 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV882 @ SV1083 @ SV225 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV225 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3055]) ).
thf(3179,plain,
! [SV1084: $i,SV226: $i,SV883: $i,SV590: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV590 @ SV883 @ SV226 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV226 ) @ SV1084 ) @ SV590 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV226 ) @ SV1084 ) @ SV883 ) @ SV226 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV226 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3056]) ).
thf(3180,plain,
! [SV1240: $i,SV1190: $i,SV1085: $i,SV884: $i,SV591: $i,SV227: $i] :
( ( ( c_ListOrder_Ostep1 @ SV227 @ SV591 @ SV884 @ SV1085 )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV227 @ SV1190 ) @ SV1240 ) )
| ~ ( c_ListOrder_Ostep1 @ SV227 @ ( c_List_Olist_OCons @ SV1190 @ SV591 @ SV1085 ) @ ( c_List_Olist_OCons @ SV1240 @ SV884 @ SV1085 ) @ SV1085 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3057]) ).
thf(3181,plain,
! [SV592: $i,SV1086: $i,SV1191: $i,SV885: $i,SV228: $i] :
( ( ( c_ListOrder_Ostep1 @ SV228 @ SV885 @ SV1191 @ SV1086 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV228 @ ( c_List_Olist_OCons @ SV592 @ SV885 @ SV1086 ) @ ( c_List_Olist_OCons @ SV592 @ SV1191 @ SV1086 ) @ SV1086 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3058]) ).
thf(3182,plain,
! [SV234: $i,SV890: $i,SV597: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV597 @ SV890 @ SV234 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV890 @ SV597 @ SV234 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV234 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3059]) ).
thf(3183,plain,
! [SV891: $i,SV1091: $i,SV1192: $i,SV598: $i,SV235: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV235 @ SV598 ) @ SV1192 ) @ SV1091 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV891 ) @ SV1192 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV235 @ SV598 ) @ SV891 ) @ SV1091 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3060]) ).
thf(3184,plain,
! [SV892: $i,SV599: $i,SV1092: $i,SV1193: $i,SV236: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV236 @ SV1193 ) @ SV1092 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV236 @ SV599 ) @ SV892 ) @ SV1193 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV236 @ SV599 ) @ SV892 ) @ SV1092 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3061]) ).
thf(3185,plain,
! [SV237: $i,SV893: $i,SV600: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV600 @ SV893 @ SV237 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV893 @ SV600 @ SV237 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3062]) ).
thf(3186,plain,
! [SV238: $i,SV894: $i,SV601: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV601 @ SV894 @ SV238 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV894 @ SV601 @ SV238 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV238 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3063]) ).
thf(3187,plain,
! [SV239: $i,SV895: $i,SV602: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV602 @ SV895 @ SV239 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV895 @ SV602 @ SV239 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV239 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3064]) ).
thf(3188,plain,
! [SV896: $i,SV603: $i,SV1194: $i,SV1093: $i,SV240: $i] :
( ( ( c_Type_Otyping @ SV240 @ SV1093 @ SV1194 )
= $false )
| ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV240 @ SV603 @ SV896 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SV1093 @ SV603 ) @ SV1194 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3065]) ).
thf(3189,plain,
! [SV1094: $i,SV897: $i,SV605: $i,SV1195: $i,SV242: $i] :
( ( ( c_OrderedGroup_Osemigroup__add @ SV242 @ SV1195 )
= $false )
| ( ( ( c_List_Ofoldl @ SV242 @ ( hAPP @ ( hAPP @ SV242 @ SV605 ) @ SV897 ) @ SV1094 @ SV1195 @ SV1195 )
= ( hAPP @ ( hAPP @ SV242 @ SV605 ) @ ( c_List_Ofoldl @ SV242 @ SV897 @ SV1094 @ SV1195 @ SV1195 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3066]) ).
thf(3190,plain,
! [SV1196: $i,SV1097: $i,SV900: $i,SV609: $i,SV246: $i] :
( ( ( hBOOL @ ( hAPP @ SV246 @ ( c_Lambda_OdB_OdB__case @ SV609 @ SV900 @ SV1097 @ ( c_Lambda_OdB_OVar @ SV1196 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV246 @ ( hAPP @ SV609 @ SV1196 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3068]) ).
thf(3191,plain,
! [SV1197: $i,SV1098: $i,SV901: $i,SV610: $i,SV247: $i] :
( ( ( hBOOL @ ( hAPP @ SV247 @ ( c_Lambda_OdB_OdB__case @ SV610 @ SV901 @ SV1098 @ ( c_Lambda_OdB_OVar @ SV1197 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV247 @ ( hAPP @ SV610 @ SV1197 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3069]) ).
thf(3192,plain,
! [SV902: $i,SV248: $i,SV611: $i,SV1099: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV1099 ) @ SV611 ) )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV248 @ SV1099 @ SV902 ) )
= $true )
| ( ( c_Type_Otyping @ SV248 @ SV611 @ SV902 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3070]) ).
thf(3193,plain,
! [SV1241: $i,SV1198: $i,SV1100: $i,SV903: $i,SV613: $i,SV250: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV250 @ ( c_Lambda_OdB_OdB__case @ SV613 @ SV903 @ SV1100 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1198 ) @ SV1241 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV250 @ ( hAPP @ ( hAPP @ SV903 @ SV1198 ) @ SV1241 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3071]) ).
thf(3194,plain,
! [SV1242: $i,SV1199: $i,SV1101: $i,SV904: $i,SV614: $i,SV251: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV251 @ ( c_Lambda_OdB_OdB__case @ SV614 @ SV904 @ SV1101 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1199 ) @ SV1242 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV251 @ ( hAPP @ ( hAPP @ SV904 @ SV1199 ) @ SV1242 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3072]) ).
thf(3195,plain,
! [SV1252: $i,SV1243: $i,SV1200: $i,SV1103: $i,SV906: $i,SV616: $i,SV253: $i] :
( ( ( SV253
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV616 @ SV253 @ SV906 @ SV1103 ) @ SV616 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV906 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1200 ) @ SV1243 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV253 )
| ~ ( c_Type_Otypings @ SV906 @ SV1243 @ SV1252 )
| ~ ( c_Type_Otyping @ SV906 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1200 ) @ SV1243 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1103 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV616 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3074]) ).
thf(3196,plain,
! [SV1104: $i,SV907: $i,SV254: $i,SV617: $i,SV1201: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1201 @ SV617 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( c_Type_Oshift @ SV254 @ SV617 @ SV907 @ SV1104 ) @ SV1201 )
= ( hAPP @ SV254 @ SV1201 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3075]) ).
thf(3197,plain,
! [SV1105: $i,SV620: $i,SV1202: $i,SV909: $i,SV257: $i] :
( ( ( ~ ( c_Type_Otyping @ SV257 @ SV909 @ SV1202 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV257 @ SV620 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1202 ) @ SV1105 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV257 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV620 ) @ SV909 ) @ SV1105 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3076]) ).
thf(3198,plain,
! [SV259: $i,SV622: $i,SV1203: $i,SV1106: $i,SV910: $i] :
( ( ( ~ ( c_Type_Otyping @ SV910 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1106 ) @ SV1203 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV622 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV910 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1106 ) @ SV1203 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV259 ) )
= $true )
| ( ( SV259 = SV622 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3077]) ).
thf(3199,plain,
! [SV1114: $i,SV635: $i,SV1205: $i,SV922: $i,SV273: $i] :
( ( ( ~ ( c_Type_Otypings @ SV273 @ SV922 @ SV1205 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV273 @ SV635 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV1205 @ SV1114 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true )
| ( ( c_Type_Otyping @ SV273 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV635 @ SV922 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1114 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3082]) ).
thf(3200,plain,
! [SV1116: $i,SV638: $i,SV1207: $i,SV276: $i,SV925: $i] :
( ( ( c_OrderedGroup_Omonoid__add @ SV925 @ SV276 @ SV1207 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV276 @ SV638 ) @ ( c_List_Ofoldl @ SV276 @ SV925 @ SV1116 @ SV1207 @ SV1207 ) )
= ( c_List_Ofoldl @ SV276 @ SV638 @ SV1116 @ SV1207 @ SV1207 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3084]) ).
thf(3201,plain,
! [SV1253: $i,SV1247: $i,SV1211: $i,SV1122: $i,SV931: $i,SV645: $i,SV286: $i] :
( ( ( c_Type_Otypings @ SV286 @ SV645 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV931 @ SV1122 @ SV286 @ SV645 ) )
| ~ ( c_Type_Otyping @ SV286 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1211 ) @ SV1247 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1122 )
| ~ ( c_Type_Otypings @ SV286 @ SV1247 @ SV1253 )
| ~ ( c_Type_Otyping @ SV286 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1211 ) @ SV1247 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV645 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV931 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3089]) ).
thf(3202,plain,
! [SV1248: $i,SV1212: $i,SV1125: $i,SV937: $i,SV652: $i,SV294: $i] :
( ( ( ~ ( c_Type_Otyping @ SV294 @ SV652 @ SV937 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV294 @ SV1125 @ SV937 @ tc_Type_Otype ) @ SV1212 @ SV1248 )
| ( c_Type_Otyping @ SV294 @ ( c_Lambda_Osubst @ SV1212 @ SV652 @ SV1125 ) @ SV1248 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3091]) ).
thf(3203,plain,
! [SV1129: $i,SV944: $i,SV662: $i,SV304: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV304 ) @ SV662 ) @ SV944 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV304 ) @ SV662 ) @ SV1129 ) )
= $true )
| ( ( SV944 = SV1129 )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV304 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3094]) ).
