%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL777-1 : 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 : n004.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 10:30:26 AM UTC 2026
% Result : Unsatisfiable 58.13s 10.10s
% Output : CNFRefutation 58.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 389
% Syntax : Number of formulae : 2965 (2120 unt; 0 typ; 0 def)
% Number of atoms : 12638 (6453 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 36972 (2126 ~;2897 |; 0 &;31949 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 72 ( 69 usr; 13 con; 0-5 aty)
% Number of variables : 9554 ( 0 ^;9554 !; 0 ?;9554 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_HOL_Oone__class_Oone,type,
c_HOL_Oone__class_Oone: $i > $i ).
thf(tp_c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(tp_c_HOL_Ozero__class_Ozero,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(tp_c_InductTermi_OIT,type,
c_InductTermi_OIT: $i ).
thf(tp_c_Int_Onumber__class_Onumber__of,type,
c_Int_Onumber__class_Onumber__of: $i > $i > $i ).
thf(tp_c_Lambda_Obeta,type,
c_Lambda_Obeta: $i ).
thf(tp_c_Lambda_OdB_OAbs,type,
c_Lambda_OdB_OAbs: $i > $i ).
thf(tp_c_Lambda_OdB_OApp,type,
c_Lambda_OdB_OApp: $i ).
thf(tp_c_Lambda_OdB_OVar,type,
c_Lambda_OdB_OVar: $i > $i ).
thf(tp_c_Lambda_OdB_OdB__size,type,
c_Lambda_OdB_OdB__size: $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_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1,type,
c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1: $i > $i > $i > $i ).
thf(tp_c_ListOrder_Ostep1,type,
c_ListOrder_Ostep1: $i > $i > $i > $i > $o ).
thf(tp_c_List_Oappend,type,
c_List_Oappend: $i > $i > $i > $i ).
thf(tp_c_List_Obutlast,type,
c_List_Obutlast: $i > $i > $i ).
thf(tp_c_List_Odrop,type,
c_List_Odrop: $i > $i > $i > $i ).
thf(tp_c_List_Ofoldl,type,
c_List_Ofoldl: $i > $i > $i > $i > $i > $i ).
thf(tp_c_List_Ohd,type,
c_List_Ohd: $i > $i > $i ).
thf(tp_c_List_Olast,type,
c_List_Olast: $i > $i > $i ).
thf(tp_c_List_Olist_OCons,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(tp_c_List_Olist_ONil,type,
c_List_Olist_ONil: $i > $i ).
thf(tp_c_List_Olist__update,type,
c_List_Olist__update: $i > $i > $i > $i > $i ).
thf(tp_c_List_Olistsp,type,
c_List_Olistsp: $i > $i > $i > $o ).
thf(tp_c_List_Onth,type,
c_List_Onth: $i > $i > $i > $i ).
thf(tp_c_List_Oreplicate,type,
c_List_Oreplicate: $i > $i > $i > $i ).
thf(tp_c_List_Orev,type,
c_List_Orev: $i > $i > $i ).
thf(tp_c_List_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_List_Osplice,type,
c_List_Osplice: $i > $i > $i > $i ).
thf(tp_c_List_Otake,type,
c_List_Otake: $i > $i > $i > $i ).
thf(tp_c_List_Otl,type,
c_List_Otl: $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_Predicate_Oconversep,type,
c_Predicate_Oconversep: $i > $i > $i > $i ).
thf(tp_c_Suc,type,
c_Suc: $i > $i ).
thf(tp_c_Transitive__Closure_Ortranclp,type,
c_Transitive__Closure_Ortranclp: $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__Xvar__app__typesE__1__1,type,
c_Type_Osko__Type__Xvar__app__typesE__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xvar__app__types__1__1,type,
c_Type_Osko__Type__Xvar__app__types__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Otyping,type,
c_Type_Otyping: $i > $i > $i > $o ).
thf(tp_c_Type_Otypings,type,
c_Type_Otypings: $i > $i > $i > $o ).
thf(tp_c_Wellfounded_Oaccp,type,
c_Wellfounded_Oaccp: $i > $i > $i > $o ).
thf(tp_c_fequal,type,
c_fequal: $i > $i ).
thf(tp_class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $i > $o ).
thf(tp_class_Int_Oring__char__0,type,
class_Int_Oring__char__0: $i > $o ).
thf(tp_class_Nat_Osemiring__char__0,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(tp_class_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_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_class_Ring__and__Field_Ozero__neq__one,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
thf(tp_hAPP,type,
hAPP: $i > $i > $i ).
thf(tp_hBOOL,type,
hBOOL: $i > $o ).
thf(tp_tc_Int_Oint,type,
tc_Int_Oint: $i ).
thf(tp_tc_Lambda_OdB,type,
tc_Lambda_OdB: $i ).
thf(tp_tc_List_Olist,type,
tc_List_Olist: $i > $i ).
thf(tp_tc_bool,type,
tc_bool: $i ).
thf(tp_tc_fun,type,
tc_fun: $i > $i > $i ).
thf(tp_tc_nat,type,
tc_nat: $i ).
thf(tp_v_i,type,
v_i: $i ).
thf(tp_v_r,type,
v_r: $i ).
thf(tp_v_s,type,
v_s: $i ).
thf(tp_v_ss,type,
v_ss: $i ).
thf(1,axiom,
! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_X ) @ V_Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(2,axiom,
! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_x ) @ V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(3,axiom,
class_Int_Onumber__ring @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber__ring) ).
thf(4,axiom,
class_Int_Oring__char__0 @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Oring__char__0) ).
thf(5,axiom,
class_Orderings_Oorder @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Oorder) ).
thf(6,axiom,
class_Orderings_Olinorder @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).
thf(7,axiom,
class_Orderings_Opreorder @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Opreorder) ).
thf(8,axiom,
class_Nat_Osemiring__char__0 @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Nat_Osemiring__char__0) ).
thf(9,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__1) ).
thf(10,axiom,
class_Ring__and__Field_Oordered__idom @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__idom) ).
thf(11,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) ).
thf(12,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) ).
thf(13,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(14,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(15,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(16,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(17,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(18,axiom,
class_Nat_Osemiring__char__0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
thf(19,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(20,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
thf(21,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(22,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(23,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(24,axiom,
! [V_dB1_H: $i,V_dB2_H: $i,V_nat: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
thf(25,axiom,
! [V_f: $i,V_a: $i,V_xs: $i,V_ys: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ T_a @ T_b )
= ( c_List_Ofoldl @ V_f @ ( c_List_Ofoldl @ V_f @ V_a @ V_xs @ T_a @ T_b ) @ V_ys @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__append_0) ).
thf(26,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(27,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(28,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(29,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(30,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(31,axiom,
! [V_r: $i,V_ts: $i,V_s: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).
thf(32,axiom,
! [V_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(33,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(34,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(35,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(36,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(37,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(38,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(39,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(40,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(41,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(42,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(43,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(44,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(45,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(46,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(47,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(48,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(49,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(50,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(51,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(52,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(53,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(54,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(55,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(56,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(57,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(58,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(59,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(60,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(61,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(62,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(63,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(64,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(65,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(66,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(67,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(68,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(69,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(70,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(71,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(72,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(73,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(74,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(75,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(76,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(77,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(78,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(79,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(80,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(81,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(82,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(83,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(84,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(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] :
( ( 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(87,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(88,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(89,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(90,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(91,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(92,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(93,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(94,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(95,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(96,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(97,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(98,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(99,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(100,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(101,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(102,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(103,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(104,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(105,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(106,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(107,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(108,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(109,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Cons_H_0) ).
thf(110,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(111,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(112,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(113,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(114,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(115,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(116,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(117,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(118,axiom,
! [V_nat: $i] :
( ( c_Lambda_OdB_OdB__size @ ( c_Lambda_OdB_OVar @ V_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I1_J_0) ).
thf(119,axiom,
! [V_nat: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_Lambda_OdB_OVar @ V_nat ) @ tc_Lambda_OdB )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I4_J_0) ).
thf(120,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(121,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Ohd @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__append_1) ).
thf(122,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(123,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Otl @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Otl @ V_xs @ T_a ) @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl__append2_0) ).
thf(124,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(125,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(126,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(127,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(128,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(129,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(130,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(131,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(132,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(133,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(134,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(135,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(136,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(137,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(138,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(139,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(140,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(141,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(142,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(143,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(144,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(145,axiom,
! [V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= V_x )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__replicate_0) ).
thf(146,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__rev_0) ).
thf(147,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(148,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(149,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(150,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(151,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(152,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Ohd @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__rev_0) ).
thf(153,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(154,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(155,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(156,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(157,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(158,axiom,
! [V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(159,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(160,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(161,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(162,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(163,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Ohd @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd_Osimps_0) ).
thf(164,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(165,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(166,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otl @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl_Osimps_I2_J_0) ).
thf(167,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(168,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(169,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(170,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(171,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(172,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(173,axiom,
! [T_a: $i] :
( ( c_List_Otl @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl_Osimps_I1_J_0) ).
thf(174,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(175,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(176,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(177,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(178,axiom,
! [V_n: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__eq__Nil_2) ).
thf(179,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(180,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(181,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(182,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(183,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_List_Orotate1 @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Otl @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate1__hd__tl_0) ).
thf(184,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(185,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(186,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(187,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(188,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(189,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(190,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(191,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(192,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(193,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(194,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(195,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(196,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(197,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(198,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(199,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(200,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(201,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(202,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(203,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(204,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(205,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(206,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(207,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_xs @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__0_0) ).
thf(208,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(209,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__eq__Nil_0) ).
thf(210,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(211,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(212,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(213,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(214,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(215,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(216,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(217,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(218,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(219,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(220,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(221,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(222,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(223,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(224,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(225,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(226,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(227,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ 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_take__1__Cons_0) ).
thf(228,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(229,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(230,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(231,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_List_Ohd @ V_xs @ T_a )
= ( c_List_Onth @ V_xs @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__conv__nth_0) ).
thf(232,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ V_n @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a )
= ( c_List_Otake @ V_n @ V_xs @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__butlast_0) ).
thf(233,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(234,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(235,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(236,axiom,
! [V_v: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Otake @ ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Cons__number__of_0) ).
thf(237,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(238,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(239,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ V_ys @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ ( c_List_Ohd @ V_ys @ T_a ) @ ( c_List_Osplice @ V_xs @ ( c_List_Otl @ V_ys @ T_a ) @ T_a ) @ T_a ) @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice_Osimps_I2_J_1) ).
thf(240,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ ( c_Suc @ V_n ) @ V_xs @ T_a )
= ( c_List_Olist_OCons @ ( c_List_Ohd @ V_xs @ T_a ) @ ( c_List_Otake @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Suc_0) ).
thf(241,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(242,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(243,axiom,
! [T_a: $i,V_ys: $i] :
( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a ) @ T_a )
= ( c_List_Ohd @ V_ys @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__append_0) ).
thf(244,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(245,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a )
= ( c_List_Otl @ ( c_List_Otake @ ( c_Suc @ V_n ) @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__tl_0) ).
thf(246,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(247,axiom,
! [V_n: $i,V_x: $i,T_a: $i,V_i: $i] :
( ( ( c_List_Onth @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ V_i @ T_a )
= V_x )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__replicate_0) ).
thf(248,axiom,
! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( c_Suc @ V_n ) @ V_x @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__Suc_0) ).
thf(249,axiom,
! [V_xs: $i,T_a: $i,V_ys: $i] :
( V_xs
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__conv__conj_0) ).
thf(250,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(251,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(252,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(253,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(254,axiom,
! [V_n: $i,V_xs: $i,T_a: $i,V_i: $i] :
( ( ( c_List_Onth @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ V_i @ T_a )
= ( c_List_Onth @ V_xs @ V_i @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__take_0) ).
thf(255,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(256,axiom,
! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_Suc @ V_n ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Suc__Cons_0) ).
thf(257,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(258,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(259,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(260,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(261,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice_Osimps_I2_J_0) ).
thf(262,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(263,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(264,axiom,
c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_1) ).
thf(265,axiom,
! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
thf(266,axiom,
! [V_n: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ V_n ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
thf(267,axiom,
! [V_x: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ V_x ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
thf(268,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= V_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__Cons_H_0) ).
thf(269,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(270,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(271,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(272,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
thf(273,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
thf(274,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(275,axiom,
! [V_i: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ ( c_Suc @ V_i ) @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Suc__conv__app__nth_0) ).
thf(276,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(277,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(278,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(279,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(280,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(281,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ ( c_List_Otl @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Olist__size__simp_I2_J_1) ).
thf(282,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).
thf(283,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
thf(284,axiom,
! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(285,axiom,
! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(286,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_Suc @ V_n ) @ T_a )
= ( c_List_Onth @ V_xs @ V_n @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__Cons__Suc_0) ).
thf(287,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(288,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(289,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_i ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
thf(290,axiom,
! [V_x: $i] : ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
thf(291,axiom,
! [V_n: $i] : ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_n ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessI_0) ).
thf(292,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(293,axiom,
! [V_n: $i,V_m: $i] :
( ( V_n = V_m )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
thf(294,axiom,
! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__antisym_0) ).
thf(295,axiom,
! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucE_0) ).
thf(296,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(297,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(298,axiom,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_One__nat__def_0) ).
thf(299,axiom,
! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Suc @ V_nat )
!= ( c_Suc @ V_nat_H ) )
| ( V_nat = V_nat_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(300,axiom,
! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(301,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(302,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i,V_n: $i] :
( ( ( c_List_Onth @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_n @ T_a )
= ( c_List_Onth @ V_xs @ V_n @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__append_0) ).
thf(303,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(304,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(305,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(306,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(307,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(308,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(309,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(310,axiom,
! [V_xa: $i,T_a: $i,V_x: $i] :
( ( c_Suc @ ( c_Nat_Osize__class_Osize @ V_xa @ ( tc_List_Olist @ T_a ) ) )
= ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ ( tc_List_Olist @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__length__conv_2) ).
thf(311,axiom,
! [V_x: $i,V_xa: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ V_xa @ ( tc_List_Olist @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__Suc__conv_2) ).
thf(312,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(313,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(314,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(315,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(316,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__1_0) ).
thf(317,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(318,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(319,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Int_Oring__char__0 @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_Int_Onumber__class_Onumber__of @ V_x @ T_a )
!= ( c_Int_Onumber__class_Onumber__of @ V_y @ T_a ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__number__of_0) ).
thf(320,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
| ( ( c_Suc @ V_m )
= V_n )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
thf(321,axiom,
! [V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
thf(322,axiom,
! [V_m: $i,V_n: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
thf(323,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
thf(324,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(325,axiom,
! [V_x: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_x ) @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
thf(326,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
thf(327,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
thf(328,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Oone__class_Oone @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
thf(329,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
thf(330,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(331,axiom,
! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
thf(332,axiom,
! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
thf(333,axiom,
! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
thf(334,axiom,
! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
thf(335,axiom,
! [V_v: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Onth @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat ) @ T_a )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__Cons__number__of_0) ).
thf(336,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ V_y @ ( c_List_Osplice @ V_xs @ V_ys @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice__Cons__Cons_0) ).
thf(337,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Osplice @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice__Nil2_0) ).
thf(338,axiom,
! [T_a: $i,V_ys: $i] :
( ( c_List_Osplice @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a )
= V_ys ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice_Osimps_I1_J_0) ).
thf(339,axiom,
! [V_xs: $i,V_x: $i,V_ys: $i,T_a: $i] :
( ( c_List_Onth @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ T_a ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ T_a )
= V_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__append__length_0) ).
thf(340,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(341,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Oappend @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Otake @ ( c_Suc @ V_n ) @ V_xs @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__hd__drop_0) ).
thf(342,axiom,
! [V_xs: $i,V_i: $i,T_a: $i] :
( ( V_xs
= ( c_List_Oappend @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ ( c_List_Odrop @ ( c_Suc @ V_i ) @ V_xs @ T_a ) @ T_a ) @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__take__nth__drop_0) ).
thf(343,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(344,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(345,axiom,
! [V_n: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Nil_0) ).
thf(346,axiom,
! [V_v: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Odrop @ ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Cons__number__of_0) ).
thf(347,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_xs @ T_a )
= V_xs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__0_0) ).
thf(348,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_Suc @ V_n ) @ V_xs @ T_a )
= ( c_List_Odrop @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Suc_0) ).
thf(349,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_n @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__drop_0) ).
thf(350,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__1__Cons_0) ).
thf(351,axiom,
! [V_ys: $i,V_xs: $i,T_a: $i] :
( V_ys
= ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__conv__conj_1) ).
thf(352,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otl @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl__drop_0) ).
thf(353,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a )
= ( c_List_Obutlast @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__butlast_0) ).
thf(354,axiom,
! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_Suc @ V_n ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_n @ V_xs @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Suc__Cons_0) ).
thf(355,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a )
= ( c_List_Otl @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__tl_0) ).
thf(356,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__drop_0) ).
thf(357,axiom,
! [V_xs: $i,T_a: $i,V_zs: $i] :
( ( V_xs
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_zs @ T_a ) )
| ( ( c_List_Oappend @ V_xs @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_zs @ T_a ) @ T_a )
= V_zs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__conv__conj_2) ).
thf(358,axiom,
! [V_xs: $i,V_i: $i,V_a: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_i @ V_a @ T_a )
= ( c_List_Oappend @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_a @ ( c_List_Odrop @ ( c_Suc @ V_i ) @ V_xs @ T_a ) @ T_a ) @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_upd__conv__take__nth__drop_0) ).
thf(359,axiom,
! [V_n: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( ( c_List_Odrop @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ( ( c_List_Onth @ V_xs @ V_n @ T_a )
= V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__via__drop_0) ).
thf(360,axiom,
! [V_ys_092_060_094isub_0621: $i,T_a: $i,V_xs_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) @ T_a )
!= V_ys_092_060_094isub_0622 )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a )
!= V_ys_092_060_094isub_0621 )
| ( V_xs_092_060_094isub_0621
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) )
| ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) @ T_a )
= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_6) ).
thf(361,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Cons_H_0) ).
thf(362,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Oappend @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__take__drop__id_0) ).
thf(363,axiom,
! [V_xs: $i,V_i: $i,T_a: $i] :
( ( ( c_List_Olist_OCons @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ ( c_List_Odrop @ ( c_Suc @ V_i ) @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_i @ V_xs @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__drop_H_0) ).
thf(364,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Onth @ V_xs @ V_n @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__drop__conv__nth_0) ).
thf(365,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_y @ T_a )
= ( c_List_Olist_OCons @ V_y @ V_xs @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I2_J_0) ).
thf(366,axiom,
! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i @ V_y @ T_a )
= ( c_List_Olist__update @ V_xs @ V_i @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__overwrite_0) ).
thf(367,axiom,
! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_j: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_j @ T_a )
= ( c_List_Onth @ V_xs @ V_j @ T_a ) )
| ( V_i = V_j )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__list__update_1) ).
thf(368,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_i: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_Suc @ V_i ) @ V_y @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist__update @ V_xs @ V_i @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I3_J_0) ).
thf(369,axiom,
! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_i_H: $i,V_x_H: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i_H @ V_x_H @ T_a )
= ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i_H @ V_x_H @ T_a ) @ V_i @ V_x @ T_a ) )
| ( V_i = V_i_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__swap_0) ).
thf(370,axiom,
! [V_xs: $i,V_i: $i,T_a: $i] :
( ( c_List_Olist__update @ V_xs @ V_i @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__id_0) ).
thf(371,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i,V_i: $i,V_x: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_i @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_ys @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__append1_0) ).
thf(372,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i,V_n: $i,V_x: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_n @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Olist__update @ V_xs @ V_n @ V_x @ T_a ) @ V_ys @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__append_0) ).
thf(373,axiom,
! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i @ T_a )
= V_x )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__list__update__eq_0) ).
thf(374,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_xa: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_x @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( ( c_List_Onth @ ( c_List_Olist__update @ V_xs @ V_x @ V_xa @ T_a ) @ V_x @ T_a )
= V_xa ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__list__update_0) ).
thf(375,axiom,
! [V_i: $i,V_xs: $i,T_a: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( ( c_List_Olist__update @ V_xs @ V_i @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ T_a )
= V_xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__same__conv_1) ).
thf(376,axiom,
! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_j: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_j @ T_a )
= ( c_List_Onth @ V_xs @ V_j @ T_a ) )
| ( V_i = V_j ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__list__update__neq_0) ).
thf(377,axiom,
! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__list__update_0) ).
thf(378,axiom,
! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a )
!= V_xs )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( ( c_List_Onth @ V_xs @ V_i @ T_a )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__same__conv_0) ).
thf(379,axiom,
! [T_a: $i,V_k: $i,V_x: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_k @ V_x @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__nonempty_1) ).
thf(380,axiom,
! [T_a: $i,V_i: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_i @ V_y @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I1_J_0) ).
thf(381,axiom,
! [T_a: $i,V_i: $i,V_v: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_i @ V_v @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update_Osimps_I1_J_0) ).
thf(382,axiom,
! [V_xs: $i,V_k: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_k @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__nonempty_0) ).
thf(383,axiom,
! [V_xs: $i,V_x: $i,V_ys: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ T_a ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_y @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__length_0) ).
thf(384,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(385,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[384]) ).
thf(386,negated_conjecture,
~ ( 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 ) ) @ ( c_List_Oappend @ v_ss @ ( c_List_Olist_OCons @ ( c_Lambda_OdB_OVar @ v_i ) @ ( 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_conjecture_4) ).
thf(387,negated_conjecture,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ v_s ) @ ( c_Lambda_OdB_OVar @ v_i ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(388,negated_conjecture,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_s ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(389,negated_conjecture,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( 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 ) ) @ ( c_Lambda_OdB_OVar @ v_i ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(390,negated_conjecture,
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_conjecture_0) ).
thf(391,plain,
$false = $false,
inference(unfold_def,[status(thm)],[385]) ).
thf(392,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(393,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(394,plain,
( ( class_Int_Onumber__ring @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(395,plain,
( ( class_Int_Oring__char__0 @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(396,plain,
( ( class_Orderings_Oorder @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(397,plain,
( ( class_Orderings_Olinorder @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(398,plain,
( ( class_Orderings_Opreorder @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(399,plain,
( ( class_Nat_Osemiring__char__0 @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(400,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(401,plain,
( ( class_Ring__and__Field_Oordered__idom @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(402,plain,
( ( class_Ring__and__Field_Ozero__neq__one @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(403,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(404,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(405,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(406,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(407,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(408,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(409,plain,
( ( class_Nat_Osemiring__char__0 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(410,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(411,plain,
( ( class_Ring__and__Field_Ozero__neq__one @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(412,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(413,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)],[22]) ).
thf(414,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)],[23]) ).
thf(415,plain,
( ( ! [V_dB1_H: $i,V_dB2_H: $i,V_nat: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(416,plain,
( ( ! [V_f: $i,V_a: $i,V_xs: $i,V_ys: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ T_a @ T_b )
= ( c_List_Ofoldl @ V_f @ ( c_List_Ofoldl @ V_f @ V_a @ V_xs @ T_a @ T_b ) @ V_ys @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(417,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)],[26]) ).
thf(418,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)],[27]) ).
thf(419,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)],[28]) ).
thf(420,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)],[29]) ).
thf(421,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)],[30]) ).
thf(422,plain,
( ( ! [V_r: $i,V_ts: $i,V_s: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(423,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)],[32]) ).
thf(424,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)],[33]) ).
thf(425,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)],[34]) ).
thf(426,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)],[35]) ).
thf(427,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)],[36]) ).
thf(428,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)],[37]) ).
thf(429,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)],[38]) ).
thf(430,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)],[39]) ).
thf(431,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)],[40]) ).
thf(432,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)],[41]) ).
thf(433,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)],[42]) ).
thf(434,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)],[43]) ).
thf(435,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)],[44]) ).
thf(436,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)],[45]) ).
thf(437,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)],[46]) ).
thf(438,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(439,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)],[48]) ).
thf(440,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)],[49]) ).
thf(441,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)],[50]) ).
thf(442,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)],[51]) ).
thf(443,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)],[52]) ).
thf(444,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)],[53]) ).
thf(445,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)],[54]) ).
thf(446,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)],[55]) ).
thf(447,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)],[56]) ).
thf(448,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)],[57]) ).
thf(449,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)],[58]) ).
thf(450,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)],[59]) ).
thf(451,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)],[60]) ).
thf(452,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)],[61]) ).
thf(453,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)],[62]) ).
thf(454,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)],[63]) ).
thf(455,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)],[64]) ).
thf(456,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)],[65]) ).
thf(457,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)],[66]) ).
thf(458,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)],[67]) ).
thf(459,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)],[68]) ).
thf(460,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)],[69]) ).
thf(461,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)],[70]) ).
thf(462,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)],[71]) ).
thf(463,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)],[72]) ).
thf(464,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)],[73]) ).
thf(465,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)],[74]) ).
thf(466,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)],[75]) ).
thf(467,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)],[76]) ).
thf(468,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)],[77]) ).
thf(469,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)],[78]) ).
thf(470,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)],[79]) ).
thf(471,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)],[80]) ).
thf(472,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)],[81]) ).
thf(473,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)],[82]) ).
thf(474,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)],[83]) ).
thf(475,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)],[84]) ).
thf(476,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(477,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)],[86]) ).
thf(478,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)],[87]) ).
thf(479,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)],[88]) ).
thf(480,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)],[89]) ).
thf(481,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)],[90]) ).
thf(482,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)],[91]) ).
thf(483,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)],[92]) ).
thf(484,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)],[93]) ).
thf(485,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)],[94]) ).
thf(486,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)],[95]) ).
thf(487,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)],[96]) ).
thf(488,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)],[97]) ).
thf(489,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)],[98]) ).
thf(490,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)],[99]) ).
thf(491,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)],[100]) ).
thf(492,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)],[101]) ).
thf(493,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)],[102]) ).
thf(494,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)],[103]) ).
thf(495,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)],[104]) ).
thf(496,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)],[105]) ).
thf(497,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)],[106]) ).
thf(498,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)],[107]) ).
thf(499,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)],[108]) ).
thf(500,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(501,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)],[110]) ).
thf(502,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)],[111]) ).
thf(503,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)],[112]) ).
thf(504,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)],[113]) ).
thf(505,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)],[114]) ).
thf(506,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)],[115]) ).
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_r = V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(508,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)],[117]) ).
thf(509,plain,
( ( ! [V_nat: $i] :
( ( c_Lambda_OdB_OdB__size @ ( c_Lambda_OdB_OVar @ V_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(510,plain,
( ( ! [V_nat: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_Lambda_OdB_OVar @ V_nat ) @ tc_Lambda_OdB )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(511,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)],[120]) ).
thf(512,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Ohd @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(513,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)],[122]) ).
thf(514,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Otl @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Otl @ V_xs @ T_a ) @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(515,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)],[124]) ).
thf(516,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)],[125]) ).
thf(517,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)],[126]) ).
thf(518,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)],[127]) ).
thf(519,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)],[128]) ).
thf(520,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)],[129]) ).
thf(521,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)],[130]) ).
thf(522,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)],[131]) ).
thf(523,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)],[132]) ).
thf(524,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)],[133]) ).
thf(525,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)],[134]) ).
thf(526,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)],[135]) ).
thf(527,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)],[136]) ).
thf(528,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)],[137]) ).
thf(529,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)],[138]) ).
thf(530,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)],[139]) ).
thf(531,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)],[140]) ).
thf(532,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(533,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(534,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)],[143]) ).
thf(535,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)],[144]) ).
thf(536,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= V_x )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(537,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(538,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)],[147]) ).
thf(539,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)],[148]) ).
thf(540,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)],[149]) ).
thf(541,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)],[150]) ).
thf(542,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)],[151]) ).
thf(543,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Ohd @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(544,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)],[153]) ).
thf(545,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)],[154]) ).
thf(546,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)],[155]) ).
thf(547,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)],[156]) ).
thf(548,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)],[157]) ).
thf(549,plain,
( ( ! [V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(550,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)],[159]) ).
thf(551,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)],[160]) ).
thf(552,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)],[161]) ).
thf(553,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)],[162]) ).
thf(554,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Ohd @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(555,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)],[164]) ).
thf(556,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)],[165]) ).
thf(557,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otl @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(558,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)],[167]) ).
thf(559,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)],[168]) ).
thf(560,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)],[169]) ).
thf(561,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)],[170]) ).
thf(562,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)],[171]) ).
thf(563,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)],[172]) ).
thf(564,plain,
( ( ! [T_a: $i] :
( ( c_List_Otl @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(565,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)],[174]) ).
thf(566,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)],[175]) ).
thf(567,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)],[176]) ).
thf(568,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)],[177]) ).
thf(569,plain,
( ( ! [V_n: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(570,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)],[179]) ).
thf(571,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)],[180]) ).
thf(572,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)],[181]) ).
thf(573,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)],[182]) ).
thf(574,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Orotate1 @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Otl @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(575,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)],[184]) ).
thf(576,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)],[185]) ).
thf(577,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)],[186]) ).
thf(578,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)],[187]) ).
thf(579,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)],[188]) ).
thf(580,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)],[189]) ).
thf(581,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)],[190]) ).
thf(582,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)],[191]) ).
thf(583,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)],[192]) ).
thf(584,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)],[193]) ).
thf(585,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)],[194]) ).
thf(586,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)],[195]) ).
thf(587,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)],[196]) ).
thf(588,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)],[197]) ).
thf(589,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)],[198]) ).
thf(590,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)],[199]) ).
thf(591,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)],[200]) ).
thf(592,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)],[201]) ).
thf(593,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)],[202]) ).
thf(594,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)],[203]) ).
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)],[204]) ).
thf(596,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)],[205]) ).
thf(597,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)],[206]) ).
thf(598,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_xs @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(599,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)],[208]) ).
thf(600,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(601,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)],[210]) ).
thf(602,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)],[211]) ).
thf(603,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)],[212]) ).
thf(604,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)],[213]) ).
thf(605,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)],[214]) ).
thf(606,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)],[215]) ).
thf(607,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)],[216]) ).
thf(608,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)],[217]) ).
thf(609,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)],[218]) ).
thf(610,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)],[219]) ).
thf(611,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)],[220]) ).
thf(612,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)],[221]) ).
thf(613,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)],[222]) ).
thf(614,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)],[223]) ).
thf(615,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)],[224]) ).
thf(616,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)],[225]) ).
thf(617,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)],[226]) ).
thf(618,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(619,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)],[228]) ).
thf(620,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)],[229]) ).
thf(621,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)],[230]) ).
thf(622,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Ohd @ V_xs @ T_a )
= ( c_List_Onth @ V_xs @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(623,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ V_n @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a )
= ( c_List_Otake @ V_n @ V_xs @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(624,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)],[233]) ).
thf(625,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)],[234]) ).
thf(626,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)],[235]) ).
thf(627,plain,
( ( ! [V_v: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Otake @ ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(628,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)],[237]) ).
thf(629,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)],[238]) ).
thf(630,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ V_ys @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ ( c_List_Ohd @ V_ys @ T_a ) @ ( c_List_Osplice @ V_xs @ ( c_List_Otl @ V_ys @ T_a ) @ T_a ) @ T_a ) @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(631,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ ( c_Suc @ V_n ) @ V_xs @ T_a )
= ( c_List_Olist_OCons @ ( c_List_Ohd @ V_xs @ T_a ) @ ( c_List_Otake @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(632,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)],[241]) ).
thf(633,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)],[242]) ).
thf(634,plain,
( ( ! [T_a: $i,V_ys: $i] :
( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a ) @ T_a )
= ( c_List_Ohd @ V_ys @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(635,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)],[244]) ).
thf(636,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a )
= ( c_List_Otl @ ( c_List_Otake @ ( c_Suc @ V_n ) @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(637,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)],[246]) ).
thf(638,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i,V_i: $i] :
( ( ( c_List_Onth @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ V_i @ T_a )
= V_x )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(639,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( c_Suc @ V_n ) @ V_x @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(640,plain,
( ( ! [V_xs: $i,T_a: $i,V_ys: $i] :
( V_xs
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(641,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)],[250]) ).
thf(642,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)],[251]) ).
thf(643,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)],[252]) ).
thf(644,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)],[253]) ).
thf(645,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i,V_i: $i] :
( ( ( c_List_Onth @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ V_i @ T_a )
= ( c_List_Onth @ V_xs @ V_i @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(646,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)],[255]) ).
thf(647,plain,
( ( ! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_Suc @ V_n ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(648,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)],[257]) ).
thf(649,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)],[258]) ).
thf(650,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)],[259]) ).
thf(651,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)],[260]) ).
thf(652,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(653,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)],[262]) ).
thf(654,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)],[263]) ).
thf(655,plain,
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(656,plain,
( ( ! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(657,plain,
( ( ! [V_n: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(658,plain,
( ( ! [V_x: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ V_x ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(659,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(660,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)],[269]) ).
thf(661,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)],[270]) ).
thf(662,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)],[271]) ).
thf(663,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(664,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(665,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)],[274]) ).
thf(666,plain,
( ( ! [V_i: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ ( c_Suc @ V_i ) @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(667,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)],[276]) ).
thf(668,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)],[277]) ).
thf(669,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)],[278]) ).
thf(670,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)],[279]) ).
thf(671,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)],[280]) ).
thf(672,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ ( c_List_Otl @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(673,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(674,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(675,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(676,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(677,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_Suc @ V_n ) @ T_a )
= ( c_List_Onth @ V_xs @ V_n @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(678,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)],[287]) ).
thf(679,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)],[288]) ).
thf(680,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_i ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(681,plain,
( ( ! [V_x: $i] : ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(682,plain,
( ( ! [V_n: $i] : ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(683,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)],[292]) ).
thf(684,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( V_n = V_m )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(685,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(686,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(687,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)],[296]) ).
thf(688,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)],[297]) ).
thf(689,plain,
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(690,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Suc @ V_nat )
!= ( c_Suc @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(691,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(692,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)],[301]) ).
thf(693,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_n: $i] :
( ( ( c_List_Onth @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_n @ T_a )
= ( c_List_Onth @ V_xs @ V_n @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(694,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)],[303]) ).
thf(695,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)],[304]) ).
thf(696,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)],[305]) ).
thf(697,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)],[306]) ).
thf(698,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)],[307]) ).
thf(699,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)],[308]) ).
thf(700,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)],[309]) ).
thf(701,plain,
( ( ! [V_xa: $i,T_a: $i,V_x: $i] :
( ( c_Suc @ ( c_Nat_Osize__class_Osize @ V_xa @ ( tc_List_Olist @ T_a ) ) )
= ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(702,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ V_xa @ ( tc_List_Olist @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(703,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)],[312]) ).
thf(704,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)],[313]) ).
thf(705,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)],[314]) ).
thf(706,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)],[315]) ).
thf(707,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(708,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)],[317]) ).
thf(709,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)],[318]) ).
thf(710,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Int_Oring__char__0 @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_Int_Onumber__class_Onumber__of @ V_x @ T_a )
!= ( c_Int_Onumber__class_Onumber__of @ V_y @ T_a ) )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(711,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
| ( ( c_Suc @ V_m )
= V_n )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(712,plain,
( ( ! [V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[321]) ).
thf(713,plain,
( ( ! [V_m: $i,V_n: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(714,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(715,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)],[324]) ).
thf(716,plain,
( ( ! [V_x: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_x ) @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(717,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(718,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(719,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Oone__class_Oone @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[328]) ).
thf(720,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(721,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)],[330]) ).
thf(722,plain,
( ( ! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(723,plain,
( ( ! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(724,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(725,plain,
( ( ! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(726,plain,
( ( ! [V_v: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Onth @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat ) @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(727,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ V_y @ ( c_List_Osplice @ V_xs @ V_ys @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(728,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Osplice @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(729,plain,
( ( ! [T_a: $i,V_ys: $i] :
( ( c_List_Osplice @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a )
= V_ys ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(730,plain,
( ( ! [V_xs: $i,V_x: $i,V_ys: $i,T_a: $i] :
( ( c_List_Onth @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ T_a ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ T_a )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(731,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)],[340]) ).
thf(732,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Oappend @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Otake @ ( c_Suc @ V_n ) @ V_xs @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(733,plain,
( ( ! [V_xs: $i,V_i: $i,T_a: $i] :
( ( V_xs
= ( c_List_Oappend @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ ( c_List_Odrop @ ( c_Suc @ V_i ) @ V_xs @ T_a ) @ T_a ) @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(734,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)],[343]) ).
thf(735,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)],[344]) ).
thf(736,plain,
( ( ! [V_n: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(737,plain,
( ( ! [V_v: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Odrop @ ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(738,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_xs @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(739,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_Suc @ V_n ) @ V_xs @ T_a )
= ( c_List_Odrop @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(740,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_n @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(741,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(742,plain,
( ( ! [V_ys: $i,V_xs: $i,T_a: $i] :
( V_ys
= ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(743,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otl @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(744,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a )
= ( c_List_Obutlast @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(745,plain,
( ( ! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_Suc @ V_n ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_n @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(746,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a )
= ( c_List_Otl @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(747,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(748,plain,
( ( ! [V_xs: $i,T_a: $i,V_zs: $i] :
( ( V_xs
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_zs @ T_a ) )
| ( ( c_List_Oappend @ V_xs @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_zs @ T_a ) @ T_a )
= V_zs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357]) ).
thf(749,plain,
( ( ! [V_xs: $i,V_i: $i,V_a: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_i @ V_a @ T_a )
= ( c_List_Oappend @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_a @ ( c_List_Odrop @ ( c_Suc @ V_i ) @ V_xs @ T_a ) @ T_a ) @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(750,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( ( c_List_Odrop @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ( ( c_List_Onth @ V_xs @ V_n @ T_a )
= V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(751,plain,
( ( ! [V_ys_092_060_094isub_0621: $i,T_a: $i,V_xs_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) @ T_a )
!= V_ys_092_060_094isub_0622 )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a )
!= V_ys_092_060_094isub_0621 )
| ( V_xs_092_060_094isub_0621
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) )
| ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) @ T_a )
= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(752,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361]) ).
thf(753,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Oappend @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[362]) ).
thf(754,plain,
( ( ! [V_xs: $i,V_i: $i,T_a: $i] :
( ( ( c_List_Olist_OCons @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ ( c_List_Odrop @ ( c_Suc @ V_i ) @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_i @ V_xs @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[363]) ).
thf(755,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Onth @ V_xs @ V_n @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[364]) ).
thf(756,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_y @ T_a )
= ( c_List_Olist_OCons @ V_y @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[365]) ).
thf(757,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i @ V_y @ T_a )
= ( c_List_Olist__update @ V_xs @ V_i @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(758,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_j: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_j @ T_a )
= ( c_List_Onth @ V_xs @ V_j @ T_a ) )
| ( V_i = V_j )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(759,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_i: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_Suc @ V_i ) @ V_y @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist__update @ V_xs @ V_i @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368]) ).
thf(760,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_i_H: $i,V_x_H: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i_H @ V_x_H @ T_a )
= ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i_H @ V_x_H @ T_a ) @ V_i @ V_x @ T_a ) )
| ( V_i = V_i_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[369]) ).
thf(761,plain,
( ( ! [V_xs: $i,V_i: $i,T_a: $i] :
( ( c_List_Olist__update @ V_xs @ V_i @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[370]) ).
thf(762,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_i: $i,V_x: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_i @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_ys @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371]) ).
thf(763,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_n: $i,V_x: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_n @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Olist__update @ V_xs @ V_n @ V_x @ T_a ) @ V_ys @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[372]) ).
thf(764,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i @ T_a )
= V_x )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[373]) ).
thf(765,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_xa: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_x @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( ( c_List_Onth @ ( c_List_Olist__update @ V_xs @ V_x @ V_xa @ T_a ) @ V_x @ T_a )
= V_xa ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374]) ).
thf(766,plain,
( ( ! [V_i: $i,V_xs: $i,T_a: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( ( c_List_Olist__update @ V_xs @ V_i @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ T_a )
= V_xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375]) ).
thf(767,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_j: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_j @ T_a )
= ( c_List_Onth @ V_xs @ V_j @ T_a ) )
| ( V_i = V_j ) ) )
= $true ),
inference(unfold_def,[status(thm)],[376]) ).
thf(768,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377]) ).
thf(769,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a )
!= V_xs )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( ( c_List_Onth @ V_xs @ V_i @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378]) ).
thf(770,plain,
( ( ! [T_a: $i,V_k: $i,V_x: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_k @ V_x @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379]) ).
thf(771,plain,
( ( ! [T_a: $i,V_i: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_i @ V_y @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(772,plain,
( ( ! [T_a: $i,V_i: $i,V_v: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_i @ V_v @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[381]) ).
thf(773,plain,
( ( ! [V_xs: $i,V_k: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_k @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382]) ).
thf(774,plain,
( ( ! [V_xs: $i,V_x: $i,V_ys: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ T_a ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_y @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383]) ).
thf(775,plain,
( ( ~ ( 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 ) ) @ ( c_List_Oappend @ v_ss @ ( c_List_Olist_OCons @ ( c_Lambda_OdB_OVar @ v_i ) @ ( 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)],[386]) ).
thf(776,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ v_s ) @ ( c_Lambda_OdB_OVar @ v_i ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387]) ).
thf(777,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_s ) )
= $true ),
inference(unfold_def,[status(thm)],[388]) ).
thf(778,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( 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 ) ) @ ( c_Lambda_OdB_OVar @ v_i ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389]) ).
thf(779,plain,
( ( 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)],[390]) ).
thf(780,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[391]) ).
thf(781,plain,
( ( ! [V_X: $i,V_Y: $i] :
( ( V_X = V_Y )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_X ) @ V_Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[392]) ).
thf(782,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(extcnf_combined,[status(esa)],[415]) ).
thf(783,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(extcnf_combined,[status(esa)],[419]) ).
thf(784,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i] :
( V_xs
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[420]) ).
thf(785,plain,
( ( ! [V_x: $i,V_t: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_t @ T_a )
!= V_t ) )
= $true ),
inference(extcnf_combined,[status(esa)],[421]) ).
thf(786,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(extcnf_combined,[status(esa)],[422]) ).
thf(787,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(extcnf_combined,[status(esa)],[423]) ).
thf(788,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(extcnf_combined,[status(esa)],[424]) ).
thf(789,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(extcnf_combined,[status(esa)],[431]) ).
thf(790,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(extcnf_combined,[status(esa)],[432]) ).
thf(791,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(extcnf_combined,[status(esa)],[440]) ).
thf(792,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(extcnf_combined,[status(esa)],[441]) ).
thf(793,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(extcnf_combined,[status(esa)],[442]) ).
thf(794,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(extcnf_combined,[status(esa)],[443]) ).
thf(795,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(extcnf_combined,[status(esa)],[444]) ).
thf(796,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(extcnf_combined,[status(esa)],[445]) ).
thf(797,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(extcnf_combined,[status(esa)],[446]) ).
thf(798,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(extcnf_combined,[status(esa)],[447]) ).
thf(799,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(extcnf_combined,[status(esa)],[448]) ).
thf(800,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(extcnf_combined,[status(esa)],[449]) ).
thf(801,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(extcnf_combined,[status(esa)],[450]) ).
thf(802,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(extcnf_combined,[status(esa)],[451]) ).
thf(803,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(extcnf_combined,[status(esa)],[452]) ).
thf(804,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(extcnf_combined,[status(esa)],[453]) ).
thf(805,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(extcnf_combined,[status(esa)],[454]) ).
thf(806,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(extcnf_combined,[status(esa)],[455]) ).
thf(807,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(extcnf_combined,[status(esa)],[458]) ).
thf(808,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(extcnf_combined,[status(esa)],[459]) ).
thf(809,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(extcnf_combined,[status(esa)],[460]) ).
thf(810,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(extcnf_combined,[status(esa)],[461]) ).
thf(811,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(extcnf_combined,[status(esa)],[463]) ).
thf(812,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(extcnf_combined,[status(esa)],[465]) ).
thf(813,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(extcnf_combined,[status(esa)],[466]) ).
thf(814,plain,
( ( ! [V_x: $i,V_s: $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 ) )
| ! [V_t: $i] :
( ( 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(extcnf_combined,[status(esa)],[469]) ).
thf(815,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(extcnf_combined,[status(esa)],[474]) ).
thf(816,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(extcnf_combined,[status(esa)],[478]) ).
thf(817,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(extcnf_combined,[status(esa)],[479]) ).
thf(818,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(extcnf_combined,[status(esa)],[481]) ).
thf(819,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(extcnf_combined,[status(esa)],[482]) ).
thf(820,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(extcnf_combined,[status(esa)],[483]) ).
thf(821,plain,
( ( ! [V_T: $i,V_U: $i,V_e: $i] :
( ( V_T = V_U )
| ! [V_i: $i,V_ts: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[484]) ).
thf(822,plain,
( ( ! [V_ys: $i,V_xs: $i,V_r: $i,T_a: $i] :
( ( V_ys = V_xs )
| ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ! [V_y: $i,V_x: $i] :
~ ( 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(extcnf_combined,[status(esa)],[486]) ).
thf(823,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(extcnf_combined,[status(esa)],[489]) ).
thf(824,plain,
( ( ! [V_r: $i,V_y: $i,V_x: $i,V_ys: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ! [V_xs: $i,T_a: $i] :
( ( 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(extcnf_combined,[status(esa)],[490]) ).
thf(825,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(extcnf_combined,[status(esa)],[492]) ).
thf(826,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(extcnf_combined,[status(esa)],[493]) ).
thf(827,plain,
( ( ! [V_r: $i,V_y: $i,V_x: $i,V_ys: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ( V_y = V_x )
| ! [T_a: $i,V_xs: $i] :
~ ( 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(extcnf_combined,[status(esa)],[494]) ).
thf(828,plain,
( ( ! [V_ys: $i,V_xs: $i,V_y: $i,V_x: $i] :
( ( V_ys = V_xs )
| ( V_y = V_x )
| ! [V_r: $i,T_a: $i] :
~ ( 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(extcnf_combined,[status(esa)],[495]) ).
thf(829,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(extcnf_combined,[status(esa)],[498]) ).
thf(830,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(extcnf_combined,[status(esa)],[499]) ).
thf(831,plain,
( ( ! [V_x: $i] :
( ! [V_s: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= V_s )
| ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[501]) ).
thf(832,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(extcnf_combined,[status(esa)],[504]) ).
thf(833,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(extcnf_combined,[status(esa)],[506]) ).
thf(834,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(extcnf_combined,[status(esa)],[507]) ).
thf(835,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(extcnf_combined,[status(esa)],[508]) ).
thf(836,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_b: $i,V_a: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[515]) ).
thf(837,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[516]) ).
thf(838,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[517]) ).
thf(839,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_a: $i,V_b: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[518]) ).
thf(840,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ! [V_t: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_t ) @ V_t_H ) )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[519]) ).
thf(841,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(extcnf_combined,[status(esa)],[520]) ).
thf(842,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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(extcnf_combined,[status(esa)],[521]) ).
thf(843,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( 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(extcnf_combined,[status(esa)],[522]) ).
thf(844,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( 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(extcnf_combined,[status(esa)],[523]) ).
thf(845,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ tc_nat )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[524]) ).
thf(846,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( 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(extcnf_combined,[status(esa)],[526]) ).
thf(847,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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(extcnf_combined,[status(esa)],[527]) ).
thf(848,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( 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(extcnf_combined,[status(esa)],[528]) ).
thf(849,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[529]) ).
thf(850,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[530]) ).
thf(851,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[531]) ).
thf(852,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(extcnf_combined,[status(esa)],[534]) ).
thf(853,plain,
( ( ! [V_n: $i] :
( ! [V_x: $i,T_a: $i] :
( ( c_List_Ohd @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= V_x )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[536]) ).
thf(854,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(extcnf_combined,[status(esa)],[542]) ).
thf(855,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[544]) ).
thf(856,plain,
( ( ! [T_a: $i,V_z: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ! [V_y: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[545]) ).
thf(857,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(extcnf_combined,[status(esa)],[546]) ).
thf(858,plain,
( ( ! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[549]) ).
thf(859,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(extcnf_combined,[status(esa)],[553]) ).
thf(860,plain,
( ( ! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( 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(extcnf_combined,[status(esa)],[556]) ).
thf(861,plain,
( ( ! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( V_xs = V_ys )
| ! [V_y: $i,V_x: $i] :
~ ( 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(extcnf_combined,[status(esa)],[558]) ).
thf(862,plain,
( ( ! [V_r: $i,V_y: $i,V_xa: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_xa ) )
| ! [V_x: $i,T_a: $i] : ( 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(extcnf_combined,[status(esa)],[559]) ).
thf(863,plain,
( ( ! [V_x: $i,V_y: $i,V_xs: $i,V_ys: $i] :
( ( V_x = V_y )
| ( V_xs = V_ys )
| ! [V_r: $i,T_a: $i] :
~ ( 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(extcnf_combined,[status(esa)],[560]) ).
thf(864,plain,
( ( ! [V_x: $i,V_y: $i,V_r: $i,V_ys: $i] :
( ( V_x = V_y )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ! [T_a: $i,V_xs: $i] :
~ ( 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(extcnf_combined,[status(esa)],[561]) ).
thf(865,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(extcnf_combined,[status(esa)],[565]) ).
thf(866,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(extcnf_combined,[status(esa)],[568]) ).
thf(867,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(extcnf_combined,[status(esa)],[572]) ).
thf(868,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(extcnf_combined,[status(esa)],[575]) ).
thf(869,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(extcnf_combined,[status(esa)],[576]) ).
thf(870,plain,
( ( ! [V_A: $i,V_ys: $i,T_a: $i] :
( ( c_List_Olistsp @ V_A @ V_ys @ T_a )
| ! [V_xs: $i] :
~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[582]) ).
thf(871,plain,
( ( ! [V_A: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olistsp @ V_A @ V_xs @ T_a )
| ! [V_ys: $i] :
~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[583]) ).
thf(872,plain,
( ( ! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ~ ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ! [V_x: $i] : ( 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(extcnf_combined,[status(esa)],[585]) ).
thf(873,plain,
( ( ! [V_dB_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[588]) ).
thf(874,plain,
( ( ! [V_nat: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[590]) ).
thf(875,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(extcnf_combined,[status(esa)],[596]) ).
thf(876,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(extcnf_combined,[status(esa)],[597]) ).
thf(877,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[600]) ).
thf(878,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(extcnf_combined,[status(esa)],[605]) ).
thf(879,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(extcnf_combined,[status(esa)],[606]) ).
thf(880,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(extcnf_combined,[status(esa)],[611]) ).
thf(881,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(extcnf_combined,[status(esa)],[612]) ).
thf(882,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(extcnf_combined,[status(esa)],[613]) ).
thf(883,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(extcnf_combined,[status(esa)],[614]) ).
thf(884,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( V_xs
= ( c_List_Olist_ONil @ T_a ) )
| ( 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 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[617]) ).
thf(885,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ! [V_n: $i] :
( ( 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(extcnf_combined,[status(esa)],[625]) ).
thf(886,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ! [V_n: $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 @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[626]) ).
thf(887,plain,
( ( ! [V_v: $i,V_x: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ! [V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[627]) ).
thf(888,plain,
( ( ! [V_x: $i] :
( ! [V_s: $i] :
( ( 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 ) ) )
| ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[629]) ).
thf(889,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ! [V_t: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[637]) ).
thf(890,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(extcnf_combined,[status(esa)],[653]) ).
thf(891,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ! [V_m: $i,V_n: $i] :
( ( 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(extcnf_combined,[status(esa)],[660]) ).
thf(892,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ! [V_m: $i,V_n: $i] :
( ( 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(extcnf_combined,[status(esa)],[661]) ).
thf(893,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ! [V_m: $i] :
~ ( 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(extcnf_combined,[status(esa)],[665]) ).
thf(894,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a )
| ! [V_b: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[667]) ).
thf(895,plain,
( ( ! [V_r: $i,V_y: $i,T_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_y @ T_a )
| ! [V_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_a ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[668]) ).
thf(896,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ! [V_b: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[669]) ).
thf(897,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ! [V_b: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[670]) ).
thf(898,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[675]) ).
thf(899,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(extcnf_combined,[status(esa)],[676]) ).
thf(900,plain,
( ( ! [V_i: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_i ) @ V_k @ tc_nat )
| ! [V_j: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_j @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[680]) ).
thf(901,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Suc @ V_nat )
!= ( c_Suc @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[690]) ).
thf(902,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[691]) ).
thf(903,plain,
( ( ! [T_a: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ T_a )
| ! [V_m: $i,V_n: $i] :
( ( ( 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(extcnf_combined,[status(esa)],[692]) ).
thf(904,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_z: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_z ) )
| ! [V_y: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[696]) ).
thf(905,plain,
( ( ! [V_r: $i,V_b: $i,T_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a )
| ! [V_a: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[697]) ).
thf(906,plain,
( ( ! [V_r: $i,V_b: $i,T_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a )
| ! [V_a: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[698]) ).
thf(907,plain,
( ( ! [V_r: $i,V_a2: $i,V_a1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a2 ) @ V_a1 ) )
| ! [T_a: $i,T_b: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a1 ) @ V_a2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[704]) ).
thf(908,plain,
( ( ! [V_r: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_a ) )
| ! [T_a: $i,T_b: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[706]) ).
thf(909,plain,
( ( ! [T_a: $i] :
( ~ ( class_Int_Oring__char__0 @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ V_x @ T_a )
!= ( c_Int_Onumber__class_Onumber__of @ V_y @ T_a ) )
| ( V_x = V_y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[710]) ).
thf(910,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Oone__class_Oone @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[719]) ).
thf(911,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[720]) ).
thf(912,plain,
( ( ! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[722]) ).
thf(913,plain,
( ( ! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[723]) ).
thf(914,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[724]) ).
thf(915,plain,
( ( ! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[725]) ).
thf(916,plain,
( ( ! [V_v: $i,V_x: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ! [V_xs: $i,T_a: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat ) @ T_a )
= V_x ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[726]) ).
thf(917,plain,
( ( ! [V_e: $i,V_us: $i,V_T: $i,V_U: $i,V_i: $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 ) )
| ! [V_ts: $i] :
( ~ ( 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 )
| ! [V_Ts: $i] :
~ ( 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(extcnf_combined,[status(esa)],[735]) ).
thf(918,plain,
( ( ! [V_v: $i,V_x: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ! [V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[737]) ).
thf(919,plain,
( ( ! [V_xs: $i,T_a: $i,V_zs: $i] :
( ( V_xs
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_zs @ T_a ) )
| ( ( c_List_Oappend @ V_xs @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_zs @ T_a ) @ T_a )
= V_zs ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[748]) ).
thf(920,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ! [V_ys: $i] :
( ( c_List_Odrop @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ( ( c_List_Onth @ V_xs @ V_n @ T_a )
= V_y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[750]) ).
thf(921,plain,
( ( ! [V_ys_092_060_094isub_0621: $i,T_a: $i,V_xs_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) @ T_a )
!= V_ys_092_060_094isub_0622 )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a )
!= V_ys_092_060_094isub_0621 )
| ( V_xs_092_060_094isub_0621
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) )
| ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) @ T_a )
= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[751]) ).
thf(922,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_i_H: $i] :
( ! [V_x_H: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i_H @ V_x_H @ T_a )
= ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i_H @ V_x_H @ T_a ) @ V_i @ V_x @ T_a ) )
| ( V_i = V_i_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[760]) ).
thf(923,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_i: $i] :
( ! [V_x: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_i @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_ys @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[762]) ).
thf(924,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_n: $i] :
( ! [V_x: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_n @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Olist__update @ V_xs @ V_n @ V_x @ T_a ) @ V_ys @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[763]) ).
thf(925,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_x @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ! [V_xa: $i] :
( ( c_List_Onth @ ( c_List_Olist__update @ V_xs @ V_x @ V_xa @ T_a ) @ V_x @ T_a )
= V_xa ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[765]) ).
thf(926,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a )
!= V_xs )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( ( c_List_Onth @ V_xs @ V_i @ T_a )
= V_x ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[769]) ).
thf(927,plain,
( ( ! [V_xs: $i,V_k: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_k @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[773]) ).
thf(928,plain,
( ( 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)],[779]) ).
thf(929,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( 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 ) ) @ ( c_Lambda_OdB_OVar @ v_i ) ) ) )
= $true ),
inference(copy,[status(thm)],[778]) ).
thf(930,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_s ) )
= $true ),
inference(copy,[status(thm)],[777]) ).
thf(931,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ v_s ) @ ( c_Lambda_OdB_OVar @ v_i ) ) ) )
= $true ),
inference(copy,[status(thm)],[776]) ).
thf(932,plain,
( ( ~ ( 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 ) ) @ ( c_List_Oappend @ v_ss @ ( c_List_Olist_OCons @ ( c_Lambda_OdB_OVar @ v_i ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(copy,[status(thm)],[775]) ).
thf(933,plain,
( ( ! [V_xs: $i,V_x: $i,V_ys: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ T_a ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_y @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[774]) ).
thf(934,plain,
( ( ! [V_xs: $i,V_k: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_k @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[927]) ).
thf(935,plain,
( ( ! [T_a: $i,V_i: $i,V_v: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_i @ V_v @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[772]) ).
thf(936,plain,
( ( ! [T_a: $i,V_i: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_i @ V_y @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[771]) ).
thf(937,plain,
( ( ! [T_a: $i,V_k: $i,V_x: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_k @ V_x @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[770]) ).
thf(938,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a )
!= V_xs )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( ( c_List_Onth @ V_xs @ V_i @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[926]) ).
thf(939,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[768]) ).
thf(940,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_j: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_j @ T_a )
= ( c_List_Onth @ V_xs @ V_j @ T_a ) )
| ( V_i = V_j ) ) )
= $true ),
inference(copy,[status(thm)],[767]) ).
thf(941,plain,
( ( ! [V_i: $i,V_xs: $i,T_a: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( ( c_List_Olist__update @ V_xs @ V_i @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ T_a )
= V_xs ) ) )
= $true ),
inference(copy,[status(thm)],[766]) ).
thf(942,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_x @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ! [V_xa: $i] :
( ( c_List_Onth @ ( c_List_Olist__update @ V_xs @ V_x @ V_xa @ T_a ) @ V_x @ T_a )
= V_xa ) ) )
= $true ),
inference(copy,[status(thm)],[925]) ).
thf(943,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i @ T_a )
= V_x )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[764]) ).
thf(944,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_n: $i] :
( ! [V_x: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_n @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Olist__update @ V_xs @ V_n @ V_x @ T_a ) @ V_ys @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[924]) ).
thf(945,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_i: $i] :
( ! [V_x: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_i @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_ys @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[923]) ).
thf(946,plain,
( ( ! [V_xs: $i,V_i: $i,T_a: $i] :
( ( c_List_Olist__update @ V_xs @ V_i @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[761]) ).
thf(947,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_i_H: $i] :
( ! [V_x_H: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i_H @ V_x_H @ T_a )
= ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i_H @ V_x_H @ T_a ) @ V_i @ V_x @ T_a ) )
| ( V_i = V_i_H ) ) )
= $true ),
inference(copy,[status(thm)],[922]) ).
thf(948,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_i: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_Suc @ V_i ) @ V_y @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist__update @ V_xs @ V_i @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[759]) ).
thf(949,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_j: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_j @ T_a )
= ( c_List_Onth @ V_xs @ V_j @ T_a ) )
| ( V_i = V_j )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[758]) ).
thf(950,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i @ V_y @ T_a )
= ( c_List_Olist__update @ V_xs @ V_i @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[757]) ).
thf(951,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_y @ T_a )
= ( c_List_Olist_OCons @ V_y @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[756]) ).
thf(952,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Onth @ V_xs @ V_n @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[755]) ).
thf(953,plain,
( ( ! [V_xs: $i,V_i: $i,T_a: $i] :
( ( ( c_List_Olist_OCons @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ ( c_List_Odrop @ ( c_Suc @ V_i ) @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_i @ V_xs @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[754]) ).
thf(954,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Oappend @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[753]) ).
thf(955,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[752]) ).
thf(956,plain,
( ( ! [V_ys_092_060_094isub_0621: $i,T_a: $i,V_xs_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) @ T_a )
!= V_ys_092_060_094isub_0622 )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a )
!= V_ys_092_060_094isub_0621 )
| ( V_xs_092_060_094isub_0621
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) )
| ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) @ T_a )
= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[921]) ).
thf(957,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ! [V_ys: $i] :
( ( c_List_Odrop @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ( ( c_List_Onth @ V_xs @ V_n @ T_a )
= V_y ) ) )
= $true ),
inference(copy,[status(thm)],[920]) ).
thf(958,plain,
( ( ! [V_xs: $i,V_i: $i,V_a: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_i @ V_a @ T_a )
= ( c_List_Oappend @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_a @ ( c_List_Odrop @ ( c_Suc @ V_i ) @ V_xs @ T_a ) @ T_a ) @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[749]) ).
thf(959,plain,
( ( ! [V_xs: $i,T_a: $i,V_zs: $i] :
( ( V_xs
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_zs @ T_a ) )
| ( ( c_List_Oappend @ V_xs @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_zs @ T_a ) @ T_a )
= V_zs ) ) )
= $true ),
inference(copy,[status(thm)],[919]) ).
thf(960,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[747]) ).
thf(961,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a )
= ( c_List_Otl @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[746]) ).
thf(962,plain,
( ( ! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_Suc @ V_n ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_n @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[745]) ).
thf(963,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a )
= ( c_List_Obutlast @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[744]) ).
thf(964,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otl @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[743]) ).
thf(965,plain,
( ( ! [V_ys: $i,V_xs: $i,T_a: $i] :
( V_ys
= ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[742]) ).
thf(966,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[741]) ).
thf(967,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_n @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[740]) ).
thf(968,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_Suc @ V_n ) @ V_xs @ T_a )
= ( c_List_Odrop @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[739]) ).
thf(969,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_xs @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[738]) ).
thf(970,plain,
( ( ! [V_v: $i,V_x: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ! [V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[918]) ).
thf(971,plain,
( ( ! [V_n: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[736]) ).
thf(972,plain,
( ( ! [V_e: $i,V_us: $i,V_T: $i,V_U: $i,V_i: $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 ) )
| ! [V_ts: $i] :
( ~ ( 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 )
| ! [V_Ts: $i] :
~ ( 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)],[917]) ).
thf(973,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)],[734]) ).
thf(974,plain,
( ( ! [V_xs: $i,V_i: $i,T_a: $i] :
( ( V_xs
= ( c_List_Oappend @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ ( c_List_Odrop @ ( c_Suc @ V_i ) @ V_xs @ T_a ) @ T_a ) @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[733]) ).
thf(975,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Oappend @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Otake @ ( c_Suc @ V_n ) @ V_xs @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[732]) ).
thf(976,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)],[731]) ).
thf(977,plain,
( ( ! [V_xs: $i,V_x: $i,V_ys: $i,T_a: $i] :
( ( c_List_Onth @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ T_a ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ T_a )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[730]) ).
thf(978,plain,
( ( ! [T_a: $i,V_ys: $i] :
( ( c_List_Osplice @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a )
= V_ys ) )
= $true ),
inference(copy,[status(thm)],[729]) ).
thf(979,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Osplice @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[728]) ).
thf(980,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ V_y @ ( c_List_Osplice @ V_xs @ V_ys @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[727]) ).
thf(981,plain,
( ( ! [V_v: $i,V_x: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ! [V_xs: $i,T_a: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat ) @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[916]) ).
thf(982,plain,
( ( ! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ) )
= $true ),
inference(copy,[status(thm)],[915]) ).
thf(983,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ) )
= $true ),
inference(copy,[status(thm)],[914]) ).
thf(984,plain,
( ( ! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[913]) ).
thf(985,plain,
( ( ! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[912]) ).
thf(986,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)],[721]) ).
thf(987,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[911]) ).
thf(988,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Oone__class_Oone @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[910]) ).
thf(989,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[718]) ).
thf(990,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[717]) ).
thf(991,plain,
( ( ! [V_x: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_x ) @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[716]) ).
thf(992,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)],[715]) ).
thf(993,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[714]) ).
thf(994,plain,
( ( ! [V_m: $i,V_n: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[713]) ).
thf(995,plain,
( ( ! [V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[712]) ).
thf(996,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
| ( ( c_Suc @ V_m )
= V_n )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[711]) ).
thf(997,plain,
( ( ! [T_a: $i] :
( ~ ( class_Int_Oring__char__0 @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ V_x @ T_a )
!= ( c_Int_Onumber__class_Onumber__of @ V_y @ T_a ) )
| ( V_x = V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[909]) ).
thf(998,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)],[709]) ).
thf(999,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)],[708]) ).
thf(1000,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[707]) ).
thf(1001,plain,
( ( ! [V_r: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_a ) )
| ! [T_a: $i,T_b: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[908]) ).
thf(1002,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)],[705]) ).
thf(1003,plain,
( ( ! [V_r: $i,V_a2: $i,V_a1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a2 ) @ V_a1 ) )
| ! [T_a: $i,T_b: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a1 ) @ V_a2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[907]) ).
thf(1004,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)],[703]) ).
thf(1005,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ V_xa @ ( tc_List_Olist @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[702]) ).
thf(1006,plain,
( ( ! [V_xa: $i,T_a: $i,V_x: $i] :
( ( c_Suc @ ( c_Nat_Osize__class_Osize @ V_xa @ ( tc_List_Olist @ T_a ) ) )
= ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[701]) ).
thf(1007,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)],[700]) ).
thf(1008,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)],[699]) ).
thf(1009,plain,
( ( ! [V_r: $i,V_b: $i,T_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a )
| ! [V_a: $i] :
( ~ ( 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)],[906]) ).
thf(1010,plain,
( ( ! [V_r: $i,V_b: $i,T_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a )
| ! [V_a: $i] :
( ~ ( 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)],[905]) ).
thf(1011,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_z: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_z ) )
| ! [V_y: $i] :
( ~ ( 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)],[904]) ).
thf(1012,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)],[695]) ).
thf(1013,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)],[694]) ).
thf(1014,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_n: $i] :
( ( ( c_List_Onth @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_n @ T_a )
= ( c_List_Onth @ V_xs @ V_n @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[693]) ).
thf(1015,plain,
( ( ! [T_a: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ T_a )
| ! [V_m: $i,V_n: $i] :
( ( ( 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)],[903]) ).
thf(1016,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[902]) ).
thf(1017,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Suc @ V_nat )
!= ( c_Suc @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(copy,[status(thm)],[901]) ).
thf(1018,plain,
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[689]) ).
thf(1019,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)],[688]) ).
thf(1020,plain,
( ( ! [T_a: $i] :
( ( c_Predicate_Oconversep @ ( c_fequal @ T_a ) @ T_a @ T_a )
= ( c_fequal @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[687]) ).
thf(1021,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[686]) ).
thf(1022,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[685]) ).
thf(1023,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( V_n = V_m )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[684]) ).
thf(1024,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)],[683]) ).
thf(1025,plain,
( ( ! [V_n: $i] : ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[682]) ).
thf(1026,plain,
( ( ! [V_x: $i] : ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[681]) ).
thf(1027,plain,
( ( ! [V_i: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_i ) @ V_k @ tc_nat )
| ! [V_j: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_j @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[900]) ).
thf(1028,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)],[679]) ).
thf(1029,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)],[678]) ).
thf(1030,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_Suc @ V_n ) @ T_a )
= ( c_List_Onth @ V_xs @ V_n @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[677]) ).
thf(1031,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(copy,[status(thm)],[899]) ).
thf(1032,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[898]) ).
thf(1033,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[674]) ).
thf(1034,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[673]) ).
thf(1035,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ ( c_List_Otl @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[672]) ).
thf(1036,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)],[671]) ).
thf(1037,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ! [V_b: $i] :
( ~ ( 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)],[897]) ).
thf(1038,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ! [V_b: $i] :
( ~ ( 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)],[896]) ).
thf(1039,plain,
( ( ! [V_r: $i,V_y: $i,T_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_y @ T_a )
| ! [V_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_a ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[895]) ).