thf(3204,plain,
! [SV1214: $i,SV1130: $i,SV947: $i,SV666: $i,SV308: $i] :
( ( ( ( c_List_Oreplicate @ SV308 @ SV666 @ SV947 )
= ( c_List_Oreplicate @ SV1130 @ SV1214 @ SV947 ) )
= $false )
| ( ( ( SV666 = SV1214 )
| ( SV308
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3095]) ).
thf(3205,plain,
! [SV1215: $i,SV1131: $i,SV948: $i,SV667: $i,SV309: $i] :
( ( ( ( c_List_Oappend @ SV309 @ SV667 @ SV948 )
= ( c_List_Olist_OCons @ SV1131 @ SV1215 @ SV948 ) )
= $false )
| ( ( ( SV309
= ( c_List_Olist_OCons @ SV1131 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1131 @ SV1215 @ SV309 @ SV667 @ SV948 ) @ SV948 ) )
| ( SV309
= ( c_List_Olist_ONil @ SV948 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3096]) ).
thf(3206,plain,
! [SV1132: $i,SV310: $i,SV668: $i,SV949: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV949 @ SV668 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV310 @ SV1132 @ tc_nat )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV310 ) @ SV668 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV949 ) @ SV1132 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3097]) ).
thf(3207,plain,
! [SV953: $i,SV672: $i,SV314: $i,SV1133: $i] :
( ( ( SV1133
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV314 @ SV672 @ SV953 @ SV1133 ) @ ( c_List_Olist_OCons @ SV672 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true )
| ( ( SV1133
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV314 ) @ SV672 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV953 @ SV1133 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3098]) ).
thf(3208,plain,
! [SV1216: $i,SV1134: $i,SV955: $i,SV674: $i,SV316: $i] :
( ( ( ( c_List_Olist_OCons @ SV316 @ SV674 @ SV955 )
= ( c_List_Oappend @ SV1134 @ SV1216 @ SV955 ) )
= $false )
| ( ( ( SV674
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV316 @ SV674 @ SV1134 @ SV1216 @ SV955 ) @ SV1216 @ SV955 ) )
| ( ( c_List_Olist_OCons @ SV316 @ SV674 @ SV955 )
= SV1216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3099]) ).
thf(3209,plain,
! [SV1217: $i,SV1135: $i,SV958: $i,SV678: $i,SV320: $i] :
( ( ( ( c_List_Olist_OCons @ SV320 @ SV678 @ SV958 )
= ( c_List_Olist_OCons @ SV1135 @ SV1217 @ SV958 ) )
= $false )
| ( ( SV320 = SV1135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3100]) ).
thf(3210,plain,
! [SV1137: $i,SV963: $i,SV683: $i,SV325: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV325 ) @ SV683 ) @ SV963 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV325 ) @ SV1137 ) @ SV963 ) )
= $true )
| ( ( SV683 = SV1137 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV325 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3102]) ).
thf(3211,plain,
! [SV1138: $i,SV965: $i,SV685: $i,SV327: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SV685 ) @ SV965 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SV685 ) @ SV1138 ) )
= $true )
| ( ( SV965 = SV1138 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV327 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3103]) ).
thf(3212,plain,
! [SV1254: $i,SV1250: $i,SV1218: $i,SV1139: $i,SV967: $i,SV687: $i,SV329: $i] :
( ( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV329 ) @ SV687 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV967 @ SV1139 @ SV1218 ) ) )
| ~ ( c_Type_Otyping @ SV1250 @ SV1139 @ SV687 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1139 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV1250 @ SV1218 @ SV687 @ tc_Type_Otype ) @ SV967 @ SV1254 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV967 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3104]) ).
thf(3213,plain,
! [SV1219: $i,SV1140: $i,SV968: $i,SV690: $i,SV332: $i] :
( ( ( ( c_List_Oreplicate @ SV332 @ SV690 @ SV968 )
= ( c_List_Oreplicate @ SV1140 @ SV1219 @ SV968 ) )
= $false )
| ( ( SV332 = SV1140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3105]) ).
thf(3214,plain,
! [SV1220: $i,SV1141: $i,SV973: $i,SV696: $i,SV338: $i] :
( ( ( ( c_List_Oappend @ SV338 @ SV696 @ SV973 )
= ( c_List_Olist_OCons @ SV1141 @ SV1220 @ SV973 ) )
= $false )
| ( ( ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1141 @ SV1220 @ SV338 @ SV696 @ SV973 ) @ SV696 @ SV973 )
= SV1220 )
| ( SV338
= ( c_List_Olist_ONil @ SV973 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3106]) ).
thf(3215,plain,
! [SV974: $i,SV697: $i,SV339: $i] :
( ( ( class_Int_Onumber__ring @ SV339 )
= $false )
| ( ( ( SV697
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV339 ) @ SV697 ) @ SV974 ) )
| ( SV974
= ( c_HOL_Ozero__class_Ozero @ SV339 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV339 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3107]) ).
thf(3216,plain,
! [SV1221: $i,SV1143: $i,SV976: $i,SV699: $i,SV341: $i] :
( ( ( ( c_List_Olist_OCons @ SV341 @ SV699 @ SV976 )
= ( c_List_Oappend @ SV1143 @ SV1221 @ SV976 ) )
= $false )
| ( ( ( SV699
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV341 @ SV699 @ SV1143 @ SV1221 @ SV976 ) @ SV1221 @ SV976 ) )
| ( SV1143
= ( c_List_Olist_ONil @ SV976 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3109]) ).
thf(3217,plain,
! [SV1222: $i,SV1145: $i,SV978: $i,SV702: $i,SV344: $i] :
( ( ( ( c_List_Oappend @ SV344 @ SV702 @ SV978 )
= ( c_List_Olist_OCons @ SV1145 @ SV1222 @ SV978 ) )
= $false )
| ( ( ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1145 @ SV1222 @ SV344 @ SV702 @ SV978 ) @ SV702 @ SV978 )
= SV1222 )
| ( SV702
= ( c_List_Olist_OCons @ SV1145 @ SV1222 @ SV978 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3111]) ).
thf(3218,plain,
! [SV1223: $i,SV1146: $i,SV979: $i,SV704: $i,SV346: $i] :
( ( ( ( c_List_Olist_OCons @ SV346 @ SV704 @ SV979 )
= ( c_List_Oappend @ SV1146 @ SV1223 @ SV979 ) )
= $false )
| ( ( ( ( c_List_Olist_OCons @ SV346 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV346 @ SV704 @ SV1146 @ SV1223 @ SV979 ) @ SV979 )
= SV1146 )
| ( SV1146
= ( c_List_Olist_ONil @ SV979 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3112]) ).
thf(3219,plain,
! [SV982: $i,SV349: $i,SV707: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV707 @ SV349 )
= ( c_Nat_Osemiring__1__class_Oof__nat @ SV982 @ SV349 ) )
= $false )
| ( ( SV707 = SV982 )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV349 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3114]) ).
thf(3220,plain,
! [SV1148: $i,SV708: $i,SV983: $i,SV350: $i] :
( ( ( SV350
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV983 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV350 @ SV708 @ SV983 @ SV1148 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV1148
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV350 ) @ SV708 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV983 @ SV1148 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3115]) ).
thf(3221,plain,
! [SV1224: $i,SV1149: $i,SV984: $i,SV709: $i,SV351: $i] :
( ( ( ( c_List_Oappend @ SV351 @ ( c_List_Olist_OCons @ SV709 @ ( c_List_Olist_ONil @ SV984 ) @ SV984 ) @ SV984 )
= ( c_List_Oappend @ SV1149 @ ( c_List_Olist_OCons @ SV1224 @ ( c_List_Olist_ONil @ SV984 ) @ SV984 ) @ SV984 ) )
= $false )
| ( ( SV709 = SV1224 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3116]) ).
thf(3222,plain,
! [SV1225: $i,SV1150: $i,SV985: $i,SV710: $i,SV352: $i] :
( ( ( ( c_List_Olist_OCons @ SV352 @ SV710 @ SV985 )
= ( c_List_Olist_OCons @ SV1150 @ SV1225 @ SV985 ) )
= $false )
| ( ( SV710 = SV1225 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3117]) ).
thf(3223,plain,
! [SV1226: $i,SV1151: $i,SV990: $i,SV716: $i,SV358: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV358 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV716 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV990 ) @ SV1151 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV990 ) @ SV1226 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV716 ) @ SV1151 )
= SV1226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3118]) ).
thf(3224,plain,
! [SV1227: $i,SV1153: $i,SV992: $i,SV719: $i,SV361: $i] :
( ( ( ( c_List_Olist_OCons @ SV361 @ SV719 @ SV992 )
= ( c_List_Oappend @ SV1153 @ SV1227 @ SV992 ) )
= $false )
| ( ( ( ( c_List_Olist_OCons @ SV361 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV361 @ SV719 @ SV1153 @ SV1227 @ SV992 ) @ SV992 )
= SV1153 )
| ( ( c_List_Olist_OCons @ SV361 @ SV719 @ SV992 )
= SV1227 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3120]) ).
thf(3225,plain,
! [SV1228: $i,SV1156: $i,SV998: $i,SV726: $i,SV368: $i] :
( ( ( ( c_List_Oappend @ SV368 @ SV726 @ SV998 )
= ( c_List_Olist_OCons @ SV1156 @ SV1228 @ SV998 ) )
= $false )
| ( ( ( SV368
= ( c_List_Olist_OCons @ SV1156 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1156 @ SV1228 @ SV368 @ SV726 @ SV998 ) @ SV998 ) )
| ( SV726
= ( c_List_Olist_OCons @ SV1156 @ SV1228 @ SV998 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3124]) ).
thf(3226,plain,
! [SV1160: $i,SV1006: $i,SV736: $i,SV378: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV378 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV378 ) @ SV736 ) @ SV1006 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV378 ) @ SV736 ) @ SV1160 ) )
| ( SV1006 = SV1160 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV378 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3127]) ).
thf(3227,plain,
! [SV1255: $i,SV1251: $i,SV1229: $i,SV1161: $i,SV1008: $i,SV738: $i,SV380: $i] :
( ( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV380 ) @ SV738 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV1008 @ SV1161 @ SV1229 ) ) )
| ~ ( c_Type_Otyping @ SV1251 @ SV1161 @ SV380 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1161 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV1251 @ SV1229 @ SV380 @ tc_Type_Otype ) @ SV1008 @ SV1255 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1008 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3128]) ).
thf(3228,plain,
! [SV1230: $i,SV1164: $i,SV1013: $i,SV744: $i,SV386: $i] :
( ( ( ( c_List_Oappend @ SV386 @ ( c_List_Olist_OCons @ SV744 @ ( c_List_Olist_ONil @ SV1013 ) @ SV1013 ) @ SV1013 )
= ( c_List_Oappend @ SV1164 @ ( c_List_Olist_OCons @ SV1230 @ ( c_List_Olist_ONil @ SV1013 ) @ SV1013 ) @ SV1013 ) )
= $false )
| ( ( SV386 = SV1164 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3130]) ).
thf(3229,plain,
! [SV402: $i,SV758: $i,SV1022: $i,SV20: $i] :
( ( ( c_Wellfounded_Oaccp @ SV20 @ SV1022 @ SV758 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV20 @ SV758 ) @ SV402 ) @ SV1022 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV20 @ SV402 @ SV758 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3136]) ).
thf(3230,plain,
! [SV1023: $i,SV403: $i,SV759: $i,SV21: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV21 @ SV759 ) @ SV403 ) @ SV1023 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV21 @ SV1023 @ SV759 )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV21 @ SV403 @ SV759 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3137]) ).
thf(3231,plain,
! [SV1025: $i,SV417: $i,SV768: $i,SV38: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV38 @ SV768 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV417 @ SV1025 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV38 ) @ SV417 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV768 ) @ SV1025 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3138]) ).
thf(3232,plain,
! [SV429: $i,SV776: $i,SV1027: $i,SV52: $i] :
( ( ( c_Wellfounded_Oaccp @ SV52 @ SV1027 @ SV776 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV52 @ SV429 ) @ SV1027 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV52 @ SV429 @ SV776 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3139]) ).
thf(3233,plain,
! [SV430: $i,SV777: $i,SV1028: $i,SV53: $i] :
( ( ( c_Wellfounded_Oaccp @ SV53 @ SV1028 @ SV777 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV53 @ SV430 ) @ SV1028 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV53 @ SV430 @ SV777 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3140]) ).
thf(3234,plain,
! [SV97: $i,SV1231: $i,SV470: $i,SV1171: $i,SV1031: $i,SV798: $i] :
( ( ( SV798 = SV1031 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV1171 @ ( c_List_Olist_OCons @ SV470 @ SV1031 @ SV1231 ) @ ( c_List_Olist_OCons @ SV97 @ SV798 @ SV1231 ) @ SV1231 ) )
= $true )
| ( ( SV97 = SV470 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3145]) ).
thf(3235,plain,
! [SV480: $i,SV108: $i,SV807: $i,SV1038: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1038 @ SV807 @ SV108 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV480 @ SV1038 @ SV108 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV480 @ SV807 @ SV108 )
= $true )
| ( ( class_Orderings_Opreorder @ SV108 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3148]) ).
thf(3236,plain,
! [SV808: $i,SV109: $i,SV1039: $i,SV481: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV481 @ SV1039 @ SV109 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1039 @ SV808 @ SV109 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV481 @ SV808 @ SV109 )
= $true )
| ( ( class_Orderings_Oorder @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3149]) ).
thf(3237,plain,
! [SV819: $i,SV493: $i,SV1232: $i,SV1175: $i,SV1050: $i,SV123: $i] :
( ( ( c_ListOrder_Ostep1 @ SV123 @ SV1050 @ SV1175 @ SV1232 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV123 @ ( c_List_Oappend @ SV1050 @ ( c_List_Olist_OCons @ SV493 @ ( c_List_Olist_ONil @ SV1232 ) @ SV1232 ) @ SV1232 ) @ ( c_List_Oappend @ SV1175 @ ( c_List_Olist_OCons @ SV819 @ ( c_List_Olist_ONil @ SV1232 ) @ SV1232 ) @ SV1232 ) @ SV1232 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SV493 ) @ SV819 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3150]) ).
thf(3238,plain,
! [SV494: $i,SV124: $i,SV820: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV820 @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ SV124 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV494 @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ SV124 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV124 ) @ SV494 ) @ SV820 ) @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ SV124 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3151]) ).
thf(3239,plain,
! [SV1233: $i,SV1176: $i,SV1055: $i,SV132: $i,SV502: $i,SV828: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV828 @ SV502 ) @ SV132 ) )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV828 @ ( c_List_Olist_OCons @ SV502 @ SV1055 @ SV1176 ) @ ( c_List_Olist_OCons @ SV132 @ SV1233 @ SV1176 ) @ SV1176 ) )
= $true )
| ( ( SV132 = SV502 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3152]) ).
thf(3240,plain,
! [SV1057: $i,SV504: $i,SV830: $i,SV135: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV135 ) @ SV830 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV504 ) @ SV1057 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV135 ) @ SV504 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV830 ) @ SV1057 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3154]) ).
thf(3241,plain,
! [SV832: $i,SV137: $i,SV506: $i,SV1058: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV1058 ) @ SV506 ) )
= $false )
| ( ( c_Type_Otyping @ SV137 @ SV1058 @ SV832 )
= $false )
| ( ( c_Type_Otyping @ SV137 @ SV506 @ SV832 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3155]) ).
thf(3242,plain,
! [SV1234: $i,SV1178: $i,SV1059: $i,SV512: $i,SV143: $i,SV836: $i] :
( ( ( c_ListOrder_Ostep1 @ SV836 @ SV143 @ SV512 @ SV1059 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV836 @ ( c_List_Oappend @ SV143 @ ( c_List_Olist_OCons @ SV1178 @ ( c_List_Olist_ONil @ SV1059 ) @ SV1059 ) @ SV1059 ) @ ( c_List_Oappend @ SV512 @ ( c_List_Olist_OCons @ SV1234 @ ( c_List_Olist_ONil @ SV1059 ) @ SV1059 ) @ SV1059 ) @ SV1059 ) )
= $true )
| ( ( SV143 = SV512 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3156]) ).
thf(3243,plain,
! [SV841: $i,SV1062: $i,SV1179: $i,SV529: $i,SV161: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV161 @ SV529 ) @ SV1179 ) @ SV1062 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV161 @ SV529 ) @ SV841 ) @ SV1179 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV161 @ SV529 ) @ SV841 ) @ SV1062 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3157]) ).
thf(3244,plain,
! [SV1236: $i,SV1181: $i,SV1065: $i,SV172: $i,SV847: $i,SV540: $i] :
( ( ( SV540 = SV847 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV172 @ ( c_List_Oappend @ SV1065 @ ( c_List_Olist_OCons @ SV540 @ ( c_List_Olist_ONil @ SV1181 ) @ SV1181 ) @ SV1181 ) @ ( c_List_Oappend @ SV1236 @ ( c_List_Olist_OCons @ SV847 @ ( c_List_Olist_ONil @ SV1181 ) @ SV1181 ) @ SV1181 ) @ SV1181 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV172 @ SV540 ) @ SV847 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3158]) ).
thf(3245,plain,
! [SV560: $i,SV858: $i,SV194: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV858 @ SV194 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV560 @ SV194 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV194 ) @ SV560 ) @ SV858 ) @ SV194 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3160]) ).
thf(3246,plain,
! [SV1237: $i,SV1069: $i,SV1182: $i,SV195: $i,SV561: $i,SV859: $i] :
( ( ( SV859 = SV561 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV195 @ ( c_List_Olist_OCons @ SV1182 @ SV561 @ SV1069 ) @ ( c_List_Olist_OCons @ SV1237 @ SV859 @ SV1069 ) @ SV1069 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV195 @ SV561 @ SV859 @ SV1069 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3161]) ).
thf(3247,plain,
! [SV1184: $i,SV1071: $i,SV867: $i,SV571: $i,SV205: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV205 ) @ SV571 ) @ SV867 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV205 ) @ SV1071 ) @ SV1184 ) @ SV205 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV867 @ SV1184 @ SV205 )
| ~ ( c_HOL_Oord__class_Oless @ SV571 @ SV1071 @ SV205 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV205 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3168]) ).
thf(3248,plain,
! [SV573: $i,SV1238: $i,SV207: $i,SV1185: $i,SV1072: $i,SV868: $i] :
( ( ( SV868 = SV1072 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV1185 @ ( c_List_Oappend @ SV207 @ ( c_List_Olist_OCons @ SV868 @ ( c_List_Olist_ONil @ SV1238 ) @ SV1238 ) @ SV1238 ) @ ( c_List_Oappend @ SV573 @ ( c_List_Olist_OCons @ SV1072 @ ( c_List_Olist_ONil @ SV1238 ) @ SV1238 ) @ SV1238 ) @ SV1238 ) )
= $true )
| ( ( SV207 = SV573 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3169]) ).
thf(3249,plain,
! [SV869: $i,SV1073: $i,SV574: $i,SV209: $i] :
( ( ( c_List_Olistsp @ SV209 @ SV574 @ SV1073 )
= $false )
| ( ( c_List_Olistsp @ SV209 @ SV869 @ SV1073 )
= $false )
| ( ( c_List_Olistsp @ SV209 @ ( c_List_Oappend @ SV574 @ SV869 @ SV1073 ) @ SV1073 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3170]) ).