thf(1040,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a )
| ! [V_b: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[894]) ).
thf(1041,plain,
( ( ! [V_i: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ ( c_Suc @ V_i ) @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[666]) ).
thf(1042,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ! [V_m: $i] :
~ ( 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)],[893]) ).
thf(1043,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[664]) ).
thf(1044,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[663]) ).
thf(1045,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)],[662]) ).
thf(1046,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ! [V_m: $i,V_n: $i] :
( ( 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)],[892]) ).
thf(1047,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ! [V_m: $i,V_n: $i] :
( ( 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)],[891]) ).
thf(1048,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[659]) ).
thf(1049,plain,
( ( ! [V_x: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ V_x ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[658]) ).
thf(1050,plain,
( ( ! [V_n: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[657]) ).
thf(1051,plain,
( ( ! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[656]) ).
thf(1052,plain,
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= $true ),
inference(copy,[status(thm)],[655]) ).
thf(1053,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)],[654]) ).
thf(1054,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)],[890]) ).
thf(1055,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[652]) ).
thf(1056,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)],[651]) ).
thf(1057,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)],[650]) ).
thf(1058,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)],[649]) ).
thf(1059,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)],[648]) ).
thf(1060,plain,
( ( ! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_Suc @ V_n ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[647]) ).
thf(1061,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)],[646]) ).
thf(1062,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i,V_i: $i] :
( ( ( c_List_Onth @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ V_i @ T_a )
= ( c_List_Onth @ V_xs @ V_i @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[645]) ).
thf(1063,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)],[644]) ).
thf(1064,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)],[643]) ).
thf(1065,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)],[642]) ).
thf(1066,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)],[641]) ).
thf(1067,plain,
( ( ! [V_xs: $i,T_a: $i,V_ys: $i] :
( V_xs
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[640]) ).
thf(1068,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( c_Suc @ V_n ) @ V_x @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[639]) ).
thf(1069,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i,V_i: $i] :
( ( ( c_List_Onth @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ V_i @ T_a )
= V_x )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[638]) ).
thf(1070,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ! [V_t: $i] :
( ~ ( 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)],[889]) ).
thf(1071,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a )
= ( c_List_Otl @ ( c_List_Otake @ ( c_Suc @ V_n ) @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[636]) ).
thf(1072,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)],[635]) ).
thf(1073,plain,
( ( ! [T_a: $i,V_ys: $i] :
( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a ) @ T_a )
= ( c_List_Ohd @ V_ys @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[634]) ).
thf(1074,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)],[633]) ).
thf(1075,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)],[632]) ).
thf(1076,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ ( c_Suc @ V_n ) @ V_xs @ T_a )
= ( c_List_Olist_OCons @ ( c_List_Ohd @ V_xs @ T_a ) @ ( c_List_Otake @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[631]) ).
thf(1077,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ V_ys @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ ( c_List_Ohd @ V_ys @ T_a ) @ ( c_List_Osplice @ V_xs @ ( c_List_Otl @ V_ys @ T_a ) @ T_a ) @ T_a ) @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[630]) ).
thf(1078,plain,
( ( ! [V_x: $i] :
( ! [V_s: $i] :
( ( 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 ) ) )
| ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[888]) ).
thf(1079,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)],[628]) ).
thf(1080,plain,
( ( ! [V_v: $i,V_x: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ! [V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[887]) ).
thf(1081,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ! [V_n: $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 @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[886]) ).
thf(1082,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ! [V_n: $i] :
( ( 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)],[885]) ).
thf(1083,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)],[624]) ).
thf(1084,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ V_n @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a )
= ( c_List_Otake @ V_n @ V_xs @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[623]) ).
thf(1085,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Ohd @ V_xs @ T_a )
= ( c_List_Onth @ V_xs @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[622]) ).
thf(1086,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)],[621]) ).
thf(1087,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)],[620]) ).
thf(1088,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)],[619]) ).
thf(1089,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[618]) ).
thf(1090,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( V_xs
= ( c_List_Olist_ONil @ T_a ) )
| ( 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 ) ) )
= $true ),
inference(copy,[status(thm)],[884]) ).
thf(1091,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)],[616]) ).
thf(1092,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)],[615]) ).
thf(1093,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)],[883]) ).
thf(1094,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)],[882]) ).
thf(1095,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)],[881]) ).
thf(1096,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)],[880]) ).
thf(1097,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)],[610]) ).
thf(1098,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)],[609]) ).
thf(1099,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)],[608]) ).
thf(1100,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)],[607]) ).
thf(1101,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)],[879]) ).
thf(1102,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)],[878]) ).
thf(1103,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)],[604]) ).
thf(1104,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)],[603]) ).
thf(1105,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)],[602]) ).
thf(1106,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)],[601]) ).
thf(1107,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[877]) ).
thf(1108,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)],[599]) ).
thf(1109,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_xs @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[598]) ).
thf(1110,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)],[876]) ).
thf(1111,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)],[875]) ).
thf(1112,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(1113,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)],[594]) ).
thf(1114,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)],[593]) ).
thf(1115,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)],[592]) ).
thf(1116,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)],[591]) ).
thf(1117,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)],[874]) ).
thf(1118,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)],[589]) ).
thf(1119,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)],[873]) ).
thf(1120,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)],[587]) ).
thf(1121,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)],[586]) ).
thf(1122,plain,
( ( ! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ~ ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ! [V_x: $i] : ( 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)],[872]) ).
thf(1123,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)],[584]) ).
thf(1124,plain,
( ( ! [V_A: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olistsp @ V_A @ V_xs @ T_a )
| ! [V_ys: $i] :
~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[871]) ).
thf(1125,plain,
( ( ! [V_A: $i,V_ys: $i,T_a: $i] :
( ( c_List_Olistsp @ V_A @ V_ys @ T_a )
| ! [V_xs: $i] :
~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[870]) ).
thf(1126,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)],[581]) ).
thf(1127,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)],[580]) ).
thf(1128,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)],[579]) ).
thf(1129,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)],[578]) ).
thf(1130,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)],[577]) ).
thf(1131,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)],[869]) ).
thf(1132,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)],[868]) ).
thf(1133,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Orotate1 @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Otl @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[574]) ).
thf(1134,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)],[573]) ).
thf(1135,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)],[867]) ).
thf(1136,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)],[571]) ).
thf(1137,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)],[570]) ).
thf(1138,plain,
( ( ! [V_n: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[569]) ).
thf(1139,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)],[866]) ).
thf(1140,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)],[567]) ).
thf(1141,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)],[566]) ).
thf(1142,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)],[865]) ).
thf(1143,plain,
( ( ! [T_a: $i] :
( ( c_List_Otl @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[564]) ).
thf(1144,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)],[563]) ).
thf(1145,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)],[562]) ).
thf(1146,plain,
( ( ! [V_x: $i,V_y: $i,V_r: $i,V_ys: $i] :
( ( V_x = V_y )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ! [T_a: $i,V_xs: $i] :
~ ( 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)],[864]) ).
thf(1147,plain,
( ( ! [V_x: $i,V_y: $i,V_xs: $i,V_ys: $i] :
( ( V_x = V_y )
| ( V_xs = V_ys )
| ! [V_r: $i,T_a: $i] :
~ ( 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)],[863]) ).
thf(1148,plain,
( ( ! [V_r: $i,V_y: $i,V_xa: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_xa ) )
| ! [V_x: $i,T_a: $i] : ( 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)],[862]) ).
thf(1149,plain,
( ( ! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( V_xs = V_ys )
| ! [V_y: $i,V_x: $i] :
~ ( 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)],[861]) ).
thf(1150,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otl @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[557]) ).
thf(1151,plain,
( ( ! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( 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)],[860]) ).
thf(1152,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)],[555]) ).
thf(1153,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Ohd @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[554]) ).
thf(1154,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)],[859]) ).
thf(1155,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)],[552]) ).
thf(1156,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)],[551]) ).
thf(1157,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)],[550]) ).
thf(1158,plain,
( ( ! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[858]) ).
thf(1159,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)],[548]) ).
thf(1160,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)],[547]) ).
thf(1161,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)],[857]) ).
thf(1162,plain,
( ( ! [T_a: $i,V_z: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ! [V_y: $i] :
( ~ ( 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)],[856]) ).
thf(1163,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
( ~ ( 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)],[855]) ).
thf(1164,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Ohd @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[543]) ).
thf(1165,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)],[854]) ).
thf(1166,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)],[541]) ).
thf(1167,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)],[540]) ).
thf(1168,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)],[539]) ).
thf(1169,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)],[538]) ).
thf(1170,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[537]) ).
thf(1171,plain,
( ( ! [V_n: $i] :
( ! [V_x: $i,T_a: $i] :
( ( c_List_Ohd @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= V_x )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[853]) ).
thf(1172,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)],[535]) ).
thf(1173,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)],[852]) ).
thf(1174,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[533]) ).
thf(1175,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[532]) ).
thf(1176,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[851]) ).
thf(1177,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[850]) ).
thf(1178,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[849]) ).
thf(1179,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( 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)],[848]) ).
thf(1180,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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)],[847]) ).
thf(1181,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( 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)],[846]) ).
thf(1182,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)],[525]) ).
thf(1183,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ tc_nat )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[845]) ).
thf(1184,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( 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)],[844]) ).
thf(1185,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( 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)],[843]) ).
thf(1186,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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)],[842]) ).
thf(1187,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)],[841]) ).
thf(1188,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ! [V_t: $i] :
( ~ ( 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)],[840]) ).
thf(1189,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_a: $i,V_b: $i] :
( ~ ( 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)],[839]) ).
thf(1190,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ~ ( 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)],[838]) ).
thf(1191,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ~ ( 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)],[837]) ).
thf(1192,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_b: $i,V_a: $i] :
( ~ ( 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)],[836]) ).
thf(1193,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Otl @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Otl @ V_xs @ T_a ) @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[514]) ).
thf(1194,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)],[513]) ).
thf(1195,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Ohd @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[512]) ).
thf(1196,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)],[511]) ).
thf(1197,plain,
( ( ! [V_nat: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_Lambda_OdB_OVar @ V_nat ) @ tc_Lambda_OdB )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[510]) ).
thf(1198,plain,
( ( ! [V_nat: $i] :
( ( c_Lambda_OdB_OdB__size @ ( c_Lambda_OdB_OVar @ V_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[509]) ).
thf(1199,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)],[835]) ).
thf(1200,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)],[834]) ).
thf(1201,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)],[833]) ).
thf(1202,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)],[505]) ).
thf(1203,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)],[832]) ).
thf(1204,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)],[503]) ).
thf(1205,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)],[502]) ).
thf(1206,plain,
( ( ! [V_x: $i] :
( ! [V_s: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= V_s )
| ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[831]) ).
thf(1207,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[500]) ).
thf(1208,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)],[830]) ).
thf(1209,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)],[829]) ).
thf(1210,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)],[497]) ).
thf(1211,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)],[496]) ).
thf(1212,plain,
( ( ! [V_ys: $i,V_xs: $i,V_y: $i,V_x: $i] :
( ( V_ys = V_xs )
| ( V_y = V_x )
| ! [V_r: $i,T_a: $i] :
~ ( 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)],[828]) ).
thf(1213,plain,
( ( ! [V_r: $i,V_y: $i,V_x: $i,V_ys: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ( V_y = V_x )
| ! [T_a: $i,V_xs: $i] :
~ ( 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)],[827]) ).
thf(1214,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)],[826]) ).
thf(1215,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)],[825]) ).
thf(1216,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)],[491]) ).
thf(1217,plain,
( ( ! [V_r: $i,V_y: $i,V_x: $i,V_ys: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ! [V_xs: $i,T_a: $i] :
( ( 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)],[824]) ).
thf(1218,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)],[823]) ).
thf(1219,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)],[488]) ).
thf(1220,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)],[487]) ).
thf(1221,plain,
( ( ! [V_ys: $i,V_xs: $i,V_r: $i,T_a: $i] :
( ( V_ys = V_xs )
| ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ! [V_y: $i,V_x: $i] :
~ ( 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)],[822]) ).
thf(1222,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)],[485]) ).
thf(1223,plain,
( ( ! [V_T: $i,V_U: $i,V_e: $i] :
( ( V_T = V_U )
| ! [V_i: $i,V_ts: $i] :
( ~ ( 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)],[821]) ).
thf(1224,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)],[820]) ).
thf(1225,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)],[819]) ).
thf(1226,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)],[818]) ).
thf(1227,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)],[480]) ).
thf(1228,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)],[817]) ).
thf(1229,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)],[816]) ).
thf(1230,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)],[477]) ).
thf(1231,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)],[476]) ).
thf(1232,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)],[475]) ).
thf(1233,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)],[815]) ).
thf(1234,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)],[473]) ).
thf(1235,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)],[472]) ).
thf(1236,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)],[471]) ).
thf(1237,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)],[470]) ).
thf(1238,plain,
( ( ! [V_x: $i,V_s: $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 ) )
| ! [V_t: $i] :
( ( 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)],[814]) ).
thf(1239,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)],[468]) ).
thf(1240,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)],[467]) ).
thf(1241,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)],[813]) ).
thf(1242,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)],[812]) ).
thf(1243,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)],[464]) ).
thf(1244,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)],[811]) ).
thf(1245,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)],[462]) ).
thf(1246,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)],[810]) ).
thf(1247,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)],[809]) ).
thf(1248,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)],[808]) ).
thf(1249,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)],[807]) ).
thf(1250,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)],[457]) ).
thf(1251,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)],[456]) ).
thf(1252,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)],[806]) ).
thf(1253,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)],[805]) ).
thf(1254,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)],[804]) ).
thf(1255,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)],[803]) ).
thf(1256,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)],[802]) ).
thf(1257,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)],[801]) ).
thf(1258,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)],[800]) ).
thf(1259,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)],[799]) ).
thf(1260,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)],[798]) ).
thf(1261,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)],[797]) ).
thf(1262,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)],[796]) ).
thf(1263,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)],[795]) ).
thf(1264,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)],[794]) ).
thf(1265,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)],[793]) ).
thf(1266,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)],[792]) ).
thf(1267,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)],[791]) ).
thf(1268,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)],[439]) ).
thf(1269,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[438]) ).
thf(1270,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)],[437]) ).
thf(1271,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)],[436]) ).
thf(1272,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)],[435]) ).
thf(1273,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)],[434]) ).
thf(1274,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)],[433]) ).
thf(1275,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)],[790]) ).
thf(1276,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)],[789]) ).
thf(1277,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)],[430]) ).
thf(1278,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)],[429]) ).
thf(1279,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)],[428]) ).
thf(1280,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)],[427]) ).
thf(1281,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)],[426]) ).
thf(1282,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)],[425]) ).
thf(1283,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)],[788]) ).
thf(1284,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)],[787]) ).
thf(1285,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)],[786]) ).
thf(1286,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)],[785]) ).
thf(1287,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)],[784]) ).
thf(1288,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)],[783]) ).
thf(1289,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)],[418]) ).
thf(1290,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)],[417]) ).
thf(1291,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)],[416]) ).
thf(1292,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)],[782]) ).
thf(1293,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)],[414]) ).
thf(1294,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)],[413]) ).
thf(1295,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(1296,plain,
( ( class_Ring__and__Field_Ozero__neq__one @ tc_nat )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(1297,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(1298,plain,
( ( class_Nat_Osemiring__char__0 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(1299,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(1300,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(1301,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[406]) ).
thf(1302,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(1303,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(1304,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(1305,plain,
( ( class_Ring__and__Field_Ozero__neq__one @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(1306,plain,
( ( class_Ring__and__Field_Oordered__idom @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(1307,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[400]) ).
thf(1308,plain,
( ( class_Nat_Osemiring__char__0 @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[399]) ).
thf(1309,plain,
( ( class_Orderings_Opreorder @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(1310,plain,
( ( class_Orderings_Olinorder @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(1311,plain,
( ( class_Orderings_Oorder @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(1312,plain,
( ( class_Int_Oring__char__0 @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[395]) ).
thf(1313,plain,
( ( class_Int_Onumber__ring @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[394]) ).
thf(1314,plain,
( ( ! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_x ) @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(1315,plain,
( ( ! [V_X: $i,V_Y: $i] :
( ( V_X = V_Y )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_X ) @ V_Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[781]) ).
thf(1316,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[780]) ).
thf(1317,plain,
( ( 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 ) ) @ ( c_List_Oappend @ v_ss @ ( c_List_Olist_OCons @ ( c_Lambda_OdB_OVar @ v_i ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[932]) ).
thf(1318,plain,
! [SV1: $i] :
( ( ! [SY1095: $i,SY1096: $i,SY1097: $i,SY1098: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV1 @ ( c_List_Olist_OCons @ SY1095 @ SY1096 @ SY1097 ) @ SY1097 ) @ ( c_Nat_Osize__class_Osize @ SV1 @ ( tc_List_Olist @ SY1097 ) ) @ SY1098 @ SY1097 )
= ( c_List_Oappend @ SV1 @ ( c_List_Olist_OCons @ SY1098 @ SY1096 @ SY1097 ) @ SY1097 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1319,plain,
! [SV2: $i] :
( ( ! [SY1099: $i,SY1100: $i,SY1101: $i] :
( ( ( c_List_Olist__update @ SV2 @ SY1099 @ SY1100 @ SY1101 )
!= ( c_List_Olist_ONil @ SY1101 ) )
| ( SV2
= ( c_List_Olist_ONil @ SY1101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1320,plain,
! [SV3: $i] :
( ( ! [SY1102: $i,SY1103: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV3 ) @ SY1102 @ SY1103 @ SV3 )
= ( c_List_Olist_ONil @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1321,plain,
! [SV4: $i] :
( ( ! [SY1104: $i,SY1105: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV4 ) @ SY1104 @ SY1105 @ SV4 )
= ( c_List_Olist_ONil @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1322,plain,
! [SV5: $i] :
( ( ! [SY1106: $i,SY1107: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV5 ) @ SY1106 @ SY1107 @ SV5 )
= ( c_List_Olist_ONil @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1323,plain,
! [SV6: $i] :
( ( ! [SY1108: $i,SY1109: $i,SY1110: $i] :
( ( ( c_List_Olist__update @ SV6 @ SY1108 @ SY1109 @ SY1110 )
!= SV6 )
| ~ ( c_HOL_Oord__class_Oless @ SY1108 @ ( c_Nat_Osize__class_Osize @ SV6 @ ( tc_List_Olist @ SY1110 ) ) @ tc_nat )
| ( ( c_List_Onth @ SV6 @ SY1108 @ SY1110 )
= SY1109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1324,plain,
! [SV7: $i] :
( ( ! [SY1111: $i,SY1112: $i,SY1113: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ SV7 @ SY1111 @ SY1112 @ SY1113 ) @ ( tc_List_Olist @ SY1113 ) )
= ( c_Nat_Osize__class_Osize @ SV7 @ ( tc_List_Olist @ SY1113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1325,plain,
! [SV8: $i] :
( ( ! [SY1114: $i,SY1115: $i,SY1116: $i,SY1117: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ SV8 @ SY1114 @ SY1115 @ SY1116 ) @ SY1117 @ SY1116 )
= ( c_List_Onth @ SV8 @ SY1117 @ SY1116 ) )
| ( SY1114 = SY1117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1326,plain,
! [SV9: $i] :
( ( ! [SY1118: $i,SY1119: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV9 @ ( c_Nat_Osize__class_Osize @ SY1118 @ ( tc_List_Olist @ SY1119 ) ) @ tc_nat )
| ( ( c_List_Olist__update @ SY1118 @ SV9 @ ( c_List_Onth @ SY1118 @ SV9 @ SY1119 ) @ SY1119 )
= SY1118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1327,plain,
! [SV10: $i] :
( ( ! [SY1120: $i,SY1121: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV10 @ ( c_Nat_Osize__class_Osize @ SY1120 @ ( tc_List_Olist @ SY1121 ) ) @ tc_nat )
| ! [SY1122: $i] :
( ( c_List_Onth @ ( c_List_Olist__update @ SY1120 @ SV10 @ SY1122 @ SY1121 ) @ SV10 @ SY1121 )
= SY1122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1328,plain,
! [SV11: $i] :
( ( ! [SY1123: $i,SY1124: $i,SY1125: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ SV11 @ SY1123 @ SY1124 @ SY1125 ) @ SY1123 @ SY1125 )
= SY1124 )
| ~ ( c_HOL_Oord__class_Oless @ SY1123 @ ( c_Nat_Osize__class_Osize @ SV11 @ ( tc_List_Olist @ SY1125 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1329,plain,
! [SV12: $i] :
( ( ! [SY1126: $i,SY1127: $i,SY1128: $i] :
( ! [SY1129: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV12 @ SY1126 @ SY1127 ) @ SY1128 @ SY1129 @ SY1127 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV12 @ SY1128 @ SY1129 @ SY1127 ) @ SY1126 @ SY1127 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1128 @ ( c_Nat_Osize__class_Osize @ SV12 @ ( tc_List_Olist @ SY1127 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(1330,plain,
! [SV13: $i] :
( ( ! [SY1130: $i,SY1131: $i,SY1132: $i] :
( ! [SY1133: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV13 @ SY1130 @ SY1131 ) @ SY1132 @ SY1133 @ SY1131 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV13 @ SY1132 @ SY1133 @ SY1131 ) @ SY1130 @ SY1131 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1132 @ ( c_Nat_Osize__class_Osize @ SV13 @ ( tc_List_Olist @ SY1131 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1331,plain,
! [SV14: $i] :
( ( ! [SY1134: $i,SY1135: $i] :
( ( c_List_Olist__update @ SV14 @ SY1134 @ ( c_List_Onth @ SV14 @ SY1134 @ SY1135 ) @ SY1135 )
= SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1332,plain,
! [SV15: $i] :
( ( ! [SY1136: $i,SY1137: $i,SY1138: $i,SY1139: $i] :
( ! [SY1140: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV15 @ SY1136 @ SY1137 @ SY1138 ) @ SY1139 @ SY1140 @ SY1138 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV15 @ SY1139 @ SY1140 @ SY1138 ) @ SY1136 @ SY1137 @ SY1138 ) )
| ( SY1136 = SY1139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1333,plain,
! [SV16: $i] :
( ( ! [SY1141: $i,SY1142: $i,SY1143: $i,SY1144: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV16 @ SY1141 @ SY1142 ) @ ( c_Suc @ SY1143 ) @ SY1144 @ SY1142 )
= ( c_List_Olist_OCons @ SV16 @ ( c_List_Olist__update @ SY1141 @ SY1143 @ SY1144 @ SY1142 ) @ SY1142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1334,plain,
! [SV17: $i] :
( ( ! [SY1145: $i,SY1146: $i,SY1147: $i,SY1148: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ SV17 @ SY1145 @ SY1146 @ SY1147 ) @ SY1148 @ SY1147 )
= ( c_List_Onth @ SV17 @ SY1148 @ SY1147 ) )
| ( SY1145 = SY1148 )
| ~ ( c_HOL_Oord__class_Oless @ SY1145 @ ( c_Nat_Osize__class_Osize @ SV17 @ ( tc_List_Olist @ SY1147 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(1335,plain,
! [SV18: $i] :
( ( ! [SY1149: $i,SY1150: $i,SY1151: $i,SY1152: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV18 @ SY1149 @ SY1150 @ SY1151 ) @ SY1149 @ SY1152 @ SY1151 )
= ( c_List_Olist__update @ SV18 @ SY1149 @ SY1152 @ SY1151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1336,plain,
! [SV19: $i] :
( ( ! [SY1153: $i,SY1154: $i,SY1155: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV19 @ SY1153 @ SY1154 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1155 @ SY1154 )
= ( c_List_Olist_OCons @ SY1155 @ SY1153 @ SY1154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1337,plain,
! [SV20: $i] :
( ( ! [SY1156: $i,SY1157: $i] :
( ( ( c_List_Ohd @ ( c_List_Odrop @ SV20 @ SY1156 @ SY1157 ) @ SY1157 )
= ( c_List_Onth @ SY1156 @ SV20 @ SY1157 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV20 @ ( c_Nat_Osize__class_Osize @ SY1156 @ ( tc_List_Olist @ SY1157 ) ) @ tc_nat )
| ( SY1156
= ( c_List_Olist_ONil @ SY1157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1338,plain,
! [SV21: $i] :
( ( ! [SY1158: $i,SY1159: $i] :
( ( ( c_List_Olist_OCons @ ( c_List_Onth @ SV21 @ SY1158 @ SY1159 ) @ ( c_List_Odrop @ ( c_Suc @ SY1158 ) @ SV21 @ SY1159 ) @ SY1159 )
= ( c_List_Odrop @ SY1158 @ SV21 @ SY1159 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1158 @ ( c_Nat_Osize__class_Osize @ SV21 @ ( tc_List_Olist @ SY1159 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1339,plain,
! [SV22: $i] :
( ( ! [SY1160: $i,SY1161: $i] :
( ( c_List_Oappend @ ( c_List_Otake @ SV22 @ SY1160 @ SY1161 ) @ ( c_List_Odrop @ SV22 @ SY1160 @ SY1161 ) @ SY1161 )
= SY1160 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1340,plain,
! [SV23: $i] :
( ( ! [SY1162: $i,SY1163: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ SV23 @ SY1162 @ SY1163 ) @ SY1163 )
= ( c_List_Olist_OCons @ SV23 @ SY1162 @ SY1163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1341,plain,
! [SV24: $i] :
( ( ! [SY1164: $i,SY1165: $i,SY1166: $i] :
( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SY1164 ) ) @ SY1165 @ SY1164 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SY1165 @ ( tc_List_Olist @ SY1164 ) ) @ SV24 @ SY1164 ) @ SY1166 @ SY1164 ) @ SY1164 )
!= SY1166 )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SY1164 ) ) @ SY1165 @ SY1164 )
!= SV24 )
| ( SY1165
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SY1165 @ ( tc_List_Olist @ SY1164 ) ) @ SV24 @ SY1164 ) )
| ( ( c_List_Oappend @ SY1165 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SY1165 @ ( tc_List_Olist @ SY1164 ) ) @ SV24 @ SY1164 ) @ SY1166 @ SY1164 ) @ SY1164 )
= ( c_List_Oappend @ SV24 @ SY1166 @ SY1164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1342,plain,
! [SV25: $i] :
( ( ! [SY1167: $i,SY1168: $i,SY1169: $i] :
( ! [SY1170: $i] :
( ( c_List_Odrop @ SV25 @ SY1167 @ SY1168 )
!= ( c_List_Olist_OCons @ SY1169 @ SY1170 @ SY1168 ) )
| ( ( c_List_Onth @ SY1167 @ SV25 @ SY1168 )
= SY1169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1343,plain,
! [SV26: $i] :
( ( ! [SY1171: $i,SY1172: $i,SY1173: $i] :
( ( ( c_List_Olist__update @ SV26 @ SY1171 @ SY1172 @ SY1173 )
= ( c_List_Oappend @ ( c_List_Otake @ SY1171 @ SV26 @ SY1173 ) @ ( c_List_Olist_OCons @ SY1172 @ ( c_List_Odrop @ ( c_Suc @ SY1171 ) @ SV26 @ SY1173 ) @ SY1173 ) @ SY1173 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1171 @ ( c_Nat_Osize__class_Osize @ SV26 @ ( tc_List_Olist @ SY1173 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1344,plain,
! [SV27: $i] :
( ( ! [SY1174: $i,SY1175: $i] :
( ( SV27
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV27 @ ( tc_List_Olist @ SY1174 ) ) @ SY1175 @ SY1174 ) )
| ( ( c_List_Oappend @ SV27 @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV27 @ ( tc_List_Olist @ SY1174 ) ) @ SY1175 @ SY1174 ) @ SY1174 )
= SY1175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1345,plain,
! [SV28: $i] :
( ( ! [SY1176: $i,SY1177: $i] :
( ( ( c_List_Olast @ ( c_List_Odrop @ SV28 @ SY1176 @ SY1177 ) @ SY1177 )
= ( c_List_Olast @ SY1176 @ SY1177 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV28 @ ( c_Nat_Osize__class_Osize @ SY1176 @ ( tc_List_Olist @ SY1177 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1346,plain,
! [SV29: $i] :
( ( ! [SY1178: $i,SY1179: $i] :
( ( c_List_Odrop @ SV29 @ ( c_List_Otl @ SY1178 @ SY1179 ) @ SY1179 )
= ( c_List_Otl @ ( c_List_Odrop @ SV29 @ SY1178 @ SY1179 ) @ SY1179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1347,plain,
! [SV30: $i] :
( ( ! [SY1180: $i,SY1181: $i,SY1182: $i] :
( ( c_List_Odrop @ ( c_Suc @ SV30 ) @ ( c_List_Olist_OCons @ SY1180 @ SY1181 @ SY1182 ) @ SY1182 )
= ( c_List_Odrop @ SV30 @ SY1181 @ SY1182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1348,plain,
! [SV31: $i] :
( ( ! [SY1183: $i,SY1184: $i] :
( ( c_List_Odrop @ SV31 @ ( c_List_Obutlast @ SY1183 @ SY1184 ) @ SY1184 )
= ( c_List_Obutlast @ ( c_List_Odrop @ SV31 @ SY1183 @ SY1184 ) @ SY1184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(1349,plain,
! [SV32: $i] :
( ( ! [SY1185: $i,SY1186: $i] :
( ( c_List_Otl @ ( c_List_Odrop @ SV32 @ SY1185 @ SY1186 ) @ SY1186 )
= ( c_List_Odrop @ SV32 @ ( c_List_Otl @ SY1185 @ SY1186 ) @ SY1186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1350,plain,
! [SV33: $i] :
( ( ! [SY1187: $i,SY1188: $i] :
( SV33
= ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SY1187 @ ( tc_List_Olist @ SY1188 ) ) @ ( c_List_Oappend @ SY1187 @ SV33 @ SY1188 ) @ SY1188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1351,plain,
! [SV34: $i] :
( ( ! [SY1189: $i,SY1190: $i] :
( ( c_List_Odrop @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ SV34 @ SY1189 @ SY1190 ) @ SY1190 )
= SY1189 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1352,plain,
! [SV35: $i] :
( ( ! [SY1191: $i,SY1192: $i] :
( ( c_List_Obutlast @ ( c_List_Odrop @ SV35 @ SY1191 @ SY1192 ) @ SY1192 )
= ( c_List_Odrop @ SV35 @ ( c_List_Obutlast @ SY1191 @ SY1192 ) @ SY1192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1353,plain,
! [SV36: $i] :
( ( ! [SY1193: $i,SY1194: $i] :
( ( c_List_Odrop @ ( c_Suc @ SV36 ) @ SY1193 @ SY1194 )
= ( c_List_Odrop @ SV36 @ ( c_List_Otl @ SY1193 @ SY1194 ) @ SY1194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1354,plain,
! [SV37: $i] :
( ( ! [SY1195: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV37 @ SY1195 )
= SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1355,plain,
! [SV38: $i] :
( ( ! [SY1196: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ SV38 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ! [SY1197: $i,SY1198: $i] :
( ( c_List_Odrop @ ( c_Int_Onumber__class_Onumber__of @ SV38 @ tc_nat ) @ ( c_List_Olist_OCons @ SY1196 @ SY1197 @ SY1198 ) @ SY1198 )
= ( c_List_Olist_OCons @ SY1196 @ SY1197 @ SY1198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1356,plain,
! [SV39: $i] :
( ( ! [SY1199: $i] :
( ( c_List_Odrop @ SV39 @ ( c_List_Olist_ONil @ SY1199 ) @ SY1199 )
= ( c_List_Olist_ONil @ SY1199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1357,plain,
! [SV40: $i] :
( ( ! [SY1200: $i,SY1201: $i,SY1202: $i,SY1203: $i] :
( ( c_Type_Otypings @ SV40 @ SY1200 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SY1201 @ SY1202 @ SV40 @ SY1200 ) )
| ! [SY1204: $i] :
( ~ ( c_Type_Otyping @ SV40 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1203 ) @ SY1204 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1202 )
| ! [SY1205: $i] :
~ ( c_Type_Otypings @ SV40 @ SY1204 @ SY1205 )
| ~ ( c_Type_Otyping @ SV40 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1203 ) @ SY1204 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1200 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1358,plain,
! [SV41: $i] :
( ( ! [SY1206: $i,SY1207: $i,SY1208: $i] :
( ( c_Type_Otypings @ SV41 @ SY1206 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SY1207 @ SV41 @ SY1208 @ SY1206 ) )
| ~ ( c_Type_Otyping @ SV41 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1208 ) @ SY1206 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1359,plain,
! [SV42: $i] :
( ( ! [SY1209: $i,SY1210: $i] :
( ( SV42
= ( c_List_Oappend @ ( c_List_Otake @ SY1209 @ SV42 @ SY1210 ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ SV42 @ SY1209 @ SY1210 ) @ ( c_List_Odrop @ ( c_Suc @ SY1209 ) @ SV42 @ SY1210 ) @ SY1210 ) @ SY1210 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1209 @ ( c_Nat_Osize__class_Osize @ SV42 @ ( tc_List_Olist @ SY1210 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1360,plain,
! [SV43: $i] :
( ( ! [SY1211: $i,SY1212: $i] :
( ( ( c_List_Oappend @ ( c_List_Otake @ SV43 @ SY1211 @ SY1212 ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ ( c_List_Odrop @ SV43 @ SY1211 @ SY1212 ) @ SY1212 ) @ ( c_List_Olist_ONil @ SY1212 ) @ SY1212 ) @ SY1212 )
= ( c_List_Otake @ ( c_Suc @ SV43 ) @ SY1211 @ SY1212 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV43 @ ( c_Nat_Osize__class_Osize @ SY1211 @ ( tc_List_Olist @ SY1212 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1361,plain,
! [SV44: $i] :
( ( ! [SY1213: $i,SY1214: $i,SY1215: $i] :
( ( c_Lambda_Oliftn @ SV44 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1213 ) @ SY1214 ) @ SY1215 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ SV44 @ SY1213 @ SY1215 ) ) @ ( c_Lambda_Oliftn @ SV44 @ SY1214 @ SY1215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1362,plain,
! [SV45: $i] :
( ( ! [SY1216: $i,SY1217: $i,SY1218: $i] :
( ( c_List_Onth @ ( c_List_Oappend @ SV45 @ ( c_List_Olist_OCons @ SY1216 @ SY1217 @ SY1218 ) @ SY1218 ) @ ( c_Nat_Osize__class_Osize @ SV45 @ ( tc_List_Olist @ SY1218 ) ) @ SY1218 )
= SY1216 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1363,plain,
! [SV46: $i] :
( ( ! [SY1219: $i] :
( ( c_List_Osplice @ ( c_List_Olist_ONil @ SV46 ) @ SY1219 @ SV46 )
= SY1219 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1364,plain,
! [SV47: $i] :
( ( ! [SY1220: $i] :
( ( c_List_Osplice @ SV47 @ ( c_List_Olist_ONil @ SY1220 ) @ SY1220 )
= SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1365,plain,
! [SV48: $i] :
( ( ! [SY1221: $i,SY1222: $i,SY1223: $i,SY1224: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV48 @ SY1221 @ SY1222 ) @ ( c_List_Olist_OCons @ SY1223 @ SY1224 @ SY1222 ) @ SY1222 )
= ( c_List_Olist_OCons @ SV48 @ ( c_List_Olist_OCons @ SY1223 @ ( c_List_Osplice @ SY1221 @ SY1224 @ SY1222 ) @ SY1222 ) @ SY1222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1366,plain,
! [SV49: $i] :
( ( ! [SY1225: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ SV49 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ! [SY1226: $i,SY1227: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ SY1225 @ SY1226 @ SY1227 ) @ ( c_Int_Onumber__class_Onumber__of @ SV49 @ tc_nat ) @ SY1227 )
= SY1225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1367,plain,
! [SV50: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1368,plain,
! [SV51: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1369,plain,
! [SV52: $i] :
( ( ( c_Suc @ SV52 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1370,plain,
! [SV53: $i] :
( ( ( c_Suc @ SV53 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1371,plain,
! [SV54: $i] :
( ( ! [SY1228: $i] :
( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV54 @ SY1228 )
= SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1372,plain,
! [SV55: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV55 )
| ( ( c_HOL_Ozero__class_Ozero @ SV55 )
!= ( c_HOL_Oone__class_Oone @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1373,plain,
! [SV56: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV56 )
| ( ( c_HOL_Oone__class_Oone @ SV56 )
!= ( c_HOL_Ozero__class_Ozero @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1374,plain,
! [SV57: $i] :
( ( ! [SY1229: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV57 ) @ ( c_Suc @ SY1229 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV57 @ SY1229 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1375,plain,
! [SV58: $i] :
( ( ! [SY1230: $i] :
( ( c_HOL_Oord__class_Oless @ SV58 @ SY1230 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV58 ) @ ( c_Suc @ SY1230 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1376,plain,
! [SV59: $i] :
( ( ! [SY1231: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV59 ) @ ( c_Suc @ SY1231 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV59 @ SY1231 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1377,plain,
! [SV60: $i] :
( ( ! [SY1232: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ SV60 @ SY1232 ) @ SY1232 )
= ( c_Transitive__Closure_Ortranclp @ SV60 @ SY1232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1378,plain,
! [SV61: $i] :
( ( ! [SY1233: $i] :
( ( c_HOL_Oord__class_Oless @ SV61 @ ( c_Suc @ SY1233 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY1233 @ SV61 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1379,plain,
! [SV62: $i] :
( ( ! [SY1234: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV62 @ SY1234 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY1234 @ ( c_Suc @ SV62 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1380,plain,
! [SV63: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV63 @ SV63 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV63 @ ( c_Suc @ SV63 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1381,plain,
! [SV64: $i] :
( ( ! [SY1235: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV64 ) @ SY1235 @ tc_nat )
| ( ( c_Suc @ SV64 )
= SY1235 )
| ~ ( c_HOL_Oord__class_Oless @ SV64 @ SY1235 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1382,plain,
! [SV65: $i] :
( ( ~ ( class_Int_Oring__char__0 @ SV65 )
| ~ ( class_Int_Onumber__ring @ SV65 )
| ! [SY1236: $i,SY1237: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ SY1236 @ SV65 )
!= ( c_Int_Onumber__class_Onumber__of @ SY1237 @ SV65 ) )
| ( SY1236 = SY1237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1383,plain,
! [SV66: $i] :
( ( ! [SY1238: $i,SY1239: $i,SY1240: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV66 @ SY1238 @ SY1238 ) @ SY1238 ) @ SY1239 ) @ SY1240 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV66 @ SY1238 ) @ SY1240 ) @ SY1239 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1384,plain,
! [SV67: $i] :
( ( ! [SY1241: $i,SY1242: $i,SY1243: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV67 @ SY1241 ) @ SY1242 ) @ SY1243 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV67 @ SY1241 @ SY1241 ) @ SY1241 ) @ SY1243 ) @ SY1242 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1385,plain,
! [SV68: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV68 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV68 )
= ( c_HOL_Oone__class_Oone @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1386,plain,
! [SV69: $i] :
( ( ! [SY1244: $i,SY1245: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV69 @ SY1244 ) @ SY1245 ) )
| ! [SY1246: $i,SY1247: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV69 @ SY1246 @ SY1247 ) @ SY1245 ) @ SY1244 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1387,plain,
! [SV70: $i] :
( ( ! [SY1248: $i,SY1249: $i,SY1250: $i,SY1251: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV70 @ SY1248 @ SY1249 ) @ SY1250 ) @ SY1251 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1251 ) @ SY1250 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1388,plain,
! [SV71: $i] :
( ( ! [SY1252: $i,SY1253: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV71 @ SY1252 ) @ SY1253 ) )
| ! [SY1254: $i,SY1255: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV71 @ SY1254 @ SY1255 ) @ SY1253 ) @ SY1252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1389,plain,
! [SV72: $i] :
( ( ! [SY1256: $i,SY1257: $i,SY1258: $i,SY1259: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV72 @ SY1256 @ SY1257 ) @ SY1258 ) @ SY1259 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV72 @ SY1259 ) @ SY1258 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1390,plain,
! [SV73: $i] :
( ( ! [SY1260: $i,SY1261: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SV73 @ SY1260 @ SY1261 ) @ ( tc_List_Olist @ SY1261 ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ SY1260 @ ( tc_List_Olist @ SY1261 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1391,plain,
! [SV74: $i] :
( ( ! [SY1262: $i,SY1263: $i] :
( ( c_Suc @ ( c_Nat_Osize__class_Osize @ SV74 @ ( tc_List_Olist @ SY1262 ) ) )
= ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SY1263 @ SV74 @ SY1262 ) @ ( tc_List_Olist @ SY1262 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1392,plain,
! [SV75: $i] :
( ( ! [SY1264: $i,SY1265: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV75 @ SY1264 ) @ SY1265 ) @ SY1265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1393,plain,
! [SV76: $i] :
( ( ! [SY1266: $i,SY1267: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV76 @ SY1266 ) @ SY1267 ) @ SY1267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1394,plain,
! [SV77: $i] :
( ( ! [SY1268: $i,SY1269: $i] :
( ( c_Wellfounded_Oaccp @ SV77 @ SY1268 @ SY1269 )
| ! [SY1270: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV77 @ SY1269 ) @ SY1268 ) @ SY1270 ) )
| ~ ( c_Wellfounded_Oaccp @ SV77 @ SY1270 @ SY1269 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1395,plain,
! [SV78: $i] :
( ( ! [SY1271: $i,SY1272: $i] :
( ( c_Wellfounded_Oaccp @ SV78 @ SY1271 @ SY1272 )
| ! [SY1273: $i] :
( ~ ( c_Wellfounded_Oaccp @ SV78 @ SY1273 @ SY1272 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV78 @ SY1272 ) @ SY1271 ) @ SY1273 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1396,plain,
! [SV79: $i] :
( ( ! [SY1274: $i,SY1275: $i,SY1276: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV79 @ SY1274 ) @ SY1275 ) @ SY1276 ) )
| ! [SY1277: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV79 @ SY1274 ) @ SY1277 ) @ SY1276 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV79 @ SY1274 ) @ SY1275 ) @ SY1277 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1397,plain,
! [SV80: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV80 @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1398,plain,
! [SV81: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV81 ) )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV81 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1399,plain,
! [SV82: $i] :
( ( ! [SY1278: $i,SY1279: $i,SY1280: $i] :
( ( ( c_List_Onth @ ( c_List_Oappend @ SV82 @ SY1278 @ SY1279 ) @ SY1280 @ SY1279 )
= ( c_List_Onth @ SV82 @ SY1280 @ SY1279 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1280 @ ( c_Nat_Osize__class_Osize @ SV82 @ ( tc_List_Olist @ SY1279 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1400,plain,
! [SV83: $i] :
( ( ~ ( class_Nat_Osemiring__char__0 @ SV83 )
| ! [SY1281: $i,SY1282: $i] :
( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SY1281 @ SV83 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY1282 @ SV83 ) )
| ( SY1281 = SY1282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1401,plain,
! [SV84: $i] :
( ( ! [SY1283: $i] :
( ( ( c_Suc @ SV84 )
!= ( c_Suc @ SY1283 ) )
| ( SV84 = SY1283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1402,plain,
! [SV85: $i] :
( ( ! [SY1284: $i] :
( ( ( c_Suc @ SV85 )
!= ( c_Suc @ SY1284 ) )
| ( SV85 = SY1284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1403,plain,
! [SV86: $i] :
( ( ! [SY1285: $i,SY1286: $i,SY1287: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV86 @ SY1285 ) @ SY1286 ) @ SY1287 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV86 @ SY1286 ) @ SY1287 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1404,plain,
! [SV87: $i] :
( ( ( c_Predicate_Oconversep @ ( c_fequal @ SV87 ) @ SV87 @ SV87 )
= ( c_fequal @ SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1405,plain,
! [SV88: $i] :
( ( ! [SY1288: $i] :
( ( SV88 = SY1288 )
| ( c_HOL_Oord__class_Oless @ SV88 @ SY1288 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV88 @ ( c_Suc @ SY1288 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1406,plain,
! [SV89: $i] :
( ( ! [SY1289: $i] :
( ( SV89 = SY1289 )
| ~ ( c_HOL_Oord__class_Oless @ SY1289 @ ( c_Suc @ SV89 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY1289 @ SV89 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1407,plain,
! [SV90: $i] :
( ( ! [SY1290: $i] :
( ( SV90 = SY1290 )
| ~ ( c_HOL_Oord__class_Oless @ SV90 @ ( c_Suc @ SY1290 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV90 @ SY1290 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1408,plain,
! [SV91: $i] :
( ( ! [SY1291: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate1 @ SV91 @ SY1291 ) @ ( tc_List_Olist @ SY1291 ) )
= ( c_Nat_Osize__class_Osize @ SV91 @ ( tc_List_Olist @ SY1291 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1409,plain,
! [SV92: $i] :
( ( c_HOL_Oord__class_Oless @ SV92 @ ( c_Suc @ SV92 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1410,plain,
! [SV93: $i] :
( ( c_HOL_Oord__class_Oless @ SV93 @ ( c_Suc @ SV93 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1411,plain,
! [SV94: $i] :
( ( ! [SY1292: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV94 ) @ SY1292 @ tc_nat )
| ! [SY1293: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1293 @ SY1292 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV94 @ SY1293 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1412,plain,
! [SV95: $i] :
( ( ! [SY1294: $i,SY1295: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ SV95 @ SY1294 @ SY1295 ) @ ( tc_List_Olist @ SY1295 ) )
= SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1413,plain,
! [SV96: $i] :
( ( ! [SY1296: $i,SY1297: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ SV96 @ SY1296 @ SY1297 ) @ SY1297 @ SY1296 )
= SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1414,plain,
! [SV97: $i] :
( ( ! [SY1298: $i,SY1299: $i,SY1300: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ SV97 @ SY1298 @ SY1299 ) @ ( c_Suc @ SY1300 ) @ SY1299 )
= ( c_List_Onth @ SY1298 @ SY1300 @ SY1299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1030]) ).
thf(1415,plain,
! [SV98: $i] :
( ( ( c_Suc @ SV98 )
!= SV98 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1416,plain,
! [SV99: $i] :
( ( SV99
!= ( c_Suc @ SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1417,plain,
! [SV100: $i] :
( ( ! [SY1301: $i] :
( ( c_HOL_Oord__class_Oless @ SV100 @ SY1301 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV100 ) @ SY1301 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1418,plain,
! [SV101: $i] :
( ( ! [SY1302: $i] :
( ( c_HOL_Oord__class_Oless @ SV101 @ ( c_Suc @ SY1302 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV101 @ SY1302 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1034]) ).
thf(1419,plain,
! [SV102: $i] :
( ( ! [SY1303: $i] :
( ( ( c_Nat_Osize__class_Osize @ SV102 @ ( tc_List_Olist @ SY1303 ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ ( c_List_Otl @ SV102 @ SY1303 ) @ ( tc_List_Olist @ SY1303 ) ) ) )
| ( SV102
= ( c_List_Olist_ONil @ SY1303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1420,plain,
! [SV103: $i] :
( ( ! [SY1304: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orev @ SV103 @ SY1304 ) @ ( tc_List_Olist @ SY1304 ) )
= ( c_Nat_Osize__class_Osize @ SV103 @ ( tc_List_Olist @ SY1304 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1036]) ).
thf(1421,plain,
! [SV104: $i] :
( ( ! [SY1305: $i,SY1306: $i,SY1307: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV104 @ SY1305 ) @ SY1306 ) @ SY1307 ) )
| ! [SY1308: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV104 @ SY1305 ) @ SY1308 ) @ SY1307 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV104 @ SY1306 ) @ SY1308 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1422,plain,
! [SV105: $i] :
( ( ! [SY1309: $i,SY1310: $i,SY1311: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV105 @ SY1309 ) @ SY1310 ) @ SY1311 ) )
| ! [SY1312: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV105 @ SY1312 ) @ SY1311 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV105 @ SY1309 ) @ SY1310 ) @ SY1312 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1423,plain,
! [SV106: $i] :
( ( ! [SY1313: $i,SY1314: $i] :
( ( c_Wellfounded_Oaccp @ SV106 @ SY1313 @ SY1314 )
| ! [SY1315: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV106 @ SY1313 ) @ SY1315 ) )
| ~ ( c_Wellfounded_Oaccp @ SV106 @ SY1315 @ SY1314 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1424,plain,
! [SV107: $i] :
( ( ! [SY1316: $i,SY1317: $i] :
( ( c_Wellfounded_Oaccp @ SV107 @ SY1316 @ SY1317 )
| ! [SY1318: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV107 @ SY1316 ) @ SY1318 ) )
| ~ ( c_Wellfounded_Oaccp @ SV107 @ SY1318 @ SY1317 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1425,plain,
! [SV108: $i] :
( ( ! [SY1319: $i,SY1320: $i] :
( ( ( c_List_Otake @ ( c_Suc @ SV108 ) @ SY1319 @ SY1320 )
= ( c_List_Oappend @ ( c_List_Otake @ SV108 @ SY1319 @ SY1320 ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ SY1319 @ SV108 @ SY1320 ) @ ( c_List_Olist_ONil @ SY1320 ) @ SY1320 ) @ SY1320 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV108 @ ( c_Nat_Osize__class_Osize @ SY1319 @ ( tc_List_Olist @ SY1320 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1426,plain,
! [SV109: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV109 )
| ! [SY1321: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1321 @ SV109 ) @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1427,plain,
! [SV110: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV110 ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1428,plain,
! [SV111: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV111 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV111 ) @ ( c_HOL_Oone__class_Oone @ SV111 ) @ SV111 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1429,plain,
! [SV112: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV112 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV112 )
= ( c_HOL_Ozero__class_Ozero @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1430,plain,
! [SV113: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV113 )
| ! [SY1322: $i,SY1323: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1322 @ SV113 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1323 @ SV113 ) @ SV113 )
| ~ ( c_HOL_Oord__class_Oless @ SY1322 @ SY1323 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1431,plain,
! [SV114: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV114 )
| ! [SY1324: $i,SY1325: $i] :
( ( c_HOL_Oord__class_Oless @ SY1324 @ SY1325 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1324 @ SV114 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1325 @ SV114 ) @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1432,plain,
! [SV115: $i] :
( ( ! [SY1326: $i,SY1327: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ SV115 @ SY1326 @ SY1327 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1327 )
= SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1433,plain,
! [SV116: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ SV116 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1434,plain,
! [SV117: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ SV117 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1435,plain,
! [SV118: $i] :
( ( ( SV118
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ SV118 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1436,plain,
! [SV119: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ SV119 ) @ ( tc_List_Olist @ SV119 ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1437,plain,
! [SV120: $i] :
( ( ! [SY1328: $i] :
( ( ( c_Nat_Osize__class_Osize @ SV120 @ ( tc_List_Olist @ SY1328 ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV120
= ( c_List_Olist_ONil @ SY1328 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1438,plain,
! [SV121: $i] :
( ( ! [SY1329: $i,SY1330: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV121 @ SY1329 @ SY1330 ) @ ( c_List_Olist_ONil @ SY1330 ) @ SY1330 )
= ( c_List_Olist_OCons @ SV121 @ SY1329 @ SY1330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1439,plain,
! [SV122: $i] :
( ( ! [SY1331: $i,SY1332: $i,SY1333: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV122 ) @ SY1331 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1332 ) @ SY1333 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1331 ) @ SY1333 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV122 ) @ SY1332 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1440,plain,
! [SV123: $i] :
( ( ! [SY1334: $i,SY1335: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV123 ) @ SY1334 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1335 ) @ SY1334 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV123 ) @ SY1335 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1441,plain,
! [SV124: $i] :
( ( ! [SY1336: $i,SY1337: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV124 ) @ SY1336 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV124 ) @ SY1337 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1336 ) @ SY1337 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1442,plain,
! [SV125: $i] :
( ( ! [SY1338: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV125 ) ) @ ( c_Lambda_OdB_OAbs @ SY1338 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV125 ) @ SY1338 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1443,plain,
! [SV126: $i] :
( ( ! [SY1339: $i,SY1340: $i,SY1341: $i] :
( ( c_List_Otake @ ( c_Suc @ SV126 ) @ ( c_List_Olist_OCons @ SY1339 @ SY1340 @ SY1341 ) @ SY1341 )
= ( c_List_Olist_OCons @ SY1339 @ ( c_List_Otake @ SV126 @ SY1340 @ SY1341 ) @ SY1341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1444,plain,
! [SV127: $i] :
( ( ! [SY1342: $i,SY1343: $i] :
( ( ( c_Lambda_Oliftn @ SV127 @ ( c_Lambda_OdB_OVar @ SY1342 ) @ SY1343 )
= ( c_Lambda_OdB_OVar @ SY1342 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1342 @ SY1343 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1445,plain,
! [SV128: $i] :
( ( ! [SY1344: $i,SY1345: $i,SY1346: $i] :
( ( ( c_List_Onth @ ( c_List_Otake @ SV128 @ SY1344 @ SY1345 ) @ SY1346 @ SY1345 )
= ( c_List_Onth @ SY1344 @ SY1346 @ SY1345 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1346 @ SV128 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1446,plain,
! [SV129: $i] :
( ( ! [SY1347: $i,SY1348: $i,SY1349: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV129 @ SY1347 @ SY1348 ) ) @ ( c_Lambda_Osubst @ SV129 @ SY1349 @ SY1348 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1347 ) @ SY1349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1447,plain,
! [SV130: $i] :
( ( ! [SY1350: $i,SY1351: $i,SY1352: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV130 @ SY1350 @ SY1351 ) ) @ ( c_Lambda_Osubst @ SY1352 @ SY1350 @ SY1351 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV130 ) @ SY1352 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1448,plain,
! [SV131: $i] :
( ( ! [SY1353: $i,SY1354: $i,SY1355: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV131 @ SY1353 @ SY1354 ) ) @ ( c_Lambda_Osubst @ SV131 @ SY1355 @ SY1354 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1353 ) @ SY1355 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1065]) ).
thf(1449,plain,
! [SV132: $i] :
( ( ! [SY1356: $i,SY1357: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV132 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SY1356 @ SV132 @ SY1357 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1356 ) @ SV132 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1357 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1450,plain,
! [SV133: $i] :
( ( ! [SY1358: $i,SY1359: $i] :
( SV133
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV133 @ ( tc_List_Olist @ SY1358 ) ) @ ( c_List_Oappend @ SV133 @ SY1359 @ SY1358 ) @ SY1358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1451,plain,
! [SV134: $i] :
( ( ! [SY1360: $i,SY1361: $i] :
( ( c_List_Oreplicate @ ( c_Suc @ SV134 ) @ SY1360 @ SY1361 )
= ( c_List_Olist_OCons @ SY1360 @ ( c_List_Oreplicate @ SV134 @ SY1360 @ SY1361 ) @ SY1361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1452,plain,
! [SV135: $i] :
( ( ! [SY1362: $i,SY1363: $i,SY1364: $i] :
( ( ( c_List_Onth @ ( c_List_Oreplicate @ SV135 @ SY1362 @ SY1363 ) @ SY1364 @ SY1363 )
= SY1362 )
| ~ ( c_HOL_Oord__class_Oless @ SY1364 @ SV135 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1453,plain,
! [SV136: $i] :
( ( ! [SY1365: $i,SY1366: $i] :
( ( c_Type_Otyping @ SV136 @ SY1365 @ SY1366 )
| ! [SY1367: $i] :
( ~ ( c_Type_Otyping @ SV136 @ SY1367 @ SY1366 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1367 ) @ SY1365 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1454,plain,
! [SV137: $i] :
( ( ! [SY1368: $i,SY1369: $i] :
( ( c_List_Otake @ SV137 @ ( c_List_Otl @ SY1368 @ SY1369 ) @ SY1369 )
= ( c_List_Otl @ ( c_List_Otake @ ( c_Suc @ SV137 ) @ SY1368 @ SY1369 ) @ SY1369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1455,plain,
! [SV138: $i] :
( ( ! [SY1370: $i,SY1371: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV138 @ SY1370 @ SY1371 ) @ SY1371 )
= ( c_List_Oappend @ SV138 @ ( c_List_Obutlast @ SY1370 @ SY1371 ) @ SY1371 ) )
| ( SY1370
= ( c_List_Olist_ONil @ SY1371 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1072]) ).
thf(1456,plain,
! [SV139: $i] :
( ( ! [SY1372: $i] :
( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ SV139 ) @ SY1372 @ SV139 ) @ SV139 )
= ( c_List_Ohd @ SY1372 @ SV139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1457,plain,
! [SV140: $i] :
( ( ! [SY1373: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ SV140 @ ( c_List_Olist_ONil @ SY1373 ) @ SY1373 ) @ SY1373 )
= ( c_List_Olast @ SV140 @ SY1373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1458,plain,
! [SV141: $i] :
( ( ! [SY1374: $i,SY1375: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ SV141 @ SY1374 @ SY1375 ) @ SY1375 )
= ( c_List_Olast @ SY1374 @ SY1375 ) )
| ( SY1374
= ( c_List_Olist_ONil @ SY1375 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1459,plain,
! [SV142: $i] :
( ( ! [SY1376: $i,SY1377: $i] :
( ( ( c_List_Otake @ ( c_Suc @ SV142 ) @ SY1376 @ SY1377 )
= ( c_List_Olist_OCons @ ( c_List_Ohd @ SY1376 @ SY1377 ) @ ( c_List_Otake @ SV142 @ ( c_List_Otl @ SY1376 @ SY1377 ) @ SY1377 ) @ SY1377 ) )
| ( SY1376
= ( c_List_Olist_ONil @ SY1377 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1460,plain,
! [SV143: $i] :
( ( ! [SY1378: $i,SY1379: $i,SY1380: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV143 @ SY1378 @ SY1379 ) @ SY1380 @ SY1379 )
= ( c_List_Olist_OCons @ SV143 @ ( c_List_Olist_OCons @ ( c_List_Ohd @ SY1380 @ SY1379 ) @ ( c_List_Osplice @ SY1378 @ ( c_List_Otl @ SY1380 @ SY1379 ) @ SY1379 ) @ SY1379 ) @ SY1379 ) )
| ( SY1380
= ( c_List_Olist_ONil @ SY1379 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1077]) ).
thf(1461,plain,
! [SV144: $i] :
( ( ! [SY1381: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV144 ) @ SY1381 @ SV144 )
= ( c_Lambda_Oliftn @ SV144 @ SY1381 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( c_HOL_Oord__class_Oless @ SV144 @ SV144 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1462,plain,
! [SV145: $i] :
( ( ! [SY1382: $i,SY1383: $i] :
( ( SV145
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1382 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SY1382 @ SY1383 @ SV145 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1382 ) @ SY1383 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1463,plain,
! [SV146: $i] :
( ( ! [SY1384: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ SV146 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ! [SY1385: $i,SY1386: $i] :
( ( c_List_Otake @ ( c_Int_Onumber__class_Onumber__of @ SV146 @ tc_nat ) @ ( c_List_Olist_OCons @ SY1384 @ SY1385 @ SY1386 ) @ SY1386 )
= ( c_List_Olist_ONil @ SY1386 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1464,plain,
! [SV147: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV147 )
| ! [SY1387: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1387 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1387 @ SV147 ) @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1465,plain,
! [SV148: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV148 )
| ! [SY1388: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV148 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1388 @ SV148 ) @ SV148 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1388 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1466,plain,
! [SV149: $i] :
( ( ! [SY1389: $i,SY1390: $i] :
( ( c_Lambda_Osubstn @ SV149 @ SY1389 @ SY1390 )
= ( c_Lambda_Osubst @ SV149 @ ( c_Lambda_Oliftn @ SY1390 @ SY1389 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1390 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1467,plain,
! [SV150: $i] :
( ( ! [SY1391: $i,SY1392: $i] :
( ( ( c_List_Otake @ SV150 @ ( c_List_Obutlast @ SY1391 @ SY1392 ) @ SY1392 )
= ( c_List_Otake @ SV150 @ SY1391 @ SY1392 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV150 @ ( c_Nat_Osize__class_Osize @ SY1391 @ ( tc_List_Olist @ SY1392 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1468,plain,
! [SV151: $i] :
( ( ! [SY1393: $i] :
( ( ( c_List_Ohd @ SV151 @ SY1393 )
= ( c_List_Onth @ SV151 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1393 ) )
| ( SV151
= ( c_List_Olist_ONil @ SY1393 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1469,plain,
! [SV152: $i] :
( ( ! [SY1394: $i,SY1395: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV152 @ SY1394 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1395 @ SY1394 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV152 ) @ SY1395 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1470,plain,
! [SV153: $i] :
( ( ! [SY1396: $i,SY1397: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV153 @ SY1396 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV153 @ SY1397 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SY1396 @ SY1397 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1471,plain,
! [SV154: $i] :
( ( ! [SY1398: $i,SY1399: $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 @ SV154 @ SY1398 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1399 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1398 @ 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 @ SV154 ) ) @ SY1398 ) @ SY1399 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1472,plain,
! [SV155: $i] :
( ( ! [SY1400: $i,SY1401: $i] :
( ( c_List_Otake @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ SV155 @ SY1400 @ SY1401 ) @ SY1401 )
= ( c_List_Olist_OCons @ SV155 @ ( c_List_Olist_ONil @ SY1401 ) @ SY1401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1473,plain,
! [SV156: $i] :
( ( ! [SY1402: $i] :
( ( SV156
= ( c_List_Olist_ONil @ SY1402 ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV156 @ ( tc_List_Olist @ SY1402 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1474,plain,
! [SV157: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ SV157 ) @ ( tc_List_Olist @ SV157 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1475,plain,
! [SV158: $i] :
( ( ! [SY1403: $i,SY1404: $i,SY1405: $i] :
( ( c_Type_Otyping @ SV158 @ SY1403 @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ SY1404 @ SV158 @ SY1403 @ SY1405 ) )
| ~ ( c_Type_Otypings @ SV158 @ ( c_List_Oappend @ SY1405 @ ( c_List_Olist_OCons @ SY1403 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SY1404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1476,plain,
! [SV159: $i] :
( ( ! [SY1406: $i,SY1407: $i,SY1408: $i,SY1409: $i] :
( ( ( c_List_Oappend @ SV159 @ SY1406 @ SY1407 )
!= ( c_List_Olist_OCons @ SY1408 @ SY1409 @ SY1407 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY1408 @ SY1409 @ SV159 @ SY1406 @ SY1407 ) @ SY1406 @ SY1407 )
= SY1409 )
| ( SY1406
= ( c_List_Olist_OCons @ SY1408 @ SY1409 @ SY1407 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1093]) ).
thf(1477,plain,
! [SV160: $i] :
( ( ! [SY1410: $i,SY1411: $i,SY1412: $i,SY1413: $i] :
( ( ( c_List_Olist_OCons @ SV160 @ SY1410 @ SY1411 )
!= ( c_List_Oappend @ SY1412 @ SY1413 @ SY1411 ) )
| ( ( c_List_Olist_OCons @ SV160 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV160 @ SY1410 @ SY1412 @ SY1413 @ SY1411 ) @ SY1411 )
= SY1412 )
| ( ( c_List_Olist_OCons @ SV160 @ SY1410 @ SY1411 )
= SY1413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1478,plain,
! [SV161: $i] :
( ( ! [SY1414: $i,SY1415: $i,SY1416: $i,SY1417: $i] :
( ( ( c_List_Oappend @ SV161 @ SY1414 @ SY1415 )
!= ( c_List_Olist_OCons @ SY1416 @ SY1417 @ SY1415 ) )
| ( SV161
= ( c_List_Olist_OCons @ SY1416 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY1416 @ SY1417 @ SV161 @ SY1414 @ SY1415 ) @ SY1415 ) )
| ( SY1414
= ( c_List_Olist_OCons @ SY1416 @ SY1417 @ SY1415 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1479,plain,
! [SV162: $i] :
( ( ! [SY1418: $i,SY1419: $i,SY1420: $i,SY1421: $i] :
( ( ( c_List_Olist_OCons @ SV162 @ SY1418 @ SY1419 )
!= ( c_List_Oappend @ SY1420 @ SY1421 @ SY1419 ) )
| ( SY1418
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV162 @ SY1418 @ SY1420 @ SY1421 @ SY1419 ) @ SY1421 @ SY1419 ) )
| ( ( c_List_Olist_OCons @ SV162 @ SY1418 @ SY1419 )
= SY1421 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1480,plain,
! [SV163: $i] :
( ( ! [SY1422: $i,SY1423: $i,SY1424: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV163 @ SY1422 @ SY1423 ) @ ( c_List_Olist_OCons @ SY1422 @ SY1424 @ SY1423 ) @ SY1423 )
= ( c_List_Olist_OCons @ SY1422 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV163 @ SY1422 @ SY1423 ) @ SY1424 @ SY1423 ) @ SY1423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1481,plain,
! [SV164: $i] :
( ( ! [SY1425: $i] :
( ( c_List_Olist_OCons @ SV164 @ ( c_List_Olist_ONil @ SY1425 ) @ SY1425 )
= ( c_List_Orev @ ( c_List_Olist_OCons @ SV164 @ ( c_List_Olist_ONil @ SY1425 ) @ SY1425 ) @ SY1425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1482,plain,
! [SV165: $i] :
( ( ! [SY1426: $i,SY1427: $i] :
( ( ( c_List_Olast @ ( c_List_Olist_OCons @ SV165 @ SY1426 @ SY1427 ) @ SY1427 )
= ( c_List_Olast @ SY1426 @ SY1427 ) )
| ( SY1426
= ( c_List_Olist_ONil @ SY1427 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1483,plain,
! [SV166: $i] :
( ( ! [SY1428: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ SV166 @ ( c_List_Olist_ONil @ SY1428 ) @ SY1428 ) @ SY1428 )
= ( c_List_Olist_OCons @ SV166 @ ( c_List_Olist_ONil @ SY1428 ) @ SY1428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1484,plain,
! [SV167: $i] :
( ( ! [SY1429: $i,SY1430: $i] :
( ( ( c_List_Olist_OCons @ SV167 @ ( c_List_Olist_ONil @ SY1429 ) @ SY1429 )
!= ( c_List_Orev @ SY1430 @ SY1429 ) )
| ( SY1430
= ( c_List_Olist_OCons @ SV167 @ ( c_List_Olist_ONil @ SY1429 ) @ SY1429 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1485,plain,
! [SV168: $i] :
( ( ! [SY1431: $i,SY1432: $i] :
( ( ( c_List_Orev @ SV168 @ SY1431 )
!= ( c_List_Olist_OCons @ SY1432 @ ( c_List_Olist_ONil @ SY1431 ) @ SY1431 ) )
| ( SV168
= ( c_List_Olist_OCons @ SY1432 @ ( c_List_Olist_ONil @ SY1431 ) @ SY1431 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1486,plain,
! [SV169: $i] :
( ( ! [SY1433: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV169 @ ( c_List_Olist_ONil @ SY1433 ) @ SY1433 ) @ SY1433 )
= ( c_List_Olist_ONil @ SY1433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1487,plain,
! [SV170: $i] :
( ( ! [SY1434: $i] :
( ( c_List_Olast @ ( c_List_Olist_OCons @ SV170 @ ( c_List_Olist_ONil @ SY1434 ) @ SY1434 ) @ SY1434 )
= SV170 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1488,plain,
! [SV171: $i] :
( ( ! [SY1435: $i,SY1436: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV171 @ SY1435 @ SY1436 ) @ SY1436 )
= ( c_List_Olist_OCons @ SV171 @ ( c_List_Obutlast @ SY1435 @ SY1436 ) @ SY1436 ) )
| ( SY1435
= ( c_List_Olist_ONil @ SY1436 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1489,plain,
! [SV172: $i] :
( ( ! [SY1437: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV172 @ SY1437 )
= ( c_List_Olist_ONil @ SY1437 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1106]) ).