thf(3250,plain,
! [SV871: $i,SV214: $i,SV1075: $i,SV578: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV578 @ SV1075 @ SV214 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV214 ) @ SV871 @ SV214 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV578 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV214 ) @ SV871 ) @ SV1075 ) @ SV214 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV214 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3171]) ).
thf(3251,plain,
! [SV878: $i,SV221: $i,SV1079: $i,SV585: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV585 @ SV1079 @ SV221 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV221 ) @ SV585 ) @ SV878 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV221 ) @ SV1079 ) @ SV878 ) @ SV221 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3174]) ).
thf(3252,plain,
! [SV879: $i,SV222: $i,SV1080: $i,SV586: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV586 @ SV1080 @ SV222 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV222 ) @ SV586 ) @ SV879 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV222 ) @ SV1080 ) @ SV879 ) @ SV222 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV222 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3175]) ).
thf(3253,plain,
! [SV880: $i,SV1081: $i,SV587: $i,SV223: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV223 ) @ SV587 ) @ SV1081 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV223 ) @ SV880 ) @ SV1081 ) @ SV223 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV587 @ SV880 @ SV223 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV223 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3176]) ).
thf(3254,plain,
! [SV588: $i,SV224: $i,SV1082: $i,SV881: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV881 @ SV1082 @ SV224 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV224 ) @ SV588 ) @ SV881 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV224 ) @ SV588 ) @ SV1082 ) @ SV224 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3177]) ).
thf(3255,plain,
! [SV589: $i,SV225: $i,SV1083: $i,SV882: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV882 @ SV1083 @ SV225 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV225 ) @ SV589 ) @ SV882 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV225 ) @ SV589 ) @ SV1083 ) @ SV225 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3178]) ).
thf(3256,plain,
! [SV883: $i,SV590: $i,SV1084: $i,SV226: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV226 ) @ SV1084 ) @ SV590 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV226 ) @ SV1084 ) @ SV883 ) @ SV226 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV590 @ SV883 @ SV226 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV226 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3179]) ).
thf(3257,plain,
! [SV884: $i,SV1085: $i,SV591: $i,SV1240: $i,SV1190: $i,SV227: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV227 @ SV1190 ) @ SV1240 ) )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV227 @ ( c_List_Olist_OCons @ SV1190 @ SV591 @ SV1085 ) @ ( c_List_Olist_OCons @ SV1240 @ SV884 @ SV1085 ) @ SV1085 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV227 @ SV591 @ SV884 @ SV1085 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3180]) ).
thf(3258,plain,
! [SV234: $i,SV597: $i,SV890: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV890 @ SV597 @ SV234 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV597 @ SV890 @ SV234 )
= $false )
| ( ( class_Orderings_Oorder @ SV234 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3182]) ).
thf(3259,plain,
! [SV891: $i,SV1091: $i,SV1192: $i,SV598: $i,SV235: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV235 @ SV598 ) @ SV1192 ) @ SV1091 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV891 ) @ SV1192 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV235 @ SV598 ) @ SV891 ) @ SV1091 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3183]) ).
thf(3260,plain,
! [SV892: $i,SV599: $i,SV1092: $i,SV1193: $i,SV236: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV236 @ SV1193 ) @ SV1092 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV236 @ SV599 ) @ SV892 ) @ SV1193 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV236 @ SV599 ) @ SV892 ) @ SV1092 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3184]) ).
thf(3261,plain,
! [SV237: $i,SV600: $i,SV893: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV893 @ SV600 @ SV237 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV600 @ SV893 @ SV237 )
= $false )
| ( ( class_Orderings_Olinorder @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3185]) ).
thf(3262,plain,
! [SV238: $i,SV601: $i,SV894: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV894 @ SV601 @ SV238 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV601 @ SV894 @ SV238 )
= $false )
| ( ( class_Orderings_Opreorder @ SV238 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3186]) ).
thf(3263,plain,
! [SV239: $i,SV602: $i,SV895: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV895 @ SV602 @ SV239 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV602 @ SV895 @ SV239 )
= $false )
| ( ( class_Orderings_Opreorder @ SV239 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3187]) ).
thf(3264,plain,
! [SV611: $i,SV902: $i,SV1099: $i,SV248: $i] :
( ( ( c_Type_Otyping @ SV248 @ SV1099 @ SV902 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV1099 ) @ SV611 ) )
= $false )
| ( ( c_Type_Otyping @ SV248 @ SV611 @ SV902 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3192]) ).
thf(3265,plain,
! [SV1241: $i,SV1198: $i,SV1100: $i,SV903: $i,SV613: $i,SV250: $i] :
( ( ( hBOOL @ ( hAPP @ SV250 @ ( c_Lambda_OdB_OdB__case @ SV613 @ SV903 @ SV1100 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1198 ) @ SV1241 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV250 @ ( hAPP @ ( hAPP @ SV903 @ SV1198 ) @ SV1241 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3193]) ).
thf(3266,plain,
! [SV1242: $i,SV1199: $i,SV1101: $i,SV904: $i,SV614: $i,SV251: $i] :
( ( ( hBOOL @ ( hAPP @ SV251 @ ( c_Lambda_OdB_OdB__case @ SV614 @ SV904 @ SV1101 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1199 ) @ SV1242 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV251 @ ( hAPP @ ( hAPP @ SV904 @ SV1199 ) @ SV1242 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3194]) ).
thf(3267,plain,
! [SV1252: $i,SV1243: $i,SV1200: $i,SV1103: $i,SV906: $i,SV616: $i,SV253: $i] :
( ( ( SV253
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV616 @ SV253 @ SV906 @ SV1103 ) @ SV616 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV906 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1200 ) @ SV1243 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV253 )
| ~ ( c_Type_Otypings @ SV906 @ SV1243 @ SV1252 )
| ~ ( c_Type_Otyping @ SV906 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1200 ) @ SV1243 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1103 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV616 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3195]) ).
thf(3268,plain,
! [SV1105: $i,SV620: $i,SV1202: $i,SV909: $i,SV257: $i] :
( ( ( c_Type_Otyping @ SV257 @ SV909 @ SV1202 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV257 @ SV620 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1202 ) @ SV1105 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV257 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV620 ) @ SV909 ) @ SV1105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3197]) ).
thf(3269,plain,
! [SV259: $i,SV622: $i,SV1203: $i,SV1106: $i,SV910: $i] :
( ( ( c_Type_Otyping @ SV910 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1106 ) @ SV1203 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV622 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV910 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1106 ) @ SV1203 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV259 ) )
= $true )
| ( ( SV259 = SV622 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3198]) ).
thf(3270,plain,
! [SV1114: $i,SV635: $i,SV1205: $i,SV922: $i,SV273: $i] :
( ( ( c_Type_Otypings @ SV273 @ SV922 @ SV1205 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV273 @ SV635 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV1205 @ SV1114 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true )
| ( ( c_Type_Otyping @ SV273 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV635 @ SV922 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1114 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3199]) ).
thf(3271,plain,
! [SV1253: $i,SV1247: $i,SV1211: $i,SV1122: $i,SV931: $i,SV645: $i,SV286: $i] :
( ( ( c_Type_Otypings @ SV286 @ SV645 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV931 @ SV1122 @ SV286 @ SV645 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV286 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1211 ) @ SV1247 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1122 )
| ~ ( c_Type_Otypings @ SV286 @ SV1247 @ SV1253 )
| ~ ( c_Type_Otyping @ SV286 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1211 ) @ SV1247 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV645 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV931 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3201]) ).
thf(3272,plain,
! [SV1248: $i,SV1212: $i,SV1125: $i,SV937: $i,SV652: $i,SV294: $i] :
( ( ( c_Type_Otyping @ SV294 @ SV652 @ SV937 )
= $false )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV294 @ SV1125 @ SV937 @ tc_Type_Otype ) @ SV1212 @ SV1248 )
| ( c_Type_Otyping @ SV294 @ ( c_Lambda_Osubst @ SV1212 @ SV652 @ SV1125 ) @ SV1248 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3202]) ).
thf(3273,plain,
! [SV1129: $i,SV944: $i,SV662: $i,SV304: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV304 ) @ SV662 ) @ SV944 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV304 ) @ SV662 ) @ SV1129 ) )
= $false )
| ( ( SV944 = SV1129 )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3203]) ).
thf(3274,plain,
! [SV1130: $i,SV947: $i,SV308: $i,SV1214: $i,SV666: $i] :
( ( ( SV666 = SV1214 )
= $true )
| ( ( SV308
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_List_Oreplicate @ SV308 @ SV666 @ SV947 )
= ( c_List_Oreplicate @ SV1130 @ SV1214 @ SV947 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3204]) ).
thf(3275,plain,
! [SV948: $i,SV667: $i,SV1215: $i,SV1131: $i,SV309: $i] :
( ( ( SV309
= ( c_List_Olist_OCons @ SV1131 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1131 @ SV1215 @ SV309 @ SV667 @ SV948 ) @ SV948 ) )
= $true )
| ( ( SV309
= ( c_List_Olist_ONil @ SV948 ) )
= $true )
| ( ( ( c_List_Oappend @ SV309 @ SV667 @ SV948 )
= ( c_List_Olist_OCons @ SV1131 @ SV1215 @ SV948 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3205]) ).
thf(3276,plain,
! [SV1132: $i,SV310: $i,SV668: $i,SV949: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV949 @ SV668 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV310 @ SV1132 @ tc_nat )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV310 ) @ SV668 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV949 ) @ SV1132 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3206]) ).