thf(1490,plain,
! [SV173: $i] :
( ( ! [SY1438: $i,SY1439: $i] :
( ( ( c_List_Otake @ SV173 @ SY1438 @ SY1439 )
!= ( c_List_Olist_ONil @ SY1439 ) )
| ( SY1438
= ( c_List_Olist_ONil @ SY1439 ) )
| ( SV173
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1491,plain,
! [SV174: $i] :
( ( ! [SY1440: $i] :
( ( c_List_Olist_ONil @ SV174 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1440 @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1492,plain,
! [SV175: $i] :
( ( ! [SY1441: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV175 @ SY1441 )
= ( c_List_Olist_ONil @ SY1441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1493,plain,
! [SV176: $i] :
( ( ! [SY1442: $i,SY1443: $i] :
( ( c_List_Oreplicate @ SV176 @ SY1442 @ SY1443 )
!= ( c_List_Olist_ONil @ SY1443 ) )
| ( SV176
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1494,plain,
! [SV177: $i] :
( ( ! [SY1444: $i] :
( ! [SY1445: $i] :
( ( c_List_Olist_ONil @ SV177 )
!= ( c_List_Oreplicate @ SY1444 @ SY1445 @ SV177 ) )
| ( SY1444
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1495,plain,
! [SV178: $i] :
( ( ! [SY1446: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV178 ) ) @ SY1446 ) ) @ ( c_Lambda_Osubst @ SV178 @ SY1446 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1496,plain,
! [SV179: $i] :
( ( ! [SY1447: $i] :
( ( ( c_List_Oappend @ ( c_List_Obutlast @ SV179 @ SY1447 ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ SV179 @ SY1447 ) @ ( c_List_Olist_ONil @ SY1447 ) @ SY1447 ) @ SY1447 )
= SV179 )
| ( SV179
= ( c_List_Olist_ONil @ SY1447 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1113]) ).
thf(1497,plain,
! [SV180: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV180 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1498,plain,
! [SV181: $i] :
( ( ! [SY1448: $i] : ( c_Type_Otyping @ SV181 @ ( c_Lambda_OdB_OVar @ SY1448 ) @ ( hAPP @ SV181 @ SY1448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1499,plain,
! [SV182: $i] :
( ( ! [SY1449: $i,SY1450: $i] :
( ( ( hAPP @ SV182 @ SY1449 )
= SY1450 )
| ~ ( c_Type_Otyping @ SV182 @ ( c_Lambda_OdB_OVar @ SY1449 ) @ SY1450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1500,plain,
! [SV183: $i] :
( ( ! [SY1451: $i] :
( ( c_Lambda_OdB_OVar @ SV183 )
!= ( c_Lambda_OdB_OAbs @ SY1451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1501,plain,
! [SV184: $i] :
( ( ! [SY1452: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV184 ) ) @ SY1452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1502,plain,
! [SV185: $i] :
( ( ! [SY1453: $i] :
( ( c_Lambda_OdB_OAbs @ SV185 )
!= ( c_Lambda_OdB_OVar @ SY1453 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1503,plain,
! [SV186: $i] :
( ( ! [SY1454: $i,SY1455: $i,SY1456: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV186 @ SY1454 @ SY1455 ) ) @ ( c_Lambda_Osubst @ SY1456 @ SY1454 @ SY1455 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV186 ) @ SY1456 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1504,plain,
! [SV187: $i] :
( ( ! [SY1457: $i,SY1458: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ SV187 @ SY1457 @ SY1458 ) @ SY1458 )
= ( c_List_Oappend @ ( c_List_Orev @ SY1457 @ SY1458 ) @ ( c_List_Orev @ SV187 @ SY1458 ) @ SY1458 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1505,plain,
! [SV188: $i] :
( ( ! [SY1459: $i,SY1460: $i,SY1461: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV188 @ SY1459 @ SY1460 @ SY1461 )
| ! [SY1462: $i] : ( c_ListOrder_Ostep1 @ SV188 @ ( c_List_Oappend @ SY1459 @ SY1462 @ SY1461 ) @ ( c_List_Oappend @ SY1460 @ SY1462 @ SY1461 ) @ SY1461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1506,plain,
! [SV189: $i] :
( ( ! [SY1463: $i,SY1464: $i,SY1465: $i,SY1466: $i] :
( ( c_ListOrder_Ostep1 @ SV189 @ ( c_List_Oappend @ SY1463 @ SY1464 @ SY1465 ) @ ( c_List_Oappend @ SY1463 @ SY1466 @ SY1465 ) @ SY1465 )
| ~ ( c_ListOrder_Ostep1 @ SV189 @ SY1464 @ SY1466 @ SY1465 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1507,plain,
! [SV190: $i] :
( ( ! [SY1467: $i,SY1468: $i] :
( ( c_List_Olistsp @ SV190 @ SY1467 @ SY1468 )
| ! [SY1469: $i] :
~ ( c_List_Olistsp @ SV190 @ ( c_List_Oappend @ SY1467 @ SY1469 @ SY1468 ) @ SY1468 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1508,plain,
! [SV191: $i] :
( ( ! [SY1470: $i,SY1471: $i] :
( ( c_List_Olistsp @ SV191 @ SY1470 @ SY1471 )
| ! [SY1472: $i] :
~ ( c_List_Olistsp @ SV191 @ ( c_List_Oappend @ SY1472 @ SY1470 @ SY1471 ) @ SY1471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1125]) ).
thf(1509,plain,
! [SV192: $i] :
( ( ! [SY1473: $i,SY1474: $i,SY1475: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV192 @ SY1473 @ SY1474 ) @ ( c_List_Oreplicate @ SY1475 @ SY1473 @ SY1474 ) @ SY1474 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SY1475 @ SY1473 @ SY1474 ) @ ( c_List_Oreplicate @ SV192 @ SY1473 @ SY1474 ) @ SY1474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1510,plain,
! [SV193: $i] :
( ( ! [SY1476: $i,SY1477: $i,SY1478: $i] :
( ( c_List_Olistsp @ SV193 @ ( c_List_Oappend @ SY1476 @ SY1477 @ SY1478 ) @ SY1478 )
| ~ ( c_List_Olistsp @ SV193 @ SY1477 @ SY1478 )
| ~ ( c_List_Olistsp @ SV193 @ SY1476 @ SY1478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1511,plain,
! [SV194: $i] :
( ( ! [SY1479: $i,SY1480: $i,SY1481: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV194 ) @ SY1479 ) @ SY1480 @ SY1481 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ SV194 @ SY1480 @ SY1481 ) ) @ ( c_Lambda_Osubstn @ SY1479 @ SY1480 @ SY1481 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1512,plain,
! [SV195: $i] :
( ( ! [SY1482: $i,SY1483: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV195 ) @ SY1482 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1483 ) @ SY1482 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV195 ) @ SY1483 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1513,plain,
! [SV196: $i] :
( ( ! [SY1484: $i,SY1485: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV196 ) @ SY1484 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV196 ) @ SY1485 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1484 ) @ SY1485 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1514,plain,
! [SV197: $i] :
( ( ! [SY1486: $i,SY1487: $i] :
( ( c_Lambda_OdB_OAbs @ SV197 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1486 ) @ SY1487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1515,plain,
! [SV198: $i] :
( ( ! [SY1488: $i,SY1489: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV198 ) @ SY1488 )
!= ( c_Lambda_OdB_OAbs @ SY1489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1516,plain,
! [SV199: $i] :
( ( ! [SY1490: $i] :
( ( ( c_List_Orotate1 @ SV199 @ SY1490 )
= ( c_List_Oappend @ ( c_List_Otl @ SV199 @ SY1490 ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ SV199 @ SY1490 ) @ ( c_List_Olist_ONil @ SY1490 ) @ SY1490 ) @ SY1490 ) )
| ( SV199
= ( c_List_Olist_ONil @ SY1490 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1517,plain,
! [SV200: $i] :
( ( ( c_List_Orev @ ( c_List_Olist_ONil @ SV200 ) @ SV200 )
= ( c_List_Olist_ONil @ SV200 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1518,plain,
! [SV201: $i] :
( ( ! [SY1491: $i] :
( ( ( c_List_Orev @ SV201 @ SY1491 )
!= ( c_List_Olist_ONil @ SY1491 ) )
| ( SV201
= ( c_List_Olist_ONil @ SY1491 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1519,plain,
! [SV202: $i] :
( ( ( c_List_Orotate1 @ ( c_List_Olist_ONil @ SV202 ) @ SV202 )
= ( c_List_Olist_ONil @ SV202 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1520,plain,
! [SV203: $i] :
( ( ! [SY1492: $i] : ( c_List_Olistsp @ SV203 @ ( c_List_Olist_ONil @ SY1492 ) @ SY1492 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1521,plain,
! [SV204: $i] :
( ( ! [SY1493: $i] :
( ( c_List_Otake @ SV204 @ ( c_List_Olist_ONil @ SY1493 ) @ SY1493 )
= ( c_List_Olist_ONil @ SY1493 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1522,plain,
! [SV205: $i] :
( ( ! [SY1494: $i] :
( ( ( c_List_Orotate1 @ SV205 @ SY1494 )
!= ( c_List_Olist_ONil @ SY1494 ) )
| ( SV205
= ( c_List_Olist_ONil @ SY1494 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1523,plain,
! [SV206: $i] :
( ( ! [SY1495: $i,SY1496: $i] :
~ ( c_ListOrder_Ostep1 @ SV206 @ ( c_List_Olist_ONil @ SY1495 ) @ SY1496 @ SY1495 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1524,plain,
! [SV207: $i] :
( ( ! [SY1497: $i,SY1498: $i] :
~ ( c_ListOrder_Ostep1 @ SV207 @ SY1497 @ ( c_List_Olist_ONil @ SY1498 ) @ SY1498 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1525,plain,
! [SV208: $i] :
( ( ! [SY1499: $i] :
( ( ( c_List_Olist_ONil @ SV208 )
!= ( c_List_Orev @ SY1499 @ SV208 ) )
| ( SY1499
= ( c_List_Olist_ONil @ SV208 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1526,plain,
! [SV209: $i] :
( ( ( c_List_Otl @ ( c_List_Olist_ONil @ SV209 ) @ SV209 )
= ( c_List_Olist_ONil @ SV209 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1527,plain,
! [SV210: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_ONil @ SV210 ) @ SV210 )
= ( c_List_Olist_ONil @ SV210 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1528,plain,
! [SV211: $i] :
( ( ( c_List_Olist_ONil @ SV211 )
= ( c_List_Orev @ ( c_List_Olist_ONil @ SV211 ) @ SV211 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1529,plain,
! [SV212: $i] :
( ( ! [SY1500: $i,SY1501: $i,SY1502: $i] :
( ( SV212 = SY1500 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1501 @ SY1500 ) @ SV212 ) )
| ! [SY1503: $i,SY1504: $i] :
~ ( c_ListOrder_Ostep1 @ SY1501 @ ( c_List_Olist_OCons @ SY1500 @ SY1502 @ SY1503 ) @ ( c_List_Olist_OCons @ SV212 @ SY1504 @ SY1503 ) @ SY1503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1530,plain,
! [SV213: $i] :
( ( ! [SY1505: $i,SY1506: $i,SY1507: $i] :
( ( SV213 = SY1505 )
| ( SY1506 = SY1507 )
| ! [SY1508: $i,SY1509: $i] :
~ ( c_ListOrder_Ostep1 @ SY1508 @ ( c_List_Olist_OCons @ SY1505 @ SY1507 @ SY1509 ) @ ( c_List_Olist_OCons @ SV213 @ SY1506 @ SY1509 ) @ SY1509 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1531,plain,
! [SV214: $i] :
( ( ! [SY1510: $i,SY1511: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV214 @ SY1510 ) @ SY1511 ) )
| ! [SY1512: $i,SY1513: $i] : ( c_ListOrder_Ostep1 @ SV214 @ ( c_List_Olist_OCons @ SY1510 @ SY1512 @ SY1513 ) @ ( c_List_Olist_OCons @ SY1511 @ SY1512 @ SY1513 ) @ SY1513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1148]) ).
thf(1532,plain,
! [SV215: $i] :
( ( ! [SY1514: $i,SY1515: $i,SY1516: $i] :
( ( c_ListOrder_Ostep1 @ SV215 @ SY1514 @ SY1515 @ SY1516 )
| ( SY1515 = SY1514 )
| ! [SY1517: $i,SY1518: $i] :
~ ( c_ListOrder_Ostep1 @ SV215 @ ( c_List_Olist_OCons @ SY1517 @ SY1514 @ SY1516 ) @ ( c_List_Olist_OCons @ SY1518 @ SY1515 @ SY1516 ) @ SY1516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1149]) ).
thf(1533,plain,
! [SV216: $i] :
( ( ! [SY1519: $i,SY1520: $i] :
( ( c_List_Otl @ ( c_List_Olist_OCons @ SV216 @ SY1519 @ SY1520 ) @ SY1520 )
= SY1519 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1150]) ).
thf(1534,plain,
! [SV217: $i] :
( ( ! [SY1521: $i,SY1522: $i,SY1523: $i] :
( ( c_ListOrder_Ostep1 @ SV217 @ SY1521 @ SY1522 @ SY1523 )
| ! [SY1524: $i,SY1525: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV217 @ SY1524 ) @ SY1525 ) )
| ~ ( c_ListOrder_Ostep1 @ SV217 @ ( c_List_Olist_OCons @ SY1524 @ SY1521 @ SY1523 ) @ ( c_List_Olist_OCons @ SY1525 @ SY1522 @ SY1523 ) @ SY1523 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1535,plain,
! [SV218: $i] :
( ( ! [SY1526: $i,SY1527: $i,SY1528: $i,SY1529: $i] :
( ( c_ListOrder_Ostep1 @ SV218 @ ( c_List_Olist_OCons @ SY1526 @ SY1527 @ SY1528 ) @ ( c_List_Olist_OCons @ SY1526 @ SY1529 @ SY1528 ) @ SY1528 )
| ~ ( c_ListOrder_Ostep1 @ SV218 @ SY1527 @ SY1529 @ SY1528 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1536,plain,
! [SV219: $i] :
( ( ! [SY1530: $i,SY1531: $i] :
( ( c_List_Ohd @ ( c_List_Olist_OCons @ SV219 @ SY1530 @ SY1531 ) @ SY1531 )
= SV219 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1537,plain,
! [SV220: $i] :
( ( ! [SY1532: $i,SY1533: $i,SY1534: $i,SY1535: $i] :
( ( ( c_List_Oreplicate @ SV220 @ SY1532 @ SY1533 )
!= ( c_List_Oreplicate @ SY1534 @ SY1535 @ SY1533 ) )
| ( SY1532 = SY1535 )
| ( SV220
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1538,plain,
! [SV221: $i] :
( ( ! [SY1536: $i,SY1537: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV221 @ SY1536 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1537 @ SY1536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1539,plain,
! [SV222: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV222 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1540,plain,
! [SV223: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV223 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1541,plain,
! [SV224: $i] :
( ( ( SV224
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV224 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1158]) ).
thf(1542,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)],[1159]) ).
thf(1543,plain,
! [SV225: $i] :
( ( ! [SY1538: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV225 ) ) @ ( c_Lambda_OdB_OAbs @ SY1538 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV225 ) @ SY1538 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1160]) ).
thf(1544,plain,
! [SV226: $i] :
( ( ! [SY1539: $i,SY1540: $i] :
( ( c_List_Olast @ ( c_List_Oreplicate @ SV226 @ SY1539 @ SY1540 ) @ SY1540 )
= SY1539 )
| ( SV226
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1545,plain,
! [SV227: $i] :
( ( ! [SY1541: $i] :
( ~ ( class_Orderings_Oorder @ SV227 )
| ! [SY1542: $i] :
( ( c_HOL_Oord__class_Oless @ SY1541 @ SY1542 @ SV227 )
| ! [SY1543: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1541 @ SY1543 @ SV227 )
| ~ ( c_HOL_Oord__class_Oless @ SY1543 @ SY1542 @ SV227 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1546,plain,
! [SV228: $i] :
( ( ! [SY1544: $i] :
( ~ ( class_Orderings_Opreorder @ SV228 )
| ! [SY1545: $i] :
( ( c_HOL_Oord__class_Oless @ SY1544 @ SY1545 @ SV228 )
| ! [SY1546: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1546 @ SY1545 @ SV228 )
| ~ ( c_HOL_Oord__class_Oless @ SY1544 @ SY1546 @ SV228 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1547,plain,
! [SV229: $i] :
( ( ! [SY1547: $i] :
( ( ( c_List_Olast @ ( c_List_Orev @ SV229 @ SY1547 ) @ SY1547 )
= ( c_List_Ohd @ SV229 @ SY1547 ) )
| ( SV229
= ( c_List_Olist_ONil @ SY1547 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1548,plain,
! [SV230: $i] :
( ( ! [SY1548: $i,SY1549: $i,SY1550: $i] :
( ! [SY1551: $i] :
( ( c_List_Oreplicate @ SV230 @ SY1548 @ SY1549 )
!= ( c_List_Oreplicate @ SY1550 @ SY1551 @ SY1549 ) )
| ( SV230 = SY1550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1549,plain,
! [SV231: $i] :
( ( ! [SY1552: $i] :
( SV231
= ( c_List_Orev @ ( c_List_Orev @ SV231 @ SY1552 ) @ SY1552 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1550,plain,
! [SV232: $i] :
( ( ! [SY1553: $i] :
( ( c_List_Orev @ ( c_List_Orev @ SV232 @ SY1553 ) @ SY1553 )
= SV232 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1167]) ).
thf(1551,plain,
! [SV233: $i] :
( ( ! [SY1554: $i] :
( ( c_List_Orev @ ( c_List_Orev @ SV233 @ SY1554 ) @ SY1554 )
= SV233 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1552,plain,
! [SV234: $i] :
( ( ! [SY1555: $i,SY1556: $i] :
( ( c_List_Orev @ ( c_List_Oreplicate @ SV234 @ SY1555 @ SY1556 ) @ SY1556 )
= ( c_List_Oreplicate @ SV234 @ SY1555 @ SY1556 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1553,plain,
! [SV235: $i] :
( ( ! [SY1557: $i] :
( ( ( c_List_Ohd @ ( c_List_Orev @ SV235 @ SY1557 ) @ SY1557 )
= ( c_List_Olast @ SV235 @ SY1557 ) )
| ( SV235
= ( c_List_Olist_ONil @ SY1557 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1170]) ).
thf(1554,plain,
! [SV236: $i] :
( ( ! [SY1558: $i,SY1559: $i] :
( ( c_List_Ohd @ ( c_List_Oreplicate @ SV236 @ SY1558 @ SY1559 ) @ SY1559 )
= SY1558 )
| ( SV236
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1171]) ).
thf(1555,plain,
! [SV237: $i] :
( ( ! [SY1560: $i,SY1561: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV237 ) @ SY1560 @ SY1561 )
= ( c_Lambda_OdB_OVar @ SV237 ) )
| ( SV237 = SY1561 )
| ( c_HOL_Oord__class_Oless @ SY1561 @ SV237 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1556,plain,
! [SV238: $i] :
( ( ! [SY1562: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV238 )
!= ( c_Lambda_OdB_OAbs @ SY1562 ) )
| ( SV238 = SY1562 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1557,plain,
! [SV239: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV239 @ SV239 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1558,plain,
! [SV240: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV240 @ SV240 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1559,plain,
! [SV241: $i] :
( ( ~ ( class_Orderings_Oorder @ SV241 )
| ! [SY1563: $i] :
~ ( c_HOL_Oord__class_Oless @ SY1563 @ SY1563 @ SV241 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1176]) ).
thf(1560,plain,
! [SV242: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV242 )
| ! [SY1564: $i] :
~ ( c_HOL_Oord__class_Oless @ SY1564 @ SY1564 @ SV242 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1561,plain,
! [SV243: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV243 )
| ! [SY1565: $i] :
~ ( c_HOL_Oord__class_Oless @ SY1565 @ SY1565 @ SV243 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1562,plain,
! [SV244: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV244 )
| ! [SY1566: $i,SY1567: $i] :
( ( c_HOL_Oord__class_Oless @ SY1566 @ SY1567 @ SV244 )
| ( SY1567 = SY1566 )
| ( c_HOL_Oord__class_Oless @ SY1567 @ SY1566 @ SV244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1563,plain,
! [SV245: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV245 )
| ! [SY1568: $i,SY1569: $i] :
( ( SY1568 = SY1569 )
| ( c_HOL_Oord__class_Oless @ SY1569 @ SY1568 @ SV245 )
| ( c_HOL_Oord__class_Oless @ SY1568 @ SY1569 @ SV245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1180]) ).
thf(1564,plain,
! [SV246: $i] :
( ( ! [SY1570: $i] :
( ( c_HOL_Oord__class_Oless @ SV246 @ SY1570 @ tc_nat )
| ( SY1570 = SV246 )
| ( c_HOL_Oord__class_Oless @ SY1570 @ SV246 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1565,plain,
! [SV247: $i] :
( ( ! [SY1571: $i,SY1572: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV247 @ SY1571 ) @ SY1572 ) )
| ( c_HOL_Oord__class_Oless @ SY1571 @ SY1572 @ tc_nat )
| ( SY1572 = SY1571 )
| ( c_HOL_Oord__class_Oless @ SY1572 @ SY1571 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1566,plain,
! [SV248: $i] :
( ( ! [SY1573: $i] :
( ( c_HOL_Oord__class_Oless @ SV248 @ SY1573 @ tc_nat )
| ( SY1573 = SV248 )
| ( c_HOL_Oord__class_Oless @ SY1573 @ SV248 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1183]) ).
thf(1567,plain,
! [SV249: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV249 )
| ! [SY1574: $i,SY1575: $i] :
( ( c_HOL_Oord__class_Oless @ SY1574 @ SY1575 @ SV249 )
| ( SY1575 = SY1574 )
| ( c_HOL_Oord__class_Oless @ SY1575 @ SY1574 @ SV249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1568,plain,
! [SV250: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV250 )
| ! [SY1576: $i,SY1577: $i] :
( ( c_HOL_Oord__class_Oless @ SY1576 @ SY1577 @ SV250 )
| ( SY1577 = SY1576 )
| ( c_HOL_Oord__class_Oless @ SY1577 @ SY1576 @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1569,plain,
! [SV251: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV251 )
| ! [SY1578: $i,SY1579: $i] :
( ( SY1578 = SY1579 )
| ( c_HOL_Oord__class_Oless @ SY1578 @ SY1579 @ SV251 )
| ( c_HOL_Oord__class_Oless @ SY1579 @ SY1578 @ SV251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1186]) ).
thf(1570,plain,
! [SV252: $i] :
( ( ! [SY1580: $i,SY1581: $i] :
( ( ( c_List_Orev @ SV252 @ SY1580 )
!= ( c_List_Orev @ SY1581 @ SY1580 ) )
| ( SV252 = SY1581 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1571,plain,
! [SV253: $i] :
( ( ! [SY1582: $i,SY1583: $i] :
( ( c_Type_Otyping @ SV253 @ SY1582 @ SY1583 )
| ! [SY1584: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1584 ) @ SY1582 ) )
| ~ ( c_Type_Otyping @ SV253 @ SY1584 @ SY1583 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1572,plain,
! [SV254: $i] :
( ( ~ ( class_Orderings_Oorder @ SV254 )
| ! [SY1585: $i,SY1586: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1585 @ SY1586 @ SV254 )
| ~ ( c_HOL_Oord__class_Oless @ SY1586 @ SY1585 @ SV254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1573,plain,
! [SV255: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV255 )
| ! [SY1587: $i,SY1588: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1587 @ SY1588 @ SV255 )
| ~ ( c_HOL_Oord__class_Oless @ SY1588 @ SY1587 @ SV255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1190]) ).
thf(1574,plain,
! [SV256: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV256 )
| ! [SY1589: $i,SY1590: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1589 @ SY1590 @ SV256 )
| ~ ( c_HOL_Oord__class_Oless @ SY1590 @ SY1589 @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1191]) ).
thf(1575,plain,
! [SV257: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV257 )
| ! [SY1591: $i,SY1592: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1591 @ SY1592 @ SV257 )
| ~ ( c_HOL_Oord__class_Oless @ SY1592 @ SY1591 @ SV257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1192]) ).
thf(1576,plain,
! [SV258: $i] :
( ( ! [SY1593: $i,SY1594: $i] :
( ( ( c_List_Otl @ ( c_List_Oappend @ SV258 @ SY1593 @ SY1594 ) @ SY1594 )
= ( c_List_Oappend @ ( c_List_Otl @ SV258 @ SY1594 ) @ SY1593 @ SY1594 ) )
| ( SV258
= ( c_List_Olist_ONil @ SY1594 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1193]) ).
thf(1577,plain,
! [SV259: $i] :
( ( ! [SY1595: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ SV259 @ ( c_List_Olist_ONil @ SY1595 ) @ SY1595 ) @ SY1595 )
= ( c_List_Obutlast @ SV259 @ SY1595 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1578,plain,
! [SV260: $i] :
( ( ! [SY1596: $i,SY1597: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ SV260 @ SY1596 @ SY1597 ) @ SY1597 )
= ( c_List_Ohd @ SV260 @ SY1597 ) )
| ( SV260
= ( c_List_Olist_ONil @ SY1597 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1579,plain,
! [SV261: $i] :
( ( ! [SY1598: $i] :
( ( c_Lambda_Osubstn @ SV261 @ SY1598 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_Lambda_Osubst @ SV261 @ SY1598 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1580,plain,
! [SV262: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_Lambda_OdB_OVar @ SV262 ) @ tc_Lambda_OdB )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1581,plain,
! [SV263: $i] :
( ( ( c_Lambda_OdB_OdB__size @ ( c_Lambda_OdB_OVar @ SV263 ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1582,plain,
! [SV264: $i] :
( ( ! [SY1599: $i,SY1600: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV264 @ SY1599 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY1600 ) )
| ( SV264
= ( c_Lambda_OdB_OAbs @ SY1600 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(1583,plain,
! [SV265: $i] :
( ( ! [SY1601: $i,SY1602: $i] :
( ! [SY1603: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV265 ) @ SY1601 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1602 ) @ SY1603 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV265 = SY1602 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1584,plain,
! [SV266: $i] :
( ( ! [SY1604: $i,SY1605: $i,SY1606: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV266 ) @ SY1604 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1605 ) @ SY1606 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1604 = SY1606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1585,plain,
! [SV267: $i] :
( ( ! [SY1607: $i,SY1608: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV267 @ SY1607 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1608 @ SY1607 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV267 ) @ SY1608 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1202]) ).
thf(1586,plain,
! [SV268: $i] :
( ( ! [SY1609: $i] :
( ! [SY1610: $i] :
( ( c_Lambda_OdB_OAbs @ SV268 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1609 @ SY1610 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV268 )
= SY1609 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1587,plain,
! [SV269: $i] :
( ( ! [SY1611: $i,SY1612: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV269 ) @ SY1611 @ SY1612 )
= ( c_Lambda_OdB_OVar @ SV269 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV269 @ SY1612 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1588,plain,
! [SV270: $i] :
( ( ! [SY1613: $i,SY1614: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV270 ) @ SY1613 @ SY1614 )
= ( c_Lambda_OdB_OVar @ SV270 ) )
| ( SV270 = SY1614 )
| ( c_HOL_Oord__class_Oless @ SY1614 @ SV270 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1589,plain,
! [SV271: $i] :
( ( ! [SY1615: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV271 ) @ SY1615 @ SV271 )
= SY1615 )
| ( c_HOL_Oord__class_Oless @ SV271 @ SV271 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1206]) ).
thf(1590,plain,
! [SV272: $i] :
( ( ! [SY1616: $i,SY1617: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ SV272 @ SY1616 @ SY1617 ) @ SY1617 )
= ( c_List_Olist_ONil @ SY1617 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1591,plain,
! [SV273: $i] :
( ( ! [SY1618: $i,SY1619: $i,SY1620: $i,SY1621: $i] :
( ( ( c_List_Olist_OCons @ SV273 @ SY1618 @ SY1619 )
!= ( c_List_Oappend @ SY1620 @ SY1621 @ SY1619 ) )
| ( SY1618
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV273 @ SY1618 @ SY1620 @ SY1621 @ SY1619 ) @ SY1621 @ SY1619 ) )
| ( SY1620
= ( c_List_Olist_ONil @ SY1619 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1208]) ).
thf(1592,plain,
! [SV274: $i] :
( ( ! [SY1622: $i,SY1623: $i,SY1624: $i,SY1625: $i] :
( ( ( c_List_Oappend @ SV274 @ SY1622 @ SY1623 )
!= ( c_List_Olist_OCons @ SY1624 @ SY1625 @ SY1623 ) )
| ( SV274
= ( c_List_Olist_OCons @ SY1624 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY1624 @ SY1625 @ SV274 @ SY1622 @ SY1623 ) @ SY1623 ) )
| ( SV274
= ( c_List_Olist_ONil @ SY1623 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1593,plain,
! [SV275: $i] :
( ( ! [SY1626: $i,SY1627: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ SV275 @ ( c_List_Olist_OCons @ SY1626 @ ( c_List_Olist_ONil @ SY1627 ) @ SY1627 ) @ SY1627 ) @ SY1627 )
= SY1626 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1594,plain,
! [SV276: $i] :
( ( ! [SY1628: $i,SY1629: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ SV276 @ ( c_List_Olist_OCons @ SY1628 @ ( c_List_Olist_ONil @ SY1629 ) @ SY1629 ) @ SY1629 ) @ SY1629 )
= SV276 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1595,plain,
! [SV277: $i] :
( ( ! [SY1630: $i,SY1631: $i,SY1632: $i] :
( ( SV277 = SY1630 )
| ( SY1631 = SY1632 )
| ! [SY1633: $i,SY1634: $i] :
~ ( c_ListOrder_Ostep1 @ SY1633 @ ( c_List_Oappend @ SV277 @ ( c_List_Olist_OCons @ SY1631 @ ( c_List_Olist_ONil @ SY1634 ) @ SY1634 ) @ SY1634 ) @ ( c_List_Oappend @ SY1630 @ ( c_List_Olist_OCons @ SY1632 @ ( c_List_Olist_ONil @ SY1634 ) @ SY1634 ) @ SY1634 ) @ SY1634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1596,plain,
! [SV278: $i] :
( ( ! [SY1635: $i,SY1636: $i,SY1637: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV278 @ SY1635 ) @ SY1636 ) )
| ( SY1635 = SY1636 )
| ! [SY1638: $i,SY1639: $i] :
~ ( c_ListOrder_Ostep1 @ SV278 @ ( c_List_Oappend @ SY1637 @ ( c_List_Olist_OCons @ SY1635 @ ( c_List_Olist_ONil @ SY1638 ) @ SY1638 ) @ SY1638 ) @ ( c_List_Oappend @ SY1639 @ ( c_List_Olist_OCons @ SY1636 @ ( c_List_Olist_ONil @ SY1638 ) @ SY1638 ) @ SY1638 ) @ SY1638 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1597,plain,
! [SV279: $i] :
( ( ! [SY1640: $i,SY1641: $i,SY1642: $i,SY1643: $i] :
( ( ( c_List_Oappend @ SV279 @ SY1640 @ SY1641 )
!= ( c_List_Olist_OCons @ SY1642 @ SY1643 @ SY1641 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY1642 @ SY1643 @ SV279 @ SY1640 @ SY1641 ) @ SY1640 @ SY1641 )
= SY1643 )
| ( SV279
= ( c_List_Olist_ONil @ SY1641 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1598,plain,
! [SV280: $i] :
( ( ! [SY1644: $i,SY1645: $i,SY1646: $i,SY1647: $i] :
( ( ( c_List_Olist_OCons @ SV280 @ SY1644 @ SY1645 )
!= ( c_List_Oappend @ SY1646 @ SY1647 @ SY1645 ) )
| ( ( c_List_Olist_OCons @ SV280 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV280 @ SY1644 @ SY1646 @ SY1647 @ SY1645 ) @ SY1645 )
= SY1646 )
| ( SY1646
= ( c_List_Olist_ONil @ SY1645 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1599,plain,
! [SV281: $i] :
( ( ! [SY1648: $i,SY1649: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ SV281 @ SY1648 @ SY1649 ) @ SY1649 )
= ( c_List_Oappend @ ( c_List_Orev @ SY1648 @ SY1649 ) @ ( c_List_Olist_OCons @ SV281 @ ( c_List_Olist_ONil @ SY1649 ) @ SY1649 ) @ SY1649 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1216]) ).
thf(1600,plain,
! [SV282: $i] :
( ( ! [SY1650: $i,SY1651: $i,SY1652: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV282 @ SY1650 ) @ SY1651 ) )
| ! [SY1653: $i,SY1654: $i] :
( ( c_ListOrder_Ostep1 @ SV282 @ SY1652 @ SY1653 @ SY1654 )
| ~ ( c_ListOrder_Ostep1 @ SV282 @ ( c_List_Oappend @ SY1652 @ ( c_List_Olist_OCons @ SY1650 @ ( c_List_Olist_ONil @ SY1654 ) @ SY1654 ) @ SY1654 ) @ ( c_List_Oappend @ SY1653 @ ( c_List_Olist_OCons @ SY1651 @ ( c_List_Olist_ONil @ SY1654 ) @ SY1654 ) @ SY1654 ) @ SY1654 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1217]) ).
thf(1601,plain,
! [SV283: $i] :
( ( ! [SY1655: $i,SY1656: $i,SY1657: $i] :
( ( ( c_List_Orev @ SV283 @ SY1655 )
!= ( c_List_Olist_OCons @ SY1656 @ SY1657 @ SY1655 ) )
| ( SV283
= ( c_List_Oappend @ ( c_List_Orev @ SY1657 @ SY1655 ) @ ( c_List_Olist_OCons @ SY1656 @ ( c_List_Olist_ONil @ SY1655 ) @ SY1655 ) @ SY1655 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1218]) ).
thf(1602,plain,
! [SV284: $i] :
( ( ! [SY1658: $i,SY1659: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ SV284 @ SY1658 ) @ ( c_List_Olist_OCons @ SY1659 @ ( c_List_Olist_ONil @ SY1658 ) @ SY1658 ) @ SY1658 ) @ SY1658 )
= ( c_List_Olist_OCons @ SY1659 @ SV284 @ SY1658 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1219]) ).
thf(1603,plain,
! [SV285: $i] :
( ( ! [SY1660: $i,SY1661: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ SV285 @ SY1660 @ SY1661 ) @ SY1661 )
= ( c_List_Oappend @ SY1660 @ ( c_List_Olist_OCons @ SV285 @ ( c_List_Olist_ONil @ SY1661 ) @ SY1661 ) @ SY1661 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1604,plain,
! [SV286: $i] :
( ( ! [SY1662: $i,SY1663: $i,SY1664: $i] :
( ( SV286 = SY1662 )
| ( c_ListOrder_Ostep1 @ SY1663 @ SV286 @ SY1662 @ SY1664 )
| ! [SY1665: $i,SY1666: $i] :
~ ( c_ListOrder_Ostep1 @ SY1663 @ ( c_List_Oappend @ SV286 @ ( c_List_Olist_OCons @ SY1665 @ ( c_List_Olist_ONil @ SY1664 ) @ SY1664 ) @ SY1664 ) @ ( c_List_Oappend @ SY1662 @ ( c_List_Olist_OCons @ SY1666 @ ( c_List_Olist_ONil @ SY1664 ) @ SY1664 ) @ SY1664 ) @ SY1664 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1605,plain,
! [SV287: $i] :
( ( ! [SY1667: $i,SY1668: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV287 @ SY1667 @ SY1668 ) @ ( c_List_Olist_OCons @ SY1667 @ ( c_List_Olist_ONil @ SY1668 ) @ SY1668 ) @ SY1668 )
= ( c_List_Olist_OCons @ SY1667 @ ( c_List_Oreplicate @ SV287 @ SY1667 @ SY1668 ) @ SY1668 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1606,plain,
! [SV288: $i] :
( ( ! [SY1669: $i,SY1670: $i] :
( ( SV288 = SY1669 )
| ! [SY1671: $i,SY1672: $i] :
( ~ ( c_Type_Otyping @ SY1670 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1671 ) @ SY1672 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1669 )
| ~ ( c_Type_Otyping @ SY1670 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1671 ) @ SY1672 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV288 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1223]) ).
thf(1607,plain,
! [SV289: $i] :
( ( ! [SY1673: $i,SY1674: $i,SY1675: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV289 ) @ SY1673 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1674 ) @ SY1675 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1608,plain,
! [SV290: $i] :
( ( ! [SY1676: $i,SY1677: $i,SY1678: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV290 ) ) @ SY1676 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1677 ) @ SY1678 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1609,plain,
! [SV291: $i] :
( ( ! [SY1679: $i,SY1680: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV291 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1679 @ SY1680 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1680
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1610,plain,
! [SV292: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV292 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV292 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1611,plain,
! [SV293: $i] :
( ( ! [SY1681: $i,SY1682: $i,SY1683: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV293 ) @ SY1681 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1682 @ SY1683 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV293
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1682 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV293 @ SY1681 @ SY1682 @ SY1683 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1683
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1228]) ).
thf(1612,plain,
! [SV294: $i] :
( ( ! [SY1684: $i] :
( ! [SY1685: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV294 @ SY1684 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY1685 ) )
| ( SY1684
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1613,plain,
! [SV295: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV295 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV295 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1230]) ).
thf(1614,plain,
! [SV296: $i] :
( ( ! [SY1686: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV296 ) @ SY1686 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SY1686 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1231]) ).
thf(1615,plain,
! [SV297: $i] :
( ( ! [SY1687: $i,SY1688: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV297 ) ) @ SY1687 ) @ SY1688 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1687 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV297 @ SY1687 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1688 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1616,plain,
! [SV298: $i] :
( ( ! [SY1689: $i,SY1690: $i,SY1691: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV298 ) @ SY1689 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1690 @ SY1691 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1691
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV298 @ SY1689 @ SY1690 @ SY1691 ) @ ( c_List_Olist_OCons @ SY1689 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( SY1691
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1233]) ).
thf(1617,plain,
! [SV299: $i] :
( ( ! [SY1692: $i,SY1693: $i,SY1694: $i] :
( ( c_List_Oappend @ SV299 @ ( c_List_Oappend @ SY1692 @ SY1693 @ SY1694 ) @ SY1694 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV299 @ SY1692 @ SY1694 ) @ SY1693 @ SY1694 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1234]) ).
thf(1618,plain,
! [SV300: $i] :
( ( ! [SY1695: $i,SY1696: $i,SY1697: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV300 @ SY1695 @ SY1696 ) @ SY1697 @ SY1696 )
= ( c_List_Oappend @ SV300 @ ( c_List_Oappend @ SY1695 @ SY1697 @ SY1696 ) @ SY1696 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1619,plain,
! [SV301: $i] :
( ( ! [SY1698: $i,SY1699: $i,SY1700: $i] :
( ( c_List_Oappend @ SV301 @ ( c_List_Oappend @ SY1698 @ SY1699 @ SY1700 ) @ SY1700 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV301 @ SY1698 @ SY1700 ) @ SY1699 @ SY1700 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1620,plain,
! [SV302: $i] :
( ( ! [SY1701: $i,SY1702: $i,SY1703: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV302 @ SY1701 @ SY1702 ) @ SY1703 @ SY1702 )
= ( c_List_Oappend @ SV302 @ ( c_List_Oappend @ SY1701 @ SY1703 @ SY1702 ) @ SY1702 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1237]) ).
thf(1621,plain,
! [SV303: $i] :
( ( ! [SY1704: $i] :
( ( ( c_List_Oappend @ SV303 @ ( c_List_Olist_OCons @ SY1704 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
| ! [SY1705: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1705 @ SV303 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1704 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1705 @ ( c_List_Oappend @ SV303 @ ( c_List_Olist_OCons @ SY1704 @ ( 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)],[1238]) ).
thf(1622,plain,
! [SV304: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV304 ) @ ( c_List_Olist_ONil @ SV304 ) @ SV304 )
= ( c_List_Olist_ONil @ SV304 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1239]) ).
thf(1623,plain,
! [SV305: $i] :
( ( ! [SY1706: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV305 ) @ SY1706 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV305 ) @ SY1706 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1240]) ).
thf(1624,plain,
! [SV306: $i] :
( ( ! [SY1707: $i,SY1708: $i,SY1709: $i,SY1710: $i] :
( ( ( c_List_Oappend @ SV306 @ ( c_List_Olist_OCons @ SY1707 @ ( c_List_Olist_ONil @ SY1708 ) @ SY1708 ) @ SY1708 )
!= ( c_List_Oappend @ SY1709 @ ( c_List_Olist_OCons @ SY1710 @ ( c_List_Olist_ONil @ SY1708 ) @ SY1708 ) @ SY1708 ) )
| ( SY1707 = SY1710 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1625,plain,
! [SV307: $i] :
( ( ! [SY1711: $i,SY1712: $i,SY1713: $i] :
( ! [SY1714: $i] :
( ( c_List_Oappend @ SV307 @ ( c_List_Olist_OCons @ SY1711 @ ( c_List_Olist_ONil @ SY1712 ) @ SY1712 ) @ SY1712 )
!= ( c_List_Oappend @ SY1713 @ ( c_List_Olist_OCons @ SY1714 @ ( c_List_Olist_ONil @ SY1712 ) @ SY1712 ) @ SY1712 ) )
| ( SV307 = SY1713 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1242]) ).
thf(1626,plain,
! [SV308: $i] :
( ( ! [SY1715: $i,SY1716: $i,SY1717: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV308 ) @ SY1715 ) @ SY1716 @ SY1717 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV308 @ SY1716 @ SY1717 ) ) @ ( c_Lambda_Osubst @ SY1715 @ SY1716 @ SY1717 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1627,plain,
! [SV309: $i] :
( ( ! [SY1718: $i] :
( ( ( c_Lambda_OdB_OVar @ SV309 )
!= ( c_Lambda_OdB_OVar @ SY1718 ) )
| ( SV309 = SY1718 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1628,plain,
! [SV310: $i] :
( ( ! [SY1719: $i,SY1720: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV310 @ SY1719 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1720 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV310 @ ( c_List_Oappend @ SY1719 @ ( c_List_Olist_OCons @ SY1720 @ ( 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)],[1245]) ).
thf(1629,plain,
! [SV311: $i] :
( ( ! [SY1721: $i,SY1722: $i] :
( ! [SY1723: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV311 ) @ SY1721 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1722 ) @ SY1723 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV311 = SY1722 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1630,plain,
! [SV312: $i] :
( ( ! [SY1724: $i,SY1725: $i,SY1726: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV312 ) @ SY1724 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1725 ) @ SY1726 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1724 = SY1726 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1631,plain,
! [SV313: $i] :
( ( ! [SY1727: $i,SY1728: $i,SY1729: $i,SY1730: $i] :
( ( ( c_List_Olist_OCons @ SV313 @ SY1727 @ SY1728 )
!= ( c_List_Olist_OCons @ SY1729 @ SY1730 @ SY1728 ) )
| ( SY1727 = SY1730 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1632,plain,
! [SV314: $i] :
( ( ! [SY1731: $i,SY1732: $i,SY1733: $i] :
( ! [SY1734: $i] :
( ( c_List_Olist_OCons @ SV314 @ SY1731 @ SY1732 )
!= ( c_List_Olist_OCons @ SY1733 @ SY1734 @ SY1732 ) )
| ( SV314 = SY1733 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1633,plain,
! [SV315: $i] :
( ( ! [SY1735: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV315 ) @ SY1735 @ SV315 )
= SY1735 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1634,plain,
! [SV316: $i] :
( ( ! [SY1736: $i,SY1737: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV316 ) @ ( c_List_Olist_OCons @ SY1736 @ SY1737 @ SV316 ) @ SV316 )
= ( c_List_Olist_OCons @ SY1736 @ SY1737 @ SV316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1635,plain,
! [SV317: $i] :
( ( ! [SY1738: $i,SY1739: $i] :
( ( SV317
!= ( c_List_Oappend @ SY1738 @ SV317 @ SY1739 ) )
| ( SY1738
= ( c_List_Olist_ONil @ SY1739 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1636,plain,
! [SV318: $i] :
( ( ! [SY1740: $i,SY1741: $i] :
( ( ( c_List_Oappend @ SV318 @ SY1740 @ SY1741 )
!= SY1740 )
| ( SV318
= ( c_List_Olist_ONil @ SY1741 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1637,plain,
! [SV319: $i] :
( ( ! [SY1742: $i,SY1743: $i] :
( ( SV319
!= ( c_List_Oappend @ SV319 @ SY1742 @ SY1743 ) )
| ( SY1742
= ( c_List_Olist_ONil @ SY1743 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1638,plain,
! [SV320: $i] :
( ( ! [SY1744: $i,SY1745: $i] :
( ( ( c_List_Oappend @ SV320 @ SY1744 @ SY1745 )
!= SV320 )
| ( SY1744
= ( c_List_Olist_ONil @ SY1745 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1639,plain,
! [SV321: $i] :
( ( ! [SY1746: $i,SY1747: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV321 @ ( c_Lambda_OdB_OVar @ SY1746 ) @ SY1747 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1640,plain,
! [SV322: $i] :
( ( ! [SY1748: $i,SY1749: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV322 ) @ SY1748 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1749 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV322 ) @ SY1748 )
= SY1749 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1641,plain,
! [SV323: $i] :
( ( ! [SY1750: $i,SY1751: $i] :
( ( c_List_Olist_ONil @ SV323 )
!= ( c_List_Olist_OCons @ SY1750 @ SY1751 @ SV323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1642,plain,
! [SV324: $i] :
( ( ! [SY1752: $i,SY1753: $i] :
( ! [SY1754: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV324 ) @ SY1752 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1753 ) @ SY1754 ) )
| ( SV324 = SY1753 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1643,plain,
! [SV325: $i] :
( ( ! [SY1755: $i,SY1756: $i,SY1757: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV325 ) @ SY1755 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1756 ) @ SY1757 ) )
| ( SY1755 = SY1757 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1644,plain,
! [SV326: $i] :
( ( ! [SY1758: $i] :
( ! [SY1759: $i] :
( ( c_Lambda_OdB_OVar @ SV326 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1758 @ SY1759 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV326 )
= SY1758 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1645,plain,
! [SV327: $i] :
( ( ! [SY1760: $i,SY1761: $i] :
( ( c_Lambda_OdB_OVar @ SV327 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1760 ) @ SY1761 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1646,plain,
! [SV328: $i] :
( ( ! [SY1762: $i,SY1763: $i] :
( ( ( c_List_Oappend @ SV328 @ SY1762 @ SY1763 )
!= ( c_List_Olist_ONil @ SY1763 ) )
| ( SY1762
= ( c_List_Olist_ONil @ SY1763 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1647,plain,
! [SV329: $i] :
( ( ! [SY1764: $i,SY1765: $i] :
( ( ( c_List_Oappend @ SV329 @ SY1764 @ SY1765 )
!= ( c_List_Olist_ONil @ SY1765 ) )
| ( SV329
= ( c_List_Olist_ONil @ SY1765 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1264]) ).
thf(1648,plain,
! [SV330: $i] :
( ( ! [SY1766: $i,SY1767: $i] :
( ( SV330
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV330 ) @ SY1766 ) @ SY1767 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV330 ) @ SY1766 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV330 ) @ SY1766 ) @ ( c_List_Oappend @ SY1767 @ ( c_List_Olist_OCons @ SY1766 @ ( 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)],[1265]) ).
thf(1649,plain,
! [SV331: $i] :
( ( ! [SY1768: $i,SY1769: $i] :
( ( ( c_List_Olist_ONil @ SV331 )
!= ( c_List_Oappend @ SY1768 @ SY1769 @ SV331 ) )
| ( SY1769
= ( c_List_Olist_ONil @ SV331 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1650,plain,
! [SV332: $i] :
( ( ! [SY1770: $i] :
( ! [SY1771: $i] :
( ( c_List_Olist_ONil @ SV332 )
!= ( c_List_Oappend @ SY1770 @ SY1771 @ SV332 ) )
| ( SY1770
= ( c_List_Olist_ONil @ SV332 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1651,plain,
! [SV333: $i] :
( ( ! [SY1772: $i,SY1773: $i,SY1774: $i] :
( ( c_List_Ofoldl @ SV333 @ SY1772 @ ( c_List_Olist_ONil @ SY1773 ) @ SY1774 @ SY1773 )
= SY1772 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1268]) ).
thf(1652,plain,
! [SV334: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ SV334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1269]) ).
thf(1653,plain,
! [SV335: $i] :
( ( ! [SY1775: $i] :
( SV335
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY1775 ) @ SV335 @ SY1775 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1654,plain,
! [SV336: $i] :
( ( ! [SY1776: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV336 ) @ SY1776 @ SV336 )
= SY1776 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1271]) ).
thf(1655,plain,
! [SV337: $i] :
( ( ! [SY1777: $i] :
( SV337
= ( c_List_Oappend @ SV337 @ ( c_List_Olist_ONil @ SY1777 ) @ SY1777 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1656,plain,
! [SV338: $i] :
( ( ! [SY1778: $i] :
( SV338
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY1778 ) @ SV338 @ SY1778 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1657,plain,
! [SV339: $i] :
( ( ! [SY1779: $i] :
( ( c_List_Oappend @ SV339 @ ( c_List_Olist_ONil @ SY1779 ) @ SY1779 )
= SV339 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1274]) ).
thf(1658,plain,
! [SV340: $i] :
( ( ! [SY1780: $i,SY1781: $i,SY1782: $i] :
( ( ( c_List_Oappend @ SV340 @ SY1780 @ SY1781 )
!= ( c_List_Oappend @ SV340 @ SY1782 @ SY1781 ) )
| ( SY1780 = SY1782 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(1659,plain,
! [SV341: $i] :
( ( ! [SY1783: $i,SY1784: $i,SY1785: $i] :
( ( ( c_List_Oappend @ SV341 @ SY1783 @ SY1784 )
!= ( c_List_Oappend @ SY1785 @ SY1783 @ SY1784 ) )
| ( SV341 = SY1785 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1660,plain,
! [SV342: $i] :
( ( ( c_Lambda_OdB_OVar @ SV342 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV342 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1661,plain,
! [SV343: $i] :
( ( ! [SY1786: $i,SY1787: $i,SY1788: $i,SY1789: $i,SY1790: $i] :
( ( c_List_Ofoldl @ SV343 @ SY1786 @ ( c_List_Olist_OCons @ SY1787 @ SY1788 @ SY1789 ) @ SY1790 @ SY1789 )
= ( c_List_Ofoldl @ SV343 @ ( hAPP @ ( hAPP @ SV343 @ SY1786 ) @ SY1787 ) @ SY1788 @ SY1790 @ SY1789 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1278]) ).
thf(1662,plain,
! [SV344: $i] :
( ( ! [SY1791: $i,SY1792: $i,SY1793: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV344 @ SY1791 @ SY1792 ) @ SY1793 @ SY1792 )
= ( c_List_Olist_OCons @ SV344 @ ( c_List_Oappend @ SY1791 @ SY1793 @ SY1792 ) @ SY1792 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1279]) ).
thf(1663,plain,
! [SV345: $i] :
( ( ! [SY1794: $i,SY1795: $i,SY1796: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV345 @ SY1794 @ SY1795 ) @ SY1796 @ SY1795 )
= ( c_List_Olist_OCons @ SV345 @ ( c_List_Oappend @ SY1794 @ SY1796 @ SY1795 ) @ SY1795 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1280]) ).
thf(1664,plain,
! [SV346: $i] :
( ( ! [SY1797: $i,SY1798: $i,SY1799: $i] :
( ( c_List_Olist_OCons @ SV346 @ ( c_List_Oappend @ SY1797 @ SY1798 @ SY1799 ) @ SY1799 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV346 @ SY1797 @ SY1799 ) @ SY1798 @ SY1799 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1281]) ).
thf(1665,plain,
! [SV347: $i] :
( ( ! [SY1800: $i,SY1801: $i,SY1802: $i] :
( ( c_List_Olist_OCons @ SV347 @ ( c_List_Oappend @ SY1800 @ SY1801 @ SY1802 ) @ SY1802 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV347 @ SY1800 @ SY1802 ) @ SY1801 @ SY1802 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1666,plain,
! [SV348: $i] :
( ( ! [SY1803: $i,SY1804: $i] :
( ( c_List_Olist_OCons @ SV348 @ SY1803 @ SY1804 )
!= ( c_List_Olist_ONil @ SY1804 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1667,plain,
! [SV349: $i] :
( ( ! [SY1805: $i,SY1806: $i] :
( ( c_List_Olist_OCons @ SV349 @ SY1805 @ SY1806 )
!= ( c_List_Olist_ONil @ SY1806 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1668,plain,
! [SV350: $i] :
( ( ! [SY1807: $i,SY1808: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV350 @ SY1807 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1808 @ SY1807 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV350 = SY1808 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1285]) ).
thf(1669,plain,
! [SV351: $i] :
( ( ! [SY1809: $i,SY1810: $i] :
( ( c_List_Olist_OCons @ SV351 @ SY1809 @ SY1810 )
!= SY1809 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1286]) ).
thf(1670,plain,
! [SV352: $i] :
( ( ! [SY1811: $i,SY1812: $i] :
( SV352
!= ( c_List_Olist_OCons @ SY1811 @ SV352 @ SY1812 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1671,plain,
! [SV353: $i] :
( ( ! [SY1813: $i,SY1814: $i] :
( ( ( c_Lambda_OdB_OVar @ SV353 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1813 @ SY1814 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1814
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1672,plain,
! [SV354: $i] :
( ( ! [SY1815: $i,SY1816: $i] :
( ( c_List_Olist_OCons @ SV354 @ SY1815 @ SY1816 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY1816 ) @ ( c_List_Olist_OCons @ SV354 @ SY1815 @ SY1816 ) @ SY1816 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1673,plain,
! [SV355: $i] :
( ( ( c_List_Olist_ONil @ SV355 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV355 ) @ ( c_List_Olist_ONil @ SV355 ) @ SV355 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1290]) ).
thf(1674,plain,
! [SV356: $i] :
( ( ! [SY1817: $i,SY1818: $i,SY1819: $i,SY1820: $i,SY1821: $i] :
( ( c_List_Ofoldl @ SV356 @ SY1817 @ ( c_List_Oappend @ SY1818 @ SY1819 @ SY1820 ) @ SY1821 @ SY1820 )
= ( c_List_Ofoldl @ SV356 @ ( c_List_Ofoldl @ SV356 @ SY1817 @ SY1818 @ SY1821 @ SY1820 ) @ SY1819 @ SY1821 @ SY1820 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1291]) ).
thf(1675,plain,
! [SV357: $i] :
( ( ! [SY1822: $i,SY1823: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV357 ) @ SY1822 )
!= ( c_Lambda_OdB_OVar @ SY1823 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1676,plain,
! [SV358: $i] :
( ( ! [SY1824: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ SV358 @ SY1824 ) )
| ~ ( class_Orderings_Opreorder @ SY1824 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1677,plain,
! [SV359: $i] :
( ( ! [SY1825: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ SV359 @ SY1825 ) )
| ~ ( class_Orderings_Oorder @ SY1825 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1678,plain,
! [SV360: $i] :
( ( ! [SY1826: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV360 ) @ SY1826 ) @ SY1826 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1679,plain,
! [SV361: $i] :
( ( ! [SY1827: $i] :
( ( SV361 = SY1827 )
| ! [SY1828: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY1828 ) @ SV361 ) @ SY1827 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1680,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[1316]) ).
thf(1681,plain,
! [SV362: $i,SV1: $i] :
( ( ! [SY1829: $i,SY1830: $i,SY1831: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV1 @ ( c_List_Olist_OCons @ SV362 @ SY1829 @ SY1830 ) @ SY1830 ) @ ( c_Nat_Osize__class_Osize @ SV1 @ ( tc_List_Olist @ SY1830 ) ) @ SY1831 @ SY1830 )
= ( c_List_Oappend @ SV1 @ ( c_List_Olist_OCons @ SY1831 @ SY1829 @ SY1830 ) @ SY1830 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1318]) ).
thf(1682,plain,
! [SV363: $i,SV2: $i] :
( ( ! [SY1832: $i,SY1833: $i] :
( ( ( c_List_Olist__update @ SV2 @ SV363 @ SY1832 @ SY1833 )
!= ( c_List_Olist_ONil @ SY1833 ) )
| ( SV2
= ( c_List_Olist_ONil @ SY1833 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1319]) ).
thf(1683,plain,
! [SV364: $i,SV3: $i] :
( ( ! [SY1834: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV3 ) @ SV364 @ SY1834 @ SV3 )
= ( c_List_Olist_ONil @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1320]) ).
thf(1684,plain,
! [SV365: $i,SV4: $i] :
( ( ! [SY1835: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV4 ) @ SV365 @ SY1835 @ SV4 )
= ( c_List_Olist_ONil @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1685,plain,
! [SV366: $i,SV5: $i] :
( ( ! [SY1836: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV5 ) @ SV366 @ SY1836 @ SV5 )
= ( c_List_Olist_ONil @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1686,plain,
! [SV367: $i,SV6: $i] :
( ( ! [SY1837: $i,SY1838: $i] :
( ( ( c_List_Olist__update @ SV6 @ SV367 @ SY1837 @ SY1838 )
!= SV6 )
| ~ ( c_HOL_Oord__class_Oless @ SV367 @ ( c_Nat_Osize__class_Osize @ SV6 @ ( tc_List_Olist @ SY1838 ) ) @ tc_nat )
| ( ( c_List_Onth @ SV6 @ SV367 @ SY1838 )
= SY1837 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1687,plain,
! [SV368: $i,SV7: $i] :
( ( ! [SY1839: $i,SY1840: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ SV7 @ SV368 @ SY1839 @ SY1840 ) @ ( tc_List_Olist @ SY1840 ) )
= ( c_Nat_Osize__class_Osize @ SV7 @ ( tc_List_Olist @ SY1840 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1688,plain,
! [SV369: $i,SV8: $i] :
( ( ! [SY1841: $i,SY1842: $i,SY1843: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ SV8 @ SV369 @ SY1841 @ SY1842 ) @ SY1843 @ SY1842 )
= ( c_List_Onth @ SV8 @ SY1843 @ SY1842 ) )
| ( SV369 = SY1843 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1689,plain,
! [SV370: $i,SV9: $i] :
( ( ! [SY1844: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV9 @ ( c_Nat_Osize__class_Osize @ SV370 @ ( tc_List_Olist @ SY1844 ) ) @ tc_nat )
| ( ( c_List_Olist__update @ SV370 @ SV9 @ ( c_List_Onth @ SV370 @ SV9 @ SY1844 ) @ SY1844 )
= SV370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1326]) ).
thf(1690,plain,
! [SV371: $i,SV10: $i] :
( ( ! [SY1845: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV10 @ ( c_Nat_Osize__class_Osize @ SV371 @ ( tc_List_Olist @ SY1845 ) ) @ tc_nat )
| ! [SY1846: $i] :
( ( c_List_Onth @ ( c_List_Olist__update @ SV371 @ SV10 @ SY1846 @ SY1845 ) @ SV10 @ SY1845 )
= SY1846 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1327]) ).
thf(1691,plain,
! [SV372: $i,SV11: $i] :
( ( ! [SY1847: $i,SY1848: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ SV11 @ SV372 @ SY1847 @ SY1848 ) @ SV372 @ SY1848 )
= SY1847 )
| ~ ( c_HOL_Oord__class_Oless @ SV372 @ ( c_Nat_Osize__class_Osize @ SV11 @ ( tc_List_Olist @ SY1848 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1328]) ).
thf(1692,plain,
! [SV373: $i,SV12: $i] :
( ( ! [SY1849: $i,SY1850: $i] :
( ! [SY1851: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV12 @ SV373 @ SY1849 ) @ SY1850 @ SY1851 @ SY1849 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV12 @ SY1850 @ SY1851 @ SY1849 ) @ SV373 @ SY1849 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1850 @ ( c_Nat_Osize__class_Osize @ SV12 @ ( tc_List_Olist @ SY1849 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1329]) ).
thf(1693,plain,
! [SV374: $i,SV13: $i] :
( ( ! [SY1852: $i,SY1853: $i] :
( ! [SY1854: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV13 @ SV374 @ SY1852 ) @ SY1853 @ SY1854 @ SY1852 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV13 @ SY1853 @ SY1854 @ SY1852 ) @ SV374 @ SY1852 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1853 @ ( c_Nat_Osize__class_Osize @ SV13 @ ( tc_List_Olist @ SY1852 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1330]) ).
thf(1694,plain,
! [SV375: $i,SV14: $i] :
( ( ! [SY1855: $i] :
( ( c_List_Olist__update @ SV14 @ SV375 @ ( c_List_Onth @ SV14 @ SV375 @ SY1855 ) @ SY1855 )
= SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1331]) ).
thf(1695,plain,
! [SV376: $i,SV15: $i] :
( ( ! [SY1856: $i,SY1857: $i,SY1858: $i] :
( ! [SY1859: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV15 @ SV376 @ SY1856 @ SY1857 ) @ SY1858 @ SY1859 @ SY1857 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV15 @ SY1858 @ SY1859 @ SY1857 ) @ SV376 @ SY1856 @ SY1857 ) )
| ( SV376 = SY1858 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1332]) ).
thf(1696,plain,
! [SV377: $i,SV16: $i] :
( ( ! [SY1860: $i,SY1861: $i,SY1862: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV16 @ SV377 @ SY1860 ) @ ( c_Suc @ SY1861 ) @ SY1862 @ SY1860 )
= ( c_List_Olist_OCons @ SV16 @ ( c_List_Olist__update @ SV377 @ SY1861 @ SY1862 @ SY1860 ) @ SY1860 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1333]) ).
thf(1697,plain,
! [SV378: $i,SV17: $i] :
( ( ! [SY1863: $i,SY1864: $i,SY1865: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ SV17 @ SV378 @ SY1863 @ SY1864 ) @ SY1865 @ SY1864 )
= ( c_List_Onth @ SV17 @ SY1865 @ SY1864 ) )
| ( SV378 = SY1865 )
| ~ ( c_HOL_Oord__class_Oless @ SV378 @ ( c_Nat_Osize__class_Osize @ SV17 @ ( tc_List_Olist @ SY1864 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1334]) ).
thf(1698,plain,
! [SV379: $i,SV18: $i] :
( ( ! [SY1866: $i,SY1867: $i,SY1868: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV18 @ SV379 @ SY1866 @ SY1867 ) @ SV379 @ SY1868 @ SY1867 )
= ( c_List_Olist__update @ SV18 @ SV379 @ SY1868 @ SY1867 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1335]) ).
thf(1699,plain,
! [SV380: $i,SV19: $i] :
( ( ! [SY1869: $i,SY1870: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV19 @ SV380 @ SY1869 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1870 @ SY1869 )
= ( c_List_Olist_OCons @ SY1870 @ SV380 @ SY1869 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1700,plain,
! [SV381: $i,SV20: $i] :
( ( ! [SY1871: $i] :
( ( ( c_List_Ohd @ ( c_List_Odrop @ SV20 @ SV381 @ SY1871 ) @ SY1871 )
= ( c_List_Onth @ SV381 @ SV20 @ SY1871 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV20 @ ( c_Nat_Osize__class_Osize @ SV381 @ ( tc_List_Olist @ SY1871 ) ) @ tc_nat )
| ( SV381
= ( c_List_Olist_ONil @ SY1871 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1337]) ).
thf(1701,plain,
! [SV382: $i,SV21: $i] :
( ( ! [SY1872: $i] :
( ( ( c_List_Olist_OCons @ ( c_List_Onth @ SV21 @ SV382 @ SY1872 ) @ ( c_List_Odrop @ ( c_Suc @ SV382 ) @ SV21 @ SY1872 ) @ SY1872 )
= ( c_List_Odrop @ SV382 @ SV21 @ SY1872 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV382 @ ( c_Nat_Osize__class_Osize @ SV21 @ ( tc_List_Olist @ SY1872 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(1702,plain,
! [SV383: $i,SV22: $i] :
( ( ! [SY1873: $i] :
( ( c_List_Oappend @ ( c_List_Otake @ SV22 @ SV383 @ SY1873 ) @ ( c_List_Odrop @ SV22 @ SV383 @ SY1873 ) @ SY1873 )
= SV383 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1339]) ).
thf(1703,plain,
! [SV384: $i,SV23: $i] :
( ( ! [SY1874: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ SV23 @ SV384 @ SY1874 ) @ SY1874 )
= ( c_List_Olist_OCons @ SV23 @ SV384 @ SY1874 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1704,plain,
! [SV385: $i,SV24: $i] :
( ( ! [SY1875: $i,SY1876: $i] :
( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SV385 ) ) @ SY1875 @ SV385 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SY1875 @ ( tc_List_Olist @ SV385 ) ) @ SV24 @ SV385 ) @ SY1876 @ SV385 ) @ SV385 )
!= SY1876 )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SV385 ) ) @ SY1875 @ SV385 )
!= SV24 )
| ( SY1875
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SY1875 @ ( tc_List_Olist @ SV385 ) ) @ SV24 @ SV385 ) )
| ( ( c_List_Oappend @ SY1875 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SY1875 @ ( tc_List_Olist @ SV385 ) ) @ SV24 @ SV385 ) @ SY1876 @ SV385 ) @ SV385 )
= ( c_List_Oappend @ SV24 @ SY1876 @ SV385 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1341]) ).
thf(1705,plain,
! [SV386: $i,SV25: $i] :
( ( ! [SY1877: $i,SY1878: $i] :
( ! [SY1879: $i] :
( ( c_List_Odrop @ SV25 @ SV386 @ SY1877 )
!= ( c_List_Olist_OCons @ SY1878 @ SY1879 @ SY1877 ) )
| ( ( c_List_Onth @ SV386 @ SV25 @ SY1877 )
= SY1878 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(1706,plain,
! [SV387: $i,SV26: $i] :
( ( ! [SY1880: $i,SY1881: $i] :
( ( ( c_List_Olist__update @ SV26 @ SV387 @ SY1880 @ SY1881 )
= ( c_List_Oappend @ ( c_List_Otake @ SV387 @ SV26 @ SY1881 ) @ ( c_List_Olist_OCons @ SY1880 @ ( c_List_Odrop @ ( c_Suc @ SV387 ) @ SV26 @ SY1881 ) @ SY1881 ) @ SY1881 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV387 @ ( c_Nat_Osize__class_Osize @ SV26 @ ( tc_List_Olist @ SY1881 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1343]) ).
thf(1707,plain,
! [SV388: $i,SV27: $i] :
( ( ! [SY1882: $i] :
( ( SV27
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV27 @ ( tc_List_Olist @ SV388 ) ) @ SY1882 @ SV388 ) )
| ( ( c_List_Oappend @ SV27 @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV27 @ ( tc_List_Olist @ SV388 ) ) @ SY1882 @ SV388 ) @ SV388 )
= SY1882 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1344]) ).
thf(1708,plain,
! [SV389: $i,SV28: $i] :
( ( ! [SY1883: $i] :
( ( ( c_List_Olast @ ( c_List_Odrop @ SV28 @ SV389 @ SY1883 ) @ SY1883 )
= ( c_List_Olast @ SV389 @ SY1883 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV28 @ ( c_Nat_Osize__class_Osize @ SV389 @ ( tc_List_Olist @ SY1883 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1345]) ).
thf(1709,plain,
! [SV390: $i,SV29: $i] :
( ( ! [SY1884: $i] :
( ( c_List_Odrop @ SV29 @ ( c_List_Otl @ SV390 @ SY1884 ) @ SY1884 )
= ( c_List_Otl @ ( c_List_Odrop @ SV29 @ SV390 @ SY1884 ) @ SY1884 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1346]) ).
thf(1710,plain,
! [SV391: $i,SV30: $i] :
( ( ! [SY1885: $i,SY1886: $i] :
( ( c_List_Odrop @ ( c_Suc @ SV30 ) @ ( c_List_Olist_OCons @ SV391 @ SY1885 @ SY1886 ) @ SY1886 )
= ( c_List_Odrop @ SV30 @ SY1885 @ SY1886 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1347]) ).
thf(1711,plain,
! [SV392: $i,SV31: $i] :
( ( ! [SY1887: $i] :
( ( c_List_Odrop @ SV31 @ ( c_List_Obutlast @ SV392 @ SY1887 ) @ SY1887 )
= ( c_List_Obutlast @ ( c_List_Odrop @ SV31 @ SV392 @ SY1887 ) @ SY1887 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1348]) ).
thf(1712,plain,
! [SV393: $i,SV32: $i] :
( ( ! [SY1888: $i] :
( ( c_List_Otl @ ( c_List_Odrop @ SV32 @ SV393 @ SY1888 ) @ SY1888 )
= ( c_List_Odrop @ SV32 @ ( c_List_Otl @ SV393 @ SY1888 ) @ SY1888 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1349]) ).
thf(1713,plain,
! [SV394: $i,SV33: $i] :
( ( ! [SY1889: $i] :
( SV33
= ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV394 @ ( tc_List_Olist @ SY1889 ) ) @ ( c_List_Oappend @ SV394 @ SV33 @ SY1889 ) @ SY1889 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1350]) ).
thf(1714,plain,
! [SV395: $i,SV34: $i] :
( ( ! [SY1890: $i] :
( ( c_List_Odrop @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ SV34 @ SV395 @ SY1890 ) @ SY1890 )
= SV395 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1351]) ).
thf(1715,plain,
! [SV396: $i,SV35: $i] :
( ( ! [SY1891: $i] :
( ( c_List_Obutlast @ ( c_List_Odrop @ SV35 @ SV396 @ SY1891 ) @ SY1891 )
= ( c_List_Odrop @ SV35 @ ( c_List_Obutlast @ SV396 @ SY1891 ) @ SY1891 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1352]) ).
thf(1716,plain,
! [SV397: $i,SV36: $i] :
( ( ! [SY1892: $i] :
( ( c_List_Odrop @ ( c_Suc @ SV36 ) @ SV397 @ SY1892 )
= ( c_List_Odrop @ SV36 @ ( c_List_Otl @ SV397 @ SY1892 ) @ SY1892 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1353]) ).
thf(1717,plain,
! [SV398: $i,SV37: $i] :
( ( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV37 @ SV398 )
= SV37 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1354]) ).
thf(1718,plain,
! [SV399: $i,SV38: $i] :
( ( ( ( c_Int_Onumber__class_Onumber__of @ SV38 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ! [SY1893: $i,SY1894: $i] :
( ( c_List_Odrop @ ( c_Int_Onumber__class_Onumber__of @ SV38 @ tc_nat ) @ ( c_List_Olist_OCons @ SV399 @ SY1893 @ SY1894 ) @ SY1894 )
= ( c_List_Olist_OCons @ SV399 @ SY1893 @ SY1894 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1355]) ).
thf(1719,plain,
! [SV400: $i,SV39: $i] :
( ( ( c_List_Odrop @ SV39 @ ( c_List_Olist_ONil @ SV400 ) @ SV400 )
= ( c_List_Olist_ONil @ SV400 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1356]) ).
thf(1720,plain,
! [SV401: $i,SV40: $i] :
( ( ! [SY1895: $i,SY1896: $i,SY1897: $i] :
( ( c_Type_Otypings @ SV40 @ SV401 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SY1895 @ SY1896 @ SV40 @ SV401 ) )
| ! [SY1898: $i] :
( ~ ( c_Type_Otyping @ SV40 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1897 ) @ SY1898 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1896 )
| ! [SY1205: $i] :
~ ( c_Type_Otypings @ SV40 @ SY1898 @ SY1205 )
| ~ ( c_Type_Otyping @ SV40 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1897 ) @ SY1898 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV401 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1895 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1357]) ).
thf(1721,plain,
! [SV402: $i,SV41: $i] :
( ( ! [SY1900: $i,SY1901: $i] :
( ( c_Type_Otypings @ SV41 @ SV402 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SY1900 @ SV41 @ SY1901 @ SV402 ) )
| ~ ( c_Type_Otyping @ SV41 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1901 ) @ SV402 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1900 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1358]) ).
thf(1722,plain,
! [SV403: $i,SV42: $i] :
( ( ! [SY1902: $i] :
( ( SV42
= ( c_List_Oappend @ ( c_List_Otake @ SV403 @ SV42 @ SY1902 ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ SV42 @ SV403 @ SY1902 ) @ ( c_List_Odrop @ ( c_Suc @ SV403 ) @ SV42 @ SY1902 ) @ SY1902 ) @ SY1902 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV403 @ ( c_Nat_Osize__class_Osize @ SV42 @ ( tc_List_Olist @ SY1902 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1359]) ).
thf(1723,plain,
! [SV404: $i,SV43: $i] :
( ( ! [SY1903: $i] :
( ( ( c_List_Oappend @ ( c_List_Otake @ SV43 @ SV404 @ SY1903 ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ ( c_List_Odrop @ SV43 @ SV404 @ SY1903 ) @ SY1903 ) @ ( c_List_Olist_ONil @ SY1903 ) @ SY1903 ) @ SY1903 )
= ( c_List_Otake @ ( c_Suc @ SV43 ) @ SV404 @ SY1903 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV43 @ ( c_Nat_Osize__class_Osize @ SV404 @ ( tc_List_Olist @ SY1903 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1360]) ).
thf(1724,plain,
! [SV405: $i,SV44: $i] :
( ( ! [SY1904: $i,SY1905: $i] :
( ( c_Lambda_Oliftn @ SV44 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV405 ) @ SY1904 ) @ SY1905 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ SV44 @ SV405 @ SY1905 ) ) @ ( c_Lambda_Oliftn @ SV44 @ SY1904 @ SY1905 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1361]) ).
thf(1725,plain,
! [SV406: $i,SV45: $i] :
( ( ! [SY1906: $i,SY1907: $i] :
( ( c_List_Onth @ ( c_List_Oappend @ SV45 @ ( c_List_Olist_OCons @ SV406 @ SY1906 @ SY1907 ) @ SY1907 ) @ ( c_Nat_Osize__class_Osize @ SV45 @ ( tc_List_Olist @ SY1907 ) ) @ SY1907 )
= SV406 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1362]) ).
thf(1726,plain,
! [SV407: $i,SV46: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_ONil @ SV46 ) @ SV407 @ SV46 )
= SV407 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1363]) ).
thf(1727,plain,
! [SV408: $i,SV47: $i] :
( ( ( c_List_Osplice @ SV47 @ ( c_List_Olist_ONil @ SV408 ) @ SV408 )
= SV47 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1364]) ).
thf(1728,plain,
! [SV409: $i,SV48: $i] :
( ( ! [SY1908: $i,SY1909: $i,SY1910: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV48 @ SV409 @ SY1908 ) @ ( c_List_Olist_OCons @ SY1909 @ SY1910 @ SY1908 ) @ SY1908 )
= ( c_List_Olist_OCons @ SV48 @ ( c_List_Olist_OCons @ SY1909 @ ( c_List_Osplice @ SV409 @ SY1910 @ SY1908 ) @ SY1908 ) @ SY1908 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1365]) ).
thf(1729,plain,
! [SV410: $i,SV49: $i] :
( ( ( ( c_Int_Onumber__class_Onumber__of @ SV49 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ! [SY1911: $i,SY1912: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ SV410 @ SY1911 @ SY1912 ) @ ( c_Int_Onumber__class_Onumber__of @ SV49 @ tc_nat ) @ SY1912 )
= SV410 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1366]) ).
thf(1730,plain,
! [SV50: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
= ( c_Suc @ SV50 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1367]) ).
thf(1731,plain,
! [SV51: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
= ( c_Suc @ SV51 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1368]) ).
thf(1732,plain,
! [SV52: $i] :
( ( ( c_Suc @ SV52 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1369]) ).
thf(1733,plain,
! [SV53: $i] :
( ( ( c_Suc @ SV53 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1370]) ).
thf(1734,plain,
! [SV411: $i,SV54: $i] :
( ( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV54 @ SV411 )
= SV54 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(1735,plain,
! [SV55: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV55 ) )
= $true )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV55 )
!= ( c_HOL_Oone__class_Oone @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1372]) ).
thf(1736,plain,
! [SV56: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV56 ) )
= $true )
| ( ( ( c_HOL_Oone__class_Oone @ SV56 )
!= ( c_HOL_Ozero__class_Ozero @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1373]) ).
thf(1737,plain,
! [SV412: $i,SV57: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV57 ) @ ( c_Suc @ SV412 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV57 @ SV412 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1374]) ).
thf(1738,plain,
! [SV413: $i,SV58: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV58 @ SV413 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV58 ) @ ( c_Suc @ SV413 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1375]) ).
thf(1739,plain,
! [SV414: $i,SV59: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV59 ) @ ( c_Suc @ SV414 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV59 @ SV414 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1376]) ).
thf(1740,plain,
! [SV415: $i,SV60: $i] :
( ( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ SV60 @ SV415 ) @ SV415 )
= ( c_Transitive__Closure_Ortranclp @ SV60 @ SV415 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1377]) ).
thf(1741,plain,
! [SV416: $i,SV61: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV61 @ ( c_Suc @ SV416 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV416 @ SV61 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1378]) ).
thf(1742,plain,
! [SV417: $i,SV62: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV62 @ SV417 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV417 @ ( c_Suc @ SV62 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1379]) ).
thf(1743,plain,
! [SV63: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV63 @ SV63 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV63 @ ( c_Suc @ SV63 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1380]) ).
thf(1744,plain,
! [SV418: $i,SV64: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV64 ) @ SV418 @ tc_nat )
| ( ( c_Suc @ SV64 )
= SV418 )
| ~ ( c_HOL_Oord__class_Oless @ SV64 @ SV418 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1381]) ).
thf(1745,plain,
! [SV65: $i] :
( ( ( ~ ( class_Int_Oring__char__0 @ SV65 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV65 )
| ! [SY1236: $i,SY1237: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ SY1236 @ SV65 )
!= ( c_Int_Onumber__class_Onumber__of @ SY1237 @ SV65 ) )
| ( SY1236 = SY1237 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1382]) ).
thf(1746,plain,
! [SV419: $i,SV66: $i] :
( ( ! [SY1913: $i,SY1914: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV66 @ SV419 @ SV419 ) @ SV419 ) @ SY1913 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV66 @ SV419 ) @ SY1914 ) @ SY1913 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1383]) ).
thf(1747,plain,
! [SV420: $i,SV67: $i] :
( ( ! [SY1915: $i,SY1916: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV67 @ SV420 ) @ SY1915 ) @ SY1916 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV67 @ SV420 @ SV420 ) @ SV420 ) @ SY1916 ) @ SY1915 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1384]) ).
thf(1748,plain,
! [SV68: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV68 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV68 )
= ( c_HOL_Oone__class_Oone @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1385]) ).
thf(1749,plain,
! [SV421: $i,SV69: $i] :
( ( ! [SY1917: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV69 @ SV421 ) @ SY1917 ) )
| ! [SY1918: $i,SY1919: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV69 @ SY1918 @ SY1919 ) @ SY1917 ) @ SV421 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1386]) ).
thf(1750,plain,
! [SV422: $i,SV70: $i] :
( ( ! [SY1920: $i,SY1921: $i,SY1922: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV70 @ SV422 @ SY1920 ) @ SY1921 ) @ SY1922 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1922 ) @ SY1921 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1387]) ).
thf(1751,plain,
! [SV423: $i,SV71: $i] :
( ( ! [SY1923: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV71 @ SV423 ) @ SY1923 ) )
| ! [SY1924: $i,SY1925: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV71 @ SY1924 @ SY1925 ) @ SY1923 ) @ SV423 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1388]) ).
thf(1752,plain,
! [SV424: $i,SV72: $i] :
( ( ! [SY1926: $i,SY1927: $i,SY1928: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV72 @ SV424 @ SY1926 ) @ SY1927 ) @ SY1928 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV72 @ SY1928 ) @ SY1927 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1389]) ).
thf(1753,plain,
! [SV425: $i,SV73: $i] :
( ( ! [SY1929: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SV73 @ SV425 @ SY1929 ) @ ( tc_List_Olist @ SY1929 ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ SV425 @ ( tc_List_Olist @ SY1929 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1390]) ).
thf(1754,plain,
! [SV426: $i,SV74: $i] :
( ( ! [SY1930: $i] :
( ( c_Suc @ ( c_Nat_Osize__class_Osize @ SV74 @ ( tc_List_Olist @ SV426 ) ) )
= ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SY1930 @ SV74 @ SV426 ) @ ( tc_List_Olist @ SV426 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1391]) ).
thf(1755,plain,
! [SV427: $i,SV75: $i] :
( ( ! [SY1931: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV75 @ SV427 ) @ SY1931 ) @ SY1931 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1392]) ).
thf(1756,plain,
! [SV428: $i,SV76: $i] :
( ( ! [SY1932: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV76 @ SV428 ) @ SY1932 ) @ SY1932 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1393]) ).
thf(1757,plain,
! [SV429: $i,SV77: $i] :
( ( ! [SY1933: $i] :
( ( c_Wellfounded_Oaccp @ SV77 @ SV429 @ SY1933 )
| ! [SY1934: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV77 @ SY1933 ) @ SV429 ) @ SY1934 ) )
| ~ ( c_Wellfounded_Oaccp @ SV77 @ SY1934 @ SY1933 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1758,plain,
! [SV430: $i,SV78: $i] :
( ( ! [SY1935: $i] :
( ( c_Wellfounded_Oaccp @ SV78 @ SV430 @ SY1935 )
| ! [SY1936: $i] :
( ~ ( c_Wellfounded_Oaccp @ SV78 @ SY1936 @ SY1935 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV78 @ SY1935 ) @ SV430 ) @ SY1936 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1395]) ).
thf(1759,plain,
! [SV431: $i,SV79: $i] :
( ( ! [SY1937: $i,SY1938: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV79 @ SV431 ) @ SY1937 ) @ SY1938 ) )
| ! [SY1939: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV79 @ SV431 ) @ SY1939 ) @ SY1938 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV79 @ SV431 ) @ SY1937 ) @ SY1939 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1396]) ).
thf(1760,plain,
! [SV80: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV80 @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV80 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1397]) ).
thf(1761,plain,
! [SV81: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV81 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV81 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1398]) ).
thf(1762,plain,
! [SV432: $i,SV82: $i] :
( ( ! [SY1940: $i,SY1941: $i] :
( ( ( c_List_Onth @ ( c_List_Oappend @ SV82 @ SV432 @ SY1940 ) @ SY1941 @ SY1940 )
= ( c_List_Onth @ SV82 @ SY1941 @ SY1940 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1941 @ ( c_Nat_Osize__class_Osize @ SV82 @ ( tc_List_Olist @ SY1940 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1399]) ).
thf(1763,plain,
! [SV83: $i] :
( ( ( ~ ( class_Nat_Osemiring__char__0 @ SV83 ) )
= $true )
| ( ( ! [SY1281: $i,SY1282: $i] :
( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SY1281 @ SV83 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY1282 @ SV83 ) )
| ( SY1281 = SY1282 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1400]) ).
thf(1764,plain,
! [SV433: $i,SV84: $i] :
( ( ( ( c_Suc @ SV84 )
!= ( c_Suc @ SV433 ) )
| ( SV84 = SV433 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1401]) ).
thf(1765,plain,
! [SV434: $i,SV85: $i] :
( ( ( ( c_Suc @ SV85 )
!= ( c_Suc @ SV434 ) )
| ( SV85 = SV434 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1402]) ).
thf(1766,plain,
! [SV435: $i,SV86: $i] :
( ( ! [SY1942: $i,SY1943: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV86 @ SV435 ) @ SY1942 ) @ SY1943 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV86 @ SY1942 ) @ SY1943 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1403]) ).
thf(1767,plain,
! [SV436: $i,SV88: $i] :
( ( ( SV88 = SV436 )
| ( c_HOL_Oord__class_Oless @ SV88 @ SV436 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV88 @ ( c_Suc @ SV436 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1405]) ).
thf(1768,plain,
! [SV437: $i,SV89: $i] :
( ( ( SV89 = SV437 )
| ~ ( c_HOL_Oord__class_Oless @ SV437 @ ( c_Suc @ SV89 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV437 @ SV89 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(1769,plain,
! [SV438: $i,SV90: $i] :
( ( ( SV90 = SV438 )
| ~ ( c_HOL_Oord__class_Oless @ SV90 @ ( c_Suc @ SV438 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV90 @ SV438 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1407]) ).
thf(1770,plain,
! [SV439: $i,SV91: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate1 @ SV91 @ SV439 ) @ ( tc_List_Olist @ SV439 ) )
= ( c_Nat_Osize__class_Osize @ SV91 @ ( tc_List_Olist @ SV439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1408]) ).
thf(1771,plain,
! [SV440: $i,SV94: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV94 ) @ SV440 @ tc_nat )
| ! [SY1944: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1944 @ SV440 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV94 @ SY1944 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1411]) ).
thf(1772,plain,
! [SV441: $i,SV95: $i] :
( ( ! [SY1945: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ SV95 @ SV441 @ SY1945 ) @ ( tc_List_Olist @ SY1945 ) )
= SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1412]) ).
thf(1773,plain,
! [SV442: $i,SV96: $i] :
( ( ! [SY1946: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ SV96 @ SV442 @ SY1946 ) @ SY1946 @ SV442 )
= SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1413]) ).
thf(1774,plain,
! [SV443: $i,SV97: $i] :
( ( ! [SY1947: $i,SY1948: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ SV97 @ SV443 @ SY1947 ) @ ( c_Suc @ SY1948 ) @ SY1947 )
= ( c_List_Onth @ SV443 @ SY1948 @ SY1947 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1414]) ).
thf(1775,plain,
! [SV98: $i] :
( ( ( c_Suc @ SV98 )
= SV98 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1415]) ).
thf(1776,plain,
! [SV99: $i] :
( ( SV99
= ( c_Suc @ SV99 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1416]) ).
thf(1777,plain,
! [SV444: $i,SV100: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV100 @ SV444 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV100 ) @ SV444 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1417]) ).
thf(1778,plain,
! [SV445: $i,SV101: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV101 @ ( c_Suc @ SV445 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV101 @ SV445 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1418]) ).
thf(1779,plain,
! [SV446: $i,SV102: $i] :
( ( ( ( c_Nat_Osize__class_Osize @ SV102 @ ( tc_List_Olist @ SV446 ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ ( c_List_Otl @ SV102 @ SV446 ) @ ( tc_List_Olist @ SV446 ) ) ) )
| ( SV102
= ( c_List_Olist_ONil @ SV446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1419]) ).
thf(1780,plain,
! [SV447: $i,SV103: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Orev @ SV103 @ SV447 ) @ ( tc_List_Olist @ SV447 ) )
= ( c_Nat_Osize__class_Osize @ SV103 @ ( tc_List_Olist @ SV447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(1781,plain,
! [SV448: $i,SV104: $i] :
( ( ! [SY1949: $i,SY1950: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV104 @ SV448 ) @ SY1949 ) @ SY1950 ) )
| ! [SY1951: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV104 @ SV448 ) @ SY1951 ) @ SY1950 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV104 @ SY1949 ) @ SY1951 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(1782,plain,
! [SV449: $i,SV105: $i] :
( ( ! [SY1952: $i,SY1953: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV105 @ SV449 ) @ SY1952 ) @ SY1953 ) )
| ! [SY1954: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV105 @ SY1954 ) @ SY1953 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV105 @ SV449 ) @ SY1952 ) @ SY1954 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1422]) ).
thf(1783,plain,
! [SV450: $i,SV106: $i] :
( ( ! [SY1955: $i] :
( ( c_Wellfounded_Oaccp @ SV106 @ SV450 @ SY1955 )
| ! [SY1956: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV106 @ SV450 ) @ SY1956 ) )
| ~ ( c_Wellfounded_Oaccp @ SV106 @ SY1956 @ SY1955 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1423]) ).
thf(1784,plain,
! [SV451: $i,SV107: $i] :
( ( ! [SY1957: $i] :
( ( c_Wellfounded_Oaccp @ SV107 @ SV451 @ SY1957 )
| ! [SY1958: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV107 @ SV451 ) @ SY1958 ) )
| ~ ( c_Wellfounded_Oaccp @ SV107 @ SY1958 @ SY1957 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1424]) ).
thf(1785,plain,
! [SV452: $i,SV108: $i] :
( ( ! [SY1959: $i] :
( ( ( c_List_Otake @ ( c_Suc @ SV108 ) @ SV452 @ SY1959 )
= ( c_List_Oappend @ ( c_List_Otake @ SV108 @ SV452 @ SY1959 ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ SV452 @ SV108 @ SY1959 ) @ ( c_List_Olist_ONil @ SY1959 ) @ SY1959 ) @ SY1959 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV108 @ ( c_Nat_Osize__class_Osize @ SV452 @ ( tc_List_Olist @ SY1959 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1425]) ).
thf(1786,plain,
! [SV109: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV109 ) )
= $true )
| ( ( ! [SY1321: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1321 @ SV109 ) @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1426]) ).
thf(1787,plain,
! [SV110: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV110 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV110 ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV110 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1427]) ).
thf(1788,plain,
! [SV111: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV111 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV111 ) @ ( c_HOL_Oone__class_Oone @ SV111 ) @ SV111 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1428]) ).
thf(1789,plain,
! [SV112: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV112 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV112 )
= ( c_HOL_Ozero__class_Ozero @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1429]) ).
thf(1790,plain,
! [SV113: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV113 ) )
= $true )
| ( ( ! [SY1322: $i,SY1323: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1322 @ SV113 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1323 @ SV113 ) @ SV113 )
| ~ ( c_HOL_Oord__class_Oless @ SY1322 @ SY1323 @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1430]) ).
thf(1791,plain,
! [SV114: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV114 ) )
= $true )
| ( ( ! [SY1324: $i,SY1325: $i] :
( ( c_HOL_Oord__class_Oless @ SY1324 @ SY1325 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1324 @ SV114 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1325 @ SV114 ) @ SV114 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1431]) ).
thf(1792,plain,
! [SV453: $i,SV115: $i] :
( ( ! [SY1960: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ SV115 @ SV453 @ SY1960 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1960 )
= SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1432]) ).
thf(1793,plain,
! [SV118: $i] :
( ( ( SV118
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV118 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1435]) ).
thf(1794,plain,
! [SV454: $i,SV120: $i] :
( ( ( ( c_Nat_Osize__class_Osize @ SV120 @ ( tc_List_Olist @ SV454 ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV120
= ( c_List_Olist_ONil @ SV454 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(1795,plain,
! [SV455: $i,SV121: $i] :
( ( ! [SY1961: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV121 @ SV455 @ SY1961 ) @ ( c_List_Olist_ONil @ SY1961 ) @ SY1961 )
= ( c_List_Olist_OCons @ SV121 @ SV455 @ SY1961 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1796,plain,
! [SV456: $i,SV122: $i] :
( ( ! [SY1962: $i,SY1963: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV122 ) @ SV456 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1962 ) @ SY1963 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV456 ) @ SY1963 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV122 ) @ SY1962 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1439]) ).
thf(1797,plain,
! [SV457: $i,SV123: $i] :
( ( ! [SY1964: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV123 ) @ SV457 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1964 ) @ SV457 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV123 ) @ SY1964 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1440]) ).
thf(1798,plain,
! [SV458: $i,SV124: $i] :
( ( ! [SY1965: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV124 ) @ SV458 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV124 ) @ SY1965 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV458 ) @ SY1965 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(1799,plain,
! [SV459: $i,SV125: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV125 ) ) @ ( c_Lambda_OdB_OAbs @ SV459 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV125 ) @ SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1800,plain,
! [SV460: $i,SV126: $i] :
( ( ! [SY1966: $i,SY1967: $i] :
( ( c_List_Otake @ ( c_Suc @ SV126 ) @ ( c_List_Olist_OCons @ SV460 @ SY1966 @ SY1967 ) @ SY1967 )
= ( c_List_Olist_OCons @ SV460 @ ( c_List_Otake @ SV126 @ SY1966 @ SY1967 ) @ SY1967 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1443]) ).
thf(1801,plain,
! [SV461: $i,SV127: $i] :
( ( ! [SY1968: $i] :
( ( ( c_Lambda_Oliftn @ SV127 @ ( c_Lambda_OdB_OVar @ SV461 ) @ SY1968 )
= ( c_Lambda_OdB_OVar @ SV461 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV461 @ SY1968 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1444]) ).
thf(1802,plain,
! [SV462: $i,SV128: $i] :
( ( ! [SY1969: $i,SY1970: $i] :
( ( ( c_List_Onth @ ( c_List_Otake @ SV128 @ SV462 @ SY1969 ) @ SY1970 @ SY1969 )
= ( c_List_Onth @ SV462 @ SY1970 @ SY1969 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1970 @ SV128 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(1803,plain,
! [SV463: $i,SV129: $i] :
( ( ! [SY1971: $i,SY1972: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV129 @ SV463 @ SY1971 ) ) @ ( c_Lambda_Osubst @ SV129 @ SY1972 @ SY1971 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV463 ) @ SY1972 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(1804,plain,
! [SV464: $i,SV130: $i] :
( ( ! [SY1973: $i,SY1974: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV130 @ SV464 @ SY1973 ) ) @ ( c_Lambda_Osubst @ SY1974 @ SV464 @ SY1973 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV130 ) @ SY1974 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(1805,plain,
! [SV465: $i,SV131: $i] :
( ( ! [SY1975: $i,SY1976: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV131 @ SV465 @ SY1975 ) ) @ ( c_Lambda_Osubst @ SV131 @ SY1976 @ SY1975 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV465 ) @ SY1976 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(1806,plain,
! [SV466: $i,SV132: $i] :
( ( ! [SY1977: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV132 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV466 @ SV132 @ SY1977 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV466 ) @ SV132 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1977 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1449]) ).
thf(1807,plain,
! [SV467: $i,SV133: $i] :
( ( ! [SY1978: $i] :
( SV133
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV133 @ ( tc_List_Olist @ SV467 ) ) @ ( c_List_Oappend @ SV133 @ SY1978 @ SV467 ) @ SV467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1450]) ).
thf(1808,plain,
! [SV468: $i,SV134: $i] :
( ( ! [SY1979: $i] :
( ( c_List_Oreplicate @ ( c_Suc @ SV134 ) @ SV468 @ SY1979 )
= ( c_List_Olist_OCons @ SV468 @ ( c_List_Oreplicate @ SV134 @ SV468 @ SY1979 ) @ SY1979 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(1809,plain,
! [SV469: $i,SV135: $i] :
( ( ! [SY1980: $i,SY1981: $i] :
( ( ( c_List_Onth @ ( c_List_Oreplicate @ SV135 @ SV469 @ SY1980 ) @ SY1981 @ SY1980 )
= SV469 )
| ~ ( c_HOL_Oord__class_Oless @ SY1981 @ SV135 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(1810,plain,
! [SV470: $i,SV136: $i] :
( ( ! [SY1982: $i] :
( ( c_Type_Otyping @ SV136 @ SV470 @ SY1982 )
| ! [SY1983: $i] :
( ~ ( c_Type_Otyping @ SV136 @ SY1983 @ SY1982 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1983 ) @ SV470 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(1811,plain,
! [SV471: $i,SV137: $i] :
( ( ! [SY1984: $i] :
( ( c_List_Otake @ SV137 @ ( c_List_Otl @ SV471 @ SY1984 ) @ SY1984 )
= ( c_List_Otl @ ( c_List_Otake @ ( c_Suc @ SV137 ) @ SV471 @ SY1984 ) @ SY1984 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(1812,plain,
! [SV472: $i,SV138: $i] :
( ( ! [SY1985: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV138 @ SV472 @ SY1985 ) @ SY1985 )
= ( c_List_Oappend @ SV138 @ ( c_List_Obutlast @ SV472 @ SY1985 ) @ SY1985 ) )
| ( SV472
= ( c_List_Olist_ONil @ SY1985 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1455]) ).
thf(1813,plain,
! [SV473: $i,SV139: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ SV139 ) @ SV473 @ SV139 ) @ SV139 )
= ( c_List_Ohd @ SV473 @ SV139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(1814,plain,
! [SV474: $i,SV140: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ SV140 @ ( c_List_Olist_ONil @ SV474 ) @ SV474 ) @ SV474 )
= ( c_List_Olast @ SV140 @ SV474 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1457]) ).
thf(1815,plain,
! [SV475: $i,SV141: $i] :
( ( ! [SY1986: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ SV141 @ SV475 @ SY1986 ) @ SY1986 )
= ( c_List_Olast @ SV475 @ SY1986 ) )
| ( SV475
= ( c_List_Olist_ONil @ SY1986 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1458]) ).
thf(1816,plain,
! [SV476: $i,SV142: $i] :
( ( ! [SY1987: $i] :
( ( ( c_List_Otake @ ( c_Suc @ SV142 ) @ SV476 @ SY1987 )
= ( c_List_Olist_OCons @ ( c_List_Ohd @ SV476 @ SY1987 ) @ ( c_List_Otake @ SV142 @ ( c_List_Otl @ SV476 @ SY1987 ) @ SY1987 ) @ SY1987 ) )
| ( SV476
= ( c_List_Olist_ONil @ SY1987 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(1817,plain,
! [SV477: $i,SV143: $i] :
( ( ! [SY1988: $i,SY1989: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV143 @ SV477 @ SY1988 ) @ SY1989 @ SY1988 )
= ( c_List_Olist_OCons @ SV143 @ ( c_List_Olist_OCons @ ( c_List_Ohd @ SY1989 @ SY1988 ) @ ( c_List_Osplice @ SV477 @ ( c_List_Otl @ SY1989 @ SY1988 ) @ SY1988 ) @ SY1988 ) @ SY1988 ) )
| ( SY1989
= ( c_List_Olist_ONil @ SY1988 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1818,plain,
! [SV144: $i] :
( ( ( ! [SY1381: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV144 ) @ SY1381 @ SV144 )
= ( c_Lambda_Oliftn @ SV144 @ SY1381 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV144 @ SV144 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1461]) ).
thf(1819,plain,
! [SV478: $i,SV145: $i] :
( ( ! [SY1990: $i] :
( ( SV145
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV478 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV478 @ SY1990 @ SV145 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV478 ) @ SY1990 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1462]) ).
thf(1820,plain,
! [SV479: $i,SV146: $i] :
( ( ( ( c_Int_Onumber__class_Onumber__of @ SV146 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ! [SY1991: $i,SY1992: $i] :
( ( c_List_Otake @ ( c_Int_Onumber__class_Onumber__of @ SV146 @ tc_nat ) @ ( c_List_Olist_OCons @ SV479 @ SY1991 @ SY1992 ) @ SY1992 )
= ( c_List_Olist_ONil @ SY1992 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(1821,plain,
! [SV147: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV147 ) )
= $true )
| ( ( ! [SY1387: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1387 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1387 @ SV147 ) @ SV147 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1464]) ).
thf(1822,plain,
! [SV148: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV148 ) )
= $true )
| ( ( ! [SY1388: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV148 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1388 @ SV148 ) @ SV148 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1388 @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1465]) ).
thf(1823,plain,
! [SV480: $i,SV149: $i] :
( ( ! [SY1993: $i] :
( ( c_Lambda_Osubstn @ SV149 @ SV480 @ SY1993 )
= ( c_Lambda_Osubst @ SV149 @ ( c_Lambda_Oliftn @ SY1993 @ SV480 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1993 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1466]) ).
thf(1824,plain,
! [SV481: $i,SV150: $i] :
( ( ! [SY1994: $i] :
( ( ( c_List_Otake @ SV150 @ ( c_List_Obutlast @ SV481 @ SY1994 ) @ SY1994 )
= ( c_List_Otake @ SV150 @ SV481 @ SY1994 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV150 @ ( c_Nat_Osize__class_Osize @ SV481 @ ( tc_List_Olist @ SY1994 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1467]) ).
thf(1825,plain,
! [SV482: $i,SV151: $i] :
( ( ( ( c_List_Ohd @ SV151 @ SV482 )
= ( c_List_Onth @ SV151 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV482 ) )
| ( SV151
= ( c_List_Olist_ONil @ SV482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(1826,plain,
! [SV483: $i,SV152: $i] :
( ( ! [SY1995: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV152 @ SV483 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1995 @ SV483 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV152 ) @ SY1995 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1469]) ).
thf(1827,plain,
! [SV484: $i,SV153: $i] :
( ( ! [SY1996: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV153 @ SV484 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV153 @ SY1996 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV484 @ SY1996 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1470]) ).
thf(1828,plain,
! [SV485: $i,SV154: $i] :
( ( ! [SY1997: $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 @ SV154 @ SV485 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1997 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV485 @ 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 @ SV154 ) ) @ SV485 ) @ SY1997 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1471]) ).
thf(1829,plain,
! [SV486: $i,SV155: $i] :
( ( ! [SY1998: $i] :
( ( c_List_Otake @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ SV155 @ SV486 @ SY1998 ) @ SY1998 )
= ( c_List_Olist_OCons @ SV155 @ ( c_List_Olist_ONil @ SY1998 ) @ SY1998 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1472]) ).
thf(1830,plain,
! [SV487: $i,SV156: $i] :
( ( ( SV156
= ( c_List_Olist_ONil @ SV487 ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV156 @ ( tc_List_Olist @ SV487 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1473]) ).
thf(1831,plain,
! [SV157: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ SV157 ) @ ( tc_List_Olist @ SV157 ) ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1474]) ).
thf(1832,plain,
! [SV488: $i,SV158: $i] :
( ( ! [SY1999: $i,SY2000: $i] :
( ( c_Type_Otyping @ SV158 @ SV488 @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ SY1999 @ SV158 @ SV488 @ SY2000 ) )
| ~ ( c_Type_Otypings @ SV158 @ ( c_List_Oappend @ SY2000 @ ( c_List_Olist_OCons @ SV488 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SY1999 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(1833,plain,
! [SV489: $i,SV159: $i] :
( ( ! [SY2001: $i,SY2002: $i,SY2003: $i] :
( ( ( c_List_Oappend @ SV159 @ SV489 @ SY2001 )
!= ( c_List_Olist_OCons @ SY2002 @ SY2003 @ SY2001 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY2002 @ SY2003 @ SV159 @ SV489 @ SY2001 ) @ SV489 @ SY2001 )
= SY2003 )
| ( SV489
= ( c_List_Olist_OCons @ SY2002 @ SY2003 @ SY2001 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1476]) ).
thf(1834,plain,
! [SV490: $i,SV160: $i] :
( ( ! [SY2004: $i,SY2005: $i,SY2006: $i] :
( ( ( c_List_Olist_OCons @ SV160 @ SV490 @ SY2004 )
!= ( c_List_Oappend @ SY2005 @ SY2006 @ SY2004 ) )
| ( ( c_List_Olist_OCons @ SV160 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV160 @ SV490 @ SY2005 @ SY2006 @ SY2004 ) @ SY2004 )
= SY2005 )
| ( ( c_List_Olist_OCons @ SV160 @ SV490 @ SY2004 )
= SY2006 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(1835,plain,
! [SV491: $i,SV161: $i] :
( ( ! [SY2007: $i,SY2008: $i,SY2009: $i] :
( ( ( c_List_Oappend @ SV161 @ SV491 @ SY2007 )
!= ( c_List_Olist_OCons @ SY2008 @ SY2009 @ SY2007 ) )
| ( SV161
= ( c_List_Olist_OCons @ SY2008 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY2008 @ SY2009 @ SV161 @ SV491 @ SY2007 ) @ SY2007 ) )
| ( SV491
= ( c_List_Olist_OCons @ SY2008 @ SY2009 @ SY2007 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1478]) ).
thf(1836,plain,
! [SV492: $i,SV162: $i] :
( ( ! [SY2010: $i,SY2011: $i,SY2012: $i] :
( ( ( c_List_Olist_OCons @ SV162 @ SV492 @ SY2010 )
!= ( c_List_Oappend @ SY2011 @ SY2012 @ SY2010 ) )
| ( SV492
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV162 @ SV492 @ SY2011 @ SY2012 @ SY2010 ) @ SY2012 @ SY2010 ) )
| ( ( c_List_Olist_OCons @ SV162 @ SV492 @ SY2010 )
= SY2012 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(1837,plain,
! [SV493: $i,SV163: $i] :
( ( ! [SY2013: $i,SY2014: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV163 @ SV493 @ SY2013 ) @ ( c_List_Olist_OCons @ SV493 @ SY2014 @ SY2013 ) @ SY2013 )
= ( c_List_Olist_OCons @ SV493 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV163 @ SV493 @ SY2013 ) @ SY2014 @ SY2013 ) @ SY2013 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1480]) ).
thf(1838,plain,
! [SV494: $i,SV164: $i] :
( ( ( c_List_Olist_OCons @ SV164 @ ( c_List_Olist_ONil @ SV494 ) @ SV494 )
= ( c_List_Orev @ ( c_List_Olist_OCons @ SV164 @ ( c_List_Olist_ONil @ SV494 ) @ SV494 ) @ SV494 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1481]) ).
thf(1839,plain,
! [SV495: $i,SV165: $i] :
( ( ! [SY2015: $i] :
( ( ( c_List_Olast @ ( c_List_Olist_OCons @ SV165 @ SV495 @ SY2015 ) @ SY2015 )
= ( c_List_Olast @ SV495 @ SY2015 ) )
| ( SV495
= ( c_List_Olist_ONil @ SY2015 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1482]) ).
thf(1840,plain,
! [SV496: $i,SV166: $i] :
( ( ( c_List_Orev @ ( c_List_Olist_OCons @ SV166 @ ( c_List_Olist_ONil @ SV496 ) @ SV496 ) @ SV496 )
= ( c_List_Olist_OCons @ SV166 @ ( c_List_Olist_ONil @ SV496 ) @ SV496 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1483]) ).
thf(1841,plain,
! [SV497: $i,SV167: $i] :
( ( ! [SY2016: $i] :
( ( ( c_List_Olist_OCons @ SV167 @ ( c_List_Olist_ONil @ SV497 ) @ SV497 )
!= ( c_List_Orev @ SY2016 @ SV497 ) )
| ( SY2016
= ( c_List_Olist_OCons @ SV167 @ ( c_List_Olist_ONil @ SV497 ) @ SV497 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1484]) ).
thf(1842,plain,
! [SV498: $i,SV168: $i] :
( ( ! [SY2017: $i] :
( ( ( c_List_Orev @ SV168 @ SV498 )
!= ( c_List_Olist_OCons @ SY2017 @ ( c_List_Olist_ONil @ SV498 ) @ SV498 ) )
| ( SV168
= ( c_List_Olist_OCons @ SY2017 @ ( c_List_Olist_ONil @ SV498 ) @ SV498 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1485]) ).
thf(1843,plain,
! [SV499: $i,SV169: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV169 @ ( c_List_Olist_ONil @ SV499 ) @ SV499 ) @ SV499 )
= ( c_List_Olist_ONil @ SV499 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1486]) ).
thf(1844,plain,
! [SV500: $i,SV170: $i] :
( ( ( c_List_Olast @ ( c_List_Olist_OCons @ SV170 @ ( c_List_Olist_ONil @ SV500 ) @ SV500 ) @ SV500 )
= SV170 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1487]) ).
thf(1845,plain,
! [SV501: $i,SV171: $i] :
( ( ! [SY2018: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV171 @ SV501 @ SY2018 ) @ SY2018 )
= ( c_List_Olist_OCons @ SV171 @ ( c_List_Obutlast @ SV501 @ SY2018 ) @ SY2018 ) )
| ( SV501
= ( c_List_Olist_ONil @ SY2018 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1488]) ).
thf(1846,plain,
! [SV502: $i,SV172: $i] :
( ( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV172 @ SV502 )
= ( c_List_Olist_ONil @ SV502 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1489]) ).
thf(1847,plain,
! [SV503: $i,SV173: $i] :
( ( ! [SY2019: $i] :
( ( ( c_List_Otake @ SV173 @ SV503 @ SY2019 )
!= ( c_List_Olist_ONil @ SY2019 ) )
| ( SV503
= ( c_List_Olist_ONil @ SY2019 ) )
| ( SV173
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(1848,plain,
! [SV504: $i,SV174: $i] :
( ( ( c_List_Olist_ONil @ SV174 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV504 @ SV174 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1491]) ).
thf(1849,plain,
! [SV505: $i,SV175: $i] :
( ( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV175 @ SV505 )
= ( c_List_Olist_ONil @ SV505 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1492]) ).
thf(1850,plain,
! [SV176: $i] :
( ( ( ! [SY1442: $i,SY1443: $i] :
( ( c_List_Oreplicate @ SV176 @ SY1442 @ SY1443 )
!= ( c_List_Olist_ONil @ SY1443 ) ) )
= $true )
| ( ( SV176
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1493]) ).
thf(1851,plain,
! [SV506: $i,SV177: $i] :
( ( ! [SY2020: $i] :
( ( c_List_Olist_ONil @ SV177 )
!= ( c_List_Oreplicate @ SV506 @ SY2020 @ SV177 ) )
| ( SV506
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(1852,plain,
! [SV507: $i,SV178: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV178 ) ) @ SV507 ) ) @ ( c_Lambda_Osubst @ SV178 @ SV507 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1495]) ).
thf(1853,plain,
! [SV508: $i,SV179: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Obutlast @ SV179 @ SV508 ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ SV179 @ SV508 ) @ ( c_List_Olist_ONil @ SV508 ) @ SV508 ) @ SV508 )
= SV179 )
| ( SV179
= ( c_List_Olist_ONil @ SV508 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1496]) ).
thf(1854,plain,
! [SV180: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV180 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV180 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1497]) ).
thf(1855,plain,
! [SV509: $i,SV181: $i] :
( ( c_Type_Otyping @ SV181 @ ( c_Lambda_OdB_OVar @ SV509 ) @ ( hAPP @ SV181 @ SV509 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1498]) ).
thf(1856,plain,
! [SV510: $i,SV182: $i] :
( ( ! [SY2021: $i] :
( ( ( hAPP @ SV182 @ SV510 )
= SY2021 )
| ~ ( c_Type_Otyping @ SV182 @ ( c_Lambda_OdB_OVar @ SV510 ) @ SY2021 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1499]) ).
thf(1857,plain,
! [SV511: $i,SV183: $i] :
( ( ( c_Lambda_OdB_OVar @ SV183 )
!= ( c_Lambda_OdB_OAbs @ SV511 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1500]) ).
thf(1858,plain,
! [SV512: $i,SV184: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV184 ) ) @ SV512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1501]) ).
thf(1859,plain,
! [SV513: $i,SV185: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV185 )
!= ( c_Lambda_OdB_OVar @ SV513 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1502]) ).
thf(1860,plain,
! [SV514: $i,SV186: $i] :
( ( ! [SY2022: $i,SY2023: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV186 @ SV514 @ SY2022 ) ) @ ( c_Lambda_Osubst @ SY2023 @ SV514 @ SY2022 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV186 ) @ SY2023 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1503]) ).
thf(1861,plain,
! [SV515: $i,SV187: $i] :
( ( ! [SY2024: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ SV187 @ SV515 @ SY2024 ) @ SY2024 )
= ( c_List_Oappend @ ( c_List_Orev @ SV515 @ SY2024 ) @ ( c_List_Orev @ SV187 @ SY2024 ) @ SY2024 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1504]) ).
thf(1862,plain,
! [SV516: $i,SV188: $i] :
( ( ! [SY2025: $i,SY2026: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV188 @ SV516 @ SY2025 @ SY2026 )
| ! [SY2027: $i] : ( c_ListOrder_Ostep1 @ SV188 @ ( c_List_Oappend @ SV516 @ SY2027 @ SY2026 ) @ ( c_List_Oappend @ SY2025 @ SY2027 @ SY2026 ) @ SY2026 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1505]) ).
thf(1863,plain,
! [SV517: $i,SV189: $i] :
( ( ! [SY2028: $i,SY2029: $i,SY2030: $i] :
( ( c_ListOrder_Ostep1 @ SV189 @ ( c_List_Oappend @ SV517 @ SY2028 @ SY2029 ) @ ( c_List_Oappend @ SV517 @ SY2030 @ SY2029 ) @ SY2029 )
| ~ ( c_ListOrder_Ostep1 @ SV189 @ SY2028 @ SY2030 @ SY2029 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(1864,plain,
! [SV518: $i,SV190: $i] :
( ( ! [SY2031: $i] :
( ( c_List_Olistsp @ SV190 @ SV518 @ SY2031 )
| ! [SY2032: $i] :
~ ( c_List_Olistsp @ SV190 @ ( c_List_Oappend @ SV518 @ SY2032 @ SY2031 ) @ SY2031 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1507]) ).
thf(1865,plain,
! [SV519: $i,SV191: $i] :
( ( ! [SY2033: $i] :
( ( c_List_Olistsp @ SV191 @ SV519 @ SY2033 )
| ! [SY2034: $i] :
~ ( c_List_Olistsp @ SV191 @ ( c_List_Oappend @ SY2034 @ SV519 @ SY2033 ) @ SY2033 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(1866,plain,
! [SV520: $i,SV192: $i] :
( ( ! [SY2035: $i,SY2036: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV192 @ SV520 @ SY2035 ) @ ( c_List_Oreplicate @ SY2036 @ SV520 @ SY2035 ) @ SY2035 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SY2036 @ SV520 @ SY2035 ) @ ( c_List_Oreplicate @ SV192 @ SV520 @ SY2035 ) @ SY2035 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1509]) ).
thf(1867,plain,
! [SV521: $i,SV193: $i] :
( ( ! [SY2037: $i,SY2038: $i] :
( ( c_List_Olistsp @ SV193 @ ( c_List_Oappend @ SV521 @ SY2037 @ SY2038 ) @ SY2038 )
| ~ ( c_List_Olistsp @ SV193 @ SY2037 @ SY2038 )
| ~ ( c_List_Olistsp @ SV193 @ SV521 @ SY2038 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(1868,plain,
! [SV522: $i,SV194: $i] :
( ( ! [SY2039: $i,SY2040: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV194 ) @ SV522 ) @ SY2039 @ SY2040 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ SV194 @ SY2039 @ SY2040 ) ) @ ( c_Lambda_Osubstn @ SV522 @ SY2039 @ SY2040 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1511]) ).
thf(1869,plain,
! [SV523: $i,SV195: $i] :
( ( ! [SY2041: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV195 ) @ SV523 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2041 ) @ SV523 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV195 ) @ SY2041 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1512]) ).
thf(1870,plain,
! [SV524: $i,SV196: $i] :
( ( ! [SY2042: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV196 ) @ SV524 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV196 ) @ SY2042 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV524 ) @ SY2042 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(1871,plain,
! [SV525: $i,SV197: $i] :
( ( ! [SY2043: $i] :
( ( c_Lambda_OdB_OAbs @ SV197 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV525 ) @ SY2043 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1514]) ).
thf(1872,plain,
! [SV526: $i,SV198: $i] :
( ( ! [SY2044: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV198 ) @ SV526 )
!= ( c_Lambda_OdB_OAbs @ SY2044 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1515]) ).
thf(1873,plain,
! [SV527: $i,SV199: $i] :
( ( ( ( c_List_Orotate1 @ SV199 @ SV527 )
= ( c_List_Oappend @ ( c_List_Otl @ SV199 @ SV527 ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ SV199 @ SV527 ) @ ( c_List_Olist_ONil @ SV527 ) @ SV527 ) @ SV527 ) )
| ( SV199
= ( c_List_Olist_ONil @ SV527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1516]) ).
thf(1874,plain,
! [SV528: $i,SV201: $i] :
( ( ( ( c_List_Orev @ SV201 @ SV528 )
!= ( c_List_Olist_ONil @ SV528 ) )
| ( SV201
= ( c_List_Olist_ONil @ SV528 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(1875,plain,
! [SV529: $i,SV203: $i] :
( ( c_List_Olistsp @ SV203 @ ( c_List_Olist_ONil @ SV529 ) @ SV529 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(1876,plain,
! [SV530: $i,SV204: $i] :
( ( ( c_List_Otake @ SV204 @ ( c_List_Olist_ONil @ SV530 ) @ SV530 )
= ( c_List_Olist_ONil @ SV530 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1521]) ).
thf(1877,plain,
! [SV531: $i,SV205: $i] :
( ( ( ( c_List_Orotate1 @ SV205 @ SV531 )
!= ( c_List_Olist_ONil @ SV531 ) )
| ( SV205
= ( c_List_Olist_ONil @ SV531 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(1878,plain,
! [SV532: $i,SV206: $i] :
( ( ! [SY2045: $i] :
~ ( c_ListOrder_Ostep1 @ SV206 @ ( c_List_Olist_ONil @ SV532 ) @ SY2045 @ SV532 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(1879,plain,
! [SV533: $i,SV207: $i] :
( ( ! [SY2046: $i] :
~ ( c_ListOrder_Ostep1 @ SV207 @ SV533 @ ( c_List_Olist_ONil @ SY2046 ) @ SY2046 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1524]) ).
thf(1880,plain,
! [SV534: $i,SV208: $i] :
( ( ( ( c_List_Olist_ONil @ SV208 )
!= ( c_List_Orev @ SV534 @ SV208 ) )
| ( SV534
= ( c_List_Olist_ONil @ SV208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1525]) ).
thf(1881,plain,
! [SV535: $i,SV212: $i] :
( ( ! [SY2047: $i,SY2048: $i] :
( ( SV212 = SV535 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2047 @ SV535 ) @ SV212 ) )
| ! [SY2049: $i,SY2050: $i] :
~ ( c_ListOrder_Ostep1 @ SY2047 @ ( c_List_Olist_OCons @ SV535 @ SY2048 @ SY2049 ) @ ( c_List_Olist_OCons @ SV212 @ SY2050 @ SY2049 ) @ SY2049 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(1882,plain,
! [SV536: $i,SV213: $i] :
( ( ! [SY2051: $i,SY2052: $i] :
( ( SV213 = SV536 )
| ( SY2051 = SY2052 )
| ! [SY2053: $i,SY2054: $i] :
~ ( c_ListOrder_Ostep1 @ SY2053 @ ( c_List_Olist_OCons @ SV536 @ SY2052 @ SY2054 ) @ ( c_List_Olist_OCons @ SV213 @ SY2051 @ SY2054 ) @ SY2054 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1530]) ).
thf(1883,plain,
! [SV537: $i,SV214: $i] :
( ( ! [SY2055: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV214 @ SV537 ) @ SY2055 ) )
| ! [SY2056: $i,SY2057: $i] : ( c_ListOrder_Ostep1 @ SV214 @ ( c_List_Olist_OCons @ SV537 @ SY2056 @ SY2057 ) @ ( c_List_Olist_OCons @ SY2055 @ SY2056 @ SY2057 ) @ SY2057 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(1884,plain,
! [SV538: $i,SV215: $i] :
( ( ! [SY2058: $i,SY2059: $i] :
( ( c_ListOrder_Ostep1 @ SV215 @ SV538 @ SY2058 @ SY2059 )
| ( SY2058 = SV538 )
| ! [SY2060: $i,SY2061: $i] :
~ ( c_ListOrder_Ostep1 @ SV215 @ ( c_List_Olist_OCons @ SY2060 @ SV538 @ SY2059 ) @ ( c_List_Olist_OCons @ SY2061 @ SY2058 @ SY2059 ) @ SY2059 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(1885,plain,
! [SV539: $i,SV216: $i] :
( ( ! [SY2062: $i] :
( ( c_List_Otl @ ( c_List_Olist_OCons @ SV216 @ SV539 @ SY2062 ) @ SY2062 )
= SV539 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1533]) ).
thf(1886,plain,
! [SV540: $i,SV217: $i] :
( ( ! [SY2063: $i,SY2064: $i] :
( ( c_ListOrder_Ostep1 @ SV217 @ SV540 @ SY2063 @ SY2064 )
| ! [SY2065: $i,SY2066: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV217 @ SY2065 ) @ SY2066 ) )
| ~ ( c_ListOrder_Ostep1 @ SV217 @ ( c_List_Olist_OCons @ SY2065 @ SV540 @ SY2064 ) @ ( c_List_Olist_OCons @ SY2066 @ SY2063 @ SY2064 ) @ SY2064 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(1887,plain,
! [SV541: $i,SV218: $i] :
( ( ! [SY2067: $i,SY2068: $i,SY2069: $i] :
( ( c_ListOrder_Ostep1 @ SV218 @ ( c_List_Olist_OCons @ SV541 @ SY2067 @ SY2068 ) @ ( c_List_Olist_OCons @ SV541 @ SY2069 @ SY2068 ) @ SY2068 )
| ~ ( c_ListOrder_Ostep1 @ SV218 @ SY2067 @ SY2069 @ SY2068 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1535]) ).
thf(1888,plain,
! [SV542: $i,SV219: $i] :
( ( ! [SY2070: $i] :
( ( c_List_Ohd @ ( c_List_Olist_OCons @ SV219 @ SV542 @ SY2070 ) @ SY2070 )
= SV219 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1536]) ).
thf(1889,plain,
! [SV543: $i,SV220: $i] :
( ( ! [SY2071: $i,SY2072: $i,SY2073: $i] :
( ( ( c_List_Oreplicate @ SV220 @ SV543 @ SY2071 )
!= ( c_List_Oreplicate @ SY2072 @ SY2073 @ SY2071 ) )
| ( SV543 = SY2073 )
| ( SV220
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(1890,plain,
! [SV544: $i,SV221: $i] :
( ( ! [SY2074: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV221 @ SV544 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2074 @ SV544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1538]) ).
thf(1891,plain,
! [SV222: $i] :
( ( c_HOL_Oord__class_Oless @ SV222 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1539]) ).
thf(1892,plain,
! [SV223: $i] :
( ( c_HOL_Oord__class_Oless @ SV223 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1540]) ).
thf(1893,plain,
! [SV224: $i] :
( ( ( SV224
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV224 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1541]) ).
thf(1894,plain,
! [SV545: $i,SV225: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV225 ) ) @ ( c_Lambda_OdB_OAbs @ SV545 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV225 ) @ SV545 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1543]) ).
thf(1895,plain,
! [SV226: $i] :
( ( ( ! [SY1539: $i,SY1540: $i] :
( ( c_List_Olast @ ( c_List_Oreplicate @ SV226 @ SY1539 @ SY1540 ) @ SY1540 )
= SY1539 ) )
= $true )
| ( ( SV226
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1544]) ).
thf(1896,plain,
! [SV546: $i,SV227: $i] :
( ( ~ ( class_Orderings_Oorder @ SV227 )
| ! [SY2075: $i] :
( ( c_HOL_Oord__class_Oless @ SV546 @ SY2075 @ SV227 )
| ! [SY2076: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV546 @ SY2076 @ SV227 )
| ~ ( c_HOL_Oord__class_Oless @ SY2076 @ SY2075 @ SV227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(1897,plain,
! [SV547: $i,SV228: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV228 )
| ! [SY2077: $i] :
( ( c_HOL_Oord__class_Oless @ SV547 @ SY2077 @ SV228 )
| ! [SY2078: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY2078 @ SY2077 @ SV228 )
| ~ ( c_HOL_Oord__class_Oless @ SV547 @ SY2078 @ SV228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(1898,plain,
! [SV548: $i,SV229: $i] :
( ( ( ( c_List_Olast @ ( c_List_Orev @ SV229 @ SV548 ) @ SV548 )
= ( c_List_Ohd @ SV229 @ SV548 ) )
| ( SV229
= ( c_List_Olist_ONil @ SV548 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1547]) ).
thf(1899,plain,
! [SV549: $i,SV230: $i] :
( ( ! [SY2079: $i,SY2080: $i] :
( ! [SY2081: $i] :
( ( c_List_Oreplicate @ SV230 @ SV549 @ SY2079 )
!= ( c_List_Oreplicate @ SY2080 @ SY2081 @ SY2079 ) )
| ( SV230 = SY2080 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1548]) ).
thf(1900,plain,
! [SV550: $i,SV231: $i] :
( ( SV231
= ( c_List_Orev @ ( c_List_Orev @ SV231 @ SV550 ) @ SV550 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(1901,plain,
! [SV551: $i,SV232: $i] :
( ( ( c_List_Orev @ ( c_List_Orev @ SV232 @ SV551 ) @ SV551 )
= SV232 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1550]) ).
thf(1902,plain,
! [SV552: $i,SV233: $i] :
( ( ( c_List_Orev @ ( c_List_Orev @ SV233 @ SV552 ) @ SV552 )
= SV233 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(1903,plain,
! [SV553: $i,SV234: $i] :
( ( ! [SY2082: $i] :
( ( c_List_Orev @ ( c_List_Oreplicate @ SV234 @ SV553 @ SY2082 ) @ SY2082 )
= ( c_List_Oreplicate @ SV234 @ SV553 @ SY2082 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1552]) ).
thf(1904,plain,
! [SV554: $i,SV235: $i] :
( ( ( ( c_List_Ohd @ ( c_List_Orev @ SV235 @ SV554 ) @ SV554 )
= ( c_List_Olast @ SV235 @ SV554 ) )
| ( SV235
= ( c_List_Olist_ONil @ SV554 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1553]) ).
thf(1905,plain,
! [SV236: $i] :
( ( ( ! [SY1558: $i,SY1559: $i] :
( ( c_List_Ohd @ ( c_List_Oreplicate @ SV236 @ SY1558 @ SY1559 ) @ SY1559 )
= SY1558 ) )
= $true )
| ( ( SV236
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1554]) ).
thf(1906,plain,
! [SV555: $i,SV237: $i] :
( ( ! [SY2083: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV237 ) @ SV555 @ SY2083 )
= ( c_Lambda_OdB_OVar @ SV237 ) )
| ( SV237 = SY2083 )
| ( c_HOL_Oord__class_Oless @ SY2083 @ SV237 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1555]) ).
thf(1907,plain,
! [SV556: $i,SV238: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV238 )
!= ( c_Lambda_OdB_OAbs @ SV556 ) )
| ( SV238 = SV556 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1556]) ).
thf(1908,plain,
! [SV239: $i] :
( ( c_HOL_Oord__class_Oless @ SV239 @ SV239 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1557]) ).
thf(1909,plain,
! [SV240: $i] :
( ( c_HOL_Oord__class_Oless @ SV240 @ SV240 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1558]) ).
thf(1910,plain,
! [SV241: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV241 ) )
= $true )
| ( ( ! [SY1563: $i] :
~ ( c_HOL_Oord__class_Oless @ SY1563 @ SY1563 @ SV241 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1559]) ).
thf(1911,plain,
! [SV242: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV242 ) )
= $true )
| ( ( ! [SY1564: $i] :
~ ( c_HOL_Oord__class_Oless @ SY1564 @ SY1564 @ SV242 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1560]) ).
thf(1912,plain,
! [SV243: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV243 ) )
= $true )
| ( ( ! [SY1565: $i] :
~ ( c_HOL_Oord__class_Oless @ SY1565 @ SY1565 @ SV243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1561]) ).
thf(1913,plain,
! [SV244: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV244 ) )
= $true )
| ( ( ! [SY1566: $i,SY1567: $i] :
( ( c_HOL_Oord__class_Oless @ SY1566 @ SY1567 @ SV244 )
| ( SY1567 = SY1566 )
| ( c_HOL_Oord__class_Oless @ SY1567 @ SY1566 @ SV244 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1562]) ).
thf(1914,plain,
! [SV245: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV245 ) )
= $true )
| ( ( ! [SY1568: $i,SY1569: $i] :
( ( SY1568 = SY1569 )
| ( c_HOL_Oord__class_Oless @ SY1569 @ SY1568 @ SV245 )
| ( c_HOL_Oord__class_Oless @ SY1568 @ SY1569 @ SV245 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1563]) ).
thf(1915,plain,
! [SV557: $i,SV246: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV246 @ SV557 @ tc_nat )
| ( SV557 = SV246 )
| ( c_HOL_Oord__class_Oless @ SV557 @ SV246 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(1916,plain,
! [SV558: $i,SV247: $i] :
( ( ! [SY2084: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV247 @ SV558 ) @ SY2084 ) )
| ( c_HOL_Oord__class_Oless @ SV558 @ SY2084 @ tc_nat )
| ( SY2084 = SV558 )
| ( c_HOL_Oord__class_Oless @ SY2084 @ SV558 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1565]) ).
thf(1917,plain,
! [SV559: $i,SV248: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV248 @ SV559 @ tc_nat )
| ( SV559 = SV248 )
| ( c_HOL_Oord__class_Oless @ SV559 @ SV248 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1566]) ).
thf(1918,plain,
! [SV249: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV249 ) )
= $true )
| ( ( ! [SY1574: $i,SY1575: $i] :
( ( c_HOL_Oord__class_Oless @ SY1574 @ SY1575 @ SV249 )
| ( SY1575 = SY1574 )
| ( c_HOL_Oord__class_Oless @ SY1575 @ SY1574 @ SV249 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1567]) ).
thf(1919,plain,
! [SV250: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV250 ) )
= $true )
| ( ( ! [SY1576: $i,SY1577: $i] :
( ( c_HOL_Oord__class_Oless @ SY1576 @ SY1577 @ SV250 )
| ( SY1577 = SY1576 )
| ( c_HOL_Oord__class_Oless @ SY1577 @ SY1576 @ SV250 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1568]) ).
thf(1920,plain,
! [SV251: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV251 ) )
= $true )
| ( ( ! [SY1578: $i,SY1579: $i] :
( ( SY1578 = SY1579 )
| ( c_HOL_Oord__class_Oless @ SY1578 @ SY1579 @ SV251 )
| ( c_HOL_Oord__class_Oless @ SY1579 @ SY1578 @ SV251 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1569]) ).
thf(1921,plain,
! [SV560: $i,SV252: $i] :
( ( ! [SY2085: $i] :
( ( ( c_List_Orev @ SV252 @ SV560 )
!= ( c_List_Orev @ SY2085 @ SV560 ) )
| ( SV252 = SY2085 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1570]) ).
thf(1922,plain,
! [SV561: $i,SV253: $i] :
( ( ! [SY2086: $i] :
( ( c_Type_Otyping @ SV253 @ SV561 @ SY2086 )
| ! [SY2087: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY2087 ) @ SV561 ) )
| ~ ( c_Type_Otyping @ SV253 @ SY2087 @ SY2086 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1571]) ).
thf(1923,plain,
! [SV254: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV254 ) )
= $true )
| ( ( ! [SY1585: $i,SY1586: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1585 @ SY1586 @ SV254 )
| ~ ( c_HOL_Oord__class_Oless @ SY1586 @ SY1585 @ SV254 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1572]) ).
thf(1924,plain,
! [SV255: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV255 ) )
= $true )
| ( ( ! [SY1587: $i,SY1588: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1587 @ SY1588 @ SV255 )
| ~ ( c_HOL_Oord__class_Oless @ SY1588 @ SY1587 @ SV255 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1573]) ).
thf(1925,plain,
! [SV256: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV256 ) )
= $true )
| ( ( ! [SY1589: $i,SY1590: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1589 @ SY1590 @ SV256 )
| ~ ( c_HOL_Oord__class_Oless @ SY1590 @ SY1589 @ SV256 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1574]) ).
thf(1926,plain,
! [SV257: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV257 ) )
= $true )
| ( ( ! [SY1591: $i,SY1592: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1591 @ SY1592 @ SV257 )
| ~ ( c_HOL_Oord__class_Oless @ SY1592 @ SY1591 @ SV257 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1575]) ).
thf(1927,plain,
! [SV562: $i,SV258: $i] :
( ( ! [SY2088: $i] :
( ( ( c_List_Otl @ ( c_List_Oappend @ SV258 @ SV562 @ SY2088 ) @ SY2088 )
= ( c_List_Oappend @ ( c_List_Otl @ SV258 @ SY2088 ) @ SV562 @ SY2088 ) )
| ( SV258
= ( c_List_Olist_ONil @ SY2088 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(1928,plain,
! [SV563: $i,SV259: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV259 @ ( c_List_Olist_ONil @ SV563 ) @ SV563 ) @ SV563 )
= ( c_List_Obutlast @ SV259 @ SV563 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(1929,plain,
! [SV564: $i,SV260: $i] :
( ( ! [SY2089: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ SV260 @ SV564 @ SY2089 ) @ SY2089 )
= ( c_List_Ohd @ SV260 @ SY2089 ) )
| ( SV260
= ( c_List_Olist_ONil @ SY2089 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(1930,plain,
! [SV565: $i,SV261: $i] :
( ( ( c_Lambda_Osubstn @ SV261 @ SV565 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_Lambda_Osubst @ SV261 @ SV565 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(1931,plain,
! [SV566: $i,SV264: $i] :
( ( ! [SY2090: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV264 @ SV566 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY2090 ) )
| ( SV264
= ( c_Lambda_OdB_OAbs @ SY2090 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1582]) ).
thf(1932,plain,
! [SV567: $i,SV265: $i] :
( ( ! [SY2091: $i] :
( ! [SY2092: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV265 ) @ SV567 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY2091 ) @ SY2092 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV265 = SY2091 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1583]) ).
thf(1933,plain,
! [SV568: $i,SV266: $i] :
( ( ! [SY2093: $i,SY2094: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV266 ) @ SV568 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY2093 ) @ SY2094 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV568 = SY2094 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1584]) ).
thf(1934,plain,
! [SV569: $i,SV267: $i] :
( ( ! [SY2095: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV267 @ SV569 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2095 @ SV569 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV267 ) @ SY2095 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1585]) ).
thf(1935,plain,
! [SV570: $i,SV268: $i] :
( ( ! [SY2096: $i] :
( ( c_Lambda_OdB_OAbs @ SV268 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV570 @ SY2096 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV268 )
= SV570 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(1936,plain,
! [SV571: $i,SV269: $i] :
( ( ! [SY2097: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV269 ) @ SV571 @ SY2097 )
= ( c_Lambda_OdB_OVar @ SV269 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV269 @ SY2097 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1587]) ).
thf(1937,plain,
! [SV572: $i,SV270: $i] :
( ( ! [SY2098: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV270 ) @ SV572 @ SY2098 )
= ( c_Lambda_OdB_OVar @ SV270 ) )
| ( SV270 = SY2098 )
| ( c_HOL_Oord__class_Oless @ SY2098 @ SV270 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1588]) ).
thf(1938,plain,
! [SV271: $i] :
( ( ( ! [SY1615: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV271 ) @ SY1615 @ SV271 )
= SY1615 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV271 @ SV271 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1589]) ).
thf(1939,plain,
! [SV573: $i,SV272: $i] :
( ( ! [SY2099: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ SV272 @ SV573 @ SY2099 ) @ SY2099 )
= ( c_List_Olist_ONil @ SY2099 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(1940,plain,
! [SV574: $i,SV273: $i] :
( ( ! [SY2100: $i,SY2101: $i,SY2102: $i] :
( ( ( c_List_Olist_OCons @ SV273 @ SV574 @ SY2100 )
!= ( c_List_Oappend @ SY2101 @ SY2102 @ SY2100 ) )
| ( SV574
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV273 @ SV574 @ SY2101 @ SY2102 @ SY2100 ) @ SY2102 @ SY2100 ) )
| ( SY2101
= ( c_List_Olist_ONil @ SY2100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1591]) ).