thf(3277,plain,
! [SV955: $i,SV1216: $i,SV1134: $i,SV316: $i,SV674: $i] :
( ( ( SV674
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV316 @ SV674 @ SV1134 @ SV1216 @ SV955 ) @ SV1216 @ SV955 ) )
= $true )
| ( ( ( c_List_Olist_OCons @ SV316 @ SV674 @ SV955 )
= SV1216 )
= $true )
| ( ( ( c_List_Olist_OCons @ SV316 @ SV674 @ SV955 )
= ( c_List_Oappend @ SV1134 @ SV1216 @ SV955 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3208]) ).
thf(3278,plain,
! [SV1137: $i,SV963: $i,SV683: $i,SV325: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV325 ) @ SV683 ) @ SV963 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV325 ) @ SV1137 ) @ SV963 ) )
= $false )
| ( ( SV683 = SV1137 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV325 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3210]) ).
thf(3279,plain,
! [SV1138: $i,SV965: $i,SV685: $i,SV327: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SV685 ) @ SV965 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SV685 ) @ SV1138 ) )
= $false )
| ( ( SV965 = SV1138 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV327 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3211]) ).
thf(3280,plain,
! [SV1254: $i,SV1250: $i,SV1218: $i,SV1139: $i,SV967: $i,SV687: $i,SV329: $i] :
( ( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV329 ) @ SV687 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV967 @ SV1139 @ SV1218 ) ) )
| ~ ( c_Type_Otyping @ SV1250 @ SV1139 @ SV687 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1139 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV1250 @ SV1218 @ SV687 @ tc_Type_Otype ) @ SV967 @ SV1254 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV967 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3212]) ).
thf(3281,plain,
! [SV973: $i,SV696: $i,SV338: $i,SV1220: $i,SV1141: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1141 @ SV1220 @ SV338 @ SV696 @ SV973 ) @ SV696 @ SV973 )
= SV1220 )
= $true )
| ( ( SV338
= ( c_List_Olist_ONil @ SV973 ) )
= $true )
| ( ( ( c_List_Oappend @ SV338 @ SV696 @ SV973 )
= ( c_List_Olist_OCons @ SV1141 @ SV1220 @ SV973 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3214]) ).
thf(3282,plain,
! [SV974: $i,SV339: $i,SV697: $i] :
( ( ( SV697
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV339 ) @ SV697 ) @ SV974 ) )
= $true )
| ( ( SV974
= ( c_HOL_Ozero__class_Ozero @ SV339 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV339 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV339 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3215]) ).
thf(3283,plain,
! [SV976: $i,SV1221: $i,SV1143: $i,SV341: $i,SV699: $i] :
( ( ( SV699
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV341 @ SV699 @ SV1143 @ SV1221 @ SV976 ) @ SV1221 @ SV976 ) )
= $true )
| ( ( SV1143
= ( c_List_Olist_ONil @ SV976 ) )
= $true )
| ( ( ( c_List_Olist_OCons @ SV341 @ SV699 @ SV976 )
= ( c_List_Oappend @ SV1143 @ SV1221 @ SV976 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3216]) ).
thf(3284,plain,
! [SV978: $i,SV702: $i,SV344: $i,SV1222: $i,SV1145: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1145 @ SV1222 @ SV344 @ SV702 @ SV978 ) @ SV702 @ SV978 )
= SV1222 )
= $true )
| ( ( SV702
= ( c_List_Olist_OCons @ SV1145 @ SV1222 @ SV978 ) )
= $true )
| ( ( ( c_List_Oappend @ SV344 @ SV702 @ SV978 )
= ( c_List_Olist_OCons @ SV1145 @ SV1222 @ SV978 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3217]) ).
thf(3285,plain,
! [SV979: $i,SV1223: $i,SV1146: $i,SV704: $i,SV346: $i] :
( ( ( ( c_List_Olist_OCons @ SV346 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV346 @ SV704 @ SV1146 @ SV1223 @ SV979 ) @ SV979 )
= SV1146 )
= $true )
| ( ( SV1146
= ( c_List_Olist_ONil @ SV979 ) )
= $true )
| ( ( ( c_List_Olist_OCons @ SV346 @ SV704 @ SV979 )
= ( c_List_Oappend @ SV1146 @ SV1223 @ SV979 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3218]) ).
thf(3286,plain,
! [SV1226: $i,SV1151: $i,SV990: $i,SV716: $i,SV358: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV716 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV990 ) @ SV1151 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV990 ) @ SV1226 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV716 ) @ SV1151 )
= SV1226 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV358 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3223]) ).
thf(3287,plain,
! [SV992: $i,SV1227: $i,SV1153: $i,SV719: $i,SV361: $i] :
( ( ( ( c_List_Olist_OCons @ SV361 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV361 @ SV719 @ SV1153 @ SV1227 @ SV992 ) @ SV992 )
= SV1153 )
= $true )
| ( ( ( c_List_Olist_OCons @ SV361 @ SV719 @ SV992 )
= SV1227 )
= $true )
| ( ( ( c_List_Olist_OCons @ SV361 @ SV719 @ SV992 )
= ( c_List_Oappend @ SV1153 @ SV1227 @ SV992 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3224]) ).
thf(3288,plain,
! [SV998: $i,SV726: $i,SV1228: $i,SV1156: $i,SV368: $i] :
( ( ( SV368
= ( c_List_Olist_OCons @ SV1156 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1156 @ SV1228 @ SV368 @ SV726 @ SV998 ) @ SV998 ) )
= $true )
| ( ( SV726
= ( c_List_Olist_OCons @ SV1156 @ SV1228 @ SV998 ) )
= $true )
| ( ( ( c_List_Oappend @ SV368 @ SV726 @ SV998 )
= ( c_List_Olist_OCons @ SV1156 @ SV1228 @ SV998 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3225]) ).
thf(3289,plain,
! [SV1160: $i,SV1006: $i,SV736: $i,SV378: $i] :
( ( ( class_Int_Onumber__ring @ SV378 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV378 ) @ SV736 ) @ SV1006 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV378 ) @ SV736 ) @ SV1160 ) )
| ( SV1006 = SV1160 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV378 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3226]) ).
thf(3290,plain,
! [SV1255: $i,SV1251: $i,SV1229: $i,SV1161: $i,SV1008: $i,SV738: $i,SV380: $i] :
( ( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV380 ) @ SV738 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV1008 @ SV1161 @ SV1229 ) ) )
| ~ ( c_Type_Otyping @ SV1251 @ SV1161 @ SV380 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1161 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV1251 @ SV1229 @ SV380 @ tc_Type_Otype ) @ SV1008 @ SV1255 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1008 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3227]) ).
thf(3291,plain,
! [SV798: $i,SV97: $i,SV1231: $i,SV1031: $i,SV470: $i,SV1171: $i] :
( ( ( c_ListOrder_Ostep1 @ SV1171 @ ( c_List_Olist_OCons @ SV470 @ SV1031 @ SV1231 ) @ ( c_List_Olist_OCons @ SV97 @ SV798 @ SV1231 ) @ SV1231 )
= $false )
| ( ( SV798 = SV1031 )
= $true )
| ( ( SV97 = SV470 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3234]) ).
thf(3292,plain,
! [SV480: $i,SV108: $i,SV807: $i,SV1038: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1038 @ SV807 @ SV108 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV480 @ SV1038 @ SV108 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV480 @ SV807 @ SV108 )
= $true )
| ( ( class_Orderings_Opreorder @ SV108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3235]) ).
thf(3293,plain,
! [SV808: $i,SV109: $i,SV1039: $i,SV481: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV481 @ SV1039 @ SV109 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1039 @ SV808 @ SV109 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV481 @ SV808 @ SV109 )
= $true )
| ( ( class_Orderings_Oorder @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3236]) ).
thf(3294,plain,
! [SV819: $i,SV1175: $i,SV1232: $i,SV493: $i,SV1050: $i,SV123: $i] :
( ( ( c_ListOrder_Ostep1 @ SV123 @ ( c_List_Oappend @ SV1050 @ ( c_List_Olist_OCons @ SV493 @ ( c_List_Olist_ONil @ SV1232 ) @ SV1232 ) @ SV1232 ) @ ( c_List_Oappend @ SV1175 @ ( c_List_Olist_OCons @ SV819 @ ( c_List_Olist_ONil @ SV1232 ) @ SV1232 ) @ SV1232 ) @ SV1232 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV123 @ SV1050 @ SV1175 @ SV1232 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SV493 ) @ SV819 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3237]) ).
thf(3295,plain,
! [SV820: $i,SV124: $i,SV494: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV494 @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ SV124 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV820 @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ SV124 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV124 ) @ SV494 ) @ SV820 ) @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ SV124 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3238]) ).
thf(3296,plain,
! [SV1233: $i,SV132: $i,SV1176: $i,SV1055: $i,SV502: $i,SV828: $i] :
( ( ( c_ListOrder_Ostep1 @ SV828 @ ( c_List_Olist_OCons @ SV502 @ SV1055 @ SV1176 ) @ ( c_List_Olist_OCons @ SV132 @ SV1233 @ SV1176 ) @ SV1176 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV828 @ SV502 ) @ SV132 ) )
= $true )
| ( ( SV132 = SV502 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3239]) ).
thf(3297,plain,
! [SV1234: $i,SV512: $i,SV1059: $i,SV1178: $i,SV143: $i,SV836: $i] :
( ( ( c_ListOrder_Ostep1 @ SV836 @ ( c_List_Oappend @ SV143 @ ( c_List_Olist_OCons @ SV1178 @ ( c_List_Olist_ONil @ SV1059 ) @ SV1059 ) @ SV1059 ) @ ( c_List_Oappend @ SV512 @ ( c_List_Olist_OCons @ SV1234 @ ( c_List_Olist_ONil @ SV1059 ) @ SV1059 ) @ SV1059 ) @ SV1059 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV836 @ SV143 @ SV512 @ SV1059 )
= $true )
| ( ( SV143 = SV512 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3242]) ).