thf(1941,plain,
! [SV575: $i,SV274: $i] :
( ( ! [SY2103: $i,SY2104: $i,SY2105: $i] :
( ( ( c_List_Oappend @ SV274 @ SV575 @ SY2103 )
!= ( c_List_Olist_OCons @ SY2104 @ SY2105 @ SY2103 ) )
| ( SV274
= ( c_List_Olist_OCons @ SY2104 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY2104 @ SY2105 @ SV274 @ SV575 @ SY2103 ) @ SY2103 ) )
| ( SV274
= ( c_List_Olist_ONil @ SY2103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(1942,plain,
! [SV576: $i,SV275: $i] :
( ( ! [SY2106: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ SV275 @ ( c_List_Olist_OCons @ SV576 @ ( c_List_Olist_ONil @ SY2106 ) @ SY2106 ) @ SY2106 ) @ SY2106 )
= SV576 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(1943,plain,
! [SV577: $i,SV276: $i] :
( ( ! [SY2107: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ SV276 @ ( c_List_Olist_OCons @ SV577 @ ( c_List_Olist_ONil @ SY2107 ) @ SY2107 ) @ SY2107 ) @ SY2107 )
= SV276 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1594]) ).
thf(1944,plain,
! [SV578: $i,SV277: $i] :
( ( ! [SY2108: $i,SY2109: $i] :
( ( SV277 = SV578 )
| ( SY2108 = SY2109 )
| ! [SY2110: $i,SY2111: $i] :
~ ( c_ListOrder_Ostep1 @ SY2110 @ ( c_List_Oappend @ SV277 @ ( c_List_Olist_OCons @ SY2108 @ ( c_List_Olist_ONil @ SY2111 ) @ SY2111 ) @ SY2111 ) @ ( c_List_Oappend @ SV578 @ ( c_List_Olist_OCons @ SY2109 @ ( c_List_Olist_ONil @ SY2111 ) @ SY2111 ) @ SY2111 ) @ SY2111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1595]) ).
thf(1945,plain,
! [SV579: $i,SV278: $i] :
( ( ! [SY2112: $i,SY2113: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV278 @ SV579 ) @ SY2112 ) )
| ( SV579 = SY2112 )
| ! [SY2114: $i,SY2115: $i] :
~ ( c_ListOrder_Ostep1 @ SV278 @ ( c_List_Oappend @ SY2113 @ ( c_List_Olist_OCons @ SV579 @ ( c_List_Olist_ONil @ SY2114 ) @ SY2114 ) @ SY2114 ) @ ( c_List_Oappend @ SY2115 @ ( c_List_Olist_OCons @ SY2112 @ ( c_List_Olist_ONil @ SY2114 ) @ SY2114 ) @ SY2114 ) @ SY2114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1596]) ).
thf(1946,plain,
! [SV580: $i,SV279: $i] :
( ( ! [SY2116: $i,SY2117: $i,SY2118: $i] :
( ( ( c_List_Oappend @ SV279 @ SV580 @ SY2116 )
!= ( c_List_Olist_OCons @ SY2117 @ SY2118 @ SY2116 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY2117 @ SY2118 @ SV279 @ SV580 @ SY2116 ) @ SV580 @ SY2116 )
= SY2118 )
| ( SV279
= ( c_List_Olist_ONil @ SY2116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1597]) ).
thf(1947,plain,
! [SV581: $i,SV280: $i] :
( ( ! [SY2119: $i,SY2120: $i,SY2121: $i] :
( ( ( c_List_Olist_OCons @ SV280 @ SV581 @ SY2119 )
!= ( c_List_Oappend @ SY2120 @ SY2121 @ SY2119 ) )
| ( ( c_List_Olist_OCons @ SV280 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV280 @ SV581 @ SY2120 @ SY2121 @ SY2119 ) @ SY2119 )
= SY2120 )
| ( SY2120
= ( c_List_Olist_ONil @ SY2119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1598]) ).
thf(1948,plain,
! [SV582: $i,SV281: $i] :
( ( ! [SY2122: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ SV281 @ SV582 @ SY2122 ) @ SY2122 )
= ( c_List_Oappend @ ( c_List_Orev @ SV582 @ SY2122 ) @ ( c_List_Olist_OCons @ SV281 @ ( c_List_Olist_ONil @ SY2122 ) @ SY2122 ) @ SY2122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1599]) ).
thf(1949,plain,
! [SV583: $i,SV282: $i] :
( ( ! [SY2123: $i,SY2124: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV282 @ SV583 ) @ SY2123 ) )
| ! [SY2125: $i,SY2126: $i] :
( ( c_ListOrder_Ostep1 @ SV282 @ SY2124 @ SY2125 @ SY2126 )
| ~ ( c_ListOrder_Ostep1 @ SV282 @ ( c_List_Oappend @ SY2124 @ ( c_List_Olist_OCons @ SV583 @ ( c_List_Olist_ONil @ SY2126 ) @ SY2126 ) @ SY2126 ) @ ( c_List_Oappend @ SY2125 @ ( c_List_Olist_OCons @ SY2123 @ ( c_List_Olist_ONil @ SY2126 ) @ SY2126 ) @ SY2126 ) @ SY2126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1600]) ).
thf(1950,plain,
! [SV584: $i,SV283: $i] :
( ( ! [SY2127: $i,SY2128: $i] :
( ( ( c_List_Orev @ SV283 @ SV584 )
!= ( c_List_Olist_OCons @ SY2127 @ SY2128 @ SV584 ) )
| ( SV283
= ( c_List_Oappend @ ( c_List_Orev @ SY2128 @ SV584 ) @ ( c_List_Olist_OCons @ SY2127 @ ( c_List_Olist_ONil @ SV584 ) @ SV584 ) @ SV584 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1601]) ).
thf(1951,plain,
! [SV585: $i,SV284: $i] :
( ( ! [SY2129: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ SV284 @ SV585 ) @ ( c_List_Olist_OCons @ SY2129 @ ( c_List_Olist_ONil @ SV585 ) @ SV585 ) @ SV585 ) @ SV585 )
= ( c_List_Olist_OCons @ SY2129 @ SV284 @ SV585 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(1952,plain,
! [SV586: $i,SV285: $i] :
( ( ! [SY2130: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ SV285 @ SV586 @ SY2130 ) @ SY2130 )
= ( c_List_Oappend @ SV586 @ ( c_List_Olist_OCons @ SV285 @ ( c_List_Olist_ONil @ SY2130 ) @ SY2130 ) @ SY2130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(1953,plain,
! [SV587: $i,SV286: $i] :
( ( ! [SY2131: $i,SY2132: $i] :
( ( SV286 = SV587 )
| ( c_ListOrder_Ostep1 @ SY2131 @ SV286 @ SV587 @ SY2132 )
| ! [SY2133: $i,SY2134: $i] :
~ ( c_ListOrder_Ostep1 @ SY2131 @ ( c_List_Oappend @ SV286 @ ( c_List_Olist_OCons @ SY2133 @ ( c_List_Olist_ONil @ SY2132 ) @ SY2132 ) @ SY2132 ) @ ( c_List_Oappend @ SV587 @ ( c_List_Olist_OCons @ SY2134 @ ( c_List_Olist_ONil @ SY2132 ) @ SY2132 ) @ SY2132 ) @ SY2132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1604]) ).
thf(1954,plain,
! [SV588: $i,SV287: $i] :
( ( ! [SY2135: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV287 @ SV588 @ SY2135 ) @ ( c_List_Olist_OCons @ SV588 @ ( c_List_Olist_ONil @ SY2135 ) @ SY2135 ) @ SY2135 )
= ( c_List_Olist_OCons @ SV588 @ ( c_List_Oreplicate @ SV287 @ SV588 @ SY2135 ) @ SY2135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1605]) ).
thf(1955,plain,
! [SV589: $i,SV288: $i] :
( ( ! [SY2136: $i] :
( ( SV288 = SV589 )
| ! [SY2137: $i,SY2138: $i] :
( ~ ( c_Type_Otyping @ SY2136 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2137 ) @ SY2138 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV589 )
| ~ ( c_Type_Otyping @ SY2136 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2137 ) @ SY2138 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV288 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1606]) ).
thf(1956,plain,
! [SV590: $i,SV289: $i] :
( ( ! [SY2139: $i,SY2140: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV289 ) @ SV590 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY2139 ) @ SY2140 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1607]) ).
thf(1957,plain,
! [SV591: $i,SV290: $i] :
( ( ! [SY2141: $i,SY2142: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV290 ) ) @ SV591 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2141 ) @ SY2142 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1608]) ).
thf(1958,plain,
! [SV592: $i,SV291: $i] :
( ( ! [SY2143: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV291 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV592 @ SY2143 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2143
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(1959,plain,
! [SV593: $i,SV293: $i] :
( ( ! [SY2144: $i,SY2145: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV293 ) @ SV593 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2144 @ SY2145 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV293
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2144 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV293 @ SV593 @ SY2144 @ SY2145 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2145
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1611]) ).
thf(1960,plain,
! [SV594: $i,SV294: $i] :
( ( ! [SY2146: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV294 @ SV594 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY2146 ) )
| ( SV594
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(1961,plain,
! [SV595: $i,SV296: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV296 ) @ SV595 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV595 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1614]) ).
thf(1962,plain,
! [SV596: $i,SV297: $i] :
( ( ! [SY2147: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV297 ) ) @ SV596 ) @ SY2147 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV596 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV297 @ SV596 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY2147 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1615]) ).
thf(1963,plain,
! [SV597: $i,SV298: $i] :
( ( ! [SY2148: $i,SY2149: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV298 ) @ SV597 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2148 @ SY2149 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2149
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV298 @ SV597 @ SY2148 @ SY2149 ) @ ( c_List_Olist_OCons @ SV597 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( SY2149
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1616]) ).
thf(1964,plain,
! [SV598: $i,SV299: $i] :
( ( ! [SY2150: $i,SY2151: $i] :
( ( c_List_Oappend @ SV299 @ ( c_List_Oappend @ SV598 @ SY2150 @ SY2151 ) @ SY2151 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV299 @ SV598 @ SY2151 ) @ SY2150 @ SY2151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1617]) ).
thf(1965,plain,
! [SV599: $i,SV300: $i] :
( ( ! [SY2152: $i,SY2153: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV300 @ SV599 @ SY2152 ) @ SY2153 @ SY2152 )
= ( c_List_Oappend @ SV300 @ ( c_List_Oappend @ SV599 @ SY2153 @ SY2152 ) @ SY2152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1618]) ).
thf(1966,plain,
! [SV600: $i,SV301: $i] :
( ( ! [SY2154: $i,SY2155: $i] :
( ( c_List_Oappend @ SV301 @ ( c_List_Oappend @ SV600 @ SY2154 @ SY2155 ) @ SY2155 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV301 @ SV600 @ SY2155 ) @ SY2154 @ SY2155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1619]) ).
thf(1967,plain,
! [SV601: $i,SV302: $i] :
( ( ! [SY2156: $i,SY2157: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV302 @ SV601 @ SY2156 ) @ SY2157 @ SY2156 )
= ( c_List_Oappend @ SV302 @ ( c_List_Oappend @ SV601 @ SY2157 @ SY2156 ) @ SY2156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(1968,plain,
! [SV602: $i,SV303: $i] :
( ( ( ( c_List_Oappend @ SV303 @ ( c_List_Olist_OCons @ SV602 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
| ! [SY2158: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2158 @ SV303 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV602 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2158 @ ( c_List_Oappend @ SV303 @ ( c_List_Olist_OCons @ SV602 @ ( 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)],[1621]) ).
thf(1969,plain,
! [SV603: $i,SV305: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV305 ) @ SV603 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV305 ) @ SV603 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1623]) ).
thf(1970,plain,
! [SV604: $i,SV306: $i] :
( ( ! [SY2159: $i,SY2160: $i,SY2161: $i] :
( ( ( c_List_Oappend @ SV306 @ ( c_List_Olist_OCons @ SV604 @ ( c_List_Olist_ONil @ SY2159 ) @ SY2159 ) @ SY2159 )
!= ( c_List_Oappend @ SY2160 @ ( c_List_Olist_OCons @ SY2161 @ ( c_List_Olist_ONil @ SY2159 ) @ SY2159 ) @ SY2159 ) )
| ( SV604 = SY2161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(1971,plain,
! [SV605: $i,SV307: $i] :
( ( ! [SY2162: $i,SY2163: $i] :
( ! [SY2164: $i] :
( ( c_List_Oappend @ SV307 @ ( c_List_Olist_OCons @ SV605 @ ( c_List_Olist_ONil @ SY2162 ) @ SY2162 ) @ SY2162 )
!= ( c_List_Oappend @ SY2163 @ ( c_List_Olist_OCons @ SY2164 @ ( c_List_Olist_ONil @ SY2162 ) @ SY2162 ) @ SY2162 ) )
| ( SV307 = SY2163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1625]) ).
thf(1972,plain,
! [SV606: $i,SV308: $i] :
( ( ! [SY2165: $i,SY2166: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV308 ) @ SV606 ) @ SY2165 @ SY2166 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV308 @ SY2165 @ SY2166 ) ) @ ( c_Lambda_Osubst @ SV606 @ SY2165 @ SY2166 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1626]) ).
thf(1973,plain,
! [SV607: $i,SV309: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV309 )
!= ( c_Lambda_OdB_OVar @ SV607 ) )
| ( SV309 = SV607 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1627]) ).
thf(1974,plain,
! [SV608: $i,SV310: $i] :
( ( ! [SY2167: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV310 @ SV608 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY2167 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV310 @ ( c_List_Oappend @ SV608 @ ( c_List_Olist_OCons @ SY2167 @ ( 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)],[1628]) ).
thf(1975,plain,
! [SV609: $i,SV311: $i] :
( ( ! [SY2168: $i] :
( ! [SY2169: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV311 ) @ SV609 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2168 ) @ SY2169 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV311 = SY2168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1629]) ).
thf(1976,plain,
! [SV610: $i,SV312: $i] :
( ( ! [SY2170: $i,SY2171: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV312 ) @ SV610 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2170 ) @ SY2171 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV610 = SY2171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1630]) ).
thf(1977,plain,
! [SV611: $i,SV313: $i] :
( ( ! [SY2172: $i,SY2173: $i,SY2174: $i] :
( ( ( c_List_Olist_OCons @ SV313 @ SV611 @ SY2172 )
!= ( c_List_Olist_OCons @ SY2173 @ SY2174 @ SY2172 ) )
| ( SV611 = SY2174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1631]) ).
thf(1978,plain,
! [SV612: $i,SV314: $i] :
( ( ! [SY2175: $i,SY2176: $i] :
( ! [SY2177: $i] :
( ( c_List_Olist_OCons @ SV314 @ SV612 @ SY2175 )
!= ( c_List_Olist_OCons @ SY2176 @ SY2177 @ SY2175 ) )
| ( SV314 = SY2176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1632]) ).
thf(1979,plain,
! [SV613: $i,SV315: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV315 ) @ SV613 @ SV315 )
= SV613 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(1980,plain,
! [SV614: $i,SV316: $i] :
( ( ! [SY2178: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV316 ) @ ( c_List_Olist_OCons @ SV614 @ SY2178 @ SV316 ) @ SV316 )
= ( c_List_Olist_OCons @ SV614 @ SY2178 @ SV316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(1981,plain,
! [SV615: $i,SV317: $i] :
( ( ! [SY2179: $i] :
( ( SV317
!= ( c_List_Oappend @ SV615 @ SV317 @ SY2179 ) )
| ( SV615
= ( c_List_Olist_ONil @ SY2179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1635]) ).
thf(1982,plain,
! [SV616: $i,SV318: $i] :
( ( ! [SY2180: $i] :
( ( ( c_List_Oappend @ SV318 @ SV616 @ SY2180 )
!= SV616 )
| ( SV318
= ( c_List_Olist_ONil @ SY2180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(1983,plain,
! [SV617: $i,SV319: $i] :
( ( ! [SY2181: $i] :
( ( SV319
!= ( c_List_Oappend @ SV319 @ SV617 @ SY2181 ) )
| ( SV617
= ( c_List_Olist_ONil @ SY2181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(1984,plain,
! [SV618: $i,SV320: $i] :
( ( ! [SY2182: $i] :
( ( ( c_List_Oappend @ SV320 @ SV618 @ SY2182 )
!= SV320 )
| ( SV618
= ( c_List_Olist_ONil @ SY2182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(1985,plain,
! [SV321: $i] :
( ( ( ! [SY1746: $i,SY1747: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV321 @ ( c_Lambda_OdB_OVar @ SY1746 ) @ SY1747 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV321 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1639]) ).
thf(1986,plain,
! [SV619: $i,SV322: $i] :
( ( ! [SY2183: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV322 ) @ SV619 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2183 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV322 ) @ SV619 )
= SY2183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(1987,plain,
! [SV620: $i,SV323: $i] :
( ( ! [SY2184: $i] :
( ( c_List_Olist_ONil @ SV323 )
!= ( c_List_Olist_OCons @ SV620 @ SY2184 @ SV323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1641]) ).
thf(1988,plain,
! [SV621: $i,SV324: $i] :
( ( ! [SY2185: $i] :
( ! [SY2186: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV324 ) @ SV621 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2185 ) @ SY2186 ) )
| ( SV324 = SY2185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1642]) ).
thf(1989,plain,
! [SV622: $i,SV325: $i] :
( ( ! [SY2187: $i,SY2188: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV325 ) @ SV622 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2187 ) @ SY2188 ) )
| ( SV622 = SY2188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1643]) ).
thf(1990,plain,
! [SV623: $i,SV326: $i] :
( ( ! [SY2189: $i] :
( ( c_Lambda_OdB_OVar @ SV326 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV623 @ SY2189 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV326 )
= SV623 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1644]) ).
thf(1991,plain,
! [SV624: $i,SV327: $i] :
( ( ! [SY2190: $i] :
( ( c_Lambda_OdB_OVar @ SV327 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV624 ) @ SY2190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1645]) ).
thf(1992,plain,
! [SV625: $i,SV328: $i] :
( ( ! [SY2191: $i] :
( ( ( c_List_Oappend @ SV328 @ SV625 @ SY2191 )
!= ( c_List_Olist_ONil @ SY2191 ) )
| ( SV625
= ( c_List_Olist_ONil @ SY2191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1646]) ).
thf(1993,plain,
! [SV626: $i,SV329: $i] :
( ( ! [SY2192: $i] :
( ( ( c_List_Oappend @ SV329 @ SV626 @ SY2192 )
!= ( c_List_Olist_ONil @ SY2192 ) )
| ( SV329
= ( c_List_Olist_ONil @ SY2192 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(1994,plain,
! [SV627: $i,SV330: $i] :
( ( ! [SY2193: $i] :
( ( SV330
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV330 ) @ SV627 ) @ SY2193 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV330 ) @ SV627 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV330 ) @ SV627 ) @ ( c_List_Oappend @ SY2193 @ ( c_List_Olist_OCons @ SV627 @ ( 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)],[1648]) ).
thf(1995,plain,
! [SV628: $i,SV331: $i] :
( ( ! [SY2194: $i] :
( ( ( c_List_Olist_ONil @ SV331 )
!= ( c_List_Oappend @ SV628 @ SY2194 @ SV331 ) )
| ( SY2194
= ( c_List_Olist_ONil @ SV331 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1649]) ).
thf(1996,plain,
! [SV629: $i,SV332: $i] :
( ( ! [SY2195: $i] :
( ( c_List_Olist_ONil @ SV332 )
!= ( c_List_Oappend @ SV629 @ SY2195 @ SV332 ) )
| ( SV629
= ( c_List_Olist_ONil @ SV332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(1997,plain,
! [SV630: $i,SV333: $i] :
( ( ! [SY2196: $i,SY2197: $i] :
( ( c_List_Ofoldl @ SV333 @ SV630 @ ( c_List_Olist_ONil @ SY2196 ) @ SY2197 @ SY2196 )
= SV630 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(1998,plain,
! [SV631: $i,SV335: $i] :
( ( SV335
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV631 ) @ SV335 @ SV631 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(1999,plain,
! [SV632: $i,SV336: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV336 ) @ SV632 @ SV336 )
= SV632 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(2000,plain,
! [SV633: $i,SV337: $i] :
( ( SV337
= ( c_List_Oappend @ SV337 @ ( c_List_Olist_ONil @ SV633 ) @ SV633 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(2001,plain,
! [SV634: $i,SV338: $i] :
( ( SV338
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV634 ) @ SV338 @ SV634 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(2002,plain,
! [SV635: $i,SV339: $i] :
( ( ( c_List_Oappend @ SV339 @ ( c_List_Olist_ONil @ SV635 ) @ SV635 )
= SV339 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1657]) ).
thf(2003,plain,
! [SV636: $i,SV340: $i] :
( ( ! [SY2198: $i,SY2199: $i] :
( ( ( c_List_Oappend @ SV340 @ SV636 @ SY2198 )
!= ( c_List_Oappend @ SV340 @ SY2199 @ SY2198 ) )
| ( SV636 = SY2199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1658]) ).
thf(2004,plain,
! [SV637: $i,SV341: $i] :
( ( ! [SY2200: $i,SY2201: $i] :
( ( ( c_List_Oappend @ SV341 @ SV637 @ SY2200 )
!= ( c_List_Oappend @ SY2201 @ SV637 @ SY2200 ) )
| ( SV341 = SY2201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1659]) ).
thf(2005,plain,
! [SV638: $i,SV343: $i] :
( ( ! [SY2202: $i,SY2203: $i,SY2204: $i,SY2205: $i] :
( ( c_List_Ofoldl @ SV343 @ SV638 @ ( c_List_Olist_OCons @ SY2202 @ SY2203 @ SY2204 ) @ SY2205 @ SY2204 )
= ( c_List_Ofoldl @ SV343 @ ( hAPP @ ( hAPP @ SV343 @ SV638 ) @ SY2202 ) @ SY2203 @ SY2205 @ SY2204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1661]) ).
thf(2006,plain,
! [SV639: $i,SV344: $i] :
( ( ! [SY2206: $i,SY2207: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV344 @ SV639 @ SY2206 ) @ SY2207 @ SY2206 )
= ( c_List_Olist_OCons @ SV344 @ ( c_List_Oappend @ SV639 @ SY2207 @ SY2206 ) @ SY2206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1662]) ).
thf(2007,plain,
! [SV640: $i,SV345: $i] :
( ( ! [SY2208: $i,SY2209: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV345 @ SV640 @ SY2208 ) @ SY2209 @ SY2208 )
= ( c_List_Olist_OCons @ SV345 @ ( c_List_Oappend @ SV640 @ SY2209 @ SY2208 ) @ SY2208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1663]) ).
thf(2008,plain,
! [SV641: $i,SV346: $i] :
( ( ! [SY2210: $i,SY2211: $i] :
( ( c_List_Olist_OCons @ SV346 @ ( c_List_Oappend @ SV641 @ SY2210 @ SY2211 ) @ SY2211 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV346 @ SV641 @ SY2211 ) @ SY2210 @ SY2211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1664]) ).
thf(2009,plain,
! [SV642: $i,SV347: $i] :
( ( ! [SY2212: $i,SY2213: $i] :
( ( c_List_Olist_OCons @ SV347 @ ( c_List_Oappend @ SV642 @ SY2212 @ SY2213 ) @ SY2213 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV347 @ SV642 @ SY2213 ) @ SY2212 @ SY2213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1665]) ).
thf(2010,plain,
! [SV643: $i,SV348: $i] :
( ( ! [SY2214: $i] :
( ( c_List_Olist_OCons @ SV348 @ SV643 @ SY2214 )
!= ( c_List_Olist_ONil @ SY2214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1666]) ).
thf(2011,plain,
! [SV644: $i,SV349: $i] :
( ( ! [SY2215: $i] :
( ( c_List_Olist_OCons @ SV349 @ SV644 @ SY2215 )
!= ( c_List_Olist_ONil @ SY2215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1667]) ).
thf(2012,plain,
! [SV645: $i,SV350: $i] :
( ( ! [SY2216: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV350 @ SV645 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2216 @ SV645 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV350 = SY2216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1668]) ).
thf(2013,plain,
! [SV646: $i,SV351: $i] :
( ( ! [SY2217: $i] :
( ( c_List_Olist_OCons @ SV351 @ SV646 @ SY2217 )
!= SV646 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(2014,plain,
! [SV647: $i,SV352: $i] :
( ( ! [SY2218: $i] :
( SV352
!= ( c_List_Olist_OCons @ SV647 @ SV352 @ SY2218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1670]) ).
thf(2015,plain,
! [SV648: $i,SV353: $i] :
( ( ! [SY2219: $i] :
( ( ( c_Lambda_OdB_OVar @ SV353 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV648 @ SY2219 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2219
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1671]) ).
thf(2016,plain,
! [SV649: $i,SV354: $i] :
( ( ! [SY2220: $i] :
( ( c_List_Olist_OCons @ SV354 @ SV649 @ SY2220 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY2220 ) @ ( c_List_Olist_OCons @ SV354 @ SV649 @ SY2220 ) @ SY2220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1672]) ).
thf(2017,plain,
! [SV650: $i,SV356: $i] :
( ( ! [SY2221: $i,SY2222: $i,SY2223: $i,SY2224: $i] :
( ( c_List_Ofoldl @ SV356 @ SV650 @ ( c_List_Oappend @ SY2221 @ SY2222 @ SY2223 ) @ SY2224 @ SY2223 )
= ( c_List_Ofoldl @ SV356 @ ( c_List_Ofoldl @ SV356 @ SV650 @ SY2221 @ SY2224 @ SY2223 ) @ SY2222 @ SY2224 @ SY2223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(2018,plain,
! [SV651: $i,SV357: $i] :
( ( ! [SY2225: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV357 ) @ SV651 )
!= ( c_Lambda_OdB_OVar @ SY2225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1675]) ).
thf(2019,plain,
! [SV652: $i,SV358: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV358 @ SV652 ) )
| ~ ( class_Orderings_Opreorder @ SV652 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1676]) ).
thf(2020,plain,
! [SV653: $i,SV359: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV359 @ SV653 ) )
| ~ ( class_Orderings_Oorder @ SV653 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1677]) ).
thf(2021,plain,
! [SV654: $i,SV360: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV360 ) @ SV654 ) @ SV654 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1678]) ).
thf(2022,plain,
! [SV655: $i,SV361: $i] :
( ( ( SV361 = SV655 )
| ! [SY2226: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY2226 ) @ SV361 ) @ SV655 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1679]) ).
thf(2023,plain,
! [SV656: $i,SV362: $i,SV1: $i] :
( ( ! [SY2227: $i,SY2228: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV1 @ ( c_List_Olist_OCons @ SV362 @ SV656 @ SY2227 ) @ SY2227 ) @ ( c_Nat_Osize__class_Osize @ SV1 @ ( tc_List_Olist @ SY2227 ) ) @ SY2228 @ SY2227 )
= ( c_List_Oappend @ SV1 @ ( c_List_Olist_OCons @ SY2228 @ SV656 @ SY2227 ) @ SY2227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1681]) ).
thf(2024,plain,
! [SV657: $i,SV363: $i,SV2: $i] :
( ( ! [SY2229: $i] :
( ( ( c_List_Olist__update @ SV2 @ SV363 @ SV657 @ SY2229 )
!= ( c_List_Olist_ONil @ SY2229 ) )
| ( SV2
= ( c_List_Olist_ONil @ SY2229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(2025,plain,
! [SV658: $i,SV364: $i,SV3: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV3 ) @ SV364 @ SV658 @ SV3 )
= ( c_List_Olist_ONil @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1683]) ).
thf(2026,plain,
! [SV659: $i,SV365: $i,SV4: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV4 ) @ SV365 @ SV659 @ SV4 )
= ( c_List_Olist_ONil @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1684]) ).
thf(2027,plain,
! [SV660: $i,SV366: $i,SV5: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV5 ) @ SV366 @ SV660 @ SV5 )
= ( c_List_Olist_ONil @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1685]) ).
thf(2028,plain,
! [SV661: $i,SV367: $i,SV6: $i] :
( ( ! [SY2230: $i] :
( ( ( c_List_Olist__update @ SV6 @ SV367 @ SV661 @ SY2230 )
!= SV6 )
| ~ ( c_HOL_Oord__class_Oless @ SV367 @ ( c_Nat_Osize__class_Osize @ SV6 @ ( tc_List_Olist @ SY2230 ) ) @ tc_nat )
| ( ( c_List_Onth @ SV6 @ SV367 @ SY2230 )
= SV661 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1686]) ).
thf(2029,plain,
! [SV662: $i,SV368: $i,SV7: $i] :
( ( ! [SY2231: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ SV7 @ SV368 @ SV662 @ SY2231 ) @ ( tc_List_Olist @ SY2231 ) )
= ( c_Nat_Osize__class_Osize @ SV7 @ ( tc_List_Olist @ SY2231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1687]) ).
thf(2030,plain,
! [SV663: $i,SV369: $i,SV8: $i] :
( ( ! [SY2232: $i,SY2233: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ SV8 @ SV369 @ SV663 @ SY2232 ) @ SY2233 @ SY2232 )
= ( c_List_Onth @ SV8 @ SY2233 @ SY2232 ) )
| ( SV369 = SY2233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1688]) ).
thf(2031,plain,
! [SV664: $i,SV370: $i,SV9: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV9 @ ( c_Nat_Osize__class_Osize @ SV370 @ ( tc_List_Olist @ SV664 ) ) @ tc_nat )
| ( ( c_List_Olist__update @ SV370 @ SV9 @ ( c_List_Onth @ SV370 @ SV9 @ SV664 ) @ SV664 )
= SV370 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1689]) ).
thf(2032,plain,
! [SV665: $i,SV371: $i,SV10: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV10 @ ( c_Nat_Osize__class_Osize @ SV371 @ ( tc_List_Olist @ SV665 ) ) @ tc_nat )
| ! [SY2234: $i] :
( ( c_List_Onth @ ( c_List_Olist__update @ SV371 @ SV10 @ SY2234 @ SV665 ) @ SV10 @ SV665 )
= SY2234 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1690]) ).
thf(2033,plain,
! [SV666: $i,SV372: $i,SV11: $i] :
( ( ! [SY2235: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ SV11 @ SV372 @ SV666 @ SY2235 ) @ SV372 @ SY2235 )
= SV666 )
| ~ ( c_HOL_Oord__class_Oless @ SV372 @ ( c_Nat_Osize__class_Osize @ SV11 @ ( tc_List_Olist @ SY2235 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1691]) ).
thf(2034,plain,
! [SV667: $i,SV373: $i,SV12: $i] :
( ( ! [SY2236: $i] :
( ! [SY2237: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV12 @ SV373 @ SV667 ) @ SY2236 @ SY2237 @ SV667 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV12 @ SY2236 @ SY2237 @ SV667 ) @ SV373 @ SV667 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2236 @ ( c_Nat_Osize__class_Osize @ SV12 @ ( tc_List_Olist @ SV667 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1692]) ).
thf(2035,plain,
! [SV668: $i,SV374: $i,SV13: $i] :
( ( ! [SY2238: $i] :
( ! [SY2239: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV13 @ SV374 @ SV668 ) @ SY2238 @ SY2239 @ SV668 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV13 @ SY2238 @ SY2239 @ SV668 ) @ SV374 @ SV668 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2238 @ ( c_Nat_Osize__class_Osize @ SV13 @ ( tc_List_Olist @ SV668 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1693]) ).
thf(2036,plain,
! [SV669: $i,SV375: $i,SV14: $i] :
( ( ( c_List_Olist__update @ SV14 @ SV375 @ ( c_List_Onth @ SV14 @ SV375 @ SV669 ) @ SV669 )
= SV14 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1694]) ).
thf(2037,plain,
! [SV670: $i,SV376: $i,SV15: $i] :
( ( ! [SY2240: $i,SY2241: $i] :
( ! [SY2242: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV15 @ SV376 @ SV670 @ SY2240 ) @ SY2241 @ SY2242 @ SY2240 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV15 @ SY2241 @ SY2242 @ SY2240 ) @ SV376 @ SV670 @ SY2240 ) )
| ( SV376 = SY2241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1695]) ).
thf(2038,plain,
! [SV671: $i,SV377: $i,SV16: $i] :
( ( ! [SY2243: $i,SY2244: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV16 @ SV377 @ SV671 ) @ ( c_Suc @ SY2243 ) @ SY2244 @ SV671 )
= ( c_List_Olist_OCons @ SV16 @ ( c_List_Olist__update @ SV377 @ SY2243 @ SY2244 @ SV671 ) @ SV671 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1696]) ).
thf(2039,plain,
! [SV672: $i,SV378: $i,SV17: $i] :
( ( ! [SY2245: $i,SY2246: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ SV17 @ SV378 @ SV672 @ SY2245 ) @ SY2246 @ SY2245 )
= ( c_List_Onth @ SV17 @ SY2246 @ SY2245 ) )
| ( SV378 = SY2246 )
| ~ ( c_HOL_Oord__class_Oless @ SV378 @ ( c_Nat_Osize__class_Osize @ SV17 @ ( tc_List_Olist @ SY2245 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1697]) ).
thf(2040,plain,
! [SV673: $i,SV379: $i,SV18: $i] :
( ( ! [SY2247: $i,SY2248: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV18 @ SV379 @ SV673 @ SY2247 ) @ SV379 @ SY2248 @ SY2247 )
= ( c_List_Olist__update @ SV18 @ SV379 @ SY2248 @ SY2247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1698]) ).
thf(2041,plain,
! [SV674: $i,SV380: $i,SV19: $i] :
( ( ! [SY2249: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV19 @ SV380 @ SV674 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2249 @ SV674 )
= ( c_List_Olist_OCons @ SY2249 @ SV380 @ SV674 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1699]) ).
thf(2042,plain,
! [SV675: $i,SV381: $i,SV20: $i] :
( ( ( ( c_List_Ohd @ ( c_List_Odrop @ SV20 @ SV381 @ SV675 ) @ SV675 )
= ( c_List_Onth @ SV381 @ SV20 @ SV675 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV20 @ ( c_Nat_Osize__class_Osize @ SV381 @ ( tc_List_Olist @ SV675 ) ) @ tc_nat )
| ( SV381
= ( c_List_Olist_ONil @ SV675 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1700]) ).
thf(2043,plain,
! [SV676: $i,SV382: $i,SV21: $i] :
( ( ( ( c_List_Olist_OCons @ ( c_List_Onth @ SV21 @ SV382 @ SV676 ) @ ( c_List_Odrop @ ( c_Suc @ SV382 ) @ SV21 @ SV676 ) @ SV676 )
= ( c_List_Odrop @ SV382 @ SV21 @ SV676 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV382 @ ( c_Nat_Osize__class_Osize @ SV21 @ ( tc_List_Olist @ SV676 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1701]) ).
thf(2044,plain,
! [SV677: $i,SV383: $i,SV22: $i] :
( ( ( c_List_Oappend @ ( c_List_Otake @ SV22 @ SV383 @ SV677 ) @ ( c_List_Odrop @ SV22 @ SV383 @ SV677 ) @ SV677 )
= SV383 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1702]) ).
thf(2045,plain,
! [SV678: $i,SV384: $i,SV23: $i] :
( ( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ SV23 @ SV384 @ SV678 ) @ SV678 )
= ( c_List_Olist_OCons @ SV23 @ SV384 @ SV678 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1703]) ).
thf(2046,plain,
! [SV679: $i,SV385: $i,SV24: $i] :
( ( ! [SY2250: $i] :
( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SV385 ) ) @ SV679 @ SV385 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV679 @ ( tc_List_Olist @ SV385 ) ) @ SV24 @ SV385 ) @ SY2250 @ SV385 ) @ SV385 )
!= SY2250 )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SV385 ) ) @ SV679 @ SV385 )
!= SV24 )
| ( SV679
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV679 @ ( tc_List_Olist @ SV385 ) ) @ SV24 @ SV385 ) )
| ( ( c_List_Oappend @ SV679 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV679 @ ( tc_List_Olist @ SV385 ) ) @ SV24 @ SV385 ) @ SY2250 @ SV385 ) @ SV385 )
= ( c_List_Oappend @ SV24 @ SY2250 @ SV385 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1704]) ).
thf(2047,plain,
! [SV680: $i,SV386: $i,SV25: $i] :
( ( ! [SY2251: $i] :
( ! [SY2252: $i] :
( ( c_List_Odrop @ SV25 @ SV386 @ SV680 )
!= ( c_List_Olist_OCons @ SY2251 @ SY2252 @ SV680 ) )
| ( ( c_List_Onth @ SV386 @ SV25 @ SV680 )
= SY2251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1705]) ).
thf(2048,plain,
! [SV681: $i,SV387: $i,SV26: $i] :
( ( ! [SY2253: $i] :
( ( ( c_List_Olist__update @ SV26 @ SV387 @ SV681 @ SY2253 )
= ( c_List_Oappend @ ( c_List_Otake @ SV387 @ SV26 @ SY2253 ) @ ( c_List_Olist_OCons @ SV681 @ ( c_List_Odrop @ ( c_Suc @ SV387 ) @ SV26 @ SY2253 ) @ SY2253 ) @ SY2253 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV387 @ ( c_Nat_Osize__class_Osize @ SV26 @ ( tc_List_Olist @ SY2253 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1706]) ).
thf(2049,plain,
! [SV682: $i,SV388: $i,SV27: $i] :
( ( ( SV27
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV27 @ ( tc_List_Olist @ SV388 ) ) @ SV682 @ SV388 ) )
| ( ( c_List_Oappend @ SV27 @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV27 @ ( tc_List_Olist @ SV388 ) ) @ SV682 @ SV388 ) @ SV388 )
= SV682 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1707]) ).
thf(2050,plain,
! [SV683: $i,SV389: $i,SV28: $i] :
( ( ( ( c_List_Olast @ ( c_List_Odrop @ SV28 @ SV389 @ SV683 ) @ SV683 )
= ( c_List_Olast @ SV389 @ SV683 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV28 @ ( c_Nat_Osize__class_Osize @ SV389 @ ( tc_List_Olist @ SV683 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1708]) ).
thf(2051,plain,
! [SV684: $i,SV390: $i,SV29: $i] :
( ( ( c_List_Odrop @ SV29 @ ( c_List_Otl @ SV390 @ SV684 ) @ SV684 )
= ( c_List_Otl @ ( c_List_Odrop @ SV29 @ SV390 @ SV684 ) @ SV684 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1709]) ).
thf(2052,plain,
! [SV685: $i,SV391: $i,SV30: $i] :
( ( ! [SY2254: $i] :
( ( c_List_Odrop @ ( c_Suc @ SV30 ) @ ( c_List_Olist_OCons @ SV391 @ SV685 @ SY2254 ) @ SY2254 )
= ( c_List_Odrop @ SV30 @ SV685 @ SY2254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1710]) ).
thf(2053,plain,
! [SV686: $i,SV392: $i,SV31: $i] :
( ( ( c_List_Odrop @ SV31 @ ( c_List_Obutlast @ SV392 @ SV686 ) @ SV686 )
= ( c_List_Obutlast @ ( c_List_Odrop @ SV31 @ SV392 @ SV686 ) @ SV686 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1711]) ).
thf(2054,plain,
! [SV687: $i,SV393: $i,SV32: $i] :
( ( ( c_List_Otl @ ( c_List_Odrop @ SV32 @ SV393 @ SV687 ) @ SV687 )
= ( c_List_Odrop @ SV32 @ ( c_List_Otl @ SV393 @ SV687 ) @ SV687 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1712]) ).
thf(2055,plain,
! [SV688: $i,SV394: $i,SV33: $i] :
( ( SV33
= ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV394 @ ( tc_List_Olist @ SV688 ) ) @ ( c_List_Oappend @ SV394 @ SV33 @ SV688 ) @ SV688 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1713]) ).
thf(2056,plain,
! [SV689: $i,SV395: $i,SV34: $i] :
( ( ( c_List_Odrop @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ SV34 @ SV395 @ SV689 ) @ SV689 )
= SV395 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1714]) ).
thf(2057,plain,
! [SV690: $i,SV396: $i,SV35: $i] :
( ( ( c_List_Obutlast @ ( c_List_Odrop @ SV35 @ SV396 @ SV690 ) @ SV690 )
= ( c_List_Odrop @ SV35 @ ( c_List_Obutlast @ SV396 @ SV690 ) @ SV690 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1715]) ).
thf(2058,plain,
! [SV691: $i,SV397: $i,SV36: $i] :
( ( ( c_List_Odrop @ ( c_Suc @ SV36 ) @ SV397 @ SV691 )
= ( c_List_Odrop @ SV36 @ ( c_List_Otl @ SV397 @ SV691 ) @ SV691 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1716]) ).
thf(2059,plain,
! [SV399: $i,SV38: $i] :
( ( ( ( c_Int_Onumber__class_Onumber__of @ SV38 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ! [SY1893: $i,SY1894: $i] :
( ( c_List_Odrop @ ( c_Int_Onumber__class_Onumber__of @ SV38 @ tc_nat ) @ ( c_List_Olist_OCons @ SV399 @ SY1893 @ SY1894 ) @ SY1894 )
= ( c_List_Olist_OCons @ SV399 @ SY1893 @ SY1894 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1718]) ).
thf(2060,plain,
! [SV692: $i,SV401: $i,SV40: $i] :
( ( ! [SY2255: $i,SY2256: $i] :
( ( c_Type_Otypings @ SV40 @ SV401 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV692 @ SY2255 @ SV40 @ SV401 ) )
| ! [SY2257: $i] :
( ~ ( c_Type_Otyping @ SV40 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2256 ) @ SY2257 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2255 )
| ! [SY1205: $i] :
~ ( c_Type_Otypings @ SV40 @ SY2257 @ SY1205 )
| ~ ( c_Type_Otyping @ SV40 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2256 ) @ SY2257 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV401 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV692 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1720]) ).
thf(2061,plain,
! [SV693: $i,SV402: $i,SV41: $i] :
( ( ! [SY2259: $i] :
( ( c_Type_Otypings @ SV41 @ SV402 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV693 @ SV41 @ SY2259 @ SV402 ) )
| ~ ( c_Type_Otyping @ SV41 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2259 ) @ SV402 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV693 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1721]) ).
thf(2062,plain,
! [SV694: $i,SV403: $i,SV42: $i] :
( ( ( SV42
= ( c_List_Oappend @ ( c_List_Otake @ SV403 @ SV42 @ SV694 ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ SV42 @ SV403 @ SV694 ) @ ( c_List_Odrop @ ( c_Suc @ SV403 ) @ SV42 @ SV694 ) @ SV694 ) @ SV694 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV403 @ ( c_Nat_Osize__class_Osize @ SV42 @ ( tc_List_Olist @ SV694 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1722]) ).
thf(2063,plain,
! [SV695: $i,SV404: $i,SV43: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Otake @ SV43 @ SV404 @ SV695 ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ ( c_List_Odrop @ SV43 @ SV404 @ SV695 ) @ SV695 ) @ ( c_List_Olist_ONil @ SV695 ) @ SV695 ) @ SV695 )
= ( c_List_Otake @ ( c_Suc @ SV43 ) @ SV404 @ SV695 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV43 @ ( c_Nat_Osize__class_Osize @ SV404 @ ( tc_List_Olist @ SV695 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1723]) ).
thf(2064,plain,
! [SV696: $i,SV405: $i,SV44: $i] :
( ( ! [SY2260: $i] :
( ( c_Lambda_Oliftn @ SV44 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV405 ) @ SV696 ) @ SY2260 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ SV44 @ SV405 @ SY2260 ) ) @ ( c_Lambda_Oliftn @ SV44 @ SV696 @ SY2260 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1724]) ).
thf(2065,plain,
! [SV697: $i,SV406: $i,SV45: $i] :
( ( ! [SY2261: $i] :
( ( c_List_Onth @ ( c_List_Oappend @ SV45 @ ( c_List_Olist_OCons @ SV406 @ SV697 @ SY2261 ) @ SY2261 ) @ ( c_Nat_Osize__class_Osize @ SV45 @ ( tc_List_Olist @ SY2261 ) ) @ SY2261 )
= SV406 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1725]) ).
thf(2066,plain,
! [SV698: $i,SV409: $i,SV48: $i] :
( ( ! [SY2262: $i,SY2263: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV48 @ SV409 @ SV698 ) @ ( c_List_Olist_OCons @ SY2262 @ SY2263 @ SV698 ) @ SV698 )
= ( c_List_Olist_OCons @ SV48 @ ( c_List_Olist_OCons @ SY2262 @ ( c_List_Osplice @ SV409 @ SY2263 @ SV698 ) @ SV698 ) @ SV698 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1728]) ).
thf(2067,plain,
! [SV410: $i,SV49: $i] :
( ( ( ( c_Int_Onumber__class_Onumber__of @ SV49 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ! [SY1911: $i,SY1912: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ SV410 @ SY1911 @ SY1912 ) @ ( c_Int_Onumber__class_Onumber__of @ SV49 @ tc_nat ) @ SY1912 )
= SV410 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1729]) ).
thf(2068,plain,
! [SV55: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV55 )
= $false )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV55 )
!= ( c_HOL_Oone__class_Oone @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1735]) ).
thf(2069,plain,
! [SV56: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV56 )
= $false )
| ( ( ( c_HOL_Oone__class_Oone @ SV56 )
!= ( c_HOL_Ozero__class_Ozero @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1736]) ).
thf(2070,plain,
! [SV412: $i,SV57: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV57 ) @ ( c_Suc @ SV412 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV57 @ SV412 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1737]) ).
thf(2071,plain,
! [SV413: $i,SV58: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV58 @ SV413 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV58 ) @ ( c_Suc @ SV413 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1738]) ).
thf(2072,plain,
! [SV414: $i,SV59: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV59 ) @ ( c_Suc @ SV414 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV59 @ SV414 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1739]) ).
thf(2073,plain,
! [SV416: $i,SV61: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV61 @ ( c_Suc @ SV416 ) @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV416 @ SV61 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1741]) ).
thf(2074,plain,
! [SV417: $i,SV62: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV62 @ SV417 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV417 @ ( c_Suc @ SV62 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1742]) ).
thf(2075,plain,
! [SV418: $i,SV64: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV64 ) @ SV418 @ tc_nat )
= $true )
| ( ( ( ( c_Suc @ SV64 )
= SV418 )
| ~ ( c_HOL_Oord__class_Oless @ SV64 @ SV418 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1744]) ).
thf(2076,plain,
! [SV65: $i] :
( ( ( class_Int_Oring__char__0 @ SV65 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV65 )
| ! [SY1236: $i,SY1237: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ SY1236 @ SV65 )
!= ( c_Int_Onumber__class_Onumber__of @ SY1237 @ SV65 ) )
| ( SY1236 = SY1237 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1745]) ).
thf(2077,plain,
! [SV699: $i,SV419: $i,SV66: $i] :
( ( ! [SY2264: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV66 @ SV419 @ SV419 ) @ SV419 ) @ SV699 ) @ SY2264 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV66 @ SV419 ) @ SY2264 ) @ SV699 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1746]) ).
thf(2078,plain,
! [SV700: $i,SV420: $i,SV67: $i] :
( ( ! [SY2265: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV67 @ SV420 ) @ SV700 ) @ SY2265 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV67 @ SV420 @ SV420 ) @ SV420 ) @ SY2265 ) @ SV700 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1747]) ).
thf(2079,plain,
! [SV68: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV68 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV68 )
= ( c_HOL_Oone__class_Oone @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1748]) ).
thf(2080,plain,
! [SV701: $i,SV421: $i,SV69: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV69 @ SV421 ) @ SV701 ) )
| ! [SY2266: $i,SY2267: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV69 @ SY2266 @ SY2267 ) @ SV701 ) @ SV421 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1749]) ).
thf(2081,plain,
! [SV702: $i,SV422: $i,SV70: $i] :
( ( ! [SY2268: $i,SY2269: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV70 @ SV422 @ SV702 ) @ SY2268 ) @ SY2269 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY2269 ) @ SY2268 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1750]) ).
thf(2082,plain,
! [SV703: $i,SV423: $i,SV71: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV71 @ SV423 ) @ SV703 ) )
| ! [SY2270: $i,SY2271: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV71 @ SY2270 @ SY2271 ) @ SV703 ) @ SV423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1751]) ).
thf(2083,plain,
! [SV704: $i,SV424: $i,SV72: $i] :
( ( ! [SY2272: $i,SY2273: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV72 @ SV424 @ SV704 ) @ SY2272 ) @ SY2273 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV72 @ SY2273 ) @ SY2272 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(2084,plain,
! [SV705: $i,SV425: $i,SV73: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SV73 @ SV425 @ SV705 ) @ ( tc_List_Olist @ SV705 ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ SV425 @ ( tc_List_Olist @ SV705 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1753]) ).
thf(2085,plain,
! [SV706: $i,SV426: $i,SV74: $i] :
( ( ( c_Suc @ ( c_Nat_Osize__class_Osize @ SV74 @ ( tc_List_Olist @ SV426 ) ) )
= ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SV706 @ SV74 @ SV426 ) @ ( tc_List_Olist @ SV426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1754]) ).
thf(2086,plain,
! [SV707: $i,SV427: $i,SV75: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV75 @ SV427 ) @ SV707 ) @ SV707 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1755]) ).
thf(2087,plain,
! [SV708: $i,SV428: $i,SV76: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV76 @ SV428 ) @ SV708 ) @ SV708 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1756]) ).
thf(2088,plain,
! [SV709: $i,SV429: $i,SV77: $i] :
( ( ( c_Wellfounded_Oaccp @ SV77 @ SV429 @ SV709 )
| ! [SY2274: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV77 @ SV709 ) @ SV429 ) @ SY2274 ) )
| ~ ( c_Wellfounded_Oaccp @ SV77 @ SY2274 @ SV709 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1757]) ).
thf(2089,plain,
! [SV710: $i,SV430: $i,SV78: $i] :
( ( ( c_Wellfounded_Oaccp @ SV78 @ SV430 @ SV710 )
| ! [SY2275: $i] :
( ~ ( c_Wellfounded_Oaccp @ SV78 @ SY2275 @ SV710 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV78 @ SV710 ) @ SV430 ) @ SY2275 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1758]) ).
thf(2090,plain,
! [SV711: $i,SV431: $i,SV79: $i] :
( ( ! [SY2276: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV79 @ SV431 ) @ SV711 ) @ SY2276 ) )
| ! [SY2277: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV79 @ SV431 ) @ SY2277 ) @ SY2276 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV79 @ SV431 ) @ SV711 ) @ SY2277 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1759]) ).
thf(2091,plain,
! [SV80: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV80 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV80 @ tc_Lambda_OdB )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1760]) ).
thf(2092,plain,
! [SV81: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV81 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1761]) ).
thf(2093,plain,
! [SV712: $i,SV432: $i,SV82: $i] :
( ( ! [SY2278: $i] :
( ( ( c_List_Onth @ ( c_List_Oappend @ SV82 @ SV432 @ SV712 ) @ SY2278 @ SV712 )
= ( c_List_Onth @ SV82 @ SY2278 @ SV712 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2278 @ ( c_Nat_Osize__class_Osize @ SV82 @ ( tc_List_Olist @ SV712 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1762]) ).
thf(2094,plain,
! [SV83: $i] :
( ( ( class_Nat_Osemiring__char__0 @ SV83 )
= $false )
| ( ( ! [SY1281: $i,SY1282: $i] :
( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SY1281 @ SV83 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY1282 @ SV83 ) )
| ( SY1281 = SY1282 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1763]) ).
thf(2095,plain,
! [SV433: $i,SV84: $i] :
( ( ( ( c_Suc @ SV84 )
!= ( c_Suc @ SV433 ) )
= $true )
| ( ( SV84 = SV433 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1764]) ).
thf(2096,plain,
! [SV434: $i,SV85: $i] :
( ( ( ( c_Suc @ SV85 )
!= ( c_Suc @ SV434 ) )
= $true )
| ( ( SV85 = SV434 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1765]) ).
thf(2097,plain,
! [SV713: $i,SV435: $i,SV86: $i] :
( ( ! [SY2279: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV86 @ SV435 ) @ SV713 ) @ SY2279 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV86 @ SV713 ) @ SY2279 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1766]) ).
thf(2098,plain,
! [SV436: $i,SV88: $i] :
( ( ( SV88 = SV436 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV88 @ SV436 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV88 @ ( c_Suc @ SV436 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1767]) ).
thf(2099,plain,
! [SV437: $i,SV89: $i] :
( ( ( SV89 = SV437 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV437 @ ( c_Suc @ SV89 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV437 @ SV89 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1768]) ).
thf(2100,plain,
! [SV438: $i,SV90: $i] :
( ( ( SV90 = SV438 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV90 @ ( c_Suc @ SV438 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV90 @ SV438 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1769]) ).
thf(2101,plain,
! [SV440: $i,SV94: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV94 ) @ SV440 @ tc_nat )
= $true )
| ( ( ! [SY1944: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1944 @ SV440 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV94 @ SY1944 @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1771]) ).
thf(2102,plain,
! [SV714: $i,SV441: $i,SV95: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ SV95 @ SV441 @ SV714 ) @ ( tc_List_Olist @ SV714 ) )
= SV95 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1772]) ).
thf(2103,plain,
! [SV715: $i,SV442: $i,SV96: $i] :
( ( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ SV96 @ SV442 @ SV715 ) @ SV715 @ SV442 )
= SV96 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1773]) ).
thf(2104,plain,
! [SV716: $i,SV443: $i,SV97: $i] :
( ( ! [SY2280: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ SV97 @ SV443 @ SV716 ) @ ( c_Suc @ SY2280 ) @ SV716 )
= ( c_List_Onth @ SV443 @ SY2280 @ SV716 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1774]) ).
thf(2105,plain,
! [SV444: $i,SV100: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV100 @ SV444 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV100 ) @ SV444 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1777]) ).
thf(2106,plain,
! [SV445: $i,SV101: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV101 @ ( c_Suc @ SV445 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV101 @ SV445 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1778]) ).
thf(2107,plain,
! [SV446: $i,SV102: $i] :
( ( ( ( c_Nat_Osize__class_Osize @ SV102 @ ( tc_List_Olist @ SV446 ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ ( c_List_Otl @ SV102 @ SV446 ) @ ( tc_List_Olist @ SV446 ) ) ) )
= $true )
| ( ( SV102
= ( c_List_Olist_ONil @ SV446 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1779]) ).
thf(2108,plain,
! [SV717: $i,SV448: $i,SV104: $i] :
( ( ! [SY2281: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV104 @ SV448 ) @ SV717 ) @ SY2281 ) )
| ! [SY2282: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV104 @ SV448 ) @ SY2282 ) @ SY2281 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV104 @ SV717 ) @ SY2282 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1781]) ).
thf(2109,plain,
! [SV718: $i,SV449: $i,SV105: $i] :
( ( ! [SY2283: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV105 @ SV449 ) @ SV718 ) @ SY2283 ) )
| ! [SY2284: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV105 @ SY2284 ) @ SY2283 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV105 @ SV449 ) @ SV718 ) @ SY2284 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1782]) ).
thf(2110,plain,
! [SV719: $i,SV450: $i,SV106: $i] :
( ( ( c_Wellfounded_Oaccp @ SV106 @ SV450 @ SV719 )
| ! [SY2285: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV106 @ SV450 ) @ SY2285 ) )
| ~ ( c_Wellfounded_Oaccp @ SV106 @ SY2285 @ SV719 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1783]) ).
thf(2111,plain,
! [SV720: $i,SV451: $i,SV107: $i] :
( ( ( c_Wellfounded_Oaccp @ SV107 @ SV451 @ SV720 )
| ! [SY2286: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV107 @ SV451 ) @ SY2286 ) )
| ~ ( c_Wellfounded_Oaccp @ SV107 @ SY2286 @ SV720 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1784]) ).
thf(2112,plain,
! [SV721: $i,SV452: $i,SV108: $i] :
( ( ( ( c_List_Otake @ ( c_Suc @ SV108 ) @ SV452 @ SV721 )
= ( c_List_Oappend @ ( c_List_Otake @ SV108 @ SV452 @ SV721 ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ SV452 @ SV108 @ SV721 ) @ ( c_List_Olist_ONil @ SV721 ) @ SV721 ) @ SV721 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV108 @ ( c_Nat_Osize__class_Osize @ SV452 @ ( tc_List_Olist @ SV721 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1785]) ).
thf(2113,plain,
! [SV109: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV109 )
= $false )
| ( ( ! [SY1321: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1321 @ SV109 ) @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1786]) ).
thf(2114,plain,
! [SV110: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV110 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV110 ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1787]) ).
thf(2115,plain,
! [SV111: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV111 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV111 ) @ ( c_HOL_Oone__class_Oone @ SV111 ) @ SV111 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1788]) ).
thf(2116,plain,
! [SV112: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV112 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV112 )
= ( c_HOL_Ozero__class_Ozero @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1789]) ).
thf(2117,plain,
! [SV113: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV113 )
= $false )
| ( ( ! [SY1322: $i,SY1323: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1322 @ SV113 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1323 @ SV113 ) @ SV113 )
| ~ ( c_HOL_Oord__class_Oless @ SY1322 @ SY1323 @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1790]) ).
thf(2118,plain,
! [SV114: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV114 )
= $false )
| ( ( ! [SY1324: $i,SY1325: $i] :
( ( c_HOL_Oord__class_Oless @ SY1324 @ SY1325 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1324 @ SV114 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1325 @ SV114 ) @ SV114 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1791]) ).
thf(2119,plain,
! [SV722: $i,SV453: $i,SV115: $i] :
( ( ( c_List_Onth @ ( c_List_Olist_OCons @ SV115 @ SV453 @ SV722 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV722 )
= SV115 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1792]) ).
thf(2120,plain,
! [SV118: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV118 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= $false )
| ( ( SV118
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1793]) ).
thf(2121,plain,
! [SV454: $i,SV120: $i] :
( ( ( ( c_Nat_Osize__class_Osize @ SV120 @ ( tc_List_Olist @ SV454 ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV120
= ( c_List_Olist_ONil @ SV454 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1794]) ).
thf(2122,plain,
! [SV723: $i,SV455: $i,SV121: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV121 @ SV455 @ SV723 ) @ ( c_List_Olist_ONil @ SV723 ) @ SV723 )
= ( c_List_Olist_OCons @ SV121 @ SV455 @ SV723 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1795]) ).
thf(2123,plain,
! [SV724: $i,SV456: $i,SV122: $i] :
( ( ! [SY2287: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV122 ) @ SV456 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV724 ) @ SY2287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV456 ) @ SY2287 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV122 ) @ SV724 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1796]) ).
thf(2124,plain,
! [SV725: $i,SV457: $i,SV123: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV123 ) @ SV457 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV725 ) @ SV457 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV123 ) @ SV725 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(2125,plain,
! [SV726: $i,SV458: $i,SV124: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV124 ) @ SV458 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV124 ) @ SV726 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV458 ) @ SV726 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1798]) ).
thf(2126,plain,
! [SV459: $i,SV125: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV125 ) ) @ ( c_Lambda_OdB_OAbs @ SV459 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV125 ) @ SV459 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1799]) ).
thf(2127,plain,
! [SV727: $i,SV460: $i,SV126: $i] :
( ( ! [SY2288: $i] :
( ( c_List_Otake @ ( c_Suc @ SV126 ) @ ( c_List_Olist_OCons @ SV460 @ SV727 @ SY2288 ) @ SY2288 )
= ( c_List_Olist_OCons @ SV460 @ ( c_List_Otake @ SV126 @ SV727 @ SY2288 ) @ SY2288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1800]) ).
thf(2128,plain,
! [SV728: $i,SV461: $i,SV127: $i] :
( ( ( ( c_Lambda_Oliftn @ SV127 @ ( c_Lambda_OdB_OVar @ SV461 ) @ SV728 )
= ( c_Lambda_OdB_OVar @ SV461 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV461 @ SV728 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1801]) ).
thf(2129,plain,
! [SV729: $i,SV462: $i,SV128: $i] :
( ( ! [SY2289: $i] :
( ( ( c_List_Onth @ ( c_List_Otake @ SV128 @ SV462 @ SV729 ) @ SY2289 @ SV729 )
= ( c_List_Onth @ SV462 @ SY2289 @ SV729 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2289 @ SV128 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1802]) ).
thf(2130,plain,
! [SV730: $i,SV463: $i,SV129: $i] :
( ( ! [SY2290: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV129 @ SV463 @ SV730 ) ) @ ( c_Lambda_Osubst @ SV129 @ SY2290 @ SV730 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV463 ) @ SY2290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1803]) ).
thf(2131,plain,
! [SV731: $i,SV464: $i,SV130: $i] :
( ( ! [SY2291: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV130 @ SV464 @ SV731 ) ) @ ( c_Lambda_Osubst @ SY2291 @ SV464 @ SV731 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV130 ) @ SY2291 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(2132,plain,
! [SV732: $i,SV465: $i,SV131: $i] :
( ( ! [SY2292: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV131 @ SV465 @ SV732 ) ) @ ( c_Lambda_Osubst @ SV131 @ SY2292 @ SV732 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV465 ) @ SY2292 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1805]) ).
thf(2133,plain,
! [SV733: $i,SV466: $i,SV132: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV132 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV466 @ SV132 @ SV733 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV466 ) @ SV132 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV733 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1806]) ).
thf(2134,plain,
! [SV734: $i,SV467: $i,SV133: $i] :
( ( SV133
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV133 @ ( tc_List_Olist @ SV467 ) ) @ ( c_List_Oappend @ SV133 @ SV734 @ SV467 ) @ SV467 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1807]) ).
thf(2135,plain,
! [SV735: $i,SV468: $i,SV134: $i] :
( ( ( c_List_Oreplicate @ ( c_Suc @ SV134 ) @ SV468 @ SV735 )
= ( c_List_Olist_OCons @ SV468 @ ( c_List_Oreplicate @ SV134 @ SV468 @ SV735 ) @ SV735 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1808]) ).
thf(2136,plain,
! [SV736: $i,SV469: $i,SV135: $i] :
( ( ! [SY2293: $i] :
( ( ( c_List_Onth @ ( c_List_Oreplicate @ SV135 @ SV469 @ SV736 ) @ SY2293 @ SV736 )
= SV469 )
| ~ ( c_HOL_Oord__class_Oless @ SY2293 @ SV135 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1809]) ).
thf(2137,plain,
! [SV737: $i,SV470: $i,SV136: $i] :
( ( ( c_Type_Otyping @ SV136 @ SV470 @ SV737 )
| ! [SY2294: $i] :
( ~ ( c_Type_Otyping @ SV136 @ SY2294 @ SV737 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY2294 ) @ SV470 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(2138,plain,
! [SV738: $i,SV471: $i,SV137: $i] :
( ( ( c_List_Otake @ SV137 @ ( c_List_Otl @ SV471 @ SV738 ) @ SV738 )
= ( c_List_Otl @ ( c_List_Otake @ ( c_Suc @ SV137 ) @ SV471 @ SV738 ) @ SV738 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1811]) ).
thf(2139,plain,
! [SV739: $i,SV472: $i,SV138: $i] :
( ( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV138 @ SV472 @ SV739 ) @ SV739 )
= ( c_List_Oappend @ SV138 @ ( c_List_Obutlast @ SV472 @ SV739 ) @ SV739 ) )
| ( SV472
= ( c_List_Olist_ONil @ SV739 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1812]) ).
thf(2140,plain,
! [SV740: $i,SV475: $i,SV141: $i] :
( ( ( ( c_List_Olast @ ( c_List_Oappend @ SV141 @ SV475 @ SV740 ) @ SV740 )
= ( c_List_Olast @ SV475 @ SV740 ) )
| ( SV475
= ( c_List_Olist_ONil @ SV740 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1815]) ).
thf(2141,plain,
! [SV741: $i,SV476: $i,SV142: $i] :
( ( ( ( c_List_Otake @ ( c_Suc @ SV142 ) @ SV476 @ SV741 )
= ( c_List_Olist_OCons @ ( c_List_Ohd @ SV476 @ SV741 ) @ ( c_List_Otake @ SV142 @ ( c_List_Otl @ SV476 @ SV741 ) @ SV741 ) @ SV741 ) )
| ( SV476
= ( c_List_Olist_ONil @ SV741 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1816]) ).
thf(2142,plain,
! [SV742: $i,SV477: $i,SV143: $i] :
( ( ! [SY2295: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV143 @ SV477 @ SV742 ) @ SY2295 @ SV742 )
= ( c_List_Olist_OCons @ SV143 @ ( c_List_Olist_OCons @ ( c_List_Ohd @ SY2295 @ SV742 ) @ ( c_List_Osplice @ SV477 @ ( c_List_Otl @ SY2295 @ SV742 ) @ SV742 ) @ SV742 ) @ SV742 ) )
| ( SY2295
= ( c_List_Olist_ONil @ SV742 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1817]) ).
thf(2143,plain,
! [SV743: $i,SV144: $i] :
( ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV144 ) @ SV743 @ SV144 )
= ( c_Lambda_Oliftn @ SV144 @ SV743 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV144 @ SV144 @ tc_nat )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1818]) ).
thf(2144,plain,
! [SV744: $i,SV478: $i,SV145: $i] :
( ( ( SV145
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV478 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV478 @ SV744 @ SV145 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV478 ) @ SV744 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1819]) ).
thf(2145,plain,
! [SV479: $i,SV146: $i] :
( ( ( ( c_Int_Onumber__class_Onumber__of @ SV146 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ! [SY1991: $i,SY1992: $i] :
( ( c_List_Otake @ ( c_Int_Onumber__class_Onumber__of @ SV146 @ tc_nat ) @ ( c_List_Olist_OCons @ SV479 @ SY1991 @ SY1992 ) @ SY1992 )
= ( c_List_Olist_ONil @ SY1992 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1820]) ).
thf(2146,plain,
! [SV147: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV147 )
= $false )
| ( ( ! [SY1387: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1387 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1387 @ SV147 ) @ SV147 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1821]) ).
thf(2147,plain,
! [SV148: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV148 )
= $false )
| ( ( ! [SY1388: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV148 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1388 @ SV148 ) @ SV148 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1388 @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1822]) ).
thf(2148,plain,
! [SV745: $i,SV480: $i,SV149: $i] :
( ( ( c_Lambda_Osubstn @ SV149 @ SV480 @ SV745 )
= ( c_Lambda_Osubst @ SV149 @ ( c_Lambda_Oliftn @ SV745 @ SV480 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV745 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1823]) ).
thf(2149,plain,
! [SV746: $i,SV481: $i,SV150: $i] :
( ( ( ( c_List_Otake @ SV150 @ ( c_List_Obutlast @ SV481 @ SV746 ) @ SV746 )
= ( c_List_Otake @ SV150 @ SV481 @ SV746 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV150 @ ( c_Nat_Osize__class_Osize @ SV481 @ ( tc_List_Olist @ SV746 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1824]) ).
thf(2150,plain,
! [SV482: $i,SV151: $i] :
( ( ( ( c_List_Ohd @ SV151 @ SV482 )
= ( c_List_Onth @ SV151 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV482 ) )
= $true )
| ( ( SV151
= ( c_List_Olist_ONil @ SV482 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1825]) ).
thf(2151,plain,
! [SV747: $i,SV483: $i,SV152: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV152 @ SV483 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV747 @ SV483 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV152 ) @ SV747 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(2152,plain,
! [SV748: $i,SV484: $i,SV153: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV153 @ SV484 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV153 @ SV748 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV484 @ SV748 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1827]) ).
thf(2153,plain,
! [SV749: $i,SV485: $i,SV154: $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 @ SV154 @ SV485 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV749 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV485 @ 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 @ SV154 ) ) @ SV485 ) @ SV749 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1828]) ).
thf(2154,plain,
! [SV750: $i,SV486: $i,SV155: $i] :
( ( ( c_List_Otake @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ SV155 @ SV486 @ SV750 ) @ SV750 )
= ( c_List_Olist_OCons @ SV155 @ ( c_List_Olist_ONil @ SV750 ) @ SV750 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(2155,plain,
! [SV487: $i,SV156: $i] :
( ( ( SV156
= ( c_List_Olist_ONil @ SV487 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV156 @ ( tc_List_Olist @ SV487 ) ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1830]) ).
thf(2156,plain,
! [SV751: $i,SV488: $i,SV158: $i] :
( ( ! [SY2296: $i] :
( ( c_Type_Otyping @ SV158 @ SV488 @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ SV751 @ SV158 @ SV488 @ SY2296 ) )
| ~ ( c_Type_Otypings @ SV158 @ ( c_List_Oappend @ SY2296 @ ( c_List_Olist_OCons @ SV488 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SV751 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1832]) ).
thf(2157,plain,
! [SV752: $i,SV489: $i,SV159: $i] :
( ( ! [SY2297: $i,SY2298: $i] :
( ( ( c_List_Oappend @ SV159 @ SV489 @ SV752 )
!= ( c_List_Olist_OCons @ SY2297 @ SY2298 @ SV752 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY2297 @ SY2298 @ SV159 @ SV489 @ SV752 ) @ SV489 @ SV752 )
= SY2298 )
| ( SV489
= ( c_List_Olist_OCons @ SY2297 @ SY2298 @ SV752 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1833]) ).
thf(2158,plain,
! [SV753: $i,SV490: $i,SV160: $i] :
( ( ! [SY2299: $i,SY2300: $i] :
( ( ( c_List_Olist_OCons @ SV160 @ SV490 @ SV753 )
!= ( c_List_Oappend @ SY2299 @ SY2300 @ SV753 ) )
| ( ( c_List_Olist_OCons @ SV160 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV160 @ SV490 @ SY2299 @ SY2300 @ SV753 ) @ SV753 )
= SY2299 )
| ( ( c_List_Olist_OCons @ SV160 @ SV490 @ SV753 )
= SY2300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1834]) ).
thf(2159,plain,
! [SV754: $i,SV491: $i,SV161: $i] :
( ( ! [SY2301: $i,SY2302: $i] :
( ( ( c_List_Oappend @ SV161 @ SV491 @ SV754 )
!= ( c_List_Olist_OCons @ SY2301 @ SY2302 @ SV754 ) )
| ( SV161
= ( c_List_Olist_OCons @ SY2301 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY2301 @ SY2302 @ SV161 @ SV491 @ SV754 ) @ SV754 ) )
| ( SV491
= ( c_List_Olist_OCons @ SY2301 @ SY2302 @ SV754 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1835]) ).
thf(2160,plain,
! [SV755: $i,SV492: $i,SV162: $i] :
( ( ! [SY2303: $i,SY2304: $i] :
( ( ( c_List_Olist_OCons @ SV162 @ SV492 @ SV755 )
!= ( c_List_Oappend @ SY2303 @ SY2304 @ SV755 ) )
| ( SV492
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV162 @ SV492 @ SY2303 @ SY2304 @ SV755 ) @ SY2304 @ SV755 ) )
| ( ( c_List_Olist_OCons @ SV162 @ SV492 @ SV755 )
= SY2304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1836]) ).
thf(2161,plain,
! [SV756: $i,SV493: $i,SV163: $i] :
( ( ! [SY2305: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV163 @ SV493 @ SV756 ) @ ( c_List_Olist_OCons @ SV493 @ SY2305 @ SV756 ) @ SV756 )
= ( c_List_Olist_OCons @ SV493 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV163 @ SV493 @ SV756 ) @ SY2305 @ SV756 ) @ SV756 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1837]) ).
thf(2162,plain,
! [SV757: $i,SV495: $i,SV165: $i] :
( ( ( ( c_List_Olast @ ( c_List_Olist_OCons @ SV165 @ SV495 @ SV757 ) @ SV757 )
= ( c_List_Olast @ SV495 @ SV757 ) )
| ( SV495
= ( c_List_Olist_ONil @ SV757 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1839]) ).
thf(2163,plain,
! [SV758: $i,SV497: $i,SV167: $i] :
( ( ( ( c_List_Olist_OCons @ SV167 @ ( c_List_Olist_ONil @ SV497 ) @ SV497 )
!= ( c_List_Orev @ SV758 @ SV497 ) )
| ( SV758
= ( c_List_Olist_OCons @ SV167 @ ( c_List_Olist_ONil @ SV497 ) @ SV497 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1841]) ).
thf(2164,plain,
! [SV759: $i,SV498: $i,SV168: $i] :
( ( ( ( c_List_Orev @ SV168 @ SV498 )
!= ( c_List_Olist_OCons @ SV759 @ ( c_List_Olist_ONil @ SV498 ) @ SV498 ) )
| ( SV168
= ( c_List_Olist_OCons @ SV759 @ ( c_List_Olist_ONil @ SV498 ) @ SV498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1842]) ).
thf(2165,plain,
! [SV760: $i,SV501: $i,SV171: $i] :
( ( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV171 @ SV501 @ SV760 ) @ SV760 )
= ( c_List_Olist_OCons @ SV171 @ ( c_List_Obutlast @ SV501 @ SV760 ) @ SV760 ) )
| ( SV501
= ( c_List_Olist_ONil @ SV760 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1845]) ).
thf(2166,plain,
! [SV761: $i,SV503: $i,SV173: $i] :
( ( ( ( c_List_Otake @ SV173 @ SV503 @ SV761 )
!= ( c_List_Olist_ONil @ SV761 ) )
| ( SV503
= ( c_List_Olist_ONil @ SV761 ) )
| ( SV173
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1847]) ).
thf(2167,plain,
! [SV762: $i,SV176: $i] :
( ( ( ! [SY2306: $i] :
( ( c_List_Oreplicate @ SV176 @ SV762 @ SY2306 )
!= ( c_List_Olist_ONil @ SY2306 ) ) )
= $true )
| ( ( SV176
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(2168,plain,
! [SV506: $i,SV177: $i] :
( ( ( ! [SY2020: $i] :
( ( c_List_Olist_ONil @ SV177 )
!= ( c_List_Oreplicate @ SV506 @ SY2020 @ SV177 ) ) )
= $true )
| ( ( SV506
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1851]) ).
thf(2169,plain,
! [SV508: $i,SV179: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Obutlast @ SV179 @ SV508 ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ SV179 @ SV508 ) @ ( c_List_Olist_ONil @ SV508 ) @ SV508 ) @ SV508 )
= SV179 )
= $true )
| ( ( SV179
= ( c_List_Olist_ONil @ SV508 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1853]) ).
thf(2170,plain,
! [SV180: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV180 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV180 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1854]) ).
thf(2171,plain,
! [SV763: $i,SV510: $i,SV182: $i] :
( ( ( ( hAPP @ SV182 @ SV510 )
= SV763 )
| ~ ( c_Type_Otyping @ SV182 @ ( c_Lambda_OdB_OVar @ SV510 ) @ SV763 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(2172,plain,
! [SV511: $i,SV183: $i] :
( ( ( c_Lambda_OdB_OVar @ SV183 )
= ( c_Lambda_OdB_OAbs @ SV511 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1857]) ).
thf(2173,plain,
! [SV512: $i,SV184: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV184 ) ) @ SV512 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1858]) ).
thf(2174,plain,
! [SV513: $i,SV185: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV185 )
= ( c_Lambda_OdB_OVar @ SV513 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1859]) ).
thf(2175,plain,
! [SV764: $i,SV514: $i,SV186: $i] :
( ( ! [SY2307: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV186 @ SV514 @ SV764 ) ) @ ( c_Lambda_Osubst @ SY2307 @ SV514 @ SV764 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV186 ) @ SY2307 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1860]) ).
thf(2176,plain,
! [SV765: $i,SV515: $i,SV187: $i] :
( ( ( c_List_Orev @ ( c_List_Oappend @ SV187 @ SV515 @ SV765 ) @ SV765 )
= ( c_List_Oappend @ ( c_List_Orev @ SV515 @ SV765 ) @ ( c_List_Orev @ SV187 @ SV765 ) @ SV765 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1861]) ).
thf(2177,plain,
! [SV766: $i,SV516: $i,SV188: $i] :
( ( ! [SY2308: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV188 @ SV516 @ SV766 @ SY2308 )
| ! [SY2309: $i] : ( c_ListOrder_Ostep1 @ SV188 @ ( c_List_Oappend @ SV516 @ SY2309 @ SY2308 ) @ ( c_List_Oappend @ SV766 @ SY2309 @ SY2308 ) @ SY2308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(2178,plain,
! [SV767: $i,SV517: $i,SV189: $i] :
( ( ! [SY2310: $i,SY2311: $i] :
( ( c_ListOrder_Ostep1 @ SV189 @ ( c_List_Oappend @ SV517 @ SV767 @ SY2310 ) @ ( c_List_Oappend @ SV517 @ SY2311 @ SY2310 ) @ SY2310 )
| ~ ( c_ListOrder_Ostep1 @ SV189 @ SV767 @ SY2311 @ SY2310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(2179,plain,
! [SV768: $i,SV518: $i,SV190: $i] :
( ( ( c_List_Olistsp @ SV190 @ SV518 @ SV768 )
| ! [SY2312: $i] :
~ ( c_List_Olistsp @ SV190 @ ( c_List_Oappend @ SV518 @ SY2312 @ SV768 ) @ SV768 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(2180,plain,
! [SV769: $i,SV519: $i,SV191: $i] :
( ( ( c_List_Olistsp @ SV191 @ SV519 @ SV769 )
| ! [SY2313: $i] :
~ ( c_List_Olistsp @ SV191 @ ( c_List_Oappend @ SY2313 @ SV519 @ SV769 ) @ SV769 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1865]) ).
thf(2181,plain,
! [SV770: $i,SV520: $i,SV192: $i] :
( ( ! [SY2314: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV192 @ SV520 @ SV770 ) @ ( c_List_Oreplicate @ SY2314 @ SV520 @ SV770 ) @ SV770 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SY2314 @ SV520 @ SV770 ) @ ( c_List_Oreplicate @ SV192 @ SV520 @ SV770 ) @ SV770 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1866]) ).
thf(2182,plain,
! [SV771: $i,SV521: $i,SV193: $i] :
( ( ! [SY2315: $i] :
( ( c_List_Olistsp @ SV193 @ ( c_List_Oappend @ SV521 @ SV771 @ SY2315 ) @ SY2315 )
| ~ ( c_List_Olistsp @ SV193 @ SV771 @ SY2315 )
| ~ ( c_List_Olistsp @ SV193 @ SV521 @ SY2315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1867]) ).
thf(2183,plain,
! [SV772: $i,SV522: $i,SV194: $i] :
( ( ! [SY2316: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV194 ) @ SV522 ) @ SV772 @ SY2316 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ SV194 @ SV772 @ SY2316 ) ) @ ( c_Lambda_Osubstn @ SV522 @ SV772 @ SY2316 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1868]) ).
thf(2184,plain,
! [SV773: $i,SV523: $i,SV195: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV195 ) @ SV523 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV773 ) @ SV523 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV195 ) @ SV773 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1869]) ).
thf(2185,plain,
! [SV774: $i,SV524: $i,SV196: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV196 ) @ SV524 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV196 ) @ SV774 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV524 ) @ SV774 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1870]) ).
thf(2186,plain,
! [SV775: $i,SV525: $i,SV197: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV197 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV525 ) @ SV775 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1871]) ).
thf(2187,plain,
! [SV776: $i,SV526: $i,SV198: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV198 ) @ SV526 )
!= ( c_Lambda_OdB_OAbs @ SV776 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1872]) ).
thf(2188,plain,
! [SV527: $i,SV199: $i] :
( ( ( ( c_List_Orotate1 @ SV199 @ SV527 )
= ( c_List_Oappend @ ( c_List_Otl @ SV199 @ SV527 ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ SV199 @ SV527 ) @ ( c_List_Olist_ONil @ SV527 ) @ SV527 ) @ SV527 ) )
= $true )
| ( ( SV199
= ( c_List_Olist_ONil @ SV527 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1873]) ).
thf(2189,plain,
! [SV528: $i,SV201: $i] :
( ( ( ( c_List_Orev @ SV201 @ SV528 )
!= ( c_List_Olist_ONil @ SV528 ) )
= $true )
| ( ( SV201
= ( c_List_Olist_ONil @ SV528 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1874]) ).
thf(2190,plain,
! [SV531: $i,SV205: $i] :
( ( ( ( c_List_Orotate1 @ SV205 @ SV531 )
!= ( c_List_Olist_ONil @ SV531 ) )
= $true )
| ( ( SV205
= ( c_List_Olist_ONil @ SV531 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1877]) ).
thf(2191,plain,
! [SV777: $i,SV532: $i,SV206: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV206 @ ( c_List_Olist_ONil @ SV532 ) @ SV777 @ SV532 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1878]) ).
thf(2192,plain,
! [SV778: $i,SV533: $i,SV207: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV207 @ SV533 @ ( c_List_Olist_ONil @ SV778 ) @ SV778 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1879]) ).
thf(2193,plain,
! [SV534: $i,SV208: $i] :
( ( ( ( c_List_Olist_ONil @ SV208 )
!= ( c_List_Orev @ SV534 @ SV208 ) )
= $true )
| ( ( SV534
= ( c_List_Olist_ONil @ SV208 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1880]) ).
thf(2194,plain,
! [SV779: $i,SV535: $i,SV212: $i] :
( ( ! [SY2317: $i] :
( ( SV212 = SV535 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV779 @ SV535 ) @ SV212 ) )
| ! [SY2318: $i,SY2319: $i] :
~ ( c_ListOrder_Ostep1 @ SV779 @ ( c_List_Olist_OCons @ SV535 @ SY2317 @ SY2318 ) @ ( c_List_Olist_OCons @ SV212 @ SY2319 @ SY2318 ) @ SY2318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1881]) ).
thf(2195,plain,
! [SV780: $i,SV536: $i,SV213: $i] :
( ( ! [SY2320: $i] :
( ( SV213 = SV536 )
| ( SV780 = SY2320 )
| ! [SY2321: $i,SY2322: $i] :
~ ( c_ListOrder_Ostep1 @ SY2321 @ ( c_List_Olist_OCons @ SV536 @ SY2320 @ SY2322 ) @ ( c_List_Olist_OCons @ SV213 @ SV780 @ SY2322 ) @ SY2322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(2196,plain,
! [SV781: $i,SV537: $i,SV214: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV214 @ SV537 ) @ SV781 ) )
| ! [SY2323: $i,SY2324: $i] : ( c_ListOrder_Ostep1 @ SV214 @ ( c_List_Olist_OCons @ SV537 @ SY2323 @ SY2324 ) @ ( c_List_Olist_OCons @ SV781 @ SY2323 @ SY2324 ) @ SY2324 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1883]) ).
thf(2197,plain,
! [SV782: $i,SV538: $i,SV215: $i] :
( ( ! [SY2325: $i] :
( ( c_ListOrder_Ostep1 @ SV215 @ SV538 @ SV782 @ SY2325 )
| ( SV782 = SV538 )
| ! [SY2326: $i,SY2327: $i] :
~ ( c_ListOrder_Ostep1 @ SV215 @ ( c_List_Olist_OCons @ SY2326 @ SV538 @ SY2325 ) @ ( c_List_Olist_OCons @ SY2327 @ SV782 @ SY2325 ) @ SY2325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(2198,plain,
! [SV783: $i,SV539: $i,SV216: $i] :
( ( ( c_List_Otl @ ( c_List_Olist_OCons @ SV216 @ SV539 @ SV783 ) @ SV783 )
= SV539 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(2199,plain,
! [SV784: $i,SV540: $i,SV217: $i] :
( ( ! [SY2328: $i] :
( ( c_ListOrder_Ostep1 @ SV217 @ SV540 @ SV784 @ SY2328 )
| ! [SY2329: $i,SY2330: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV217 @ SY2329 ) @ SY2330 ) )
| ~ ( c_ListOrder_Ostep1 @ SV217 @ ( c_List_Olist_OCons @ SY2329 @ SV540 @ SY2328 ) @ ( c_List_Olist_OCons @ SY2330 @ SV784 @ SY2328 ) @ SY2328 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1886]) ).
thf(2200,plain,
! [SV785: $i,SV541: $i,SV218: $i] :
( ( ! [SY2331: $i,SY2332: $i] :
( ( c_ListOrder_Ostep1 @ SV218 @ ( c_List_Olist_OCons @ SV541 @ SV785 @ SY2331 ) @ ( c_List_Olist_OCons @ SV541 @ SY2332 @ SY2331 ) @ SY2331 )
| ~ ( c_ListOrder_Ostep1 @ SV218 @ SV785 @ SY2332 @ SY2331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1887]) ).
thf(2201,plain,
! [SV786: $i,SV542: $i,SV219: $i] :
( ( ( c_List_Ohd @ ( c_List_Olist_OCons @ SV219 @ SV542 @ SV786 ) @ SV786 )
= SV219 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1888]) ).
thf(2202,plain,
! [SV787: $i,SV543: $i,SV220: $i] :
( ( ! [SY2333: $i,SY2334: $i] :
( ( ( c_List_Oreplicate @ SV220 @ SV543 @ SV787 )
!= ( c_List_Oreplicate @ SY2333 @ SY2334 @ SV787 ) )
| ( SV543 = SY2334 )
| ( SV220
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1889]) ).
thf(2203,plain,
! [SV788: $i,SV544: $i,SV221: $i] :
( ( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV221 @ SV544 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV788 @ SV544 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1890]) ).
thf(2204,plain,
! [SV545: $i,SV225: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV225 ) ) @ ( c_Lambda_OdB_OAbs @ SV545 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV225 ) @ SV545 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1894]) ).
thf(2205,plain,
! [SV789: $i,SV226: $i] :
( ( ( ! [SY2335: $i] :
( ( c_List_Olast @ ( c_List_Oreplicate @ SV226 @ SV789 @ SY2335 ) @ SY2335 )
= SV789 ) )
= $true )
| ( ( SV226
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1895]) ).
thf(2206,plain,
! [SV546: $i,SV227: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV227 ) )
= $true )
| ( ( ! [SY2075: $i] :
( ( c_HOL_Oord__class_Oless @ SV546 @ SY2075 @ SV227 )
| ! [SY2076: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV546 @ SY2076 @ SV227 )
| ~ ( c_HOL_Oord__class_Oless @ SY2076 @ SY2075 @ SV227 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1896]) ).
thf(2207,plain,
! [SV547: $i,SV228: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV228 ) )
= $true )
| ( ( ! [SY2077: $i] :
( ( c_HOL_Oord__class_Oless @ SV547 @ SY2077 @ SV228 )
| ! [SY2078: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY2078 @ SY2077 @ SV228 )
| ~ ( c_HOL_Oord__class_Oless @ SV547 @ SY2078 @ SV228 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1897]) ).
thf(2208,plain,
! [SV548: $i,SV229: $i] :
( ( ( ( c_List_Olast @ ( c_List_Orev @ SV229 @ SV548 ) @ SV548 )
= ( c_List_Ohd @ SV229 @ SV548 ) )
= $true )
| ( ( SV229
= ( c_List_Olist_ONil @ SV548 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1898]) ).
thf(2209,plain,
! [SV790: $i,SV549: $i,SV230: $i] :
( ( ! [SY2336: $i] :
( ! [SY2337: $i] :
( ( c_List_Oreplicate @ SV230 @ SV549 @ SV790 )
!= ( c_List_Oreplicate @ SY2336 @ SY2337 @ SV790 ) )
| ( SV230 = SY2336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1899]) ).
thf(2210,plain,
! [SV791: $i,SV553: $i,SV234: $i] :
( ( ( c_List_Orev @ ( c_List_Oreplicate @ SV234 @ SV553 @ SV791 ) @ SV791 )
= ( c_List_Oreplicate @ SV234 @ SV553 @ SV791 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1903]) ).
thf(2211,plain,
! [SV554: $i,SV235: $i] :
( ( ( ( c_List_Ohd @ ( c_List_Orev @ SV235 @ SV554 ) @ SV554 )
= ( c_List_Olast @ SV235 @ SV554 ) )
= $true )
| ( ( SV235
= ( c_List_Olist_ONil @ SV554 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1904]) ).
thf(2212,plain,
! [SV792: $i,SV236: $i] :
( ( ( ! [SY2338: $i] :
( ( c_List_Ohd @ ( c_List_Oreplicate @ SV236 @ SV792 @ SY2338 ) @ SY2338 )
= SV792 ) )
= $true )
| ( ( SV236
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1905]) ).
thf(2213,plain,
! [SV793: $i,SV555: $i,SV237: $i] :
( ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV237 ) @ SV555 @ SV793 )
= ( c_Lambda_OdB_OVar @ SV237 ) )
| ( SV237 = SV793 )
| ( c_HOL_Oord__class_Oless @ SV793 @ SV237 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(2214,plain,
! [SV556: $i,SV238: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV238 )
!= ( c_Lambda_OdB_OAbs @ SV556 ) )
= $true )
| ( ( SV238 = SV556 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1907]) ).
thf(2215,plain,
! [SV241: $i] :
( ( ( class_Orderings_Oorder @ SV241 )
= $false )
| ( ( ! [SY1563: $i] :
~ ( c_HOL_Oord__class_Oless @ SY1563 @ SY1563 @ SV241 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1910]) ).
thf(2216,plain,
! [SV242: $i] :
( ( ( class_Orderings_Olinorder @ SV242 )
= $false )
| ( ( ! [SY1564: $i] :
~ ( c_HOL_Oord__class_Oless @ SY1564 @ SY1564 @ SV242 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1911]) ).
thf(2217,plain,
! [SV243: $i] :
( ( ( class_Orderings_Opreorder @ SV243 )
= $false )
| ( ( ! [SY1565: $i] :
~ ( c_HOL_Oord__class_Oless @ SY1565 @ SY1565 @ SV243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1912]) ).
thf(2218,plain,
! [SV244: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV244 )
= $false )
| ( ( ! [SY1566: $i,SY1567: $i] :
( ( c_HOL_Oord__class_Oless @ SY1566 @ SY1567 @ SV244 )
| ( SY1567 = SY1566 )
| ( c_HOL_Oord__class_Oless @ SY1567 @ SY1566 @ SV244 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1913]) ).
thf(2219,plain,
! [SV245: $i] :
( ( ( class_Orderings_Olinorder @ SV245 )
= $false )
| ( ( ! [SY1568: $i,SY1569: $i] :
( ( SY1568 = SY1569 )
| ( c_HOL_Oord__class_Oless @ SY1569 @ SY1568 @ SV245 )
| ( c_HOL_Oord__class_Oless @ SY1568 @ SY1569 @ SV245 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1914]) ).
thf(2220,plain,
! [SV557: $i,SV246: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV246 @ SV557 @ tc_nat )
= $true )
| ( ( ( SV557 = SV246 )
| ( c_HOL_Oord__class_Oless @ SV557 @ SV246 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1915]) ).
thf(2221,plain,
! [SV794: $i,SV558: $i,SV247: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV247 @ SV558 ) @ SV794 ) )
| ( c_HOL_Oord__class_Oless @ SV558 @ SV794 @ tc_nat )
| ( SV794 = SV558 )
| ( c_HOL_Oord__class_Oless @ SV794 @ SV558 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(2222,plain,
! [SV559: $i,SV248: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV248 @ SV559 @ tc_nat )
= $true )
| ( ( ( SV559 = SV248 )
| ( c_HOL_Oord__class_Oless @ SV559 @ SV248 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1917]) ).
thf(2223,plain,
! [SV249: $i] :
( ( ( class_Orderings_Olinorder @ SV249 )
= $false )
| ( ( ! [SY1574: $i,SY1575: $i] :
( ( c_HOL_Oord__class_Oless @ SY1574 @ SY1575 @ SV249 )
| ( SY1575 = SY1574 )
| ( c_HOL_Oord__class_Oless @ SY1575 @ SY1574 @ SV249 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1918]) ).
thf(2224,plain,
! [SV250: $i] :
( ( ( class_Orderings_Olinorder @ SV250 )
= $false )
| ( ( ! [SY1576: $i,SY1577: $i] :
( ( c_HOL_Oord__class_Oless @ SY1576 @ SY1577 @ SV250 )
| ( SY1577 = SY1576 )
| ( c_HOL_Oord__class_Oless @ SY1577 @ SY1576 @ SV250 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1919]) ).
thf(2225,plain,
! [SV251: $i] :
( ( ( class_Orderings_Olinorder @ SV251 )
= $false )
| ( ( ! [SY1578: $i,SY1579: $i] :
( ( SY1578 = SY1579 )
| ( c_HOL_Oord__class_Oless @ SY1578 @ SY1579 @ SV251 )
| ( c_HOL_Oord__class_Oless @ SY1579 @ SY1578 @ SV251 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1920]) ).
thf(2226,plain,
! [SV795: $i,SV560: $i,SV252: $i] :
( ( ( ( c_List_Orev @ SV252 @ SV560 )
!= ( c_List_Orev @ SV795 @ SV560 ) )
| ( SV252 = SV795 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(2227,plain,
! [SV796: $i,SV561: $i,SV253: $i] :
( ( ( c_Type_Otyping @ SV253 @ SV561 @ SV796 )
| ! [SY2339: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY2339 ) @ SV561 ) )
| ~ ( c_Type_Otyping @ SV253 @ SY2339 @ SV796 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1922]) ).
thf(2228,plain,
! [SV254: $i] :
( ( ( class_Orderings_Oorder @ SV254 )
= $false )
| ( ( ! [SY1585: $i,SY1586: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1585 @ SY1586 @ SV254 )
| ~ ( c_HOL_Oord__class_Oless @ SY1586 @ SY1585 @ SV254 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1923]) ).
thf(2229,plain,
! [SV255: $i] :
( ( ( class_Orderings_Olinorder @ SV255 )
= $false )
| ( ( ! [SY1587: $i,SY1588: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1587 @ SY1588 @ SV255 )
| ~ ( c_HOL_Oord__class_Oless @ SY1588 @ SY1587 @ SV255 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1924]) ).
thf(2230,plain,
! [SV256: $i] :
( ( ( class_Orderings_Opreorder @ SV256 )
= $false )
| ( ( ! [SY1589: $i,SY1590: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1589 @ SY1590 @ SV256 )
| ~ ( c_HOL_Oord__class_Oless @ SY1590 @ SY1589 @ SV256 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1925]) ).
thf(2231,plain,
! [SV257: $i] :
( ( ( class_Orderings_Opreorder @ SV257 )
= $false )
| ( ( ! [SY1591: $i,SY1592: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1591 @ SY1592 @ SV257 )
| ~ ( c_HOL_Oord__class_Oless @ SY1592 @ SY1591 @ SV257 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1926]) ).
thf(2232,plain,
! [SV797: $i,SV562: $i,SV258: $i] :
( ( ( ( c_List_Otl @ ( c_List_Oappend @ SV258 @ SV562 @ SV797 ) @ SV797 )
= ( c_List_Oappend @ ( c_List_Otl @ SV258 @ SV797 ) @ SV562 @ SV797 ) )
| ( SV258
= ( c_List_Olist_ONil @ SV797 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1927]) ).
thf(2233,plain,
! [SV798: $i,SV564: $i,SV260: $i] :
( ( ( ( c_List_Ohd @ ( c_List_Oappend @ SV260 @ SV564 @ SV798 ) @ SV798 )
= ( c_List_Ohd @ SV260 @ SV798 ) )
| ( SV260
= ( c_List_Olist_ONil @ SV798 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1929]) ).
thf(2234,plain,
! [SV799: $i,SV566: $i,SV264: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV264 @ SV566 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV799 ) )
| ( SV264
= ( c_Lambda_OdB_OAbs @ SV799 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1931]) ).
thf(2235,plain,
! [SV800: $i,SV567: $i,SV265: $i] :
( ( ! [SY2340: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV265 ) @ SV567 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV800 ) @ SY2340 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV265 = SV800 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2236,plain,
! [SV801: $i,SV568: $i,SV266: $i] :
( ( ! [SY2341: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV266 ) @ SV568 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV801 ) @ SY2341 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV568 = SY2341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1933]) ).
thf(2237,plain,
! [SV802: $i,SV569: $i,SV267: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV267 @ SV569 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV802 @ SV569 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV267 ) @ SV802 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(2238,plain,
! [SV570: $i,SV268: $i] :
( ( ( ! [SY2096: $i] :
( ( c_Lambda_OdB_OAbs @ SV268 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV570 @ SY2096 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ( c_Lambda_OdB_OAbs @ SV268 )
= SV570 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1935]) ).
thf(2239,plain,
! [SV803: $i,SV571: $i,SV269: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV269 ) @ SV571 @ SV803 )
= ( c_Lambda_OdB_OVar @ SV269 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV269 @ SV803 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1936]) ).
thf(2240,plain,
! [SV804: $i,SV572: $i,SV270: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV270 ) @ SV572 @ SV804 )
= ( c_Lambda_OdB_OVar @ SV270 ) )
| ( SV270 = SV804 )
| ( c_HOL_Oord__class_Oless @ SV804 @ SV270 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1937]) ).
thf(2241,plain,
! [SV805: $i,SV271: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV271 ) @ SV805 @ SV271 )
= SV805 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV271 @ SV271 @ tc_nat )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2242,plain,
! [SV806: $i,SV573: $i,SV272: $i] :
( ( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ SV272 @ SV573 @ SV806 ) @ SV806 )
= ( c_List_Olist_ONil @ SV806 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1939]) ).
thf(2243,plain,
! [SV807: $i,SV574: $i,SV273: $i] :
( ( ! [SY2342: $i,SY2343: $i] :
( ( ( c_List_Olist_OCons @ SV273 @ SV574 @ SV807 )
!= ( c_List_Oappend @ SY2342 @ SY2343 @ SV807 ) )
| ( SV574
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV273 @ SV574 @ SY2342 @ SY2343 @ SV807 ) @ SY2343 @ SV807 ) )
| ( SY2342
= ( c_List_Olist_ONil @ SV807 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2244,plain,
! [SV808: $i,SV575: $i,SV274: $i] :
( ( ! [SY2344: $i,SY2345: $i] :
( ( ( c_List_Oappend @ SV274 @ SV575 @ SV808 )
!= ( c_List_Olist_OCons @ SY2344 @ SY2345 @ SV808 ) )
| ( SV274
= ( c_List_Olist_OCons @ SY2344 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY2344 @ SY2345 @ SV274 @ SV575 @ SV808 ) @ SV808 ) )
| ( SV274
= ( c_List_Olist_ONil @ SV808 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1941]) ).
thf(2245,plain,
! [SV809: $i,SV576: $i,SV275: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ SV275 @ ( c_List_Olist_OCons @ SV576 @ ( c_List_Olist_ONil @ SV809 ) @ SV809 ) @ SV809 ) @ SV809 )
= SV576 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1942]) ).
thf(2246,plain,
! [SV810: $i,SV577: $i,SV276: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV276 @ ( c_List_Olist_OCons @ SV577 @ ( c_List_Olist_ONil @ SV810 ) @ SV810 ) @ SV810 ) @ SV810 )
= SV276 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2247,plain,
! [SV811: $i,SV578: $i,SV277: $i] :
( ( ! [SY2346: $i] :
( ( SV277 = SV578 )
| ( SV811 = SY2346 )
| ! [SY2347: $i,SY2348: $i] :
~ ( c_ListOrder_Ostep1 @ SY2347 @ ( c_List_Oappend @ SV277 @ ( c_List_Olist_OCons @ SV811 @ ( c_List_Olist_ONil @ SY2348 ) @ SY2348 ) @ SY2348 ) @ ( c_List_Oappend @ SV578 @ ( c_List_Olist_OCons @ SY2346 @ ( c_List_Olist_ONil @ SY2348 ) @ SY2348 ) @ SY2348 ) @ SY2348 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(2248,plain,
! [SV812: $i,SV579: $i,SV278: $i] :
( ( ! [SY2349: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV278 @ SV579 ) @ SV812 ) )
| ( SV579 = SV812 )
| ! [SY2350: $i,SY2351: $i] :
~ ( c_ListOrder_Ostep1 @ SV278 @ ( c_List_Oappend @ SY2349 @ ( c_List_Olist_OCons @ SV579 @ ( c_List_Olist_ONil @ SY2350 ) @ SY2350 ) @ SY2350 ) @ ( c_List_Oappend @ SY2351 @ ( c_List_Olist_OCons @ SV812 @ ( c_List_Olist_ONil @ SY2350 ) @ SY2350 ) @ SY2350 ) @ SY2350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2249,plain,
! [SV813: $i,SV580: $i,SV279: $i] :
( ( ! [SY2352: $i,SY2353: $i] :
( ( ( c_List_Oappend @ SV279 @ SV580 @ SV813 )
!= ( c_List_Olist_OCons @ SY2352 @ SY2353 @ SV813 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY2352 @ SY2353 @ SV279 @ SV580 @ SV813 ) @ SV580 @ SV813 )
= SY2353 )
| ( SV279
= ( c_List_Olist_ONil @ SV813 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(2250,plain,
! [SV814: $i,SV581: $i,SV280: $i] :
( ( ! [SY2354: $i,SY2355: $i] :
( ( ( c_List_Olist_OCons @ SV280 @ SV581 @ SV814 )
!= ( c_List_Oappend @ SY2354 @ SY2355 @ SV814 ) )
| ( ( c_List_Olist_OCons @ SV280 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV280 @ SV581 @ SY2354 @ SY2355 @ SV814 ) @ SV814 )
= SY2354 )
| ( SY2354
= ( c_List_Olist_ONil @ SV814 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1947]) ).
thf(2251,plain,
! [SV815: $i,SV582: $i,SV281: $i] :
( ( ( c_List_Orev @ ( c_List_Olist_OCons @ SV281 @ SV582 @ SV815 ) @ SV815 )
= ( c_List_Oappend @ ( c_List_Orev @ SV582 @ SV815 ) @ ( c_List_Olist_OCons @ SV281 @ ( c_List_Olist_ONil @ SV815 ) @ SV815 ) @ SV815 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1948]) ).
thf(2252,plain,
! [SV816: $i,SV583: $i,SV282: $i] :
( ( ! [SY2356: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV282 @ SV583 ) @ SV816 ) )
| ! [SY2357: $i,SY2358: $i] :
( ( c_ListOrder_Ostep1 @ SV282 @ SY2356 @ SY2357 @ SY2358 )
| ~ ( c_ListOrder_Ostep1 @ SV282 @ ( c_List_Oappend @ SY2356 @ ( c_List_Olist_OCons @ SV583 @ ( c_List_Olist_ONil @ SY2358 ) @ SY2358 ) @ SY2358 ) @ ( c_List_Oappend @ SY2357 @ ( c_List_Olist_OCons @ SV816 @ ( c_List_Olist_ONil @ SY2358 ) @ SY2358 ) @ SY2358 ) @ SY2358 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1949]) ).
thf(2253,plain,
! [SV817: $i,SV584: $i,SV283: $i] :
( ( ! [SY2359: $i] :
( ( ( c_List_Orev @ SV283 @ SV584 )
!= ( c_List_Olist_OCons @ SV817 @ SY2359 @ SV584 ) )
| ( SV283
= ( c_List_Oappend @ ( c_List_Orev @ SY2359 @ SV584 ) @ ( c_List_Olist_OCons @ SV817 @ ( c_List_Olist_ONil @ SV584 ) @ SV584 ) @ SV584 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1950]) ).
thf(2254,plain,
! [SV818: $i,SV585: $i,SV284: $i] :
( ( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ SV284 @ SV585 ) @ ( c_List_Olist_OCons @ SV818 @ ( c_List_Olist_ONil @ SV585 ) @ SV585 ) @ SV585 ) @ SV585 )
= ( c_List_Olist_OCons @ SV818 @ SV284 @ SV585 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1951]) ).
thf(2255,plain,
! [SV819: $i,SV586: $i,SV285: $i] :
( ( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ SV285 @ SV586 @ SV819 ) @ SV819 )
= ( c_List_Oappend @ SV586 @ ( c_List_Olist_OCons @ SV285 @ ( c_List_Olist_ONil @ SV819 ) @ SV819 ) @ SV819 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1952]) ).
thf(2256,plain,
! [SV820: $i,SV587: $i,SV286: $i] :
( ( ! [SY2360: $i] :
( ( SV286 = SV587 )
| ( c_ListOrder_Ostep1 @ SV820 @ SV286 @ SV587 @ SY2360 )
| ! [SY2361: $i,SY2362: $i] :
~ ( c_ListOrder_Ostep1 @ SV820 @ ( c_List_Oappend @ SV286 @ ( c_List_Olist_OCons @ SY2361 @ ( c_List_Olist_ONil @ SY2360 ) @ SY2360 ) @ SY2360 ) @ ( c_List_Oappend @ SV587 @ ( c_List_Olist_OCons @ SY2362 @ ( c_List_Olist_ONil @ SY2360 ) @ SY2360 ) @ SY2360 ) @ SY2360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1953]) ).
thf(2257,plain,
! [SV821: $i,SV588: $i,SV287: $i] :
( ( ( c_List_Oappend @ ( c_List_Oreplicate @ SV287 @ SV588 @ SV821 ) @ ( c_List_Olist_OCons @ SV588 @ ( c_List_Olist_ONil @ SV821 ) @ SV821 ) @ SV821 )
= ( c_List_Olist_OCons @ SV588 @ ( c_List_Oreplicate @ SV287 @ SV588 @ SV821 ) @ SV821 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(2258,plain,
! [SV822: $i,SV589: $i,SV288: $i] :
( ( ( SV288 = SV589 )
| ! [SY2363: $i,SY2364: $i] :
( ~ ( c_Type_Otyping @ SV822 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2363 ) @ SY2364 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV589 )
| ~ ( c_Type_Otyping @ SV822 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2363 ) @ SY2364 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1955]) ).
thf(2259,plain,
! [SV823: $i,SV590: $i,SV289: $i] :
( ( ! [SY2365: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV289 ) @ SV590 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV823 ) @ SY2365 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(2260,plain,
! [SV824: $i,SV591: $i,SV290: $i] :
( ( ! [SY2366: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV290 ) ) @ SV591 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV824 ) @ SY2366 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2261,plain,
! [SV825: $i,SV592: $i,SV291: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV291 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV592 @ SV825 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV825
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1958]) ).
thf(2262,plain,
! [SV826: $i,SV593: $i,SV293: $i] :
( ( ! [SY2367: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV293 ) @ SV593 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV826 @ SY2367 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV293
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV826 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV293 @ SV593 @ SV826 @ SY2367 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2367
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1959]) ).
thf(2263,plain,
! [SV594: $i,SV294: $i] :
( ( ( ! [SY2146: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV294 @ SV594 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY2146 ) ) )
= $true )
| ( ( SV594
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1960]) ).
thf(2264,plain,
! [SV595: $i,SV296: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV296 ) @ SV595 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV595 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1961]) ).
thf(2265,plain,
! [SV827: $i,SV596: $i,SV297: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV297 ) ) @ SV596 ) @ SV827 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV596 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV297 @ SV596 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV827 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(2266,plain,
! [SV828: $i,SV597: $i,SV298: $i] :
( ( ! [SY2368: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV298 ) @ SV597 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV828 @ SY2368 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2368
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV298 @ SV597 @ SV828 @ SY2368 ) @ ( c_List_Olist_OCons @ SV597 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( SY2368
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1963]) ).
thf(2267,plain,
! [SV829: $i,SV598: $i,SV299: $i] :
( ( ! [SY2369: $i] :
( ( c_List_Oappend @ SV299 @ ( c_List_Oappend @ SV598 @ SV829 @ SY2369 ) @ SY2369 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV299 @ SV598 @ SY2369 ) @ SV829 @ SY2369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1964]) ).
thf(2268,plain,
! [SV830: $i,SV599: $i,SV300: $i] :
( ( ! [SY2370: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV300 @ SV599 @ SV830 ) @ SY2370 @ SV830 )
= ( c_List_Oappend @ SV300 @ ( c_List_Oappend @ SV599 @ SY2370 @ SV830 ) @ SV830 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1965]) ).
thf(2269,plain,
! [SV831: $i,SV600: $i,SV301: $i] :
( ( ! [SY2371: $i] :
( ( c_List_Oappend @ SV301 @ ( c_List_Oappend @ SV600 @ SV831 @ SY2371 ) @ SY2371 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV301 @ SV600 @ SY2371 ) @ SV831 @ SY2371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1966]) ).
thf(2270,plain,
! [SV832: $i,SV601: $i,SV302: $i] :
( ( ! [SY2372: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV302 @ SV601 @ SV832 ) @ SY2372 @ SV832 )
= ( c_List_Oappend @ SV302 @ ( c_List_Oappend @ SV601 @ SY2372 @ SV832 ) @ SV832 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2271,plain,
! [SV602: $i,SV303: $i] :
( ( ( ( c_List_Oappend @ SV303 @ ( c_List_Olist_OCons @ SV602 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true )
| ( ( ! [SY2158: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2158 @ SV303 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV602 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2158 @ ( c_List_Oappend @ SV303 @ ( c_List_Olist_OCons @ SV602 @ ( 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)],[1968]) ).
thf(2272,plain,
! [SV833: $i,SV604: $i,SV306: $i] :
( ( ! [SY2373: $i,SY2374: $i] :
( ( ( c_List_Oappend @ SV306 @ ( c_List_Olist_OCons @ SV604 @ ( c_List_Olist_ONil @ SV833 ) @ SV833 ) @ SV833 )
!= ( c_List_Oappend @ SY2373 @ ( c_List_Olist_OCons @ SY2374 @ ( c_List_Olist_ONil @ SV833 ) @ SV833 ) @ SV833 ) )
| ( SV604 = SY2374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2273,plain,
! [SV834: $i,SV605: $i,SV307: $i] :
( ( ! [SY2375: $i] :
( ! [SY2376: $i] :
( ( c_List_Oappend @ SV307 @ ( c_List_Olist_OCons @ SV605 @ ( c_List_Olist_ONil @ SV834 ) @ SV834 ) @ SV834 )
!= ( c_List_Oappend @ SY2375 @ ( c_List_Olist_OCons @ SY2376 @ ( c_List_Olist_ONil @ SV834 ) @ SV834 ) @ SV834 ) )
| ( SV307 = SY2375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(2274,plain,
! [SV835: $i,SV606: $i,SV308: $i] :
( ( ! [SY2377: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV308 ) @ SV606 ) @ SV835 @ SY2377 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV308 @ SV835 @ SY2377 ) ) @ ( c_Lambda_Osubst @ SV606 @ SV835 @ SY2377 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1972]) ).
thf(2275,plain,
! [SV607: $i,SV309: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV309 )
!= ( c_Lambda_OdB_OVar @ SV607 ) )
= $true )
| ( ( SV309 = SV607 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1973]) ).
thf(2276,plain,
! [SV836: $i,SV608: $i,SV310: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV310 @ SV608 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV836 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV310 @ ( c_List_Oappend @ SV608 @ ( c_List_Olist_OCons @ SV836 @ ( 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)],[1974]) ).
thf(2277,plain,
! [SV837: $i,SV609: $i,SV311: $i] :
( ( ! [SY2378: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV311 ) @ SV609 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV837 ) @ SY2378 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV311 = SV837 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(2278,plain,
! [SV838: $i,SV610: $i,SV312: $i] :
( ( ! [SY2379: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV312 ) @ SV610 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV838 ) @ SY2379 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV610 = SY2379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1976]) ).
thf(2279,plain,
! [SV839: $i,SV611: $i,SV313: $i] :
( ( ! [SY2380: $i,SY2381: $i] :
( ( ( c_List_Olist_OCons @ SV313 @ SV611 @ SV839 )
!= ( c_List_Olist_OCons @ SY2380 @ SY2381 @ SV839 ) )
| ( SV611 = SY2381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1977]) ).
thf(2280,plain,
! [SV840: $i,SV612: $i,SV314: $i] :
( ( ! [SY2382: $i] :
( ! [SY2383: $i] :
( ( c_List_Olist_OCons @ SV314 @ SV612 @ SV840 )
!= ( c_List_Olist_OCons @ SY2382 @ SY2383 @ SV840 ) )
| ( SV314 = SY2382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1978]) ).
thf(2281,plain,
! [SV841: $i,SV614: $i,SV316: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV316 ) @ ( c_List_Olist_OCons @ SV614 @ SV841 @ SV316 ) @ SV316 )
= ( c_List_Olist_OCons @ SV614 @ SV841 @ SV316 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1980]) ).
thf(2282,plain,
! [SV842: $i,SV615: $i,SV317: $i] :
( ( ( SV317
!= ( c_List_Oappend @ SV615 @ SV317 @ SV842 ) )
| ( SV615
= ( c_List_Olist_ONil @ SV842 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1981]) ).
thf(2283,plain,
! [SV843: $i,SV616: $i,SV318: $i] :
( ( ( ( c_List_Oappend @ SV318 @ SV616 @ SV843 )
!= SV616 )
| ( SV318
= ( c_List_Olist_ONil @ SV843 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1982]) ).
thf(2284,plain,
! [SV844: $i,SV617: $i,SV319: $i] :
( ( ( SV319
!= ( c_List_Oappend @ SV319 @ SV617 @ SV844 ) )
| ( SV617
= ( c_List_Olist_ONil @ SV844 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2285,plain,
! [SV845: $i,SV618: $i,SV320: $i] :
( ( ( ( c_List_Oappend @ SV320 @ SV618 @ SV845 )
!= SV320 )
| ( SV618
= ( c_List_Olist_ONil @ SV845 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1984]) ).
thf(2286,plain,
! [SV846: $i,SV321: $i] :
( ( ( ! [SY2384: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV321 @ ( c_Lambda_OdB_OVar @ SV846 ) @ SY2384 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV321 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1985]) ).
thf(2287,plain,
! [SV847: $i,SV619: $i,SV322: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV322 ) @ SV619 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV847 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV322 ) @ SV619 )
= SV847 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1986]) ).
thf(2288,plain,
! [SV848: $i,SV620: $i,SV323: $i] :
( ( ( c_List_Olist_ONil @ SV323 )
!= ( c_List_Olist_OCons @ SV620 @ SV848 @ SV323 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2289,plain,
! [SV849: $i,SV621: $i,SV324: $i] :
( ( ! [SY2385: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV324 ) @ SV621 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV849 ) @ SY2385 ) )
| ( SV324 = SV849 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1988]) ).
thf(2290,plain,
! [SV850: $i,SV622: $i,SV325: $i] :
( ( ! [SY2386: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV325 ) @ SV622 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV850 ) @ SY2386 ) )
| ( SV622 = SY2386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1989]) ).
thf(2291,plain,
! [SV623: $i,SV326: $i] :
( ( ( ! [SY2189: $i] :
( ( c_Lambda_OdB_OVar @ SV326 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV623 @ SY2189 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ( c_Lambda_OdB_OVar @ SV326 )
= SV623 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1990]) ).
thf(2292,plain,
! [SV851: $i,SV624: $i,SV327: $i] :
( ( ( c_Lambda_OdB_OVar @ SV327 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV624 ) @ SV851 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1991]) ).
thf(2293,plain,
! [SV852: $i,SV625: $i,SV328: $i] :
( ( ( ( c_List_Oappend @ SV328 @ SV625 @ SV852 )
!= ( c_List_Olist_ONil @ SV852 ) )
| ( SV625
= ( c_List_Olist_ONil @ SV852 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(2294,plain,
! [SV853: $i,SV626: $i,SV329: $i] :
( ( ( ( c_List_Oappend @ SV329 @ SV626 @ SV853 )
!= ( c_List_Olist_ONil @ SV853 ) )
| ( SV329
= ( c_List_Olist_ONil @ SV853 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1993]) ).
thf(2295,plain,
! [SV854: $i,SV627: $i,SV330: $i] :
( ( ( SV330
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV330 ) @ SV627 ) @ SV854 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV330 ) @ SV627 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV330 ) @ SV627 ) @ ( c_List_Oappend @ SV854 @ ( c_List_Olist_OCons @ SV627 @ ( 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)],[1994]) ).
thf(2296,plain,
! [SV855: $i,SV628: $i,SV331: $i] :
( ( ( ( c_List_Olist_ONil @ SV331 )
!= ( c_List_Oappend @ SV628 @ SV855 @ SV331 ) )
| ( SV855
= ( c_List_Olist_ONil @ SV331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1995]) ).
thf(2297,plain,
! [SV629: $i,SV332: $i] :
( ( ( ! [SY2195: $i] :
( ( c_List_Olist_ONil @ SV332 )
!= ( c_List_Oappend @ SV629 @ SY2195 @ SV332 ) ) )
= $true )
| ( ( SV629
= ( c_List_Olist_ONil @ SV332 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1996]) ).
thf(2298,plain,
! [SV856: $i,SV630: $i,SV333: $i] :
( ( ! [SY2387: $i] :
( ( c_List_Ofoldl @ SV333 @ SV630 @ ( c_List_Olist_ONil @ SV856 ) @ SY2387 @ SV856 )
= SV630 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1997]) ).
thf(2299,plain,
! [SV857: $i,SV636: $i,SV340: $i] :
( ( ! [SY2388: $i] :
( ( ( c_List_Oappend @ SV340 @ SV636 @ SV857 )
!= ( c_List_Oappend @ SV340 @ SY2388 @ SV857 ) )
| ( SV636 = SY2388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(2300,plain,
! [SV858: $i,SV637: $i,SV341: $i] :
( ( ! [SY2389: $i] :
( ( ( c_List_Oappend @ SV341 @ SV637 @ SV858 )
!= ( c_List_Oappend @ SY2389 @ SV637 @ SV858 ) )
| ( SV341 = SY2389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2004]) ).
thf(2301,plain,
! [SV859: $i,SV638: $i,SV343: $i] :
( ( ! [SY2390: $i,SY2391: $i,SY2392: $i] :
( ( c_List_Ofoldl @ SV343 @ SV638 @ ( c_List_Olist_OCons @ SV859 @ SY2390 @ SY2391 ) @ SY2392 @ SY2391 )
= ( c_List_Ofoldl @ SV343 @ ( hAPP @ ( hAPP @ SV343 @ SV638 ) @ SV859 ) @ SY2390 @ SY2392 @ SY2391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2005]) ).
thf(2302,plain,
! [SV860: $i,SV639: $i,SV344: $i] :
( ( ! [SY2393: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV344 @ SV639 @ SV860 ) @ SY2393 @ SV860 )
= ( c_List_Olist_OCons @ SV344 @ ( c_List_Oappend @ SV639 @ SY2393 @ SV860 ) @ SV860 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2006]) ).
thf(2303,plain,
! [SV861: $i,SV640: $i,SV345: $i] :
( ( ! [SY2394: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV345 @ SV640 @ SV861 ) @ SY2394 @ SV861 )
= ( c_List_Olist_OCons @ SV345 @ ( c_List_Oappend @ SV640 @ SY2394 @ SV861 ) @ SV861 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2007]) ).
thf(2304,plain,
! [SV862: $i,SV641: $i,SV346: $i] :
( ( ! [SY2395: $i] :
( ( c_List_Olist_OCons @ SV346 @ ( c_List_Oappend @ SV641 @ SV862 @ SY2395 ) @ SY2395 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV346 @ SV641 @ SY2395 ) @ SV862 @ SY2395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2305,plain,
! [SV863: $i,SV642: $i,SV347: $i] :
( ( ! [SY2396: $i] :
( ( c_List_Olist_OCons @ SV347 @ ( c_List_Oappend @ SV642 @ SV863 @ SY2396 ) @ SY2396 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV347 @ SV642 @ SY2396 ) @ SV863 @ SY2396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2009]) ).
thf(2306,plain,
! [SV864: $i,SV643: $i,SV348: $i] :
( ( ( c_List_Olist_OCons @ SV348 @ SV643 @ SV864 )
!= ( c_List_Olist_ONil @ SV864 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2010]) ).
thf(2307,plain,
! [SV865: $i,SV644: $i,SV349: $i] :
( ( ( c_List_Olist_OCons @ SV349 @ SV644 @ SV865 )
!= ( c_List_Olist_ONil @ SV865 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2011]) ).
thf(2308,plain,
! [SV866: $i,SV645: $i,SV350: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV350 @ SV645 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV866 @ SV645 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV350 = SV866 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2012]) ).
thf(2309,plain,
! [SV867: $i,SV646: $i,SV351: $i] :
( ( ( c_List_Olist_OCons @ SV351 @ SV646 @ SV867 )
!= SV646 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2013]) ).
thf(2310,plain,
! [SV868: $i,SV647: $i,SV352: $i] :
( ( SV352
!= ( c_List_Olist_OCons @ SV647 @ SV352 @ SV868 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2311,plain,
! [SV869: $i,SV648: $i,SV353: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV353 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV648 @ SV869 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV869
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2015]) ).
thf(2312,plain,
! [SV870: $i,SV649: $i,SV354: $i] :
( ( ( c_List_Olist_OCons @ SV354 @ SV649 @ SV870 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV870 ) @ ( c_List_Olist_OCons @ SV354 @ SV649 @ SV870 ) @ SV870 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2016]) ).
thf(2313,plain,
! [SV871: $i,SV650: $i,SV356: $i] :
( ( ! [SY2397: $i,SY2398: $i,SY2399: $i] :
( ( c_List_Ofoldl @ SV356 @ SV650 @ ( c_List_Oappend @ SV871 @ SY2397 @ SY2398 ) @ SY2399 @ SY2398 )
= ( c_List_Ofoldl @ SV356 @ ( c_List_Ofoldl @ SV356 @ SV650 @ SV871 @ SY2399 @ SY2398 ) @ SY2397 @ SY2399 @ SY2398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2017]) ).
thf(2314,plain,
! [SV872: $i,SV651: $i,SV357: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV357 ) @ SV651 )
!= ( c_Lambda_OdB_OVar @ SV872 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2018]) ).
thf(2315,plain,
! [SV652: $i,SV358: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV358 @ SV652 ) )
= $true )
| ( ( ~ ( class_Orderings_Opreorder @ SV652 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2019]) ).
thf(2316,plain,
! [SV653: $i,SV359: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV359 @ SV653 ) )
= $true )
| ( ( ~ ( class_Orderings_Oorder @ SV653 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2020]) ).
thf(2317,plain,
! [SV655: $i,SV361: $i] :
( ( ( SV361 = SV655 )
= $true )
| ( ( ! [SY2226: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY2226 ) @ SV361 ) @ SV655 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2022]) ).
thf(2318,plain,
! [SV873: $i,SV656: $i,SV362: $i,SV1: $i] :
( ( ! [SY2400: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV1 @ ( c_List_Olist_OCons @ SV362 @ SV656 @ SV873 ) @ SV873 ) @ ( c_Nat_Osize__class_Osize @ SV1 @ ( tc_List_Olist @ SV873 ) ) @ SY2400 @ SV873 )
= ( c_List_Oappend @ SV1 @ ( c_List_Olist_OCons @ SY2400 @ SV656 @ SV873 ) @ SV873 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2319,plain,
! [SV874: $i,SV657: $i,SV363: $i,SV2: $i] :
( ( ( ( c_List_Olist__update @ SV2 @ SV363 @ SV657 @ SV874 )
!= ( c_List_Olist_ONil @ SV874 ) )
| ( SV2
= ( c_List_Olist_ONil @ SV874 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(2320,plain,
! [SV875: $i,SV661: $i,SV367: $i,SV6: $i] :
( ( ( ( c_List_Olist__update @ SV6 @ SV367 @ SV661 @ SV875 )
!= SV6 )
| ~ ( c_HOL_Oord__class_Oless @ SV367 @ ( c_Nat_Osize__class_Osize @ SV6 @ ( tc_List_Olist @ SV875 ) ) @ tc_nat )
| ( ( c_List_Onth @ SV6 @ SV367 @ SV875 )
= SV661 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2321,plain,
! [SV876: $i,SV662: $i,SV368: $i,SV7: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ SV7 @ SV368 @ SV662 @ SV876 ) @ ( tc_List_Olist @ SV876 ) )
= ( c_Nat_Osize__class_Osize @ SV7 @ ( tc_List_Olist @ SV876 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2322,plain,
! [SV877: $i,SV663: $i,SV369: $i,SV8: $i] :
( ( ! [SY2401: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ SV8 @ SV369 @ SV663 @ SV877 ) @ SY2401 @ SV877 )
= ( c_List_Onth @ SV8 @ SY2401 @ SV877 ) )
| ( SV369 = SY2401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2030]) ).
thf(2323,plain,
! [SV664: $i,SV370: $i,SV9: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV9 @ ( c_Nat_Osize__class_Osize @ SV370 @ ( tc_List_Olist @ SV664 ) ) @ tc_nat ) )
= $true )
| ( ( ( c_List_Olist__update @ SV370 @ SV9 @ ( c_List_Onth @ SV370 @ SV9 @ SV664 ) @ SV664 )
= SV370 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2031]) ).
thf(2324,plain,
! [SV665: $i,SV371: $i,SV10: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV10 @ ( c_Nat_Osize__class_Osize @ SV371 @ ( tc_List_Olist @ SV665 ) ) @ tc_nat ) )
= $true )
| ( ( ! [SY2234: $i] :
( ( c_List_Onth @ ( c_List_Olist__update @ SV371 @ SV10 @ SY2234 @ SV665 ) @ SV10 @ SV665 )
= SY2234 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2032]) ).
thf(2325,plain,
! [SV878: $i,SV666: $i,SV372: $i,SV11: $i] :
( ( ( ( c_List_Onth @ ( c_List_Olist__update @ SV11 @ SV372 @ SV666 @ SV878 ) @ SV372 @ SV878 )
= SV666 )
| ~ ( c_HOL_Oord__class_Oless @ SV372 @ ( c_Nat_Osize__class_Osize @ SV11 @ ( tc_List_Olist @ SV878 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2033]) ).
thf(2326,plain,
! [SV879: $i,SV667: $i,SV373: $i,SV12: $i] :
( ( ! [SY2402: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV12 @ SV373 @ SV667 ) @ SV879 @ SY2402 @ SV667 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV12 @ SV879 @ SY2402 @ SV667 ) @ SV373 @ SV667 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV879 @ ( c_Nat_Osize__class_Osize @ SV12 @ ( tc_List_Olist @ SV667 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2034]) ).
thf(2327,plain,
! [SV880: $i,SV668: $i,SV374: $i,SV13: $i] :
( ( ! [SY2403: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV13 @ SV374 @ SV668 ) @ SV880 @ SY2403 @ SV668 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV13 @ SV880 @ SY2403 @ SV668 ) @ SV374 @ SV668 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV880 @ ( c_Nat_Osize__class_Osize @ SV13 @ ( tc_List_Olist @ SV668 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2328,plain,
! [SV881: $i,SV670: $i,SV376: $i,SV15: $i] :
( ( ! [SY2404: $i] :
( ! [SY2405: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV15 @ SV376 @ SV670 @ SV881 ) @ SY2404 @ SY2405 @ SV881 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV15 @ SY2404 @ SY2405 @ SV881 ) @ SV376 @ SV670 @ SV881 ) )
| ( SV376 = SY2404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2037]) ).
thf(2329,plain,
! [SV882: $i,SV671: $i,SV377: $i,SV16: $i] :
( ( ! [SY2406: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV16 @ SV377 @ SV671 ) @ ( c_Suc @ SV882 ) @ SY2406 @ SV671 )
= ( c_List_Olist_OCons @ SV16 @ ( c_List_Olist__update @ SV377 @ SV882 @ SY2406 @ SV671 ) @ SV671 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2038]) ).
thf(2330,plain,
! [SV883: $i,SV672: $i,SV378: $i,SV17: $i] :
( ( ! [SY2407: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ SV17 @ SV378 @ SV672 @ SV883 ) @ SY2407 @ SV883 )
= ( c_List_Onth @ SV17 @ SY2407 @ SV883 ) )
| ( SV378 = SY2407 )
| ~ ( c_HOL_Oord__class_Oless @ SV378 @ ( c_Nat_Osize__class_Osize @ SV17 @ ( tc_List_Olist @ SV883 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2039]) ).
thf(2331,plain,
! [SV884: $i,SV673: $i,SV379: $i,SV18: $i] :
( ( ! [SY2408: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV18 @ SV379 @ SV673 @ SV884 ) @ SV379 @ SY2408 @ SV884 )
= ( c_List_Olist__update @ SV18 @ SV379 @ SY2408 @ SV884 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2040]) ).
thf(2332,plain,
! [SV885: $i,SV674: $i,SV380: $i,SV19: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV19 @ SV380 @ SV674 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV885 @ SV674 )
= ( c_List_Olist_OCons @ SV885 @ SV380 @ SV674 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(2333,plain,
! [SV675: $i,SV381: $i,SV20: $i] :
( ( ( ( c_List_Ohd @ ( c_List_Odrop @ SV20 @ SV381 @ SV675 ) @ SV675 )
= ( c_List_Onth @ SV381 @ SV20 @ SV675 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV20 @ ( c_Nat_Osize__class_Osize @ SV381 @ ( tc_List_Olist @ SV675 ) ) @ tc_nat )
| ( SV381
= ( c_List_Olist_ONil @ SV675 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2042]) ).
thf(2334,plain,
! [SV676: $i,SV382: $i,SV21: $i] :
( ( ( ( c_List_Olist_OCons @ ( c_List_Onth @ SV21 @ SV382 @ SV676 ) @ ( c_List_Odrop @ ( c_Suc @ SV382 ) @ SV21 @ SV676 ) @ SV676 )
= ( c_List_Odrop @ SV382 @ SV21 @ SV676 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV382 @ ( c_Nat_Osize__class_Osize @ SV21 @ ( tc_List_Olist @ SV676 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2043]) ).
thf(2335,plain,
! [SV886: $i,SV679: $i,SV385: $i,SV24: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SV385 ) ) @ SV679 @ SV385 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV679 @ ( tc_List_Olist @ SV385 ) ) @ SV24 @ SV385 ) @ SV886 @ SV385 ) @ SV385 )
!= SV886 )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SV385 ) ) @ SV679 @ SV385 )
!= SV24 )
| ( SV679
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV679 @ ( tc_List_Olist @ SV385 ) ) @ SV24 @ SV385 ) )
| ( ( c_List_Oappend @ SV679 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV679 @ ( tc_List_Olist @ SV385 ) ) @ SV24 @ SV385 ) @ SV886 @ SV385 ) @ SV385 )
= ( c_List_Oappend @ SV24 @ SV886 @ SV385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2046]) ).
thf(2336,plain,
! [SV887: $i,SV680: $i,SV386: $i,SV25: $i] :
( ( ! [SY2409: $i] :
( ( c_List_Odrop @ SV25 @ SV386 @ SV680 )
!= ( c_List_Olist_OCons @ SV887 @ SY2409 @ SV680 ) )
| ( ( c_List_Onth @ SV386 @ SV25 @ SV680 )
= SV887 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2047]) ).
thf(2337,plain,
! [SV888: $i,SV681: $i,SV387: $i,SV26: $i] :
( ( ( ( c_List_Olist__update @ SV26 @ SV387 @ SV681 @ SV888 )
= ( c_List_Oappend @ ( c_List_Otake @ SV387 @ SV26 @ SV888 ) @ ( c_List_Olist_OCons @ SV681 @ ( c_List_Odrop @ ( c_Suc @ SV387 ) @ SV26 @ SV888 ) @ SV888 ) @ SV888 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV387 @ ( c_Nat_Osize__class_Osize @ SV26 @ ( tc_List_Olist @ SV888 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2048]) ).
thf(2338,plain,
! [SV682: $i,SV388: $i,SV27: $i] :
( ( ( SV27
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV27 @ ( tc_List_Olist @ SV388 ) ) @ SV682 @ SV388 ) )
= $true )
| ( ( ( c_List_Oappend @ SV27 @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV27 @ ( tc_List_Olist @ SV388 ) ) @ SV682 @ SV388 ) @ SV388 )
= SV682 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2049]) ).
thf(2339,plain,
! [SV683: $i,SV389: $i,SV28: $i] :
( ( ( ( c_List_Olast @ ( c_List_Odrop @ SV28 @ SV389 @ SV683 ) @ SV683 )
= ( c_List_Olast @ SV389 @ SV683 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV28 @ ( c_Nat_Osize__class_Osize @ SV389 @ ( tc_List_Olist @ SV683 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2050]) ).
thf(2340,plain,
! [SV889: $i,SV685: $i,SV391: $i,SV30: $i] :
( ( ( c_List_Odrop @ ( c_Suc @ SV30 ) @ ( c_List_Olist_OCons @ SV391 @ SV685 @ SV889 ) @ SV889 )
= ( c_List_Odrop @ SV30 @ SV685 @ SV889 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2052]) ).
thf(2341,plain,
! [SV399: $i,SV38: $i] :
( ( ( ( c_Int_Onumber__class_Onumber__of @ SV38 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( ! [SY1893: $i,SY1894: $i] :
( ( c_List_Odrop @ ( c_Int_Onumber__class_Onumber__of @ SV38 @ tc_nat ) @ ( c_List_Olist_OCons @ SV399 @ SY1893 @ SY1894 ) @ SY1894 )
= ( c_List_Olist_OCons @ SV399 @ SY1893 @ SY1894 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2059]) ).
thf(2342,plain,
! [SV890: $i,SV692: $i,SV401: $i,SV40: $i] :
( ( ! [SY2410: $i] :
( ( c_Type_Otypings @ SV40 @ SV401 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV692 @ SV890 @ SV40 @ SV401 ) )
| ! [SY2411: $i] :
( ~ ( c_Type_Otyping @ SV40 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2410 ) @ SY2411 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV890 )
| ! [SY1205: $i] :
~ ( c_Type_Otypings @ SV40 @ SY2411 @ SY1205 )
| ~ ( c_Type_Otyping @ SV40 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2410 ) @ SY2411 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV401 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV692 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2343,plain,
! [SV891: $i,SV693: $i,SV402: $i,SV41: $i] :
( ( ( c_Type_Otypings @ SV41 @ SV402 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV693 @ SV41 @ SV891 @ SV402 ) )
| ~ ( c_Type_Otyping @ SV41 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV891 ) @ SV402 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV693 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2344,plain,
! [SV694: $i,SV403: $i,SV42: $i] :
( ( ( SV42
= ( c_List_Oappend @ ( c_List_Otake @ SV403 @ SV42 @ SV694 ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ SV42 @ SV403 @ SV694 ) @ ( c_List_Odrop @ ( c_Suc @ SV403 ) @ SV42 @ SV694 ) @ SV694 ) @ SV694 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV403 @ ( c_Nat_Osize__class_Osize @ SV42 @ ( tc_List_Olist @ SV694 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2062]) ).
thf(2345,plain,
! [SV695: $i,SV404: $i,SV43: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Otake @ SV43 @ SV404 @ SV695 ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ ( c_List_Odrop @ SV43 @ SV404 @ SV695 ) @ SV695 ) @ ( c_List_Olist_ONil @ SV695 ) @ SV695 ) @ SV695 )
= ( c_List_Otake @ ( c_Suc @ SV43 ) @ SV404 @ SV695 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV43 @ ( c_Nat_Osize__class_Osize @ SV404 @ ( tc_List_Olist @ SV695 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2063]) ).
thf(2346,plain,
! [SV892: $i,SV696: $i,SV405: $i,SV44: $i] :
( ( ( c_Lambda_Oliftn @ SV44 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV405 ) @ SV696 ) @ SV892 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ SV44 @ SV405 @ SV892 ) ) @ ( c_Lambda_Oliftn @ SV44 @ SV696 @ SV892 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2064]) ).
thf(2347,plain,
! [SV893: $i,SV697: $i,SV406: $i,SV45: $i] :
( ( ( c_List_Onth @ ( c_List_Oappend @ SV45 @ ( c_List_Olist_OCons @ SV406 @ SV697 @ SV893 ) @ SV893 ) @ ( c_Nat_Osize__class_Osize @ SV45 @ ( tc_List_Olist @ SV893 ) ) @ SV893 )
= SV406 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2065]) ).