thf(3298,plain,
! [SV1062: $i,SV1179: $i,SV841: $i,SV529: $i,SV161: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV161 @ SV529 ) @ SV841 ) @ SV1179 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV161 @ SV529 ) @ SV1179 ) @ SV1062 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV161 @ SV529 ) @ SV841 ) @ SV1062 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3243]) ).
thf(3299,plain,
! [SV847: $i,SV1236: $i,SV1181: $i,SV540: $i,SV1065: $i,SV172: $i] :
( ( ( c_ListOrder_Ostep1 @ SV172 @ ( c_List_Oappend @ SV1065 @ ( c_List_Olist_OCons @ SV540 @ ( c_List_Olist_ONil @ SV1181 ) @ SV1181 ) @ SV1181 ) @ ( c_List_Oappend @ SV1236 @ ( c_List_Olist_OCons @ SV847 @ ( c_List_Olist_ONil @ SV1181 ) @ SV1181 ) @ SV1181 ) @ SV1181 )
= $false )
| ( ( SV540 = SV847 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV172 @ SV540 ) @ SV847 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3244]) ).
thf(3300,plain,
! [SV858: $i,SV560: $i,SV194: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV560 @ SV194 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV858 @ SV194 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV194 ) @ SV560 ) @ SV858 ) @ SV194 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3245]) ).
thf(3301,plain,
! [SV859: $i,SV1237: $i,SV1069: $i,SV561: $i,SV1182: $i,SV195: $i] :
( ( ( c_ListOrder_Ostep1 @ SV195 @ ( c_List_Olist_OCons @ SV1182 @ SV561 @ SV1069 ) @ ( c_List_Olist_OCons @ SV1237 @ SV859 @ SV1069 ) @ SV1069 )
= $false )
| ( ( SV859 = SV561 )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV195 @ SV561 @ SV859 @ SV1069 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3246]) ).
thf(3302,plain,
! [SV1071: $i,SV571: $i,SV205: $i,SV1184: $i,SV867: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV867 @ SV1184 @ SV205 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV571 @ SV1071 @ SV205 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV205 ) @ SV571 ) @ SV867 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV205 ) @ SV1071 ) @ SV1184 ) @ SV205 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV205 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3247]) ).
thf(3303,plain,
! [SV1072: $i,SV573: $i,SV1238: $i,SV868: $i,SV207: $i,SV1185: $i] :
( ( ( c_ListOrder_Ostep1 @ SV1185 @ ( c_List_Oappend @ SV207 @ ( c_List_Olist_OCons @ SV868 @ ( c_List_Olist_ONil @ SV1238 ) @ SV1238 ) @ SV1238 ) @ ( c_List_Oappend @ SV573 @ ( c_List_Olist_OCons @ SV1072 @ ( c_List_Olist_ONil @ SV1238 ) @ SV1238 ) @ SV1238 ) @ SV1238 )
= $false )
| ( ( SV868 = SV1072 )
= $true )
| ( ( SV207 = SV573 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3248]) ).
thf(3304,plain,
! [SV871: $i,SV214: $i,SV1075: $i,SV578: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV578 @ SV1075 @ SV214 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV214 ) @ SV871 @ SV214 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV578 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV214 ) @ SV871 ) @ SV1075 ) @ SV214 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV214 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3250]) ).
thf(3305,plain,
! [SV884: $i,SV1240: $i,SV1085: $i,SV591: $i,SV1190: $i,SV227: $i] :
( ( ( c_ListOrder_Ostep1 @ SV227 @ ( c_List_Olist_OCons @ SV1190 @ SV591 @ SV1085 ) @ ( c_List_Olist_OCons @ SV1240 @ SV884 @ SV1085 ) @ SV1085 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV227 @ SV1190 ) @ SV1240 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV227 @ SV591 @ SV884 @ SV1085 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3257]) ).
thf(3306,plain,
! [SV1091: $i,SV598: $i,SV1192: $i,SV891: $i,SV235: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV891 ) @ SV1192 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV235 @ SV598 ) @ SV1192 ) @ SV1091 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV235 @ SV598 ) @ SV891 ) @ SV1091 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3259]) ).
thf(3307,plain,
! [SV1092: $i,SV1193: $i,SV892: $i,SV599: $i,SV236: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV236 @ SV599 ) @ SV892 ) @ SV1193 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV236 @ SV1193 ) @ SV1092 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV236 @ SV599 ) @ SV892 ) @ SV1092 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3260]) ).
thf(3308,plain,
! [SV616: $i,SV1103: $i,SV1252: $i,SV253: $i,SV1243: $i,SV1200: $i,SV906: $i] :
( ( ( ~ ( c_Type_Otyping @ SV906 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1200 ) @ SV1243 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV253 ) )
= $true )
| ( ( ~ ( c_Type_Otypings @ SV906 @ SV1243 @ SV1252 )
| ~ ( c_Type_Otyping @ SV906 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1200 ) @ SV1243 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1103 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV616 ) )
= $true )
| ( ( SV253
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV616 @ SV253 @ SV906 @ SV1103 ) @ SV616 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3267]) ).
thf(3309,plain,
! [SV909: $i,SV1105: $i,SV1202: $i,SV620: $i,SV257: $i] :
( ( ( c_Type_Otyping @ SV257 @ SV620 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1202 ) @ SV1105 ) )
= $false )
| ( ( c_Type_Otyping @ SV257 @ SV909 @ SV1202 )
= $false )
| ( ( c_Type_Otyping @ SV257 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV620 ) @ SV909 ) @ SV1105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3268]) ).
thf(3310,plain,
! [SV622: $i,SV259: $i,SV1203: $i,SV1106: $i,SV910: $i] :
( ( ( c_Type_Otyping @ SV910 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1106 ) @ SV1203 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV259 )
= $false )
| ( ( c_Type_Otyping @ SV910 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1106 ) @ SV1203 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV622 )
= $false )
| ( ( SV259 = SV622 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3269]) ).
thf(3311,plain,
! [SV922: $i,SV1114: $i,SV1205: $i,SV635: $i,SV273: $i] :
( ( ( c_Type_Otyping @ SV273 @ SV635 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV1205 @ SV1114 @ tc_Type_Otype @ tc_Type_Otype ) )
= $false )
| ( ( c_Type_Otypings @ SV273 @ SV922 @ SV1205 )
= $false )
| ( ( c_Type_Otyping @ SV273 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV635 @ SV922 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1114 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3270]) ).
thf(3312,plain,
! [SV931: $i,SV645: $i,SV1253: $i,SV1122: $i,SV1247: $i,SV1211: $i,SV286: $i] :
( ( ( ~ ( c_Type_Otyping @ SV286 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1211 ) @ SV1247 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1122 ) )
= $true )
| ( ( ~ ( c_Type_Otypings @ SV286 @ SV1247 @ SV1253 )
| ~ ( c_Type_Otyping @ SV286 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1211 ) @ SV1247 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV645 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV931 ) )
= $true )
| ( ( c_Type_Otypings @ SV286 @ SV645 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV931 @ SV1122 @ SV286 @ SV645 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3271]) ).
thf(3313,plain,
! [SV652: $i,SV1248: $i,SV1212: $i,SV937: $i,SV1125: $i,SV294: $i] :
( ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV294 @ SV1125 @ SV937 @ tc_Type_Otype ) @ SV1212 @ SV1248 ) )
= $true )
| ( ( c_Type_Otyping @ SV294 @ ( c_Lambda_Osubst @ SV1212 @ SV652 @ SV1125 ) @ SV1248 )
= $true )
| ( ( c_Type_Otyping @ SV294 @ SV652 @ SV937 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3272]) ).
thf(3314,plain,
! [SV1254: $i,SV1250: $i,SV1218: $i,SV1139: $i,SV967: $i,SV687: $i,SV329: $i] :
( ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV329 ) @ SV687 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV967 @ SV1139 @ SV1218 ) ) )
| ~ ( c_Type_Otyping @ SV1250 @ SV1139 @ SV687 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1139 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV1250 @ SV1218 @ SV687 @ tc_Type_Otype ) @ SV967 @ SV1254 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV967 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3280]) ).
thf(3315,plain,
! [SV974: $i,SV339: $i,SV697: $i] :
( ( ( SV697
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV339 ) @ SV697 ) @ SV974 ) )
= $false )
| ( ( SV974
= ( c_HOL_Ozero__class_Ozero @ SV339 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV339 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV339 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3282]) ).
thf(3316,plain,
! [SV1226: $i,SV1151: $i,SV990: $i,SV716: $i,SV358: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV716 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV990 ) @ SV1151 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV990 ) @ SV1226 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV716 ) @ SV1151 )
= SV1226 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV358 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3286]) ).
thf(3317,plain,
! [SV1160: $i,SV1006: $i,SV736: $i,SV378: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV378 ) @ SV736 ) @ SV1006 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV378 ) @ SV736 ) @ SV1160 ) )
= $true )
| ( ( SV1006 = SV1160 )
= $true )
| ( ( class_Int_Onumber__ring @ SV378 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV378 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3289]) ).
thf(3318,plain,
! [SV1255: $i,SV1251: $i,SV1229: $i,SV1161: $i,SV1008: $i,SV738: $i,SV380: $i] :
( ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV380 ) @ SV738 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV1008 @ SV1161 @ SV1229 ) ) )
| ~ ( c_Type_Otyping @ SV1251 @ SV1161 @ SV380 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1161 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV1251 @ SV1229 @ SV380 @ tc_Type_Otype ) @ SV1008 @ SV1255 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1008 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3290]) ).