thf(2348,plain,
! [SV894: $i,SV698: $i,SV409: $i,SV48: $i] :
( ( ! [SY2413: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV48 @ SV409 @ SV698 ) @ ( c_List_Olist_OCons @ SV894 @ SY2413 @ SV698 ) @ SV698 )
= ( c_List_Olist_OCons @ SV48 @ ( c_List_Olist_OCons @ SV894 @ ( c_List_Osplice @ SV409 @ SY2413 @ SV698 ) @ SV698 ) @ SV698 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(2349,plain,
! [SV410: $i,SV49: $i] :
( ( ( ( c_Int_Onumber__class_Onumber__of @ SV49 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( ! [SY1911: $i,SY1912: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ SV410 @ SY1911 @ SY1912 ) @ ( c_Int_Onumber__class_Onumber__of @ SV49 @ tc_nat ) @ SY1912 )
= SV410 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2067]) ).
thf(2350,plain,
! [SV55: $i] :
( ( ( ( c_HOL_Ozero__class_Ozero @ SV55 )
= ( c_HOL_Oone__class_Oone @ SV55 ) )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2068]) ).
thf(2351,plain,
! [SV56: $i] :
( ( ( ( c_HOL_Oone__class_Oone @ SV56 )
= ( c_HOL_Ozero__class_Ozero @ SV56 ) )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2069]) ).
thf(2352,plain,
! [SV412: $i,SV57: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV57 @ SV412 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV57 ) @ ( c_Suc @ SV412 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2070]) ).
thf(2353,plain,
! [SV413: $i,SV58: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV58 ) @ ( c_Suc @ SV413 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV58 @ SV413 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2071]) ).
thf(2354,plain,
! [SV414: $i,SV59: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV59 @ SV414 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV59 ) @ ( c_Suc @ SV414 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2072]) ).
thf(2355,plain,
! [SV417: $i,SV62: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV62 @ SV417 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV417 @ ( c_Suc @ SV62 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2074]) ).
thf(2356,plain,
! [SV418: $i,SV64: $i] :
( ( ( ( c_Suc @ SV64 )
= SV418 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV64 @ SV418 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV64 ) @ SV418 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2075]) ).
thf(2357,plain,
! [SV65: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV65 ) )
= $true )
| ( ( ! [SY1236: $i,SY1237: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ SY1236 @ SV65 )
!= ( c_Int_Onumber__class_Onumber__of @ SY1237 @ SV65 ) )
| ( SY1236 = SY1237 ) ) )
= $true )
| ( ( class_Int_Oring__char__0 @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2076]) ).
thf(2358,plain,
! [SV895: $i,SV699: $i,SV419: $i,SV66: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV66 @ SV419 @ SV419 ) @ SV419 ) @ SV699 ) @ SV895 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV66 @ SV419 ) @ SV895 ) @ SV699 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2077]) ).
thf(2359,plain,
! [SV896: $i,SV700: $i,SV420: $i,SV67: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV67 @ SV420 ) @ SV700 ) @ SV896 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV67 @ SV420 @ SV420 ) @ SV420 ) @ SV896 ) @ SV700 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2078]) ).
thf(2360,plain,
! [SV701: $i,SV421: $i,SV69: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV69 @ SV421 ) @ SV701 ) )
= $true )
| ( ( ! [SY2266: $i,SY2267: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV69 @ SY2266 @ SY2267 ) @ SV701 ) @ SV421 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2080]) ).
thf(2361,plain,
! [SV897: $i,SV702: $i,SV422: $i,SV70: $i] :
( ( ! [SY2414: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV70 @ SV422 @ SV702 ) @ SV897 ) @ SY2414 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY2414 ) @ SV897 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2081]) ).
thf(2362,plain,
! [SV703: $i,SV423: $i,SV71: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV71 @ SV423 ) @ SV703 ) )
= $true )
| ( ( ! [SY2270: $i,SY2271: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV71 @ SY2270 @ SY2271 ) @ SV703 ) @ SV423 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2082]) ).
thf(2363,plain,
! [SV898: $i,SV704: $i,SV424: $i,SV72: $i] :
( ( ! [SY2415: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV72 @ SV424 @ SV704 ) @ SV898 ) @ SY2415 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV72 @ SY2415 ) @ SV898 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2083]) ).
thf(2364,plain,
! [SV709: $i,SV429: $i,SV77: $i] :
( ( ( c_Wellfounded_Oaccp @ SV77 @ SV429 @ SV709 )
= $true )
| ( ( ! [SY2274: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV77 @ SV709 ) @ SV429 ) @ SY2274 ) )
| ~ ( c_Wellfounded_Oaccp @ SV77 @ SY2274 @ SV709 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2088]) ).
thf(2365,plain,
! [SV710: $i,SV430: $i,SV78: $i] :
( ( ( c_Wellfounded_Oaccp @ SV78 @ SV430 @ SV710 )
= $true )
| ( ( ! [SY2275: $i] :
( ~ ( c_Wellfounded_Oaccp @ SV78 @ SY2275 @ SV710 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV78 @ SV710 ) @ SV430 ) @ SY2275 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2089]) ).
thf(2366,plain,
! [SV899: $i,SV711: $i,SV431: $i,SV79: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV79 @ SV431 ) @ SV711 ) @ SV899 ) )
| ! [SY2416: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV79 @ SV431 ) @ SY2416 ) @ SV899 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV79 @ SV431 ) @ SV711 ) @ SY2416 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2090]) ).
thf(2367,plain,
! [SV900: $i,SV712: $i,SV432: $i,SV82: $i] :
( ( ( ( c_List_Onth @ ( c_List_Oappend @ SV82 @ SV432 @ SV712 ) @ SV900 @ SV712 )
= ( c_List_Onth @ SV82 @ SV900 @ SV712 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV900 @ ( c_Nat_Osize__class_Osize @ SV82 @ ( tc_List_Olist @ SV712 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2093]) ).
thf(2368,plain,
! [SV83: $i,SV901: $i] :
( ( ( ! [SY2417: $i] :
( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV901 @ SV83 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY2417 @ SV83 ) )
| ( SV901 = SY2417 ) ) )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV83 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2094]) ).
thf(2369,plain,
! [SV433: $i,SV84: $i] :
( ( ( ( c_Suc @ SV84 )
= ( c_Suc @ SV433 ) )
= $false )
| ( ( SV84 = SV433 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2095]) ).
thf(2370,plain,
! [SV434: $i,SV85: $i] :
( ( ( ( c_Suc @ SV85 )
= ( c_Suc @ SV434 ) )
= $false )
| ( ( SV85 = SV434 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2096]) ).
thf(2371,plain,
! [SV902: $i,SV713: $i,SV435: $i,SV86: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV86 @ SV435 ) @ SV713 ) @ SV902 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV86 @ SV713 ) @ SV902 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2097]) ).
thf(2372,plain,
! [SV436: $i,SV88: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV88 @ SV436 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV88 @ ( c_Suc @ SV436 ) @ tc_nat ) )
= $true )
| ( ( SV88 = SV436 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2098]) ).
thf(2373,plain,
! [SV89: $i,SV437: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV437 @ ( c_Suc @ SV89 ) @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV437 @ SV89 @ tc_nat )
= $true )
| ( ( SV89 = SV437 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2099]) ).
thf(2374,plain,
! [SV438: $i,SV90: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV90 @ ( c_Suc @ SV438 ) @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV90 @ SV438 @ tc_nat )
= $true )
| ( ( SV90 = SV438 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2100]) ).
thf(2375,plain,
! [SV94: $i,SV440: $i,SV903: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV903 @ SV440 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV94 @ SV903 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV94 ) @ SV440 @ tc_nat )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2101]) ).
thf(2376,plain,
! [SV904: $i,SV716: $i,SV443: $i,SV97: $i] :
( ( ( c_List_Onth @ ( c_List_Olist_OCons @ SV97 @ SV443 @ SV716 ) @ ( c_Suc @ SV904 ) @ SV716 )
= ( c_List_Onth @ SV443 @ SV904 @ SV716 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2104]) ).
thf(2377,plain,
! [SV444: $i,SV100: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV100 ) @ SV444 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV100 @ SV444 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2105]) ).
thf(2378,plain,
! [SV445: $i,SV101: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV101 @ SV445 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV101 @ ( c_Suc @ SV445 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2106]) ).
thf(2379,plain,
! [SV905: $i,SV717: $i,SV448: $i,SV104: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV104 @ SV448 ) @ SV717 ) @ SV905 ) )
| ! [SY2418: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV104 @ SV448 ) @ SY2418 ) @ SV905 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV104 @ SV717 ) @ SY2418 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2108]) ).
thf(2380,plain,
! [SV906: $i,SV718: $i,SV449: $i,SV105: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV105 @ SV449 ) @ SV718 ) @ SV906 ) )
| ! [SY2419: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV105 @ SY2419 ) @ SV906 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV105 @ SV449 ) @ SV718 ) @ SY2419 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2109]) ).
thf(2381,plain,
! [SV719: $i,SV450: $i,SV106: $i] :
( ( ( c_Wellfounded_Oaccp @ SV106 @ SV450 @ SV719 )
= $true )
| ( ( ! [SY2285: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV106 @ SV450 ) @ SY2285 ) )
| ~ ( c_Wellfounded_Oaccp @ SV106 @ SY2285 @ SV719 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2110]) ).
thf(2382,plain,
! [SV720: $i,SV451: $i,SV107: $i] :
( ( ( c_Wellfounded_Oaccp @ SV107 @ SV451 @ SV720 )
= $true )
| ( ( ! [SY2286: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV107 @ SV451 ) @ SY2286 ) )
| ~ ( c_Wellfounded_Oaccp @ SV107 @ SY2286 @ SV720 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2111]) ).
thf(2383,plain,
! [SV721: $i,SV452: $i,SV108: $i] :
( ( ( ( c_List_Otake @ ( c_Suc @ SV108 ) @ SV452 @ SV721 )
= ( c_List_Oappend @ ( c_List_Otake @ SV108 @ SV452 @ SV721 ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ SV452 @ SV108 @ SV721 ) @ ( c_List_Olist_ONil @ SV721 ) @ SV721 ) @ SV721 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV108 @ ( c_Nat_Osize__class_Osize @ SV452 @ ( tc_List_Olist @ SV721 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2112]) ).
thf(2384,plain,
! [SV109: $i,SV907: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV907 @ SV109 ) @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV109 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV109 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2113]) ).
thf(2385,plain,
! [SV110: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV110 ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV110 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2114]) ).
thf(2386,plain,
! [SV113: $i,SV908: $i] :
( ( ( ! [SY2420: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV908 @ SV113 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2420 @ SV113 ) @ SV113 )
| ~ ( c_HOL_Oord__class_Oless @ SV908 @ SY2420 @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV113 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2117]) ).
thf(2387,plain,
! [SV114: $i,SV909: $i] :
( ( ( ! [SY2421: $i] :
( ( c_HOL_Oord__class_Oless @ SV909 @ SY2421 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV909 @ SV114 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2421 @ SV114 ) @ SV114 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV114 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2118]) ).
thf(2388,plain,
! [SV454: $i,SV120: $i] :
( ( ( ( c_Nat_Osize__class_Osize @ SV120 @ ( tc_List_Olist @ SV454 ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV120
= ( c_List_Olist_ONil @ SV454 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2121]) ).
thf(2389,plain,
! [SV910: $i,SV724: $i,SV456: $i,SV122: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV122 ) @ SV456 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV724 ) @ SV910 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV456 ) @ SV910 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV122 ) @ SV724 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2123]) ).
thf(2390,plain,
! [SV725: $i,SV457: $i,SV123: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV123 ) @ SV457 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV725 ) @ SV457 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV123 ) @ SV725 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2124]) ).
thf(2391,plain,
! [SV726: $i,SV458: $i,SV124: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV124 ) @ SV458 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV124 ) @ SV726 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV458 ) @ SV726 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2125]) ).
thf(2392,plain,
! [SV459: $i,SV125: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV125 ) @ SV459 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV125 ) ) @ ( c_Lambda_OdB_OAbs @ SV459 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2126]) ).
thf(2393,plain,
! [SV911: $i,SV727: $i,SV460: $i,SV126: $i] :
( ( ( c_List_Otake @ ( c_Suc @ SV126 ) @ ( c_List_Olist_OCons @ SV460 @ SV727 @ SV911 ) @ SV911 )
= ( c_List_Olist_OCons @ SV460 @ ( c_List_Otake @ SV126 @ SV727 @ SV911 ) @ SV911 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2127]) ).
thf(2394,plain,
! [SV728: $i,SV461: $i,SV127: $i] :
( ( ( ( c_Lambda_Oliftn @ SV127 @ ( c_Lambda_OdB_OVar @ SV461 ) @ SV728 )
= ( c_Lambda_OdB_OVar @ SV461 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV461 @ SV728 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2128]) ).
thf(2395,plain,
! [SV912: $i,SV729: $i,SV462: $i,SV128: $i] :
( ( ( ( c_List_Onth @ ( c_List_Otake @ SV128 @ SV462 @ SV729 ) @ SV912 @ SV729 )
= ( c_List_Onth @ SV462 @ SV912 @ SV729 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV912 @ SV128 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2129]) ).
thf(2396,plain,
! [SV913: $i,SV730: $i,SV463: $i,SV129: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV129 @ SV463 @ SV730 ) ) @ ( c_Lambda_Osubst @ SV129 @ SV913 @ SV730 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV463 ) @ SV913 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2130]) ).
thf(2397,plain,
! [SV914: $i,SV731: $i,SV464: $i,SV130: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV130 @ SV464 @ SV731 ) ) @ ( c_Lambda_Osubst @ SV914 @ SV464 @ SV731 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV130 ) @ SV914 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2131]) ).
thf(2398,plain,
! [SV915: $i,SV732: $i,SV465: $i,SV131: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV131 @ SV465 @ SV732 ) ) @ ( c_Lambda_Osubst @ SV131 @ SV915 @ SV732 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV465 ) @ SV915 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2132]) ).
thf(2399,plain,
! [SV733: $i,SV466: $i,SV132: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV132 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV466 @ SV132 @ SV733 ) @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV466 ) @ SV132 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV733 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2133]) ).
thf(2400,plain,
! [SV916: $i,SV736: $i,SV469: $i,SV135: $i] :
( ( ( ( c_List_Onth @ ( c_List_Oreplicate @ SV135 @ SV469 @ SV736 ) @ SV916 @ SV736 )
= SV469 )
| ~ ( c_HOL_Oord__class_Oless @ SV916 @ SV135 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2136]) ).
thf(2401,plain,
! [SV737: $i,SV470: $i,SV136: $i] :
( ( ( c_Type_Otyping @ SV136 @ SV470 @ SV737 )
= $true )
| ( ( ! [SY2294: $i] :
( ~ ( c_Type_Otyping @ SV136 @ SY2294 @ SV737 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY2294 ) @ SV470 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2137]) ).
thf(2402,plain,
! [SV739: $i,SV472: $i,SV138: $i] :
( ( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV138 @ SV472 @ SV739 ) @ SV739 )
= ( c_List_Oappend @ SV138 @ ( c_List_Obutlast @ SV472 @ SV739 ) @ SV739 ) )
= $true )
| ( ( SV472
= ( c_List_Olist_ONil @ SV739 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2139]) ).
thf(2403,plain,
! [SV740: $i,SV475: $i,SV141: $i] :
( ( ( ( c_List_Olast @ ( c_List_Oappend @ SV141 @ SV475 @ SV740 ) @ SV740 )
= ( c_List_Olast @ SV475 @ SV740 ) )
= $true )
| ( ( SV475
= ( c_List_Olist_ONil @ SV740 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2140]) ).
thf(2404,plain,
! [SV741: $i,SV476: $i,SV142: $i] :
( ( ( ( c_List_Otake @ ( c_Suc @ SV142 ) @ SV476 @ SV741 )
= ( c_List_Olist_OCons @ ( c_List_Ohd @ SV476 @ SV741 ) @ ( c_List_Otake @ SV142 @ ( c_List_Otl @ SV476 @ SV741 ) @ SV741 ) @ SV741 ) )
= $true )
| ( ( SV476
= ( c_List_Olist_ONil @ SV741 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2141]) ).
thf(2405,plain,
! [SV917: $i,SV742: $i,SV477: $i,SV143: $i] :
( ( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV143 @ SV477 @ SV742 ) @ SV917 @ SV742 )
= ( c_List_Olist_OCons @ SV143 @ ( c_List_Olist_OCons @ ( c_List_Ohd @ SV917 @ SV742 ) @ ( c_List_Osplice @ SV477 @ ( c_List_Otl @ SV917 @ SV742 ) @ SV742 ) @ SV742 ) @ SV742 ) )
| ( SV917
= ( c_List_Olist_ONil @ SV742 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2142]) ).
thf(2406,plain,
! [SV744: $i,SV478: $i,SV145: $i] :
( ( ( SV145
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV478 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV478 @ SV744 @ SV145 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV478 ) @ SV744 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV145 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2144]) ).
thf(2407,plain,
! [SV479: $i,SV146: $i] :
( ( ( ( c_Int_Onumber__class_Onumber__of @ SV146 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( ! [SY1991: $i,SY1992: $i] :
( ( c_List_Otake @ ( c_Int_Onumber__class_Onumber__of @ SV146 @ tc_nat ) @ ( c_List_Olist_OCons @ SV479 @ SY1991 @ SY1992 ) @ SY1992 )
= ( c_List_Olist_ONil @ SY1992 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2145]) ).
thf(2408,plain,
! [SV147: $i,SV918: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV918 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV918 @ SV147 ) @ SV147 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV147 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2146]) ).
thf(2409,plain,
! [SV919: $i,SV148: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV148 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV919 @ SV148 ) @ SV148 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV919 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV148 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2147]) ).
thf(2410,plain,
! [SV746: $i,SV481: $i,SV150: $i] :
( ( ( ( c_List_Otake @ SV150 @ ( c_List_Obutlast @ SV481 @ SV746 ) @ SV746 )
= ( c_List_Otake @ SV150 @ SV481 @ SV746 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV150 @ ( c_Nat_Osize__class_Osize @ SV481 @ ( tc_List_Olist @ SV746 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2149]) ).
thf(2411,plain,
! [SV747: $i,SV483: $i,SV152: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV152 @ SV483 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV747 @ SV483 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV152 ) @ SV747 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2151]) ).
thf(2412,plain,
! [SV748: $i,SV484: $i,SV153: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV153 @ SV484 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV153 @ SV748 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV484 @ SV748 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2152]) ).
thf(2413,plain,
! [SV749: $i,SV485: $i,SV154: $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 @ SV154 @ SV485 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV749 @ 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 ) @ SV485 @ 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 @ SV154 ) ) @ SV485 ) @ SV749 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2153]) ).
thf(2414,plain,
! [SV920: $i,SV751: $i,SV488: $i,SV158: $i] :
( ( ( c_Type_Otyping @ SV158 @ SV488 @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ SV751 @ SV158 @ SV488 @ SV920 ) )
| ~ ( c_Type_Otypings @ SV158 @ ( c_List_Oappend @ SV920 @ ( c_List_Olist_OCons @ SV488 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SV751 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2156]) ).
thf(2415,plain,
! [SV921: $i,SV752: $i,SV489: $i,SV159: $i] :
( ( ! [SY2422: $i] :
( ( ( c_List_Oappend @ SV159 @ SV489 @ SV752 )
!= ( c_List_Olist_OCons @ SV921 @ SY2422 @ SV752 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV921 @ SY2422 @ SV159 @ SV489 @ SV752 ) @ SV489 @ SV752 )
= SY2422 )
| ( SV489
= ( c_List_Olist_OCons @ SV921 @ SY2422 @ SV752 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2157]) ).
thf(2416,plain,
! [SV922: $i,SV753: $i,SV490: $i,SV160: $i] :
( ( ! [SY2423: $i] :
( ( ( c_List_Olist_OCons @ SV160 @ SV490 @ SV753 )
!= ( c_List_Oappend @ SV922 @ SY2423 @ SV753 ) )
| ( ( c_List_Olist_OCons @ SV160 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV160 @ SV490 @ SV922 @ SY2423 @ SV753 ) @ SV753 )
= SV922 )
| ( ( c_List_Olist_OCons @ SV160 @ SV490 @ SV753 )
= SY2423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2158]) ).
thf(2417,plain,
! [SV923: $i,SV754: $i,SV491: $i,SV161: $i] :
( ( ! [SY2424: $i] :
( ( ( c_List_Oappend @ SV161 @ SV491 @ SV754 )
!= ( c_List_Olist_OCons @ SV923 @ SY2424 @ SV754 ) )
| ( SV161
= ( c_List_Olist_OCons @ SV923 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV923 @ SY2424 @ SV161 @ SV491 @ SV754 ) @ SV754 ) )
| ( SV491
= ( c_List_Olist_OCons @ SV923 @ SY2424 @ SV754 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2159]) ).
thf(2418,plain,
! [SV924: $i,SV755: $i,SV492: $i,SV162: $i] :
( ( ! [SY2425: $i] :
( ( ( c_List_Olist_OCons @ SV162 @ SV492 @ SV755 )
!= ( c_List_Oappend @ SV924 @ SY2425 @ SV755 ) )
| ( SV492
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV162 @ SV492 @ SV924 @ SY2425 @ SV755 ) @ SY2425 @ SV755 ) )
| ( ( c_List_Olist_OCons @ SV162 @ SV492 @ SV755 )
= SY2425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2160]) ).
thf(2419,plain,
! [SV925: $i,SV756: $i,SV493: $i,SV163: $i] :
( ( ( c_List_Oappend @ ( c_List_Oreplicate @ SV163 @ SV493 @ SV756 ) @ ( c_List_Olist_OCons @ SV493 @ SV925 @ SV756 ) @ SV756 )
= ( c_List_Olist_OCons @ SV493 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV163 @ SV493 @ SV756 ) @ SV925 @ SV756 ) @ SV756 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2161]) ).
thf(2420,plain,
! [SV757: $i,SV495: $i,SV165: $i] :
( ( ( ( c_List_Olast @ ( c_List_Olist_OCons @ SV165 @ SV495 @ SV757 ) @ SV757 )
= ( c_List_Olast @ SV495 @ SV757 ) )
= $true )
| ( ( SV495
= ( c_List_Olist_ONil @ SV757 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2162]) ).
thf(2421,plain,
! [SV758: $i,SV497: $i,SV167: $i] :
( ( ( ( c_List_Olist_OCons @ SV167 @ ( c_List_Olist_ONil @ SV497 ) @ SV497 )
!= ( c_List_Orev @ SV758 @ SV497 ) )
= $true )
| ( ( SV758
= ( c_List_Olist_OCons @ SV167 @ ( c_List_Olist_ONil @ SV497 ) @ SV497 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2163]) ).
thf(2422,plain,
! [SV759: $i,SV498: $i,SV168: $i] :
( ( ( ( c_List_Orev @ SV168 @ SV498 )
!= ( c_List_Olist_OCons @ SV759 @ ( c_List_Olist_ONil @ SV498 ) @ SV498 ) )
= $true )
| ( ( SV168
= ( c_List_Olist_OCons @ SV759 @ ( c_List_Olist_ONil @ SV498 ) @ SV498 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2164]) ).
thf(2423,plain,
! [SV760: $i,SV501: $i,SV171: $i] :
( ( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV171 @ SV501 @ SV760 ) @ SV760 )
= ( c_List_Olist_OCons @ SV171 @ ( c_List_Obutlast @ SV501 @ SV760 ) @ SV760 ) )
= $true )
| ( ( SV501
= ( c_List_Olist_ONil @ SV760 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2165]) ).
thf(2424,plain,
! [SV761: $i,SV503: $i,SV173: $i] :
( ( ( ( c_List_Otake @ SV173 @ SV503 @ SV761 )
!= ( c_List_Olist_ONil @ SV761 ) )
= $true )
| ( ( ( SV503
= ( c_List_Olist_ONil @ SV761 ) )
| ( SV173
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2166]) ).
thf(2425,plain,
! [SV926: $i,SV762: $i,SV176: $i] :
( ( ( ( c_List_Oreplicate @ SV176 @ SV762 @ SV926 )
!= ( c_List_Olist_ONil @ SV926 ) )
= $true )
| ( ( SV176
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2167]) ).
thf(2426,plain,
! [SV927: $i,SV506: $i,SV177: $i] :
( ( ( ( c_List_Olist_ONil @ SV177 )
!= ( c_List_Oreplicate @ SV506 @ SV927 @ SV177 ) )
= $true )
| ( ( SV506
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2168]) ).
thf(2427,plain,
! [SV763: $i,SV510: $i,SV182: $i] :
( ( ( ( hAPP @ SV182 @ SV510 )
= SV763 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV182 @ ( c_Lambda_OdB_OVar @ SV510 ) @ SV763 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2171]) ).
thf(2428,plain,
! [SV928: $i,SV764: $i,SV514: $i,SV186: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV186 @ SV514 @ SV764 ) ) @ ( c_Lambda_Osubst @ SV928 @ SV514 @ SV764 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV186 ) @ SV928 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2175]) ).
thf(2429,plain,
! [SV929: $i,SV766: $i,SV516: $i,SV188: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV188 @ SV516 @ SV766 @ SV929 )
| ! [SY2426: $i] : ( c_ListOrder_Ostep1 @ SV188 @ ( c_List_Oappend @ SV516 @ SY2426 @ SV929 ) @ ( c_List_Oappend @ SV766 @ SY2426 @ SV929 ) @ SV929 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2177]) ).
thf(2430,plain,
! [SV930: $i,SV767: $i,SV517: $i,SV189: $i] :
( ( ! [SY2427: $i] :
( ( c_ListOrder_Ostep1 @ SV189 @ ( c_List_Oappend @ SV517 @ SV767 @ SV930 ) @ ( c_List_Oappend @ SV517 @ SY2427 @ SV930 ) @ SV930 )
| ~ ( c_ListOrder_Ostep1 @ SV189 @ SV767 @ SY2427 @ SV930 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2178]) ).
thf(2431,plain,
! [SV768: $i,SV518: $i,SV190: $i] :
( ( ( c_List_Olistsp @ SV190 @ SV518 @ SV768 )
= $true )
| ( ( ! [SY2312: $i] :
~ ( c_List_Olistsp @ SV190 @ ( c_List_Oappend @ SV518 @ SY2312 @ SV768 ) @ SV768 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2179]) ).
thf(2432,plain,
! [SV769: $i,SV519: $i,SV191: $i] :
( ( ( c_List_Olistsp @ SV191 @ SV519 @ SV769 )
= $true )
| ( ( ! [SY2313: $i] :
~ ( c_List_Olistsp @ SV191 @ ( c_List_Oappend @ SY2313 @ SV519 @ SV769 ) @ SV769 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2180]) ).
thf(2433,plain,
! [SV931: $i,SV770: $i,SV520: $i,SV192: $i] :
( ( ( c_List_Oappend @ ( c_List_Oreplicate @ SV192 @ SV520 @ SV770 ) @ ( c_List_Oreplicate @ SV931 @ SV520 @ SV770 ) @ SV770 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SV931 @ SV520 @ SV770 ) @ ( c_List_Oreplicate @ SV192 @ SV520 @ SV770 ) @ SV770 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2181]) ).
thf(2434,plain,
! [SV932: $i,SV771: $i,SV521: $i,SV193: $i] :
( ( ( c_List_Olistsp @ SV193 @ ( c_List_Oappend @ SV521 @ SV771 @ SV932 ) @ SV932 )
| ~ ( c_List_Olistsp @ SV193 @ SV771 @ SV932 )
| ~ ( c_List_Olistsp @ SV193 @ SV521 @ SV932 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2182]) ).
thf(2435,plain,
! [SV933: $i,SV772: $i,SV522: $i,SV194: $i] :
( ( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV194 ) @ SV522 ) @ SV772 @ SV933 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ SV194 @ SV772 @ SV933 ) ) @ ( c_Lambda_Osubstn @ SV522 @ SV772 @ SV933 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2183]) ).
thf(2436,plain,
! [SV773: $i,SV523: $i,SV195: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV195 ) @ SV523 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV773 ) @ SV523 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV195 ) @ SV773 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2184]) ).
thf(2437,plain,
! [SV774: $i,SV524: $i,SV196: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV196 ) @ SV524 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV196 ) @ SV774 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV524 ) @ SV774 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2185]) ).
thf(2438,plain,
! [SV775: $i,SV525: $i,SV197: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV197 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV525 ) @ SV775 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2186]) ).
thf(2439,plain,
! [SV776: $i,SV526: $i,SV198: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV198 ) @ SV526 )
= ( c_Lambda_OdB_OAbs @ SV776 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2187]) ).
thf(2440,plain,
! [SV528: $i,SV201: $i] :
( ( ( ( c_List_Orev @ SV201 @ SV528 )
= ( c_List_Olist_ONil @ SV528 ) )
= $false )
| ( ( SV201
= ( c_List_Olist_ONil @ SV528 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2189]) ).
thf(2441,plain,
! [SV531: $i,SV205: $i] :
( ( ( ( c_List_Orotate1 @ SV205 @ SV531 )
= ( c_List_Olist_ONil @ SV531 ) )
= $false )
| ( ( SV205
= ( c_List_Olist_ONil @ SV531 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2190]) ).
thf(2442,plain,
! [SV777: $i,SV532: $i,SV206: $i] :
( ( c_ListOrder_Ostep1 @ SV206 @ ( c_List_Olist_ONil @ SV532 ) @ SV777 @ SV532 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2191]) ).
thf(2443,plain,
! [SV778: $i,SV533: $i,SV207: $i] :
( ( c_ListOrder_Ostep1 @ SV207 @ SV533 @ ( c_List_Olist_ONil @ SV778 ) @ SV778 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2192]) ).
thf(2444,plain,
! [SV534: $i,SV208: $i] :
( ( ( ( c_List_Olist_ONil @ SV208 )
= ( c_List_Orev @ SV534 @ SV208 ) )
= $false )
| ( ( SV534
= ( c_List_Olist_ONil @ SV208 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2193]) ).
thf(2445,plain,
! [SV934: $i,SV779: $i,SV535: $i,SV212: $i] :
( ( ( SV212 = SV535 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV779 @ SV535 ) @ SV212 ) )
| ! [SY2428: $i,SY2429: $i] :
~ ( c_ListOrder_Ostep1 @ SV779 @ ( c_List_Olist_OCons @ SV535 @ SV934 @ SY2428 ) @ ( c_List_Olist_OCons @ SV212 @ SY2429 @ SY2428 ) @ SY2428 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2194]) ).
thf(2446,plain,
! [SV935: $i,SV780: $i,SV536: $i,SV213: $i] :
( ( ( SV213 = SV536 )
| ( SV780 = SV935 )
| ! [SY2430: $i,SY2431: $i] :
~ ( c_ListOrder_Ostep1 @ SY2430 @ ( c_List_Olist_OCons @ SV536 @ SV935 @ SY2431 ) @ ( c_List_Olist_OCons @ SV213 @ SV780 @ SY2431 ) @ SY2431 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2195]) ).
thf(2447,plain,
! [SV781: $i,SV537: $i,SV214: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV214 @ SV537 ) @ SV781 ) ) )
= $true )
| ( ( ! [SY2323: $i,SY2324: $i] : ( c_ListOrder_Ostep1 @ SV214 @ ( c_List_Olist_OCons @ SV537 @ SY2323 @ SY2324 ) @ ( c_List_Olist_OCons @ SV781 @ SY2323 @ SY2324 ) @ SY2324 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2196]) ).
thf(2448,plain,
! [SV936: $i,SV782: $i,SV538: $i,SV215: $i] :
( ( ( c_ListOrder_Ostep1 @ SV215 @ SV538 @ SV782 @ SV936 )
| ( SV782 = SV538 )
| ! [SY2432: $i,SY2433: $i] :
~ ( c_ListOrder_Ostep1 @ SV215 @ ( c_List_Olist_OCons @ SY2432 @ SV538 @ SV936 ) @ ( c_List_Olist_OCons @ SY2433 @ SV782 @ SV936 ) @ SV936 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2197]) ).
thf(2449,plain,
! [SV937: $i,SV784: $i,SV540: $i,SV217: $i] :
( ( ( c_ListOrder_Ostep1 @ SV217 @ SV540 @ SV784 @ SV937 )
| ! [SY2434: $i,SY2435: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV217 @ SY2434 ) @ SY2435 ) )
| ~ ( c_ListOrder_Ostep1 @ SV217 @ ( c_List_Olist_OCons @ SY2434 @ SV540 @ SV937 ) @ ( c_List_Olist_OCons @ SY2435 @ SV784 @ SV937 ) @ SV937 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2199]) ).
thf(2450,plain,
! [SV938: $i,SV785: $i,SV541: $i,SV218: $i] :
( ( ! [SY2436: $i] :
( ( c_ListOrder_Ostep1 @ SV218 @ ( c_List_Olist_OCons @ SV541 @ SV785 @ SV938 ) @ ( c_List_Olist_OCons @ SV541 @ SY2436 @ SV938 ) @ SV938 )
| ~ ( c_ListOrder_Ostep1 @ SV218 @ SV785 @ SY2436 @ SV938 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2200]) ).
thf(2451,plain,
! [SV939: $i,SV787: $i,SV543: $i,SV220: $i] :
( ( ! [SY2437: $i] :
( ( ( c_List_Oreplicate @ SV220 @ SV543 @ SV787 )
!= ( c_List_Oreplicate @ SV939 @ SY2437 @ SV787 ) )
| ( SV543 = SY2437 )
| ( SV220
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2202]) ).
thf(2452,plain,
! [SV545: $i,SV225: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV225 ) @ SV545 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV225 ) ) @ ( c_Lambda_OdB_OAbs @ SV545 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2204]) ).
thf(2453,plain,
! [SV940: $i,SV789: $i,SV226: $i] :
( ( ( ( c_List_Olast @ ( c_List_Oreplicate @ SV226 @ SV789 @ SV940 ) @ SV940 )
= SV789 )
= $true )
| ( ( SV226
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2205]) ).
thf(2454,plain,
! [SV546: $i,SV227: $i] :
( ( ( class_Orderings_Oorder @ SV227 )
= $false )
| ( ( ! [SY2075: $i] :
( ( c_HOL_Oord__class_Oless @ SV546 @ SY2075 @ SV227 )
| ! [SY2076: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV546 @ SY2076 @ SV227 )
| ~ ( c_HOL_Oord__class_Oless @ SY2076 @ SY2075 @ SV227 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2206]) ).
thf(2455,plain,
! [SV547: $i,SV228: $i] :
( ( ( class_Orderings_Opreorder @ SV228 )
= $false )
| ( ( ! [SY2077: $i] :
( ( c_HOL_Oord__class_Oless @ SV547 @ SY2077 @ SV228 )
| ! [SY2078: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY2078 @ SY2077 @ SV228 )
| ~ ( c_HOL_Oord__class_Oless @ SV547 @ SY2078 @ SV228 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2207]) ).
thf(2456,plain,
! [SV941: $i,SV790: $i,SV549: $i,SV230: $i] :
( ( ! [SY2438: $i] :
( ( c_List_Oreplicate @ SV230 @ SV549 @ SV790 )
!= ( c_List_Oreplicate @ SV941 @ SY2438 @ SV790 ) )
| ( SV230 = SV941 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2209]) ).
thf(2457,plain,
! [SV942: $i,SV792: $i,SV236: $i] :
( ( ( ( c_List_Ohd @ ( c_List_Oreplicate @ SV236 @ SV792 @ SV942 ) @ SV942 )
= SV792 )
= $true )
| ( ( SV236
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2212]) ).
thf(2458,plain,
! [SV793: $i,SV555: $i,SV237: $i] :
( ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV237 ) @ SV555 @ SV793 )
= ( c_Lambda_OdB_OVar @ SV237 ) )
= $true )
| ( ( ( SV237 = SV793 )
| ( c_HOL_Oord__class_Oless @ SV793 @ SV237 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2213]) ).
thf(2459,plain,
! [SV556: $i,SV238: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV238 )
= ( c_Lambda_OdB_OAbs @ SV556 ) )
= $false )
| ( ( SV238 = SV556 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2214]) ).
thf(2460,plain,
! [SV241: $i,SV943: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV943 @ SV943 @ SV241 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV241 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2215]) ).
thf(2461,plain,
! [SV242: $i,SV944: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV944 @ SV944 @ SV242 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV242 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2216]) ).
thf(2462,plain,
! [SV243: $i,SV945: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV945 @ SV945 @ SV243 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV243 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2217]) ).
thf(2463,plain,
! [SV244: $i,SV946: $i] :
( ( ( ! [SY2439: $i] :
( ( c_HOL_Oord__class_Oless @ SV946 @ SY2439 @ SV244 )
| ( SY2439 = SV946 )
| ( c_HOL_Oord__class_Oless @ SY2439 @ SV946 @ SV244 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV244 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2218]) ).
thf(2464,plain,
! [SV245: $i,SV947: $i] :
( ( ( ! [SY2440: $i] :
( ( SV947 = SY2440 )
| ( c_HOL_Oord__class_Oless @ SY2440 @ SV947 @ SV245 )
| ( c_HOL_Oord__class_Oless @ SV947 @ SY2440 @ SV245 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV245 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2219]) ).
thf(2465,plain,
! [SV246: $i,SV557: $i] :
( ( ( SV557 = SV246 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV557 @ SV246 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV246 @ SV557 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2220]) ).
thf(2466,plain,
! [SV794: $i,SV558: $i,SV247: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV247 @ SV558 ) @ SV794 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV558 @ SV794 @ tc_nat )
| ( SV794 = SV558 )
| ( c_HOL_Oord__class_Oless @ SV794 @ SV558 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2221]) ).
thf(2467,plain,
! [SV248: $i,SV559: $i] :
( ( ( SV559 = SV248 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV559 @ SV248 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV248 @ SV559 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2222]) ).
thf(2468,plain,
! [SV249: $i,SV948: $i] :
( ( ( ! [SY2441: $i] :
( ( c_HOL_Oord__class_Oless @ SV948 @ SY2441 @ SV249 )
| ( SY2441 = SV948 )
| ( c_HOL_Oord__class_Oless @ SY2441 @ SV948 @ SV249 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV249 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2223]) ).
thf(2469,plain,
! [SV250: $i,SV949: $i] :
( ( ( ! [SY2442: $i] :
( ( c_HOL_Oord__class_Oless @ SV949 @ SY2442 @ SV250 )
| ( SY2442 = SV949 )
| ( c_HOL_Oord__class_Oless @ SY2442 @ SV949 @ SV250 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV250 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2224]) ).
thf(2470,plain,
! [SV251: $i,SV950: $i] :
( ( ( ! [SY2443: $i] :
( ( SV950 = SY2443 )
| ( c_HOL_Oord__class_Oless @ SV950 @ SY2443 @ SV251 )
| ( c_HOL_Oord__class_Oless @ SY2443 @ SV950 @ SV251 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV251 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2225]) ).
thf(2471,plain,
! [SV795: $i,SV560: $i,SV252: $i] :
( ( ( ( c_List_Orev @ SV252 @ SV560 )
!= ( c_List_Orev @ SV795 @ SV560 ) )
= $true )
| ( ( SV252 = SV795 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2226]) ).
thf(2472,plain,
! [SV796: $i,SV561: $i,SV253: $i] :
( ( ( c_Type_Otyping @ SV253 @ SV561 @ SV796 )
= $true )
| ( ( ! [SY2339: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY2339 ) @ SV561 ) )
| ~ ( c_Type_Otyping @ SV253 @ SY2339 @ SV796 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2227]) ).
thf(2473,plain,
! [SV254: $i,SV951: $i] :
( ( ( ! [SY2444: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV951 @ SY2444 @ SV254 )
| ~ ( c_HOL_Oord__class_Oless @ SY2444 @ SV951 @ SV254 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV254 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2228]) ).
thf(2474,plain,
! [SV255: $i,SV952: $i] :
( ( ( ! [SY2445: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV952 @ SY2445 @ SV255 )
| ~ ( c_HOL_Oord__class_Oless @ SY2445 @ SV952 @ SV255 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV255 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2229]) ).
thf(2475,plain,
! [SV256: $i,SV953: $i] :
( ( ( ! [SY2446: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV953 @ SY2446 @ SV256 )
| ~ ( c_HOL_Oord__class_Oless @ SY2446 @ SV953 @ SV256 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV256 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2230]) ).
thf(2476,plain,
! [SV257: $i,SV954: $i] :
( ( ( ! [SY2447: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV954 @ SY2447 @ SV257 )
| ~ ( c_HOL_Oord__class_Oless @ SY2447 @ SV954 @ SV257 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV257 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2231]) ).
thf(2477,plain,
! [SV797: $i,SV562: $i,SV258: $i] :
( ( ( ( c_List_Otl @ ( c_List_Oappend @ SV258 @ SV562 @ SV797 ) @ SV797 )
= ( c_List_Oappend @ ( c_List_Otl @ SV258 @ SV797 ) @ SV562 @ SV797 ) )
= $true )
| ( ( SV258
= ( c_List_Olist_ONil @ SV797 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2232]) ).
thf(2478,plain,
! [SV798: $i,SV564: $i,SV260: $i] :
( ( ( ( c_List_Ohd @ ( c_List_Oappend @ SV260 @ SV564 @ SV798 ) @ SV798 )
= ( c_List_Ohd @ SV260 @ SV798 ) )
= $true )
| ( ( SV260
= ( c_List_Olist_ONil @ SV798 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2233]) ).
thf(2479,plain,
! [SV799: $i,SV566: $i,SV264: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV264 @ SV566 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV799 ) )
= $true )
| ( ( SV264
= ( c_Lambda_OdB_OAbs @ SV799 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2234]) ).
thf(2480,plain,
! [SV800: $i,SV567: $i,SV265: $i] :
( ( ( ! [SY2340: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV265 ) @ SV567 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV800 ) @ SY2340 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( SV265 = SV800 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2235]) ).
thf(2481,plain,
! [SV955: $i,SV801: $i,SV568: $i,SV266: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV266 ) @ SV568 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV801 ) @ SV955 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV568 = SV955 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2236]) ).
thf(2482,plain,
! [SV802: $i,SV569: $i,SV267: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV267 @ SV569 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV802 @ SV569 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV267 ) @ SV802 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2237]) ).
thf(2483,plain,
! [SV956: $i,SV570: $i,SV268: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV268 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV570 @ SV956 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_Lambda_OdB_OAbs @ SV268 )
= SV570 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2238]) ).
thf(2484,plain,
! [SV803: $i,SV571: $i,SV269: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV269 ) @ SV571 @ SV803 )
= ( c_Lambda_OdB_OVar @ SV269 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV269 @ SV803 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2239]) ).
thf(2485,plain,
! [SV804: $i,SV572: $i,SV270: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV270 ) @ SV572 @ SV804 )
= ( c_Lambda_OdB_OVar @ SV270 ) )
= $true )
| ( ( ( SV270 = SV804 )
| ( c_HOL_Oord__class_Oless @ SV804 @ SV270 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2240]) ).
thf(2486,plain,
! [SV957: $i,SV807: $i,SV574: $i,SV273: $i] :
( ( ! [SY2448: $i] :
( ( ( c_List_Olist_OCons @ SV273 @ SV574 @ SV807 )
!= ( c_List_Oappend @ SV957 @ SY2448 @ SV807 ) )
| ( SV574
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV273 @ SV574 @ SV957 @ SY2448 @ SV807 ) @ SY2448 @ SV807 ) )
| ( SV957
= ( c_List_Olist_ONil @ SV807 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2243]) ).
thf(2487,plain,
! [SV958: $i,SV808: $i,SV575: $i,SV274: $i] :
( ( ! [SY2449: $i] :
( ( ( c_List_Oappend @ SV274 @ SV575 @ SV808 )
!= ( c_List_Olist_OCons @ SV958 @ SY2449 @ SV808 ) )
| ( SV274
= ( c_List_Olist_OCons @ SV958 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV958 @ SY2449 @ SV274 @ SV575 @ SV808 ) @ SV808 ) )
| ( SV274
= ( c_List_Olist_ONil @ SV808 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2244]) ).
thf(2488,plain,
! [SV959: $i,SV811: $i,SV578: $i,SV277: $i] :
( ( ( SV277 = SV578 )
| ( SV811 = SV959 )
| ! [SY2450: $i,SY2451: $i] :
~ ( c_ListOrder_Ostep1 @ SY2450 @ ( c_List_Oappend @ SV277 @ ( c_List_Olist_OCons @ SV811 @ ( c_List_Olist_ONil @ SY2451 ) @ SY2451 ) @ SY2451 ) @ ( c_List_Oappend @ SV578 @ ( c_List_Olist_OCons @ SV959 @ ( c_List_Olist_ONil @ SY2451 ) @ SY2451 ) @ SY2451 ) @ SY2451 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2247]) ).
thf(2489,plain,
! [SV960: $i,SV812: $i,SV579: $i,SV278: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV278 @ SV579 ) @ SV812 ) )
| ( SV579 = SV812 )
| ! [SY2452: $i,SY2453: $i] :
~ ( c_ListOrder_Ostep1 @ SV278 @ ( c_List_Oappend @ SV960 @ ( c_List_Olist_OCons @ SV579 @ ( c_List_Olist_ONil @ SY2452 ) @ SY2452 ) @ SY2452 ) @ ( c_List_Oappend @ SY2453 @ ( c_List_Olist_OCons @ SV812 @ ( c_List_Olist_ONil @ SY2452 ) @ SY2452 ) @ SY2452 ) @ SY2452 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2248]) ).
thf(2490,plain,
! [SV961: $i,SV813: $i,SV580: $i,SV279: $i] :
( ( ! [SY2454: $i] :
( ( ( c_List_Oappend @ SV279 @ SV580 @ SV813 )
!= ( c_List_Olist_OCons @ SV961 @ SY2454 @ SV813 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV961 @ SY2454 @ SV279 @ SV580 @ SV813 ) @ SV580 @ SV813 )
= SY2454 )
| ( SV279
= ( c_List_Olist_ONil @ SV813 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2249]) ).
thf(2491,plain,
! [SV962: $i,SV814: $i,SV581: $i,SV280: $i] :
( ( ! [SY2455: $i] :
( ( ( c_List_Olist_OCons @ SV280 @ SV581 @ SV814 )
!= ( c_List_Oappend @ SV962 @ SY2455 @ SV814 ) )
| ( ( c_List_Olist_OCons @ SV280 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV280 @ SV581 @ SV962 @ SY2455 @ SV814 ) @ SV814 )
= SV962 )
| ( SV962
= ( c_List_Olist_ONil @ SV814 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2250]) ).
thf(2492,plain,
! [SV963: $i,SV816: $i,SV583: $i,SV282: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV282 @ SV583 ) @ SV816 ) )
| ! [SY2456: $i,SY2457: $i] :
( ( c_ListOrder_Ostep1 @ SV282 @ SV963 @ SY2456 @ SY2457 )
| ~ ( c_ListOrder_Ostep1 @ SV282 @ ( c_List_Oappend @ SV963 @ ( c_List_Olist_OCons @ SV583 @ ( c_List_Olist_ONil @ SY2457 ) @ SY2457 ) @ SY2457 ) @ ( c_List_Oappend @ SY2456 @ ( c_List_Olist_OCons @ SV816 @ ( c_List_Olist_ONil @ SY2457 ) @ SY2457 ) @ SY2457 ) @ SY2457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2252]) ).
thf(2493,plain,
! [SV964: $i,SV817: $i,SV584: $i,SV283: $i] :
( ( ( ( c_List_Orev @ SV283 @ SV584 )
!= ( c_List_Olist_OCons @ SV817 @ SV964 @ SV584 ) )
| ( SV283
= ( c_List_Oappend @ ( c_List_Orev @ SV964 @ SV584 ) @ ( c_List_Olist_OCons @ SV817 @ ( c_List_Olist_ONil @ SV584 ) @ SV584 ) @ SV584 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2253]) ).
thf(2494,plain,
! [SV965: $i,SV820: $i,SV587: $i,SV286: $i] :
( ( ( SV286 = SV587 )
| ( c_ListOrder_Ostep1 @ SV820 @ SV286 @ SV587 @ SV965 )
| ! [SY2458: $i,SY2459: $i] :
~ ( c_ListOrder_Ostep1 @ SV820 @ ( c_List_Oappend @ SV286 @ ( c_List_Olist_OCons @ SY2458 @ ( c_List_Olist_ONil @ SV965 ) @ SV965 ) @ SV965 ) @ ( c_List_Oappend @ SV587 @ ( c_List_Olist_OCons @ SY2459 @ ( c_List_Olist_ONil @ SV965 ) @ SV965 ) @ SV965 ) @ SV965 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2256]) ).
thf(2495,plain,
! [SV822: $i,SV589: $i,SV288: $i] :
( ( ( SV288 = SV589 )
= $true )
| ( ( ! [SY2363: $i,SY2364: $i] :
( ~ ( c_Type_Otyping @ SV822 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2363 ) @ SY2364 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV589 )
| ~ ( c_Type_Otyping @ SV822 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2363 ) @ SY2364 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV288 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2258]) ).
thf(2496,plain,
! [SV966: $i,SV823: $i,SV590: $i,SV289: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV289 ) @ SV590 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV823 ) @ SV966 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2259]) ).
thf(2497,plain,
! [SV967: $i,SV824: $i,SV591: $i,SV290: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV290 ) ) @ SV591 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV824 ) @ SV967 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2260]) ).
thf(2498,plain,
! [SV825: $i,SV592: $i,SV291: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV291 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV592 @ SV825 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV825
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2261]) ).
thf(2499,plain,
! [SV968: $i,SV826: $i,SV593: $i,SV293: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV293 ) @ SV593 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV826 @ SV968 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV293
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV826 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV293 @ SV593 @ SV826 @ SV968 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV968
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2262]) ).
thf(2500,plain,
! [SV969: $i,SV594: $i,SV294: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV294 @ SV594 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV969 ) )
= $true )
| ( ( SV594
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2263]) ).
thf(2501,plain,
! [SV296: $i,SV595: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ SV595 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV296 ) @ SV595 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2264]) ).
thf(2502,plain,
! [SV827: $i,SV596: $i,SV297: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV297 ) ) @ SV596 ) @ SV827 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV596 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV297 @ SV596 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV827 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2265]) ).
thf(2503,plain,
! [SV970: $i,SV828: $i,SV597: $i,SV298: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV298 ) @ SV597 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV828 @ SV970 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV970
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV298 @ SV597 @ SV828 @ SV970 ) @ ( c_List_Olist_OCons @ SV597 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( SV970
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2266]) ).
thf(2504,plain,
! [SV971: $i,SV829: $i,SV598: $i,SV299: $i] :
( ( ( c_List_Oappend @ SV299 @ ( c_List_Oappend @ SV598 @ SV829 @ SV971 ) @ SV971 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV299 @ SV598 @ SV971 ) @ SV829 @ SV971 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2267]) ).
thf(2505,plain,
! [SV972: $i,SV830: $i,SV599: $i,SV300: $i] :
( ( ( c_List_Oappend @ ( c_List_Oappend @ SV300 @ SV599 @ SV830 ) @ SV972 @ SV830 )
= ( c_List_Oappend @ SV300 @ ( c_List_Oappend @ SV599 @ SV972 @ SV830 ) @ SV830 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2268]) ).
thf(2506,plain,
! [SV973: $i,SV831: $i,SV600: $i,SV301: $i] :
( ( ( c_List_Oappend @ SV301 @ ( c_List_Oappend @ SV600 @ SV831 @ SV973 ) @ SV973 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV301 @ SV600 @ SV973 ) @ SV831 @ SV973 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2269]) ).
thf(2507,plain,
! [SV974: $i,SV832: $i,SV601: $i,SV302: $i] :
( ( ( c_List_Oappend @ ( c_List_Oappend @ SV302 @ SV601 @ SV832 ) @ SV974 @ SV832 )
= ( c_List_Oappend @ SV302 @ ( c_List_Oappend @ SV601 @ SV974 @ SV832 ) @ SV832 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2270]) ).
thf(2508,plain,
! [SV602: $i,SV303: $i,SV975: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV975 @ SV303 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV602 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV975 @ ( c_List_Oappend @ SV303 @ ( c_List_Olist_OCons @ SV602 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_List_Oappend @ SV303 @ ( c_List_Olist_OCons @ SV602 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2271]) ).
thf(2509,plain,
! [SV976: $i,SV833: $i,SV604: $i,SV306: $i] :
( ( ! [SY2460: $i] :
( ( ( c_List_Oappend @ SV306 @ ( c_List_Olist_OCons @ SV604 @ ( c_List_Olist_ONil @ SV833 ) @ SV833 ) @ SV833 )
!= ( c_List_Oappend @ SV976 @ ( c_List_Olist_OCons @ SY2460 @ ( c_List_Olist_ONil @ SV833 ) @ SV833 ) @ SV833 ) )
| ( SV604 = SY2460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2272]) ).
thf(2510,plain,
! [SV977: $i,SV834: $i,SV605: $i,SV307: $i] :
( ( ! [SY2461: $i] :
( ( c_List_Oappend @ SV307 @ ( c_List_Olist_OCons @ SV605 @ ( c_List_Olist_ONil @ SV834 ) @ SV834 ) @ SV834 )
!= ( c_List_Oappend @ SV977 @ ( c_List_Olist_OCons @ SY2461 @ ( c_List_Olist_ONil @ SV834 ) @ SV834 ) @ SV834 ) )
| ( SV307 = SV977 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2273]) ).
thf(2511,plain,
! [SV978: $i,SV835: $i,SV606: $i,SV308: $i] :
( ( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV308 ) @ SV606 ) @ SV835 @ SV978 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV308 @ SV835 @ SV978 ) ) @ ( c_Lambda_Osubst @ SV606 @ SV835 @ SV978 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2274]) ).
thf(2512,plain,
! [SV607: $i,SV309: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV309 )
= ( c_Lambda_OdB_OVar @ SV607 ) )
= $false )
| ( ( SV309 = SV607 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2275]) ).
thf(2513,plain,
! [SV837: $i,SV609: $i,SV311: $i] :
( ( ( ! [SY2378: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV311 ) @ SV609 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV837 ) @ SY2378 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( SV311 = SV837 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2277]) ).
thf(2514,plain,
! [SV979: $i,SV838: $i,SV610: $i,SV312: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV312 ) @ SV610 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV838 ) @ SV979 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV610 = SV979 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2278]) ).
thf(2515,plain,
! [SV980: $i,SV839: $i,SV611: $i,SV313: $i] :
( ( ! [SY2462: $i] :
( ( ( c_List_Olist_OCons @ SV313 @ SV611 @ SV839 )
!= ( c_List_Olist_OCons @ SV980 @ SY2462 @ SV839 ) )
| ( SV611 = SY2462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2279]) ).
thf(2516,plain,
! [SV981: $i,SV840: $i,SV612: $i,SV314: $i] :
( ( ! [SY2463: $i] :
( ( c_List_Olist_OCons @ SV314 @ SV612 @ SV840 )
!= ( c_List_Olist_OCons @ SV981 @ SY2463 @ SV840 ) )
| ( SV314 = SV981 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2280]) ).
thf(2517,plain,
! [SV842: $i,SV615: $i,SV317: $i] :
( ( ( SV317
!= ( c_List_Oappend @ SV615 @ SV317 @ SV842 ) )
= $true )
| ( ( SV615
= ( c_List_Olist_ONil @ SV842 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2282]) ).
thf(2518,plain,
! [SV843: $i,SV616: $i,SV318: $i] :
( ( ( ( c_List_Oappend @ SV318 @ SV616 @ SV843 )
!= SV616 )
= $true )
| ( ( SV318
= ( c_List_Olist_ONil @ SV843 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2283]) ).
thf(2519,plain,
! [SV844: $i,SV617: $i,SV319: $i] :
( ( ( SV319
!= ( c_List_Oappend @ SV319 @ SV617 @ SV844 ) )
= $true )
| ( ( SV617
= ( c_List_Olist_ONil @ SV844 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2284]) ).
thf(2520,plain,
! [SV845: $i,SV618: $i,SV320: $i] :
( ( ( ( c_List_Oappend @ SV320 @ SV618 @ SV845 )
!= SV320 )
= $true )
| ( ( SV618
= ( c_List_Olist_ONil @ SV845 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2285]) ).
thf(2521,plain,
! [SV982: $i,SV846: $i,SV321: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV321 @ ( c_Lambda_OdB_OVar @ SV846 ) @ SV982 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV321 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2286]) ).
thf(2522,plain,
! [SV847: $i,SV619: $i,SV322: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV322 ) @ SV619 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV847 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV322 ) @ SV619 )
= SV847 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2287]) ).
thf(2523,plain,
! [SV848: $i,SV620: $i,SV323: $i] :
( ( ( c_List_Olist_ONil @ SV323 )
= ( c_List_Olist_OCons @ SV620 @ SV848 @ SV323 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2288]) ).
thf(2524,plain,
! [SV849: $i,SV621: $i,SV324: $i] :
( ( ( ! [SY2385: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV324 ) @ SV621 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV849 ) @ SY2385 ) ) )
= $true )
| ( ( SV324 = SV849 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2289]) ).
thf(2525,plain,
! [SV983: $i,SV850: $i,SV622: $i,SV325: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV325 ) @ SV622 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV850 ) @ SV983 ) )
| ( SV622 = SV983 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2290]) ).
thf(2526,plain,
! [SV984: $i,SV623: $i,SV326: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV326 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV623 @ SV984 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_Lambda_OdB_OVar @ SV326 )
= SV623 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2291]) ).
thf(2527,plain,
! [SV851: $i,SV624: $i,SV327: $i] :
( ( ( c_Lambda_OdB_OVar @ SV327 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV624 ) @ SV851 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2292]) ).
thf(2528,plain,
! [SV852: $i,SV625: $i,SV328: $i] :
( ( ( ( c_List_Oappend @ SV328 @ SV625 @ SV852 )
!= ( c_List_Olist_ONil @ SV852 ) )
= $true )
| ( ( SV625
= ( c_List_Olist_ONil @ SV852 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2293]) ).
thf(2529,plain,
! [SV853: $i,SV626: $i,SV329: $i] :
( ( ( ( c_List_Oappend @ SV329 @ SV626 @ SV853 )
!= ( c_List_Olist_ONil @ SV853 ) )
= $true )
| ( ( SV329
= ( c_List_Olist_ONil @ SV853 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2294]) ).
thf(2530,plain,
! [SV854: $i,SV627: $i,SV330: $i] :
( ( ( SV330
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV330 ) @ SV627 ) @ SV854 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV330 ) @ SV627 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV330 ) @ SV627 ) @ ( c_List_Oappend @ SV854 @ ( c_List_Olist_OCons @ SV627 @ ( 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)],[2295]) ).
thf(2531,plain,
! [SV855: $i,SV628: $i,SV331: $i] :
( ( ( ( c_List_Olist_ONil @ SV331 )
!= ( c_List_Oappend @ SV628 @ SV855 @ SV331 ) )
= $true )
| ( ( SV855
= ( c_List_Olist_ONil @ SV331 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2296]) ).
thf(2532,plain,
! [SV985: $i,SV629: $i,SV332: $i] :
( ( ( ( c_List_Olist_ONil @ SV332 )
!= ( c_List_Oappend @ SV629 @ SV985 @ SV332 ) )
= $true )
| ( ( SV629
= ( c_List_Olist_ONil @ SV332 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2297]) ).
thf(2533,plain,
! [SV986: $i,SV856: $i,SV630: $i,SV333: $i] :
( ( ( c_List_Ofoldl @ SV333 @ SV630 @ ( c_List_Olist_ONil @ SV856 ) @ SV986 @ SV856 )
= SV630 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2298]) ).
thf(2534,plain,
! [SV987: $i,SV857: $i,SV636: $i,SV340: $i] :
( ( ( ( c_List_Oappend @ SV340 @ SV636 @ SV857 )
!= ( c_List_Oappend @ SV340 @ SV987 @ SV857 ) )
| ( SV636 = SV987 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2299]) ).
thf(2535,plain,
! [SV988: $i,SV858: $i,SV637: $i,SV341: $i] :
( ( ( ( c_List_Oappend @ SV341 @ SV637 @ SV858 )
!= ( c_List_Oappend @ SV988 @ SV637 @ SV858 ) )
| ( SV341 = SV988 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2300]) ).
thf(2536,plain,
! [SV989: $i,SV859: $i,SV638: $i,SV343: $i] :
( ( ! [SY2464: $i,SY2465: $i] :
( ( c_List_Ofoldl @ SV343 @ SV638 @ ( c_List_Olist_OCons @ SV859 @ SV989 @ SY2464 ) @ SY2465 @ SY2464 )
= ( c_List_Ofoldl @ SV343 @ ( hAPP @ ( hAPP @ SV343 @ SV638 ) @ SV859 ) @ SV989 @ SY2465 @ SY2464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2301]) ).
thf(2537,plain,
! [SV990: $i,SV860: $i,SV639: $i,SV344: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV344 @ SV639 @ SV860 ) @ SV990 @ SV860 )
= ( c_List_Olist_OCons @ SV344 @ ( c_List_Oappend @ SV639 @ SV990 @ SV860 ) @ SV860 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2302]) ).
thf(2538,plain,
! [SV991: $i,SV861: $i,SV640: $i,SV345: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV345 @ SV640 @ SV861 ) @ SV991 @ SV861 )
= ( c_List_Olist_OCons @ SV345 @ ( c_List_Oappend @ SV640 @ SV991 @ SV861 ) @ SV861 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2303]) ).
thf(2539,plain,
! [SV992: $i,SV862: $i,SV641: $i,SV346: $i] :
( ( ( c_List_Olist_OCons @ SV346 @ ( c_List_Oappend @ SV641 @ SV862 @ SV992 ) @ SV992 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV346 @ SV641 @ SV992 ) @ SV862 @ SV992 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2304]) ).
thf(2540,plain,
! [SV993: $i,SV863: $i,SV642: $i,SV347: $i] :
( ( ( c_List_Olist_OCons @ SV347 @ ( c_List_Oappend @ SV642 @ SV863 @ SV993 ) @ SV993 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV347 @ SV642 @ SV993 ) @ SV863 @ SV993 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2305]) ).
thf(2541,plain,
! [SV864: $i,SV643: $i,SV348: $i] :
( ( ( c_List_Olist_OCons @ SV348 @ SV643 @ SV864 )
= ( c_List_Olist_ONil @ SV864 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2306]) ).
thf(2542,plain,
! [SV865: $i,SV644: $i,SV349: $i] :
( ( ( c_List_Olist_OCons @ SV349 @ SV644 @ SV865 )
= ( c_List_Olist_ONil @ SV865 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2307]) ).
thf(2543,plain,
! [SV866: $i,SV645: $i,SV350: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV350 @ SV645 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV866 @ SV645 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV350 = SV866 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2308]) ).
thf(2544,plain,
! [SV867: $i,SV646: $i,SV351: $i] :
( ( ( c_List_Olist_OCons @ SV351 @ SV646 @ SV867 )
= SV646 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2309]) ).
thf(2545,plain,
! [SV868: $i,SV647: $i,SV352: $i] :
( ( SV352
= ( c_List_Olist_OCons @ SV647 @ SV352 @ SV868 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2310]) ).
thf(2546,plain,
! [SV869: $i,SV648: $i,SV353: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV353 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV648 @ SV869 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV869
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2311]) ).
thf(2547,plain,
! [SV994: $i,SV871: $i,SV650: $i,SV356: $i] :
( ( ! [SY2466: $i,SY2467: $i] :
( ( c_List_Ofoldl @ SV356 @ SV650 @ ( c_List_Oappend @ SV871 @ SV994 @ SY2466 ) @ SY2467 @ SY2466 )
= ( c_List_Ofoldl @ SV356 @ ( c_List_Ofoldl @ SV356 @ SV650 @ SV871 @ SY2467 @ SY2466 ) @ SV994 @ SY2467 @ SY2466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2313]) ).
thf(2548,plain,
! [SV872: $i,SV651: $i,SV357: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV357 ) @ SV651 )
= ( c_Lambda_OdB_OVar @ SV872 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2314]) ).
thf(2549,plain,
! [SV358: $i,SV652: $i] :
( ( ( class_Orderings_Opreorder @ SV652 )
= $false )
| ( ( class_Orderings_Opreorder @ ( tc_fun @ SV358 @ SV652 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2315]) ).
thf(2550,plain,
! [SV359: $i,SV653: $i] :
( ( ( class_Orderings_Oorder @ SV653 )
= $false )
| ( ( class_Orderings_Oorder @ ( tc_fun @ SV359 @ SV653 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2316]) ).
thf(2551,plain,
! [SV655: $i,SV361: $i,SV995: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV995 ) @ SV361 ) @ SV655 ) ) )
= $true )
| ( ( SV361 = SV655 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2317]) ).
thf(2552,plain,
! [SV996: $i,SV873: $i,SV656: $i,SV362: $i,SV1: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV1 @ ( c_List_Olist_OCons @ SV362 @ SV656 @ SV873 ) @ SV873 ) @ ( c_Nat_Osize__class_Osize @ SV1 @ ( tc_List_Olist @ SV873 ) ) @ SV996 @ SV873 )
= ( c_List_Oappend @ SV1 @ ( c_List_Olist_OCons @ SV996 @ SV656 @ SV873 ) @ SV873 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2318]) ).
thf(2553,plain,
! [SV874: $i,SV657: $i,SV363: $i,SV2: $i] :
( ( ( ( c_List_Olist__update @ SV2 @ SV363 @ SV657 @ SV874 )
!= ( c_List_Olist_ONil @ SV874 ) )
= $true )
| ( ( SV2
= ( c_List_Olist_ONil @ SV874 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2319]) ).
thf(2554,plain,
! [SV875: $i,SV661: $i,SV367: $i,SV6: $i] :
( ( ( ( c_List_Olist__update @ SV6 @ SV367 @ SV661 @ SV875 )
!= SV6 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV367 @ ( c_Nat_Osize__class_Osize @ SV6 @ ( tc_List_Olist @ SV875 ) ) @ tc_nat )
| ( ( c_List_Onth @ SV6 @ SV367 @ SV875 )
= SV661 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2320]) ).
thf(2555,plain,
! [SV997: $i,SV877: $i,SV663: $i,SV369: $i,SV8: $i] :
( ( ( ( c_List_Onth @ ( c_List_Olist__update @ SV8 @ SV369 @ SV663 @ SV877 ) @ SV997 @ SV877 )
= ( c_List_Onth @ SV8 @ SV997 @ SV877 ) )
| ( SV369 = SV997 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2322]) ).
thf(2556,plain,
! [SV664: $i,SV370: $i,SV9: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV9 @ ( c_Nat_Osize__class_Osize @ SV370 @ ( tc_List_Olist @ SV664 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Olist__update @ SV370 @ SV9 @ ( c_List_Onth @ SV370 @ SV9 @ SV664 ) @ SV664 )
= SV370 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2323]) ).
thf(2557,plain,
! [SV665: $i,SV371: $i,SV10: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV10 @ ( c_Nat_Osize__class_Osize @ SV371 @ ( tc_List_Olist @ SV665 ) ) @ tc_nat )
= $false )
| ( ( ! [SY2234: $i] :
( ( c_List_Onth @ ( c_List_Olist__update @ SV371 @ SV10 @ SY2234 @ SV665 ) @ SV10 @ SV665 )
= SY2234 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2324]) ).
thf(2558,plain,
! [SV878: $i,SV666: $i,SV372: $i,SV11: $i] :
( ( ( ( c_List_Onth @ ( c_List_Olist__update @ SV11 @ SV372 @ SV666 @ SV878 ) @ SV372 @ SV878 )
= SV666 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV372 @ ( c_Nat_Osize__class_Osize @ SV11 @ ( tc_List_Olist @ SV878 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2325]) ).
thf(2559,plain,
! [SV879: $i,SV667: $i,SV373: $i,SV12: $i] :
( ( ( ! [SY2402: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV12 @ SV373 @ SV667 ) @ SV879 @ SY2402 @ SV667 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV12 @ SV879 @ SY2402 @ SV667 ) @ SV373 @ SV667 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV879 @ ( c_Nat_Osize__class_Osize @ SV12 @ ( tc_List_Olist @ SV667 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2326]) ).