thf(3319,plain,
! [SV807: $i,SV108: $i,SV1038: $i,SV480: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV480 @ SV1038 @ SV108 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1038 @ SV807 @ SV108 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV480 @ SV807 @ SV108 )
= $true )
| ( ( class_Orderings_Opreorder @ SV108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3292]) ).
thf(3320,plain,
! [SV481: $i,SV109: $i,SV808: $i,SV1039: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1039 @ SV808 @ SV109 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV481 @ SV1039 @ SV109 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV481 @ SV808 @ SV109 )
= $true )
| ( ( class_Orderings_Oorder @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3293]) ).
thf(3321,plain,
! [SV1071: $i,SV571: $i,SV205: $i,SV1184: $i,SV867: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV867 @ SV1184 @ SV205 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV571 @ SV1071 @ SV205 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV205 ) @ SV571 ) @ SV867 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV205 ) @ SV1071 ) @ SV1184 ) @ SV205 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV205 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3302]) ).
thf(3322,plain,
! [SV1075: $i,SV578: $i,SV871: $i,SV214: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV214 ) @ SV871 @ SV214 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV578 @ SV1075 @ SV214 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV578 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV214 ) @ SV871 ) @ SV1075 ) @ SV214 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV214 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3304]) ).
thf(3323,plain,
! [SV616: $i,SV1103: $i,SV1252: $i,SV253: $i,SV1243: $i,SV1200: $i,SV906: $i] :
( ( ( c_Type_Otyping @ SV906 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1200 ) @ SV1243 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV253 )
= $false )
| ( ( ~ ( c_Type_Otypings @ SV906 @ SV1243 @ SV1252 )
| ~ ( c_Type_Otyping @ SV906 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1200 ) @ SV1243 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1103 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV616 ) )
= $true )
| ( ( SV253
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV616 @ SV253 @ SV906 @ SV1103 ) @ SV616 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3308]) ).
thf(3324,plain,
! [SV931: $i,SV645: $i,SV1253: $i,SV1122: $i,SV1247: $i,SV1211: $i,SV286: $i] :
( ( ( c_Type_Otyping @ SV286 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1211 ) @ SV1247 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1122 )
= $false )
| ( ( ~ ( c_Type_Otypings @ SV286 @ SV1247 @ SV1253 )
| ~ ( c_Type_Otyping @ SV286 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1211 ) @ SV1247 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV645 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV931 ) )
= $true )
| ( ( c_Type_Otypings @ SV286 @ SV645 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV931 @ SV1122 @ SV286 @ SV645 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3312]) ).
thf(3325,plain,
! [SV652: $i,SV1248: $i,SV1212: $i,SV937: $i,SV1125: $i,SV294: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV294 @ SV1125 @ SV937 @ tc_Type_Otype ) @ SV1212 @ SV1248 )
= $false )
| ( ( c_Type_Otyping @ SV294 @ ( c_Lambda_Osubst @ SV1212 @ SV652 @ SV1125 ) @ SV1248 )
= $true )
| ( ( c_Type_Otyping @ SV294 @ SV652 @ SV937 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3313]) ).
thf(3326,plain,
! [SV329: $i,SV1254: $i,SV687: $i,SV1250: $i,SV1218: $i,SV1139: $i,SV967: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV967 @ SV1139 @ SV1218 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV1250 @ SV1139 @ SV687 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1139 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV1250 @ SV1218 @ SV687 @ tc_Type_Otype ) @ SV967 @ SV1254 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV967 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV329 ) @ SV687 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3314]) ).
thf(3327,plain,
! [SV1160: $i,SV1006: $i,SV736: $i,SV378: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV378 ) @ SV736 ) @ SV1006 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV378 ) @ SV736 ) @ SV1160 ) )
= $false )
| ( ( SV1006 = SV1160 )
= $true )
| ( ( class_Int_Onumber__ring @ SV378 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV378 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3317]) ).
thf(3328,plain,
! [SV738: $i,SV1255: $i,SV380: $i,SV1251: $i,SV1229: $i,SV1161: $i,SV1008: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV1008 @ SV1161 @ SV1229 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV1251 @ SV1161 @ SV380 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1161 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV1251 @ SV1229 @ SV380 @ tc_Type_Otype ) @ SV1008 @ SV1255 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1008 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV380 ) @ SV738 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3318]) ).
thf(3329,plain,
! [SV1184: $i,SV867: $i,SV205: $i,SV1071: $i,SV571: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV571 @ SV1071 @ SV205 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV867 @ SV1184 @ SV205 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV205 ) @ SV571 ) @ SV867 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV205 ) @ SV1071 ) @ SV1184 ) @ SV205 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV205 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3321]) ).
thf(3330,plain,
! [SV253: $i,SV616: $i,SV1103: $i,SV1200: $i,SV1252: $i,SV1243: $i,SV906: $i] :
( ( ( ~ ( c_Type_Otypings @ SV906 @ SV1243 @ SV1252 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV906 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1200 ) @ SV1243 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1103 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV616 ) )
= $true )
| ( ( c_Type_Otyping @ SV906 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1200 ) @ SV1243 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV253 )
= $false )
| ( ( SV253
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV616 @ SV253 @ SV906 @ SV1103 ) @ SV616 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3323]) ).
thf(3331,plain,
! [SV1122: $i,SV931: $i,SV645: $i,SV1211: $i,SV1253: $i,SV1247: $i,SV286: $i] :
( ( ( ~ ( c_Type_Otypings @ SV286 @ SV1247 @ SV1253 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV286 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1211 ) @ SV1247 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV645 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV931 ) )
= $true )
| ( ( c_Type_Otyping @ SV286 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1211 ) @ SV1247 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1122 )
= $false )
| ( ( c_Type_Otypings @ SV286 @ SV645 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV931 @ SV1122 @ SV286 @ SV645 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3324]) ).
thf(3332,plain,
! [SV329: $i,SV1254: $i,SV967: $i,SV1218: $i,SV687: $i,SV1139: $i,SV1250: $i] :
( ( ( ~ ( c_Type_Otyping @ SV1250 @ SV1139 @ SV687 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1139 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV1250 @ SV1218 @ SV687 @ tc_Type_Otype ) @ SV967 @ SV1254 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV967 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV967 @ SV1139 @ SV1218 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV329 ) @ SV687 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3326]) ).
thf(3333,plain,
! [SV738: $i,SV1255: $i,SV1008: $i,SV1229: $i,SV380: $i,SV1161: $i,SV1251: $i] :
( ( ( ~ ( c_Type_Otyping @ SV1251 @ SV1161 @ SV380 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1161 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV1251 @ SV1229 @ SV380 @ tc_Type_Otype ) @ SV1008 @ SV1255 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1008 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV1008 @ SV1161 @ SV1229 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV380 ) @ SV738 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3328]) ).
thf(3334,plain,
! [SV253: $i,SV616: $i,SV1103: $i,SV1200: $i,SV1252: $i,SV1243: $i,SV906: $i] :
( ( ( c_Type_Otypings @ SV906 @ SV1243 @ SV1252 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV906 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1200 ) @ SV1243 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1103 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV616 ) )
= $true )
| ( ( c_Type_Otyping @ SV906 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1200 ) @ SV1243 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV253 )
= $false )
| ( ( SV253
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV616 @ SV253 @ SV906 @ SV1103 ) @ SV616 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3330]) ).
thf(3335,plain,
! [SV1122: $i,SV931: $i,SV645: $i,SV1211: $i,SV1253: $i,SV1247: $i,SV286: $i] :
( ( ( c_Type_Otypings @ SV286 @ SV1247 @ SV1253 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV286 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1211 ) @ SV1247 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV645 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV931 ) )
= $true )
| ( ( c_Type_Otyping @ SV286 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1211 ) @ SV1247 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1122 )
= $false )
| ( ( c_Type_Otypings @ SV286 @ SV645 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV931 @ SV1122 @ SV286 @ SV645 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3331]) ).
thf(3336,plain,
! [SV329: $i,SV1254: $i,SV967: $i,SV1218: $i,SV687: $i,SV1139: $i,SV1250: $i] :
( ( ( c_Type_Otyping @ SV1250 @ SV1139 @ SV687 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1139 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV1250 @ SV1218 @ SV687 @ tc_Type_Otype ) @ SV967 @ SV1254 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV967 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV967 @ SV1139 @ SV1218 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV329 ) @ SV687 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3332]) ).
thf(3337,plain,
! [SV738: $i,SV1255: $i,SV1008: $i,SV1229: $i,SV380: $i,SV1161: $i,SV1251: $i] :
( ( ( c_Type_Otyping @ SV1251 @ SV1161 @ SV380 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1161 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV1251 @ SV1229 @ SV380 @ tc_Type_Otype ) @ SV1008 @ SV1255 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1008 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV1008 @ SV1161 @ SV1229 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV380 ) @ SV738 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3333]) ).
thf(3338,plain,
! [SV253: $i,SV1252: $i,SV616: $i,SV1103: $i,SV1243: $i,SV1200: $i,SV906: $i] :
( ( ( c_Type_Otyping @ SV906 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1200 ) @ SV1243 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1103 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV616 )
= $false )
| ( ( c_Type_Otypings @ SV906 @ SV1243 @ SV1252 )
= $false )
| ( ( c_Type_Otyping @ SV906 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1200 ) @ SV1243 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV253 )
= $false )
| ( ( SV253
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV616 @ SV253 @ SV906 @ SV1103 ) @ SV616 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3334]) ).
thf(3339,plain,
! [SV1122: $i,SV1253: $i,SV931: $i,SV645: $i,SV1247: $i,SV1211: $i,SV286: $i] :
( ( ( c_Type_Otyping @ SV286 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1211 ) @ SV1247 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV645 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV931 )
= $false )
| ( ( c_Type_Otypings @ SV286 @ SV1247 @ SV1253 )
= $false )
| ( ( c_Type_Otyping @ SV286 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1211 ) @ SV1247 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1122 )
= $false )
| ( ( c_Type_Otypings @ SV286 @ SV645 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV931 @ SV1122 @ SV286 @ SV645 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3335]) ).
thf(3340,plain,
! [SV329: $i,SV1254: $i,SV967: $i,SV687: $i,SV1218: $i,SV1250: $i,SV1139: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1139 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV1250 @ SV1218 @ SV687 @ tc_Type_Otype ) @ SV967 @ SV1254 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV967 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV1250 @ SV1139 @ SV687 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV967 @ SV1139 @ SV1218 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV329 ) @ SV687 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3336]) ).
thf(3341,plain,
! [SV738: $i,SV1255: $i,SV1008: $i,SV380: $i,SV1229: $i,SV1251: $i,SV1161: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1161 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV1251 @ SV1229 @ SV380 @ tc_Type_Otype ) @ SV1008 @ SV1255 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1008 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV1251 @ SV1161 @ SV380 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV1008 @ SV1161 @ SV1229 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV380 ) @ SV738 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3337]) ).
thf(3342,plain,
! [SV329: $i,SV1254: $i,SV967: $i,SV687: $i,SV1218: $i,SV1250: $i,SV1139: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1139 ) )
= $false )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV1250 @ SV1218 @ SV687 @ tc_Type_Otype ) @ SV967 @ SV1254 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV967 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV1250 @ SV1139 @ SV687 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV967 @ SV1139 @ SV1218 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV329 ) @ SV687 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3340]) ).
thf(3343,plain,
! [SV738: $i,SV1255: $i,SV1008: $i,SV380: $i,SV1229: $i,SV1251: $i,SV1161: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1161 ) )
= $false )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV1251 @ SV1229 @ SV380 @ tc_Type_Otype ) @ SV1008 @ SV1255 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1008 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV1251 @ SV1161 @ SV380 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV1008 @ SV1161 @ SV1229 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV380 ) @ SV738 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3341]) ).
thf(3344,plain,
! [SV329: $i,SV1139: $i,SV1254: $i,SV967: $i,SV687: $i,SV1218: $i,SV1250: $i] :
( ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV1250 @ SV1218 @ SV687 @ tc_Type_Otype ) @ SV967 @ SV1254 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV967 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1139 ) )
= $false )
| ( ( c_Type_Otyping @ SV1250 @ SV1139 @ SV687 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV967 @ SV1139 @ SV1218 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV329 ) @ SV687 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3342]) ).
thf(3345,plain,
! [SV738: $i,SV1161: $i,SV1255: $i,SV1008: $i,SV380: $i,SV1229: $i,SV1251: $i] :
( ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV1251 @ SV1229 @ SV380 @ tc_Type_Otype ) @ SV1008 @ SV1255 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1008 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1161 ) )
= $false )
| ( ( c_Type_Otyping @ SV1251 @ SV1161 @ SV380 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV1008 @ SV1161 @ SV1229 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV380 ) @ SV738 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3343]) ).
thf(3346,plain,
! [SV329: $i,SV1139: $i,SV1254: $i,SV967: $i,SV687: $i,SV1218: $i,SV1250: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV1250 @ SV1218 @ SV687 @ tc_Type_Otype ) @ SV967 @ SV1254 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV967 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1139 ) )
= $false )
| ( ( c_Type_Otyping @ SV1250 @ SV1139 @ SV687 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV967 @ SV1139 @ SV1218 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV329 ) @ SV687 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3344]) ).
thf(3347,plain,
! [SV738: $i,SV1161: $i,SV1255: $i,SV1008: $i,SV380: $i,SV1229: $i,SV1251: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV1251 @ SV1229 @ SV380 @ tc_Type_Otype ) @ SV1008 @ SV1255 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1008 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1161 ) )
= $false )
| ( ( c_Type_Otyping @ SV1251 @ SV1161 @ SV380 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV1008 @ SV1161 @ SV1229 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV380 ) @ SV738 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3345]) ).
thf(3348,plain,
! [SV329: $i,SV1139: $i,SV1254: $i,SV687: $i,SV1218: $i,SV1250: $i,SV967: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV967 ) )
= $false )
| ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV1250 @ SV1218 @ SV687 @ tc_Type_Otype ) @ SV967 @ SV1254 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1139 ) )
= $false )
| ( ( c_Type_Otyping @ SV1250 @ SV1139 @ SV687 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV967 @ SV1139 @ SV1218 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV329 ) @ SV687 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3346]) ).
thf(3349,plain,
! [SV738: $i,SV1161: $i,SV1255: $i,SV380: $i,SV1229: $i,SV1251: $i,SV1008: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1008 ) )
= $false )
| ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV1251 @ SV1229 @ SV380 @ tc_Type_Otype ) @ SV1008 @ SV1255 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1161 ) )
= $false )
| ( ( c_Type_Otyping @ SV1251 @ SV1161 @ SV380 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV1008 @ SV1161 @ SV1229 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV380 ) @ SV738 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3347]) ).
thf(3350,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[865,3349,3348,3339,3338,3329,3327,3325,3322,3320,3319,3316,3315,3311,3310,3309,3307,3306,3305,3303,3301,3300,3299,3298,3297,3296,3295,3294,3291,3288,3287,3285,3284,3283,3281,3279,3278,3277,3276,3275,3274,3273,3266,3265,3264,3263,3262,3261,3258,3256,3255,3254,3253,3252,3251,3249,3241,3240,3233,3232,3231,3230,3229,3228,3222,3221,3220,3219,3213,3209,3207,3200,3196,3191,3190,3189,3188,3181,3173,3172,3167,3166,3165,3164,3163,3162,3159,3153,3147,3146,3144,3143,3142,3141,3135,3134,3133,3132,3131,3129,3126,3125,3123,3122,3121,3119,3113,3110,3108,3101,3093,3092,3090,3088,3087,3086,3085,3083,3081,3080,3079,3078,3073,3067,3048,3040,3033,3032,3031,3030,3029,3028,3027,3025,3024,3022,3021,3020,3019,3018,3010,3009,3008,3007,3006,3005,3004,3003,3002,2997,2996,2995,2992,2991,2990,2989,2976,2975,2974,2971,2969,2965,2964,2963,2962,2961,2958,2956,2950,2949,2948,2947,2941,2933,2932,2929,2927,2925,2923,2921,2919,2917,2913,2912,2910,2909,2908,2904,2902,2901,2896,2892,2887,2885,2884,2883,2882,2879,2868,2852,2848,2846,2833,2832,2831,2830,2829,2827,2821,2816,2815,2814,2805,2803,2799,2798,2797,2781,2778,2769,2768,2767,2764,2761,2760,2759,2758,2756,2755,2754,2753,2752,2740,2738,2734,2730,2724,2722,2715,2712,2700,2698,2692,2690,2687,2681,2675,2674,2670,2668,2663,2657,2656,2653,2650,2648,2630,2629,2623,2611,2601,2600,2599,2598,2580,2575,2573,2563,2555,2554,2538,2537,2536,2535,2534,2533,2531,2530,2527,2521,2520,2516,2515,2512,2498,2488,2485,2484,2482,2481,2480,2479,2478,2475,2474,2463,2462,2460,2446,2444,2389,2386,2332,2319,2286,2279,2237,2236,2221,2220,2217,2212,2200,2188,2187,2174,2167,2166,2165,2164,2163,2162,2151,2148,2146,2139,2138,2137,2136,2131,2130,2124,2123,2120,2119,2111,2110,2108,2019,2004,1973,1967,1938,1936,1933,1917,1913,1912,1891,1890,1889,1888,1887,1870,1846,1845,1821,1805,1803,1801,1798,1797,1796,1794,1792,1791,1777,1764,1762,1756,1755,1754,1649,1637,1632,1629,1625,1614,1576,1558,1490,1411,1395,1394,1380,1365,1354,1353,1352,1351,1346,1256,1255,1254,1253,1252,1251,1250,1249,1248,1247,1246,1245,1244,1243,1242,1241,1240,1239,1236,1235,1223,1201,1199,1197,1191,1148,1019,979]) ).
thf(3351,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[3350]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL785-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n008.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 12:34:39 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 75.62/12.96 ...
% 75.62/12.96
% 75.62/12.96 No.of.Axioms: 418
% 75.62/12.96
% 75.62/12.96 Length.of.Defs: 0
% 75.62/12.96
% 75.62/12.96 Contains.Choice.Funs: false
% 75.62/12.96 ...............................................................................................................................
% 75.62/12.96
% 75.62/12.96 ********************************
% 75.62/12.96 * All subproblems solved! *
% 75.62/12.96 ********************************
% 75.62/12.96 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:418,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:298,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:3350,loop_count:0,foatp_calls:1,translation:fof_full)
% 75.62/12.96
% 75.62/12.96 %**** Beginning of derivation protocol ****
% 75.62/12.96 % SZS output start CNFRefutation
% See solution above
% 75.62/12.97
% 75.62/12.97 %**** End of derivation protocol ****
% 75.62/12.97 %**** no. of clauses in derivation: 3351 ****
% 75.62/12.97 %**** clause counter: 3350 ****
% 75.62/12.97
% 75.62/12.97 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:418,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:298,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:3350,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------