thf(2560,plain,
! [SV880: $i,SV668: $i,SV374: $i,SV13: $i] :
( ( ( ! [SY2403: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV13 @ SV374 @ SV668 ) @ SV880 @ SY2403 @ SV668 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV13 @ SV880 @ SY2403 @ SV668 ) @ SV374 @ SV668 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV880 @ ( c_Nat_Osize__class_Osize @ SV13 @ ( tc_List_Olist @ SV668 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2327]) ).
thf(2561,plain,
! [SV998: $i,SV881: $i,SV670: $i,SV376: $i,SV15: $i] :
( ( ! [SY2468: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV15 @ SV376 @ SV670 @ SV881 ) @ SV998 @ SY2468 @ SV881 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV15 @ SV998 @ SY2468 @ SV881 ) @ SV376 @ SV670 @ SV881 ) )
| ( SV376 = SV998 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2328]) ).
thf(2562,plain,
! [SV999: $i,SV882: $i,SV671: $i,SV377: $i,SV16: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV16 @ SV377 @ SV671 ) @ ( c_Suc @ SV882 ) @ SV999 @ SV671 )
= ( c_List_Olist_OCons @ SV16 @ ( c_List_Olist__update @ SV377 @ SV882 @ SV999 @ SV671 ) @ SV671 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2329]) ).
thf(2563,plain,
! [SV1000: $i,SV883: $i,SV672: $i,SV378: $i,SV17: $i] :
( ( ( ( c_List_Onth @ ( c_List_Olist__update @ SV17 @ SV378 @ SV672 @ SV883 ) @ SV1000 @ SV883 )
= ( c_List_Onth @ SV17 @ SV1000 @ SV883 ) )
| ( SV378 = SV1000 )
| ~ ( c_HOL_Oord__class_Oless @ SV378 @ ( c_Nat_Osize__class_Osize @ SV17 @ ( tc_List_Olist @ SV883 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2330]) ).
thf(2564,plain,
! [SV1001: $i,SV884: $i,SV673: $i,SV379: $i,SV18: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ SV18 @ SV379 @ SV673 @ SV884 ) @ SV379 @ SV1001 @ SV884 )
= ( c_List_Olist__update @ SV18 @ SV379 @ SV1001 @ SV884 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2331]) ).
thf(2565,plain,
! [SV675: $i,SV381: $i,SV20: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV20 @ ( c_Nat_Osize__class_Osize @ SV381 @ ( tc_List_Olist @ SV675 ) ) @ tc_nat ) )
= $true )
| ( ( SV381
= ( c_List_Olist_ONil @ SV675 ) )
= $true )
| ( ( ( c_List_Ohd @ ( c_List_Odrop @ SV20 @ SV381 @ SV675 ) @ SV675 )
= ( c_List_Onth @ SV381 @ SV20 @ SV675 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2333]) ).
thf(2566,plain,
! [SV676: $i,SV21: $i,SV382: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV382 @ ( c_Nat_Osize__class_Osize @ SV21 @ ( tc_List_Olist @ SV676 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Olist_OCons @ ( c_List_Onth @ SV21 @ SV382 @ SV676 ) @ ( c_List_Odrop @ ( c_Suc @ SV382 ) @ SV21 @ SV676 ) @ SV676 )
= ( c_List_Odrop @ SV382 @ SV21 @ SV676 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2334]) ).
thf(2567,plain,
! [SV886: $i,SV679: $i,SV385: $i,SV24: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SV385 ) ) @ SV679 @ SV385 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV679 @ ( tc_List_Olist @ SV385 ) ) @ SV24 @ SV385 ) @ SV886 @ SV385 ) @ SV385 )
!= SV886 )
= $true )
| ( ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SV385 ) ) @ SV679 @ SV385 )
!= SV24 )
| ( SV679
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV679 @ ( tc_List_Olist @ SV385 ) ) @ SV24 @ SV385 ) )
| ( ( c_List_Oappend @ SV679 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV679 @ ( tc_List_Olist @ SV385 ) ) @ SV24 @ SV385 ) @ SV886 @ SV385 ) @ SV385 )
= ( c_List_Oappend @ SV24 @ SV886 @ SV385 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2335]) ).
thf(2568,plain,
! [SV887: $i,SV680: $i,SV386: $i,SV25: $i] :
( ( ( ! [SY2409: $i] :
( ( c_List_Odrop @ SV25 @ SV386 @ SV680 )
!= ( c_List_Olist_OCons @ SV887 @ SY2409 @ SV680 ) ) )
= $true )
| ( ( ( c_List_Onth @ SV386 @ SV25 @ SV680 )
= SV887 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2336]) ).
thf(2569,plain,
! [SV888: $i,SV681: $i,SV387: $i,SV26: $i] :
( ( ( ( c_List_Olist__update @ SV26 @ SV387 @ SV681 @ SV888 )
= ( c_List_Oappend @ ( c_List_Otake @ SV387 @ SV26 @ SV888 ) @ ( c_List_Olist_OCons @ SV681 @ ( c_List_Odrop @ ( c_Suc @ SV387 ) @ SV26 @ SV888 ) @ SV888 ) @ SV888 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV387 @ ( c_Nat_Osize__class_Osize @ SV26 @ ( tc_List_Olist @ SV888 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2337]) ).
thf(2570,plain,
! [SV682: $i,SV388: $i,SV27: $i] :
( ( ( SV27
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV27 @ ( tc_List_Olist @ SV388 ) ) @ SV682 @ SV388 ) )
= $false )
| ( ( ( c_List_Oappend @ SV27 @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV27 @ ( tc_List_Olist @ SV388 ) ) @ SV682 @ SV388 ) @ SV388 )
= SV682 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2338]) ).
thf(2571,plain,
! [SV683: $i,SV389: $i,SV28: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV28 @ ( c_Nat_Osize__class_Osize @ SV389 @ ( tc_List_Olist @ SV683 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Olast @ ( c_List_Odrop @ SV28 @ SV389 @ SV683 ) @ SV683 )
= ( c_List_Olast @ SV389 @ SV683 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2339]) ).
thf(2572,plain,
! [SV1002: $i,SV399: $i,SV38: $i] :
( ( ( ! [SY2469: $i] :
( ( c_List_Odrop @ ( c_Int_Onumber__class_Onumber__of @ SV38 @ tc_nat ) @ ( c_List_Olist_OCons @ SV399 @ SV1002 @ SY2469 ) @ SY2469 )
= ( c_List_Olist_OCons @ SV399 @ SV1002 @ SY2469 ) ) )
= $true )
| ( ( ( c_Int_Onumber__class_Onumber__of @ SV38 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2341]) ).
thf(2573,plain,
! [SV1003: $i,SV890: $i,SV692: $i,SV401: $i,SV40: $i] :
( ( ( c_Type_Otypings @ SV40 @ SV401 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV692 @ SV890 @ SV40 @ SV401 ) )
| ! [SY2470: $i] :
( ~ ( c_Type_Otyping @ SV40 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1003 ) @ SY2470 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV890 )
| ! [SY1205: $i] :
~ ( c_Type_Otypings @ SV40 @ SY2470 @ SY1205 )
| ~ ( c_Type_Otyping @ SV40 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1003 ) @ SY2470 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV401 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV692 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2342]) ).
thf(2574,plain,
! [SV891: $i,SV693: $i,SV402: $i,SV41: $i] :
( ( ( c_Type_Otypings @ SV41 @ SV402 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV693 @ SV41 @ SV891 @ SV402 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV41 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV891 ) @ SV402 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV693 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2343]) ).
thf(2575,plain,
! [SV694: $i,SV42: $i,SV403: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV403 @ ( c_Nat_Osize__class_Osize @ SV42 @ ( tc_List_Olist @ SV694 ) ) @ tc_nat )
= $false )
| ( ( SV42
= ( c_List_Oappend @ ( c_List_Otake @ SV403 @ SV42 @ SV694 ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ SV42 @ SV403 @ SV694 ) @ ( c_List_Odrop @ ( c_Suc @ SV403 ) @ SV42 @ SV694 ) @ SV694 ) @ SV694 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2344]) ).
thf(2576,plain,
! [SV695: $i,SV404: $i,SV43: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV43 @ ( c_Nat_Osize__class_Osize @ SV404 @ ( tc_List_Olist @ SV695 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Oappend @ ( c_List_Otake @ SV43 @ SV404 @ SV695 ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ ( c_List_Odrop @ SV43 @ SV404 @ SV695 ) @ SV695 ) @ ( c_List_Olist_ONil @ SV695 ) @ SV695 ) @ SV695 )
= ( c_List_Otake @ ( c_Suc @ SV43 ) @ SV404 @ SV695 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2345]) ).
thf(2577,plain,
! [SV1004: $i,SV894: $i,SV698: $i,SV409: $i,SV48: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV48 @ SV409 @ SV698 ) @ ( c_List_Olist_OCons @ SV894 @ SV1004 @ SV698 ) @ SV698 )
= ( c_List_Olist_OCons @ SV48 @ ( c_List_Olist_OCons @ SV894 @ ( c_List_Osplice @ SV409 @ SV1004 @ SV698 ) @ SV698 ) @ SV698 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2348]) ).
thf(2578,plain,
! [SV49: $i,SV1005: $i,SV410: $i] :
( ( ( ! [SY2472: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ SV410 @ SV1005 @ SY2472 ) @ ( c_Int_Onumber__class_Onumber__of @ SV49 @ tc_nat ) @ SY2472 )
= SV410 ) )
= $true )
| ( ( ( c_Int_Onumber__class_Onumber__of @ SV49 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2349]) ).
thf(2579,plain,
! [SV62: $i,SV417: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV417 @ ( c_Suc @ SV62 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV62 @ SV417 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2355]) ).
thf(2580,plain,
! [SV418: $i,SV64: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV64 @ SV418 @ tc_nat )
= $false )
| ( ( ( c_Suc @ SV64 )
= SV418 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV64 ) @ SV418 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2356]) ).
thf(2581,plain,
! [SV65: $i] :
( ( ( class_Int_Onumber__ring @ SV65 )
= $false )
| ( ( ! [SY1236: $i,SY1237: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ SY1236 @ SV65 )
!= ( c_Int_Onumber__class_Onumber__of @ SY1237 @ SV65 ) )
| ( SY1236 = SY1237 ) ) )
= $true )
| ( ( class_Int_Oring__char__0 @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2357]) ).
thf(2582,plain,
! [SV895: $i,SV699: $i,SV419: $i,SV66: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV66 @ SV419 @ SV419 ) @ SV419 ) @ SV699 ) @ SV895 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV66 @ SV419 ) @ SV895 ) @ SV699 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2358]) ).
thf(2583,plain,
! [SV896: $i,SV700: $i,SV420: $i,SV67: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV67 @ SV420 ) @ SV700 ) @ SV896 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV67 @ SV420 @ SV420 ) @ SV420 ) @ SV896 ) @ SV700 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2359]) ).
thf(2584,plain,
! [SV421: $i,SV701: $i,SV1006: $i,SV69: $i] :
( ( ( ! [SY2473: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV69 @ SV1006 @ SY2473 ) @ SV701 ) @ SV421 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV69 @ SV421 ) @ SV701 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2360]) ).
thf(2585,plain,
! [SV1007: $i,SV897: $i,SV702: $i,SV422: $i,SV70: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV70 @ SV422 @ SV702 ) @ SV897 ) @ SV1007 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV1007 ) @ SV897 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2361]) ).
thf(2586,plain,
! [SV423: $i,SV703: $i,SV1008: $i,SV71: $i] :
( ( ( ! [SY2474: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV71 @ SV1008 @ SY2474 ) @ SV703 ) @ SV423 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV71 @ SV423 ) @ SV703 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2362]) ).
thf(2587,plain,
! [SV1009: $i,SV898: $i,SV704: $i,SV424: $i,SV72: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV72 @ SV424 @ SV704 ) @ SV898 ) @ SV1009 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV72 @ SV1009 ) @ SV898 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2363]) ).
thf(2588,plain,
! [SV1010: $i,SV429: $i,SV709: $i,SV77: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV77 @ SV709 ) @ SV429 ) @ SV1010 ) )
| ~ ( c_Wellfounded_Oaccp @ SV77 @ SV1010 @ SV709 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV77 @ SV429 @ SV709 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2364]) ).
thf(2589,plain,
! [SV430: $i,SV710: $i,SV1011: $i,SV78: $i] :
( ( ( ~ ( c_Wellfounded_Oaccp @ SV78 @ SV1011 @ SV710 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV78 @ SV710 ) @ SV430 ) @ SV1011 ) ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV78 @ SV430 @ SV710 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2365]) ).
thf(2590,plain,
! [SV899: $i,SV711: $i,SV431: $i,SV79: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV79 @ SV431 ) @ SV711 ) @ SV899 ) )
= $true )
| ( ( ! [SY2416: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV79 @ SV431 ) @ SY2416 ) @ SV899 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV79 @ SV431 ) @ SV711 ) @ SY2416 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2366]) ).
thf(2591,plain,
! [SV900: $i,SV712: $i,SV432: $i,SV82: $i] :
( ( ( ( c_List_Onth @ ( c_List_Oappend @ SV82 @ SV432 @ SV712 ) @ SV900 @ SV712 )
= ( c_List_Onth @ SV82 @ SV900 @ SV712 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV900 @ ( c_Nat_Osize__class_Osize @ SV82 @ ( tc_List_Olist @ SV712 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2367]) ).
thf(2592,plain,
! [SV1012: $i,SV83: $i,SV901: $i] :
( ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV901 @ SV83 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV1012 @ SV83 ) )
| ( SV901 = SV1012 ) )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV83 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2368]) ).
thf(2593,plain,
! [SV902: $i,SV713: $i,SV435: $i,SV86: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV86 @ SV435 ) @ SV713 ) @ SV902 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV86 @ SV713 ) @ SV902 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2371]) ).
thf(2594,plain,
! [SV436: $i,SV88: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV88 @ ( c_Suc @ SV436 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV88 @ SV436 @ tc_nat )
= $true )
| ( ( SV88 = SV436 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2372]) ).
thf(2595,plain,
! [SV89: $i,SV437: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV437 @ ( c_Suc @ SV89 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV437 @ SV89 @ tc_nat )
= $true )
| ( ( SV89 = SV437 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2373]) ).
thf(2596,plain,
! [SV438: $i,SV90: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV90 @ ( c_Suc @ SV438 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV90 @ SV438 @ tc_nat )
= $true )
| ( ( SV90 = SV438 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2374]) ).
thf(2597,plain,
! [SV94: $i,SV440: $i,SV903: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV903 @ SV440 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV94 @ SV903 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV94 ) @ SV440 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2375]) ).
thf(2598,plain,
! [SV905: $i,SV717: $i,SV448: $i,SV104: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV104 @ SV448 ) @ SV717 ) @ SV905 ) )
= $true )
| ( ( ! [SY2418: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV104 @ SV448 ) @ SY2418 ) @ SV905 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV104 @ SV717 ) @ SY2418 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2379]) ).
thf(2599,plain,
! [SV906: $i,SV718: $i,SV449: $i,SV105: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV105 @ SV449 ) @ SV718 ) @ SV906 ) )
= $true )
| ( ( ! [SY2419: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV105 @ SY2419 ) @ SV906 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV105 @ SV449 ) @ SV718 ) @ SY2419 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2380]) ).
thf(2600,plain,
! [SV719: $i,SV1013: $i,SV450: $i,SV106: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV106 @ SV450 ) @ SV1013 ) )
| ~ ( c_Wellfounded_Oaccp @ SV106 @ SV1013 @ SV719 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV106 @ SV450 @ SV719 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2381]) ).
thf(2601,plain,
! [SV720: $i,SV1014: $i,SV451: $i,SV107: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV107 @ SV451 ) @ SV1014 ) )
| ~ ( c_Wellfounded_Oaccp @ SV107 @ SV1014 @ SV720 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV107 @ SV451 @ SV720 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2382]) ).
thf(2602,plain,
! [SV721: $i,SV452: $i,SV108: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV108 @ ( c_Nat_Osize__class_Osize @ SV452 @ ( tc_List_Olist @ SV721 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Otake @ ( c_Suc @ SV108 ) @ SV452 @ SV721 )
= ( c_List_Oappend @ ( c_List_Otake @ SV108 @ SV452 @ SV721 ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ SV452 @ SV108 @ SV721 ) @ ( c_List_Olist_ONil @ SV721 ) @ SV721 ) @ SV721 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2383]) ).
thf(2603,plain,
! [SV109: $i,SV907: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV907 @ SV109 ) @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV109 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2384]) ).
thf(2604,plain,
! [SV1015: $i,SV113: $i,SV908: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV908 @ SV113 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1015 @ SV113 ) @ SV113 )
| ~ ( c_HOL_Oord__class_Oless @ SV908 @ SV1015 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV113 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2386]) ).
thf(2605,plain,
! [SV114: $i,SV1016: $i,SV909: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV909 @ SV1016 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV909 @ SV114 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1016 @ SV114 ) @ SV114 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV114 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2387]) ).
thf(2606,plain,
! [SV910: $i,SV724: $i,SV456: $i,SV122: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV122 ) @ SV456 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV724 ) @ SV910 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV456 ) @ SV910 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV122 ) @ SV724 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2389]) ).
thf(2607,plain,
! [SV457: $i,SV725: $i,SV123: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV123 ) @ SV725 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV123 ) @ SV457 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV725 ) @ SV457 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2390]) ).
thf(2608,plain,
! [SV124: $i,SV726: $i,SV458: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV458 ) @ SV726 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV124 ) @ SV458 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV124 ) @ SV726 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2391]) ).
thf(2609,plain,
! [SV127: $i,SV728: $i,SV461: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV461 @ SV728 @ tc_nat )
= $false )
| ( ( ( c_Lambda_Oliftn @ SV127 @ ( c_Lambda_OdB_OVar @ SV461 ) @ SV728 )
= ( c_Lambda_OdB_OVar @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2394]) ).
thf(2610,plain,
! [SV912: $i,SV729: $i,SV462: $i,SV128: $i] :
( ( ( ( c_List_Onth @ ( c_List_Otake @ SV128 @ SV462 @ SV729 ) @ SV912 @ SV729 )
= ( c_List_Onth @ SV462 @ SV912 @ SV729 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV912 @ SV128 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2395]) ).
thf(2611,plain,
! [SV913: $i,SV730: $i,SV463: $i,SV129: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV129 @ SV463 @ SV730 ) ) @ ( c_Lambda_Osubst @ SV129 @ SV913 @ SV730 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV463 ) @ SV913 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2396]) ).
thf(2612,plain,
! [SV914: $i,SV731: $i,SV464: $i,SV130: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV130 @ SV464 @ SV731 ) ) @ ( c_Lambda_Osubst @ SV914 @ SV464 @ SV731 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV130 ) @ SV914 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2397]) ).
thf(2613,plain,
! [SV915: $i,SV732: $i,SV465: $i,SV131: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV131 @ SV465 @ SV732 ) ) @ ( c_Lambda_Osubst @ SV131 @ SV915 @ SV732 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV465 ) @ SV915 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2398]) ).
thf(2614,plain,
! [SV733: $i,SV132: $i,SV466: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV466 ) @ SV132 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV733 ) )
= $false )
| ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV132 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV466 @ SV132 @ SV733 ) @ tc_Lambda_OdB )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2399]) ).
thf(2615,plain,
! [SV916: $i,SV736: $i,SV469: $i,SV135: $i] :
( ( ( ( c_List_Onth @ ( c_List_Oreplicate @ SV135 @ SV469 @ SV736 ) @ SV916 @ SV736 )
= SV469 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV916 @ SV135 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2400]) ).
thf(2616,plain,
! [SV470: $i,SV737: $i,SV1017: $i,SV136: $i] :
( ( ( ~ ( c_Type_Otyping @ SV136 @ SV1017 @ SV737 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV1017 ) @ SV470 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV136 @ SV470 @ SV737 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2401]) ).
thf(2617,plain,
! [SV917: $i,SV742: $i,SV477: $i,SV143: $i] :
( ( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV143 @ SV477 @ SV742 ) @ SV917 @ SV742 )
= ( c_List_Olist_OCons @ SV143 @ ( c_List_Olist_OCons @ ( c_List_Ohd @ SV917 @ SV742 ) @ ( c_List_Osplice @ SV477 @ ( c_List_Otl @ SV917 @ SV742 ) @ SV742 ) @ SV742 ) @ SV742 ) )
= $true )
| ( ( SV917
= ( c_List_Olist_ONil @ SV742 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2405]) ).
thf(2618,plain,
! [SV145: $i,SV744: $i,SV478: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV478 ) @ SV744 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV145 ) )
= $false )
| ( ( SV145
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV478 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV478 @ SV744 @ SV145 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2406]) ).
thf(2619,plain,
! [SV1018: $i,SV479: $i,SV146: $i] :
( ( ( ! [SY2475: $i] :
( ( c_List_Otake @ ( c_Int_Onumber__class_Onumber__of @ SV146 @ tc_nat ) @ ( c_List_Olist_OCons @ SV479 @ SV1018 @ SY2475 ) @ SY2475 )
= ( c_List_Olist_ONil @ SY2475 ) ) )
= $true )
| ( ( ( c_Int_Onumber__class_Onumber__of @ SV146 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2407]) ).
thf(2620,plain,
! [SV147: $i,SV918: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV918 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV918 @ SV147 ) @ SV147 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV147 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2408]) ).
thf(2621,plain,
! [SV919: $i,SV148: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV148 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV919 @ SV148 ) @ SV148 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV919 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2409]) ).
thf(2622,plain,
! [SV746: $i,SV481: $i,SV150: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV150 @ ( c_Nat_Osize__class_Osize @ SV481 @ ( tc_List_Olist @ SV746 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Otake @ SV150 @ ( c_List_Obutlast @ SV481 @ SV746 ) @ SV746 )
= ( c_List_Otake @ SV150 @ SV481 @ SV746 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2410]) ).
thf(2623,plain,
! [SV483: $i,SV747: $i,SV152: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV152 ) @ SV747 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV152 @ SV483 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV747 @ SV483 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2411]) ).
thf(2624,plain,
! [SV153: $i,SV748: $i,SV484: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV484 @ SV748 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV153 @ SV484 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV153 @ SV748 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2412]) ).
thf(2625,plain,
! [SV749: $i,SV485: $i,SV154: $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 @ SV154 @ SV485 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV749 @ 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 ) @ SV485 @ 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 @ SV154 ) ) @ SV485 ) @ SV749 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2413]) ).
thf(2626,plain,
! [SV920: $i,SV751: $i,SV488: $i,SV158: $i] :
( ( ( c_Type_Otyping @ SV158 @ SV488 @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ SV751 @ SV158 @ SV488 @ SV920 ) )
= $true )
| ( ( ~ ( c_Type_Otypings @ SV158 @ ( c_List_Oappend @ SV920 @ ( c_List_Olist_OCons @ SV488 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SV751 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2414]) ).
thf(2627,plain,
! [SV1019: $i,SV921: $i,SV752: $i,SV489: $i,SV159: $i] :
( ( ( ( c_List_Oappend @ SV159 @ SV489 @ SV752 )
!= ( c_List_Olist_OCons @ SV921 @ SV1019 @ SV752 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV921 @ SV1019 @ SV159 @ SV489 @ SV752 ) @ SV489 @ SV752 )
= SV1019 )
| ( SV489
= ( c_List_Olist_OCons @ SV921 @ SV1019 @ SV752 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2415]) ).
thf(2628,plain,
! [SV1020: $i,SV922: $i,SV753: $i,SV490: $i,SV160: $i] :
( ( ( ( c_List_Olist_OCons @ SV160 @ SV490 @ SV753 )
!= ( c_List_Oappend @ SV922 @ SV1020 @ SV753 ) )
| ( ( c_List_Olist_OCons @ SV160 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV160 @ SV490 @ SV922 @ SV1020 @ SV753 ) @ SV753 )
= SV922 )
| ( ( c_List_Olist_OCons @ SV160 @ SV490 @ SV753 )
= SV1020 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2416]) ).
thf(2629,plain,
! [SV1021: $i,SV923: $i,SV754: $i,SV491: $i,SV161: $i] :
( ( ( ( c_List_Oappend @ SV161 @ SV491 @ SV754 )
!= ( c_List_Olist_OCons @ SV923 @ SV1021 @ SV754 ) )
| ( SV161
= ( c_List_Olist_OCons @ SV923 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV923 @ SV1021 @ SV161 @ SV491 @ SV754 ) @ SV754 ) )
| ( SV491
= ( c_List_Olist_OCons @ SV923 @ SV1021 @ SV754 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2417]) ).
thf(2630,plain,
! [SV1022: $i,SV924: $i,SV755: $i,SV492: $i,SV162: $i] :
( ( ( ( c_List_Olist_OCons @ SV162 @ SV492 @ SV755 )
!= ( c_List_Oappend @ SV924 @ SV1022 @ SV755 ) )
| ( SV492
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV162 @ SV492 @ SV924 @ SV1022 @ SV755 ) @ SV1022 @ SV755 ) )
| ( ( c_List_Olist_OCons @ SV162 @ SV492 @ SV755 )
= SV1022 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2418]) ).
thf(2631,plain,
! [SV758: $i,SV497: $i,SV167: $i] :
( ( ( ( c_List_Olist_OCons @ SV167 @ ( c_List_Olist_ONil @ SV497 ) @ SV497 )
= ( c_List_Orev @ SV758 @ SV497 ) )
= $false )
| ( ( SV758
= ( c_List_Olist_OCons @ SV167 @ ( c_List_Olist_ONil @ SV497 ) @ SV497 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2421]) ).
thf(2632,plain,
! [SV759: $i,SV498: $i,SV168: $i] :
( ( ( ( c_List_Orev @ SV168 @ SV498 )
= ( c_List_Olist_OCons @ SV759 @ ( c_List_Olist_ONil @ SV498 ) @ SV498 ) )
= $false )
| ( ( SV168
= ( c_List_Olist_OCons @ SV759 @ ( c_List_Olist_ONil @ SV498 ) @ SV498 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2422]) ).
thf(2633,plain,
! [SV761: $i,SV503: $i,SV173: $i] :
( ( ( ( c_List_Otake @ SV173 @ SV503 @ SV761 )
= ( c_List_Olist_ONil @ SV761 ) )
= $false )
| ( ( ( SV503
= ( c_List_Olist_ONil @ SV761 ) )
| ( SV173
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2424]) ).
thf(2634,plain,
! [SV926: $i,SV762: $i,SV176: $i] :
( ( ( ( c_List_Oreplicate @ SV176 @ SV762 @ SV926 )
= ( c_List_Olist_ONil @ SV926 ) )
= $false )
| ( ( SV176
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2425]) ).
thf(2635,plain,
! [SV927: $i,SV506: $i,SV177: $i] :
( ( ( ( c_List_Olist_ONil @ SV177 )
= ( c_List_Oreplicate @ SV506 @ SV927 @ SV177 ) )
= $false )
| ( ( SV506
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2426]) ).
thf(2636,plain,
! [SV763: $i,SV510: $i,SV182: $i] :
( ( ( c_Type_Otyping @ SV182 @ ( c_Lambda_OdB_OVar @ SV510 ) @ SV763 )
= $false )
| ( ( ( hAPP @ SV182 @ SV510 )
= SV763 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2427]) ).
thf(2637,plain,
! [SV928: $i,SV764: $i,SV514: $i,SV186: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV186 @ SV514 @ SV764 ) ) @ ( c_Lambda_Osubst @ SV928 @ SV514 @ SV764 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV186 ) @ SV928 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2428]) ).
thf(2638,plain,
! [SV929: $i,SV766: $i,SV516: $i,SV188: $i] :
( ( ( ~ ( c_ListOrder_Ostep1 @ SV188 @ SV516 @ SV766 @ SV929 ) )
= $true )
| ( ( ! [SY2426: $i] : ( c_ListOrder_Ostep1 @ SV188 @ ( c_List_Oappend @ SV516 @ SY2426 @ SV929 ) @ ( c_List_Oappend @ SV766 @ SY2426 @ SV929 ) @ SV929 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2429]) ).
thf(2639,plain,
! [SV1023: $i,SV930: $i,SV767: $i,SV517: $i,SV189: $i] :
( ( ( c_ListOrder_Ostep1 @ SV189 @ ( c_List_Oappend @ SV517 @ SV767 @ SV930 ) @ ( c_List_Oappend @ SV517 @ SV1023 @ SV930 ) @ SV930 )
| ~ ( c_ListOrder_Ostep1 @ SV189 @ SV767 @ SV1023 @ SV930 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2430]) ).
thf(2640,plain,
! [SV768: $i,SV1024: $i,SV518: $i,SV190: $i] :
( ( ( ~ ( c_List_Olistsp @ SV190 @ ( c_List_Oappend @ SV518 @ SV1024 @ SV768 ) @ SV768 ) )
= $true )
| ( ( c_List_Olistsp @ SV190 @ SV518 @ SV768 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2431]) ).
thf(2641,plain,
! [SV769: $i,SV519: $i,SV1025: $i,SV191: $i] :
( ( ( ~ ( c_List_Olistsp @ SV191 @ ( c_List_Oappend @ SV1025 @ SV519 @ SV769 ) @ SV769 ) )
= $true )
| ( ( c_List_Olistsp @ SV191 @ SV519 @ SV769 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2432]) ).
thf(2642,plain,
! [SV932: $i,SV771: $i,SV521: $i,SV193: $i] :
( ( ( c_List_Olistsp @ SV193 @ ( c_List_Oappend @ SV521 @ SV771 @ SV932 ) @ SV932 )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV193 @ SV771 @ SV932 )
| ~ ( c_List_Olistsp @ SV193 @ SV521 @ SV932 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2434]) ).
thf(2643,plain,
! [SV523: $i,SV773: $i,SV195: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV195 ) @ SV773 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV195 ) @ SV523 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV773 ) @ SV523 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2436]) ).
thf(2644,plain,
! [SV196: $i,SV774: $i,SV524: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV524 ) @ SV774 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV196 ) @ SV524 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV196 ) @ SV774 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2437]) ).
thf(2645,plain,
! [SV934: $i,SV779: $i,SV535: $i,SV212: $i] :
( ( ( SV212 = SV535 )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV779 @ SV535 ) @ SV212 ) )
| ! [SY2428: $i,SY2429: $i] :
~ ( c_ListOrder_Ostep1 @ SV779 @ ( c_List_Olist_OCons @ SV535 @ SV934 @ SY2428 ) @ ( c_List_Olist_OCons @ SV212 @ SY2429 @ SY2428 ) @ SY2428 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2445]) ).
thf(2646,plain,
! [SV935: $i,SV780: $i,SV536: $i,SV213: $i] :
( ( ( SV213 = SV536 )
= $true )
| ( ( ( SV780 = SV935 )
| ! [SY2430: $i,SY2431: $i] :
~ ( c_ListOrder_Ostep1 @ SY2430 @ ( c_List_Olist_OCons @ SV536 @ SV935 @ SY2431 ) @ ( c_List_Olist_OCons @ SV213 @ SV780 @ SY2431 ) @ SY2431 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2446]) ).
thf(2647,plain,
! [SV781: $i,SV537: $i,SV214: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV214 @ SV537 ) @ SV781 ) )
= $false )
| ( ( ! [SY2323: $i,SY2324: $i] : ( c_ListOrder_Ostep1 @ SV214 @ ( c_List_Olist_OCons @ SV537 @ SY2323 @ SY2324 ) @ ( c_List_Olist_OCons @ SV781 @ SY2323 @ SY2324 ) @ SY2324 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2447]) ).
thf(2648,plain,
! [SV936: $i,SV782: $i,SV538: $i,SV215: $i] :
( ( ( c_ListOrder_Ostep1 @ SV215 @ SV538 @ SV782 @ SV936 )
= $true )
| ( ( ( SV782 = SV538 )
| ! [SY2432: $i,SY2433: $i] :
~ ( c_ListOrder_Ostep1 @ SV215 @ ( c_List_Olist_OCons @ SY2432 @ SV538 @ SV936 ) @ ( c_List_Olist_OCons @ SY2433 @ SV782 @ SV936 ) @ SV936 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2448]) ).
thf(2649,plain,
! [SV937: $i,SV784: $i,SV540: $i,SV217: $i] :
( ( ( c_ListOrder_Ostep1 @ SV217 @ SV540 @ SV784 @ SV937 )
= $true )
| ( ( ! [SY2434: $i,SY2435: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV217 @ SY2434 ) @ SY2435 ) )
| ~ ( c_ListOrder_Ostep1 @ SV217 @ ( c_List_Olist_OCons @ SY2434 @ SV540 @ SV937 ) @ ( c_List_Olist_OCons @ SY2435 @ SV784 @ SV937 ) @ SV937 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2449]) ).
thf(2650,plain,
! [SV1026: $i,SV938: $i,SV785: $i,SV541: $i,SV218: $i] :
( ( ( c_ListOrder_Ostep1 @ SV218 @ ( c_List_Olist_OCons @ SV541 @ SV785 @ SV938 ) @ ( c_List_Olist_OCons @ SV541 @ SV1026 @ SV938 ) @ SV938 )
| ~ ( c_ListOrder_Ostep1 @ SV218 @ SV785 @ SV1026 @ SV938 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2450]) ).
thf(2651,plain,
! [SV1027: $i,SV939: $i,SV787: $i,SV543: $i,SV220: $i] :
( ( ( ( c_List_Oreplicate @ SV220 @ SV543 @ SV787 )
!= ( c_List_Oreplicate @ SV939 @ SV1027 @ SV787 ) )
| ( SV543 = SV1027 )
| ( SV220
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2451]) ).
thf(2652,plain,
! [SV227: $i,SV1028: $i,SV546: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV546 @ SV1028 @ SV227 )
| ! [SY2476: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV546 @ SY2476 @ SV227 )
| ~ ( c_HOL_Oord__class_Oless @ SY2476 @ SV1028 @ SV227 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV227 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2454]) ).
thf(2653,plain,
! [SV228: $i,SV1029: $i,SV547: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV547 @ SV1029 @ SV228 )
| ! [SY2477: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY2477 @ SV1029 @ SV228 )
| ~ ( c_HOL_Oord__class_Oless @ SV547 @ SY2477 @ SV228 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV228 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2455]) ).
thf(2654,plain,
! [SV941: $i,SV790: $i,SV549: $i,SV230: $i] :
( ( ( ! [SY2438: $i] :
( ( c_List_Oreplicate @ SV230 @ SV549 @ SV790 )
!= ( c_List_Oreplicate @ SV941 @ SY2438 @ SV790 ) ) )
= $true )
| ( ( SV230 = SV941 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2456]) ).
thf(2655,plain,
! [SV555: $i,SV793: $i,SV237: $i] :
( ( ( SV237 = SV793 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV793 @ SV237 @ tc_nat )
= $true )
| ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV237 ) @ SV555 @ SV793 )
= ( c_Lambda_OdB_OVar @ SV237 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2458]) ).
thf(2656,plain,
! [SV241: $i,SV943: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV943 @ SV943 @ SV241 )
= $false )
| ( ( class_Orderings_Oorder @ SV241 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2460]) ).
thf(2657,plain,
! [SV242: $i,SV944: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV944 @ SV944 @ SV242 )
= $false )
| ( ( class_Orderings_Olinorder @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2461]) ).
thf(2658,plain,
! [SV243: $i,SV945: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV945 @ SV945 @ SV243 )
= $false )
| ( ( class_Orderings_Opreorder @ SV243 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2462]) ).
thf(2659,plain,
! [SV244: $i,SV1030: $i,SV946: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV946 @ SV1030 @ SV244 )
| ( SV1030 = SV946 )
| ( c_HOL_Oord__class_Oless @ SV1030 @ SV946 @ SV244 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV244 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2463]) ).
thf(2660,plain,
! [SV245: $i,SV1031: $i,SV947: $i] :
( ( ( ( SV947 = SV1031 )
| ( c_HOL_Oord__class_Oless @ SV1031 @ SV947 @ SV245 )
| ( c_HOL_Oord__class_Oless @ SV947 @ SV1031 @ SV245 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV245 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2464]) ).
thf(2661,plain,
! [SV247: $i,SV794: $i,SV558: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV558 @ SV794 @ tc_nat )
= $true )
| ( ( ( SV794 = SV558 )
| ( c_HOL_Oord__class_Oless @ SV794 @ SV558 @ tc_nat ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV247 @ SV558 ) @ SV794 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2466]) ).
thf(2662,plain,
! [SV249: $i,SV1032: $i,SV948: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV948 @ SV1032 @ SV249 )
| ( SV1032 = SV948 )
| ( c_HOL_Oord__class_Oless @ SV1032 @ SV948 @ SV249 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV249 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2468]) ).
thf(2663,plain,
! [SV250: $i,SV1033: $i,SV949: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV949 @ SV1033 @ SV250 )
| ( SV1033 = SV949 )
| ( c_HOL_Oord__class_Oless @ SV1033 @ SV949 @ SV250 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV250 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2469]) ).
thf(2664,plain,
! [SV251: $i,SV1034: $i,SV950: $i] :
( ( ( ( SV950 = SV1034 )
| ( c_HOL_Oord__class_Oless @ SV950 @ SV1034 @ SV251 )
| ( c_HOL_Oord__class_Oless @ SV1034 @ SV950 @ SV251 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV251 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2470]) ).
thf(2665,plain,
! [SV795: $i,SV560: $i,SV252: $i] :
( ( ( ( c_List_Orev @ SV252 @ SV560 )
= ( c_List_Orev @ SV795 @ SV560 ) )
= $false )
| ( ( SV252 = SV795 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2471]) ).
thf(2666,plain,
! [SV796: $i,SV253: $i,SV561: $i,SV1035: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV1035 ) @ SV561 ) )
| ~ ( c_Type_Otyping @ SV253 @ SV1035 @ SV796 ) )
= $true )
| ( ( c_Type_Otyping @ SV253 @ SV561 @ SV796 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2472]) ).
thf(2667,plain,
! [SV254: $i,SV1036: $i,SV951: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV951 @ SV1036 @ SV254 )
| ~ ( c_HOL_Oord__class_Oless @ SV1036 @ SV951 @ SV254 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV254 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2473]) ).
thf(2668,plain,
! [SV255: $i,SV1037: $i,SV952: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV952 @ SV1037 @ SV255 )
| ~ ( c_HOL_Oord__class_Oless @ SV1037 @ SV952 @ SV255 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV255 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2474]) ).
thf(2669,plain,
! [SV256: $i,SV1038: $i,SV953: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV953 @ SV1038 @ SV256 )
| ~ ( c_HOL_Oord__class_Oless @ SV1038 @ SV953 @ SV256 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV256 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2475]) ).
thf(2670,plain,
! [SV257: $i,SV1039: $i,SV954: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV954 @ SV1039 @ SV257 )
| ~ ( c_HOL_Oord__class_Oless @ SV1039 @ SV954 @ SV257 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV257 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2476]) ).
thf(2671,plain,
! [SV799: $i,SV566: $i,SV264: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV264 @ SV566 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV799 ) )
= $false )
| ( ( SV264
= ( c_Lambda_OdB_OAbs @ SV799 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2479]) ).
thf(2672,plain,
! [SV1040: $i,SV800: $i,SV567: $i,SV265: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV265 ) @ SV567 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV800 ) @ SV1040 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV265 = SV800 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2480]) ).
thf(2673,plain,
! [SV955: $i,SV801: $i,SV568: $i,SV266: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV266 ) @ SV568 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV801 ) @ SV955 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV568 = SV955 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2481]) ).
thf(2674,plain,
! [SV569: $i,SV802: $i,SV267: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV267 ) @ SV802 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV267 @ SV569 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV802 @ SV569 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2482]) ).
thf(2675,plain,
! [SV956: $i,SV570: $i,SV268: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV268 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV570 @ SV956 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( c_Lambda_OdB_OAbs @ SV268 )
= SV570 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2483]) ).
thf(2676,plain,
! [SV571: $i,SV803: $i,SV269: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV269 @ SV803 @ tc_nat )
= $false )
| ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV269 ) @ SV571 @ SV803 )
= ( c_Lambda_OdB_OVar @ SV269 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2484]) ).
thf(2677,plain,
! [SV572: $i,SV804: $i,SV270: $i] :
( ( ( SV270 = SV804 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV804 @ SV270 @ tc_nat )
= $true )
| ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV270 ) @ SV572 @ SV804 )
= ( c_Lambda_OdB_OVar @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2485]) ).
thf(2678,plain,
! [SV1041: $i,SV957: $i,SV807: $i,SV574: $i,SV273: $i] :
( ( ( ( c_List_Olist_OCons @ SV273 @ SV574 @ SV807 )
!= ( c_List_Oappend @ SV957 @ SV1041 @ SV807 ) )
| ( SV574
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV273 @ SV574 @ SV957 @ SV1041 @ SV807 ) @ SV1041 @ SV807 ) )
| ( SV957
= ( c_List_Olist_ONil @ SV807 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2486]) ).
thf(2679,plain,
! [SV1042: $i,SV958: $i,SV808: $i,SV575: $i,SV274: $i] :
( ( ( ( c_List_Oappend @ SV274 @ SV575 @ SV808 )
!= ( c_List_Olist_OCons @ SV958 @ SV1042 @ SV808 ) )
| ( SV274
= ( c_List_Olist_OCons @ SV958 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV958 @ SV1042 @ SV274 @ SV575 @ SV808 ) @ SV808 ) )
| ( SV274
= ( c_List_Olist_ONil @ SV808 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2487]) ).
thf(2680,plain,
! [SV959: $i,SV811: $i,SV578: $i,SV277: $i] :
( ( ( SV277 = SV578 )
= $true )
| ( ( ( SV811 = SV959 )
| ! [SY2450: $i,SY2451: $i] :
~ ( c_ListOrder_Ostep1 @ SY2450 @ ( c_List_Oappend @ SV277 @ ( c_List_Olist_OCons @ SV811 @ ( c_List_Olist_ONil @ SY2451 ) @ SY2451 ) @ SY2451 ) @ ( c_List_Oappend @ SV578 @ ( c_List_Olist_OCons @ SV959 @ ( c_List_Olist_ONil @ SY2451 ) @ SY2451 ) @ SY2451 ) @ SY2451 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2488]) ).
thf(2681,plain,
! [SV960: $i,SV812: $i,SV579: $i,SV278: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV278 @ SV579 ) @ SV812 ) )
= $true )
| ( ( ( SV579 = SV812 )
| ! [SY2452: $i,SY2453: $i] :
~ ( c_ListOrder_Ostep1 @ SV278 @ ( c_List_Oappend @ SV960 @ ( c_List_Olist_OCons @ SV579 @ ( c_List_Olist_ONil @ SY2452 ) @ SY2452 ) @ SY2452 ) @ ( c_List_Oappend @ SY2453 @ ( c_List_Olist_OCons @ SV812 @ ( c_List_Olist_ONil @ SY2452 ) @ SY2452 ) @ SY2452 ) @ SY2452 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2489]) ).
thf(2682,plain,
! [SV1043: $i,SV961: $i,SV813: $i,SV580: $i,SV279: $i] :
( ( ( ( c_List_Oappend @ SV279 @ SV580 @ SV813 )
!= ( c_List_Olist_OCons @ SV961 @ SV1043 @ SV813 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV961 @ SV1043 @ SV279 @ SV580 @ SV813 ) @ SV580 @ SV813 )
= SV1043 )
| ( SV279
= ( c_List_Olist_ONil @ SV813 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2490]) ).
thf(2683,plain,
! [SV1044: $i,SV962: $i,SV814: $i,SV581: $i,SV280: $i] :
( ( ( ( c_List_Olist_OCons @ SV280 @ SV581 @ SV814 )
!= ( c_List_Oappend @ SV962 @ SV1044 @ SV814 ) )
| ( ( c_List_Olist_OCons @ SV280 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV280 @ SV581 @ SV962 @ SV1044 @ SV814 ) @ SV814 )
= SV962 )
| ( SV962
= ( c_List_Olist_ONil @ SV814 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2491]) ).
thf(2684,plain,
! [SV963: $i,SV816: $i,SV583: $i,SV282: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV282 @ SV583 ) @ SV816 ) )
= $true )
| ( ( ! [SY2456: $i,SY2457: $i] :
( ( c_ListOrder_Ostep1 @ SV282 @ SV963 @ SY2456 @ SY2457 )
| ~ ( c_ListOrder_Ostep1 @ SV282 @ ( c_List_Oappend @ SV963 @ ( c_List_Olist_OCons @ SV583 @ ( c_List_Olist_ONil @ SY2457 ) @ SY2457 ) @ SY2457 ) @ ( c_List_Oappend @ SY2456 @ ( c_List_Olist_OCons @ SV816 @ ( c_List_Olist_ONil @ SY2457 ) @ SY2457 ) @ SY2457 ) @ SY2457 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2492]) ).
thf(2685,plain,
! [SV964: $i,SV817: $i,SV584: $i,SV283: $i] :
( ( ( ( c_List_Orev @ SV283 @ SV584 )
!= ( c_List_Olist_OCons @ SV817 @ SV964 @ SV584 ) )
= $true )
| ( ( SV283
= ( c_List_Oappend @ ( c_List_Orev @ SV964 @ SV584 ) @ ( c_List_Olist_OCons @ SV817 @ ( c_List_Olist_ONil @ SV584 ) @ SV584 ) @ SV584 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2493]) ).
thf(2686,plain,
! [SV965: $i,SV820: $i,SV587: $i,SV286: $i] :
( ( ( SV286 = SV587 )
= $true )
| ( ( ( c_ListOrder_Ostep1 @ SV820 @ SV286 @ SV587 @ SV965 )
| ! [SY2458: $i,SY2459: $i] :
~ ( c_ListOrder_Ostep1 @ SV820 @ ( c_List_Oappend @ SV286 @ ( c_List_Olist_OCons @ SY2458 @ ( c_List_Olist_ONil @ SV965 ) @ SV965 ) @ SV965 ) @ ( c_List_Oappend @ SV587 @ ( c_List_Olist_OCons @ SY2459 @ ( c_List_Olist_ONil @ SV965 ) @ SV965 ) @ SV965 ) @ SV965 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2494]) ).
thf(2687,plain,
! [SV288: $i,SV589: $i,SV1045: $i,SV822: $i] :
( ( ( ! [SY2478: $i] :
( ~ ( c_Type_Otyping @ SV822 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1045 ) @ SY2478 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV589 )
| ~ ( c_Type_Otyping @ SV822 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1045 ) @ SY2478 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV288 ) ) )
= $true )
| ( ( SV288 = SV589 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2495]) ).
thf(2688,plain,
! [SV966: $i,SV823: $i,SV590: $i,SV289: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV289 ) @ SV590 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV823 ) @ SV966 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2496]) ).
thf(2689,plain,
! [SV967: $i,SV824: $i,SV591: $i,SV290: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV290 ) ) @ SV591 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV824 ) @ SV967 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2497]) ).
thf(2690,plain,
! [SV825: $i,SV592: $i,SV291: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV291 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV592 @ SV825 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV825
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2498]) ).
thf(2691,plain,
! [SV968: $i,SV826: $i,SV593: $i,SV293: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV293 ) @ SV593 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV826 @ SV968 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( SV293
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV826 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV293 @ SV593 @ SV826 @ SV968 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV968
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2499]) ).
thf(2692,plain,
! [SV969: $i,SV594: $i,SV294: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV294 @ SV594 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV969 ) )
= $false )
| ( ( SV594
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2500]) ).
thf(2693,plain,
! [SV827: $i,SV297: $i,SV596: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV596 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV297 @ SV596 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV827 @ 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 @ SV297 ) ) @ SV596 ) @ SV827 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2502]) ).
thf(2694,plain,
! [SV970: $i,SV828: $i,SV597: $i,SV298: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV298 ) @ SV597 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV828 @ SV970 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( SV970
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV298 @ SV597 @ SV828 @ SV970 ) @ ( c_List_Olist_OCons @ SV597 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( SV970
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2503]) ).
thf(2695,plain,
! [SV1046: $i,SV976: $i,SV833: $i,SV604: $i,SV306: $i] :
( ( ( ( c_List_Oappend @ SV306 @ ( c_List_Olist_OCons @ SV604 @ ( c_List_Olist_ONil @ SV833 ) @ SV833 ) @ SV833 )
!= ( c_List_Oappend @ SV976 @ ( c_List_Olist_OCons @ SV1046 @ ( c_List_Olist_ONil @ SV833 ) @ SV833 ) @ SV833 ) )
| ( SV604 = SV1046 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2509]) ).
thf(2696,plain,
! [SV977: $i,SV834: $i,SV605: $i,SV307: $i] :
( ( ( ! [SY2461: $i] :
( ( c_List_Oappend @ SV307 @ ( c_List_Olist_OCons @ SV605 @ ( c_List_Olist_ONil @ SV834 ) @ SV834 ) @ SV834 )
!= ( c_List_Oappend @ SV977 @ ( c_List_Olist_OCons @ SY2461 @ ( c_List_Olist_ONil @ SV834 ) @ SV834 ) @ SV834 ) ) )
= $true )
| ( ( SV307 = SV977 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2510]) ).
thf(2697,plain,
! [SV1047: $i,SV837: $i,SV609: $i,SV311: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV311 ) @ SV609 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV837 ) @ SV1047 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV311 = SV837 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2513]) ).
thf(2698,plain,
! [SV979: $i,SV838: $i,SV610: $i,SV312: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV312 ) @ SV610 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV838 ) @ SV979 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV610 = SV979 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2514]) ).
thf(2699,plain,
! [SV1048: $i,SV980: $i,SV839: $i,SV611: $i,SV313: $i] :
( ( ( ( c_List_Olist_OCons @ SV313 @ SV611 @ SV839 )
!= ( c_List_Olist_OCons @ SV980 @ SV1048 @ SV839 ) )
| ( SV611 = SV1048 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2515]) ).
thf(2700,plain,
! [SV981: $i,SV840: $i,SV612: $i,SV314: $i] :
( ( ( ! [SY2463: $i] :
( ( c_List_Olist_OCons @ SV314 @ SV612 @ SV840 )
!= ( c_List_Olist_OCons @ SV981 @ SY2463 @ SV840 ) ) )
= $true )
| ( ( SV314 = SV981 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2516]) ).
thf(2701,plain,
! [SV842: $i,SV615: $i,SV317: $i] :
( ( ( SV317
= ( c_List_Oappend @ SV615 @ SV317 @ SV842 ) )
= $false )
| ( ( SV615
= ( c_List_Olist_ONil @ SV842 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2517]) ).
thf(2702,plain,
! [SV843: $i,SV616: $i,SV318: $i] :
( ( ( ( c_List_Oappend @ SV318 @ SV616 @ SV843 )
= SV616 )
= $false )
| ( ( SV318
= ( c_List_Olist_ONil @ SV843 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2518]) ).
thf(2703,plain,
! [SV844: $i,SV617: $i,SV319: $i] :
( ( ( SV319
= ( c_List_Oappend @ SV319 @ SV617 @ SV844 ) )
= $false )
| ( ( SV617
= ( c_List_Olist_ONil @ SV844 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2519]) ).
thf(2704,plain,
! [SV845: $i,SV618: $i,SV320: $i] :
( ( ( ( c_List_Oappend @ SV320 @ SV618 @ SV845 )
= SV320 )
= $false )
| ( ( SV618
= ( c_List_Olist_ONil @ SV845 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2520]) ).
thf(2705,plain,
! [SV982: $i,SV846: $i,SV321: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV321 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV321 @ ( c_Lambda_OdB_OVar @ SV846 ) @ SV982 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2521]) ).
thf(2706,plain,
! [SV847: $i,SV619: $i,SV322: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV322 ) @ SV619 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV847 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV322 ) @ SV619 )
= SV847 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2522]) ).
thf(2707,plain,
! [SV1049: $i,SV849: $i,SV621: $i,SV324: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV324 ) @ SV621 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV849 ) @ SV1049 ) )
= $true )
| ( ( SV324 = SV849 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2524]) ).
thf(2708,plain,
! [SV983: $i,SV850: $i,SV622: $i,SV325: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV325 ) @ SV622 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV850 ) @ SV983 ) )
= $true )
| ( ( SV622 = SV983 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2525]) ).
thf(2709,plain,
! [SV984: $i,SV623: $i,SV326: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV326 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV623 @ SV984 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( c_Lambda_OdB_OVar @ SV326 )
= SV623 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2526]) ).
thf(2710,plain,
! [SV852: $i,SV625: $i,SV328: $i] :
( ( ( ( c_List_Oappend @ SV328 @ SV625 @ SV852 )
= ( c_List_Olist_ONil @ SV852 ) )
= $false )
| ( ( SV625
= ( c_List_Olist_ONil @ SV852 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2528]) ).
thf(2711,plain,
! [SV853: $i,SV626: $i,SV329: $i] :
( ( ( ( c_List_Oappend @ SV329 @ SV626 @ SV853 )
= ( c_List_Olist_ONil @ SV853 ) )
= $false )
| ( ( SV329
= ( c_List_Olist_ONil @ SV853 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2529]) ).
thf(2712,plain,
! [SV854: $i,SV627: $i,SV330: $i] :
( ( ( SV330
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV330 ) @ SV627 ) @ SV854 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV330 ) @ SV627 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV330 ) @ SV627 ) @ ( c_List_Oappend @ SV854 @ ( c_List_Olist_OCons @ SV627 @ ( 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)],[2530]) ).
thf(2713,plain,
! [SV855: $i,SV628: $i,SV331: $i] :
( ( ( ( c_List_Olist_ONil @ SV331 )
= ( c_List_Oappend @ SV628 @ SV855 @ SV331 ) )
= $false )
| ( ( SV855
= ( c_List_Olist_ONil @ SV331 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2531]) ).
thf(2714,plain,
! [SV985: $i,SV629: $i,SV332: $i] :
( ( ( ( c_List_Olist_ONil @ SV332 )
= ( c_List_Oappend @ SV629 @ SV985 @ SV332 ) )
= $false )
| ( ( SV629
= ( c_List_Olist_ONil @ SV332 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2532]) ).
thf(2715,plain,
! [SV987: $i,SV857: $i,SV636: $i,SV340: $i] :
( ( ( ( c_List_Oappend @ SV340 @ SV636 @ SV857 )
!= ( c_List_Oappend @ SV340 @ SV987 @ SV857 ) )
= $true )
| ( ( SV636 = SV987 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2534]) ).
thf(2716,plain,
! [SV988: $i,SV858: $i,SV637: $i,SV341: $i] :
( ( ( ( c_List_Oappend @ SV341 @ SV637 @ SV858 )
!= ( c_List_Oappend @ SV988 @ SV637 @ SV858 ) )
= $true )
| ( ( SV341 = SV988 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2535]) ).
thf(2717,plain,
! [SV1050: $i,SV989: $i,SV859: $i,SV638: $i,SV343: $i] :
( ( ! [SY2479: $i] :
( ( c_List_Ofoldl @ SV343 @ SV638 @ ( c_List_Olist_OCons @ SV859 @ SV989 @ SV1050 ) @ SY2479 @ SV1050 )
= ( c_List_Ofoldl @ SV343 @ ( hAPP @ ( hAPP @ SV343 @ SV638 ) @ SV859 ) @ SV989 @ SY2479 @ SV1050 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2536]) ).
thf(2718,plain,
! [SV866: $i,SV645: $i,SV350: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV350 @ SV645 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV866 @ SV645 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV350 = SV866 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2543]) ).
thf(2719,plain,
! [SV869: $i,SV648: $i,SV353: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV353 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV648 @ SV869 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV869
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2546]) ).
thf(2720,plain,
! [SV1051: $i,SV994: $i,SV871: $i,SV650: $i,SV356: $i] :
( ( ! [SY2480: $i] :
( ( c_List_Ofoldl @ SV356 @ SV650 @ ( c_List_Oappend @ SV871 @ SV994 @ SV1051 ) @ SY2480 @ SV1051 )
= ( c_List_Ofoldl @ SV356 @ ( c_List_Ofoldl @ SV356 @ SV650 @ SV871 @ SY2480 @ SV1051 ) @ SV994 @ SY2480 @ SV1051 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2547]) ).
thf(2721,plain,
! [SV655: $i,SV361: $i,SV995: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV995 ) @ SV361 ) @ SV655 ) )
= $false )
| ( ( SV361 = SV655 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2551]) ).
thf(2722,plain,
! [SV874: $i,SV657: $i,SV363: $i,SV2: $i] :
( ( ( ( c_List_Olist__update @ SV2 @ SV363 @ SV657 @ SV874 )
= ( c_List_Olist_ONil @ SV874 ) )
= $false )
| ( ( SV2
= ( c_List_Olist_ONil @ SV874 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2553]) ).
thf(2723,plain,
! [SV875: $i,SV661: $i,SV367: $i,SV6: $i] :
( ( ( ( c_List_Olist__update @ SV6 @ SV367 @ SV661 @ SV875 )
= SV6 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV367 @ ( c_Nat_Osize__class_Osize @ SV6 @ ( tc_List_Olist @ SV875 ) ) @ tc_nat )
| ( ( c_List_Onth @ SV6 @ SV367 @ SV875 )
= SV661 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2554]) ).
thf(2724,plain,
! [SV997: $i,SV877: $i,SV663: $i,SV369: $i,SV8: $i] :
( ( ( ( c_List_Onth @ ( c_List_Olist__update @ SV8 @ SV369 @ SV663 @ SV877 ) @ SV997 @ SV877 )
= ( c_List_Onth @ SV8 @ SV997 @ SV877 ) )
= $true )
| ( ( SV369 = SV997 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2555]) ).
thf(2725,plain,
! [SV665: $i,SV1052: $i,SV10: $i,SV371: $i] :
( ( ( ( c_List_Onth @ ( c_List_Olist__update @ SV371 @ SV10 @ SV1052 @ SV665 ) @ SV10 @ SV665 )
= SV1052 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV10 @ ( c_Nat_Osize__class_Osize @ SV371 @ ( tc_List_Olist @ SV665 ) ) @ tc_nat )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2557]) ).
thf(2726,plain,
! [SV666: $i,SV878: $i,SV11: $i,SV372: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV372 @ ( c_Nat_Osize__class_Osize @ SV11 @ ( tc_List_Olist @ SV878 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Onth @ ( c_List_Olist__update @ SV11 @ SV372 @ SV666 @ SV878 ) @ SV372 @ SV878 )
= SV666 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2558]) ).
thf(2727,plain,
! [SV1053: $i,SV879: $i,SV667: $i,SV373: $i,SV12: $i] :
( ( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV12 @ SV373 @ SV667 ) @ SV879 @ SV1053 @ SV667 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV12 @ SV879 @ SV1053 @ SV667 ) @ SV373 @ SV667 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV879 @ ( c_Nat_Osize__class_Osize @ SV12 @ ( tc_List_Olist @ SV667 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2559]) ).
thf(2728,plain,
! [SV1054: $i,SV880: $i,SV668: $i,SV374: $i,SV13: $i] :
( ( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV13 @ SV374 @ SV668 ) @ SV880 @ SV1054 @ SV668 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV13 @ SV880 @ SV1054 @ SV668 ) @ SV374 @ SV668 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV880 @ ( c_Nat_Osize__class_Osize @ SV13 @ ( tc_List_Olist @ SV668 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2560]) ).
thf(2729,plain,
! [SV998: $i,SV881: $i,SV670: $i,SV376: $i,SV15: $i] :
( ( ( ! [SY2468: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV15 @ SV376 @ SV670 @ SV881 ) @ SV998 @ SY2468 @ SV881 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV15 @ SV998 @ SY2468 @ SV881 ) @ SV376 @ SV670 @ SV881 ) ) )
= $true )
| ( ( SV376 = SV998 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2561]) ).
thf(2730,plain,
! [SV1000: $i,SV883: $i,SV672: $i,SV378: $i,SV17: $i] :
( ( ( ( c_List_Onth @ ( c_List_Olist__update @ SV17 @ SV378 @ SV672 @ SV883 ) @ SV1000 @ SV883 )
= ( c_List_Onth @ SV17 @ SV1000 @ SV883 ) )
= $true )
| ( ( ( SV378 = SV1000 )
| ~ ( c_HOL_Oord__class_Oless @ SV378 @ ( c_Nat_Osize__class_Osize @ SV17 @ ( tc_List_Olist @ SV883 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2563]) ).
thf(2731,plain,
! [SV675: $i,SV381: $i,SV20: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV20 @ ( c_Nat_Osize__class_Osize @ SV381 @ ( tc_List_Olist @ SV675 ) ) @ tc_nat )
= $false )
| ( ( SV381
= ( c_List_Olist_ONil @ SV675 ) )
= $true )
| ( ( ( c_List_Ohd @ ( c_List_Odrop @ SV20 @ SV381 @ SV675 ) @ SV675 )
= ( c_List_Onth @ SV381 @ SV20 @ SV675 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2565]) ).
thf(2732,plain,
! [SV886: $i,SV679: $i,SV385: $i,SV24: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SV385 ) ) @ SV679 @ SV385 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV679 @ ( tc_List_Olist @ SV385 ) ) @ SV24 @ SV385 ) @ SV886 @ SV385 ) @ SV385 )
= SV886 )
= $false )
| ( ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SV385 ) ) @ SV679 @ SV385 )
!= SV24 )
| ( SV679
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV679 @ ( tc_List_Olist @ SV385 ) ) @ SV24 @ SV385 ) )
| ( ( c_List_Oappend @ SV679 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV679 @ ( tc_List_Olist @ SV385 ) ) @ SV24 @ SV385 ) @ SV886 @ SV385 ) @ SV385 )
= ( c_List_Oappend @ SV24 @ SV886 @ SV385 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2567]) ).
thf(2733,plain,
! [SV1055: $i,SV887: $i,SV680: $i,SV386: $i,SV25: $i] :
( ( ( ( c_List_Odrop @ SV25 @ SV386 @ SV680 )
!= ( c_List_Olist_OCons @ SV887 @ SV1055 @ SV680 ) )
= $true )
| ( ( ( c_List_Onth @ SV386 @ SV25 @ SV680 )
= SV887 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2568]) ).
thf(2734,plain,
! [SV681: $i,SV888: $i,SV26: $i,SV387: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV387 @ ( c_Nat_Osize__class_Osize @ SV26 @ ( tc_List_Olist @ SV888 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Olist__update @ SV26 @ SV387 @ SV681 @ SV888 )
= ( c_List_Oappend @ ( c_List_Otake @ SV387 @ SV26 @ SV888 ) @ ( c_List_Olist_OCons @ SV681 @ ( c_List_Odrop @ ( c_Suc @ SV387 ) @ SV26 @ SV888 ) @ SV888 ) @ SV888 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2569]) ).
thf(2735,plain,
! [SV1056: $i,SV1002: $i,SV399: $i,SV38: $i] :
( ( ( ( c_List_Odrop @ ( c_Int_Onumber__class_Onumber__of @ SV38 @ tc_nat ) @ ( c_List_Olist_OCons @ SV399 @ SV1002 @ SV1056 ) @ SV1056 )
= ( c_List_Olist_OCons @ SV399 @ SV1002 @ SV1056 ) )
= $true )
| ( ( ( c_Int_Onumber__class_Onumber__of @ SV38 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2572]) ).
thf(2736,plain,
! [SV1003: $i,SV890: $i,SV692: $i,SV401: $i,SV40: $i] :
( ( ( c_Type_Otypings @ SV40 @ SV401 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV692 @ SV890 @ SV40 @ SV401 ) )
= $true )
| ( ( ! [SY2470: $i] :
( ~ ( c_Type_Otyping @ SV40 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1003 ) @ SY2470 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV890 )
| ! [SY1205: $i] :
~ ( c_Type_Otypings @ SV40 @ SY2470 @ SY1205 )
| ~ ( c_Type_Otyping @ SV40 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1003 ) @ SY2470 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV401 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV692 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2573]) ).
thf(2737,plain,
! [SV693: $i,SV402: $i,SV891: $i,SV41: $i] :
( ( ( c_Type_Otyping @ SV41 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV891 ) @ SV402 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV693 )
= $false )
| ( ( c_Type_Otypings @ SV41 @ SV402 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV693 @ SV41 @ SV891 @ SV402 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2574]) ).
thf(2738,plain,
! [SV49: $i,SV1057: $i,SV1005: $i,SV410: $i] :
( ( ( ( c_List_Onth @ ( c_List_Olist_OCons @ SV410 @ SV1005 @ SV1057 ) @ ( c_Int_Onumber__class_Onumber__of @ SV49 @ tc_nat ) @ SV1057 )
= SV410 )
= $true )
| ( ( ( c_Int_Onumber__class_Onumber__of @ SV49 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2578]) ).
thf(2739,plain,
! [SV65: $i,SV1058: $i] :
( ( ( ! [SY2481: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ SV1058 @ SV65 )
!= ( c_Int_Onumber__class_Onumber__of @ SY2481 @ SV65 ) )
| ( SV1058 = SY2481 ) ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV65 )
= $false )
| ( ( class_Int_Oring__char__0 @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2581]) ).
thf(2740,plain,
! [SV699: $i,SV895: $i,SV419: $i,SV66: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV66 @ SV419 ) @ SV895 ) @ SV699 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV66 @ SV419 @ SV419 ) @ SV419 ) @ SV699 ) @ SV895 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2582]) ).
thf(2741,plain,
! [SV700: $i,SV896: $i,SV420: $i,SV67: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV67 @ SV420 @ SV420 ) @ SV420 ) @ SV896 ) @ SV700 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV67 @ SV420 ) @ SV700 ) @ SV896 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2583]) ).
thf(2742,plain,
! [SV421: $i,SV701: $i,SV1059: $i,SV1006: $i,SV69: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV69 @ SV1006 @ SV1059 ) @ SV701 ) @ SV421 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV69 @ SV421 ) @ SV701 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2584]) ).
thf(2743,plain,
! [SV1007: $i,SV897: $i,SV702: $i,SV422: $i,SV70: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV70 @ SV422 @ SV702 ) @ SV897 ) @ SV1007 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV1007 ) @ SV897 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2585]) ).
thf(2744,plain,
! [SV423: $i,SV703: $i,SV1060: $i,SV1008: $i,SV71: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV71 @ SV1008 @ SV1060 ) @ SV703 ) @ SV423 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV71 @ SV423 ) @ SV703 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2586]) ).
thf(2745,plain,
! [SV1009: $i,SV898: $i,SV704: $i,SV424: $i,SV72: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV72 @ SV424 @ SV704 ) @ SV898 ) @ SV1009 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV72 @ SV1009 ) @ SV898 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2587]) ).
thf(2746,plain,
! [SV1010: $i,SV429: $i,SV709: $i,SV77: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV77 @ SV709 ) @ SV429 ) @ SV1010 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV77 @ SV1010 @ SV709 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV77 @ SV429 @ SV709 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2588]) ).
thf(2747,plain,
! [SV430: $i,SV710: $i,SV1011: $i,SV78: $i] :
( ( ( ~ ( c_Wellfounded_Oaccp @ SV78 @ SV1011 @ SV710 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV78 @ SV710 ) @ SV430 ) @ SV1011 ) ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV78 @ SV430 @ SV710 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2589]) ).
thf(2748,plain,
! [SV711: $i,SV899: $i,SV1061: $i,SV431: $i,SV79: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV79 @ SV431 ) @ SV1061 ) @ SV899 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV79 @ SV431 ) @ SV711 ) @ SV1061 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV79 @ SV431 ) @ SV711 ) @ SV899 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2590]) ).
thf(2749,plain,
! [SV432: $i,SV712: $i,SV82: $i,SV900: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV900 @ ( c_Nat_Osize__class_Osize @ SV82 @ ( tc_List_Olist @ SV712 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Onth @ ( c_List_Oappend @ SV82 @ SV432 @ SV712 ) @ SV900 @ SV712 )
= ( c_List_Onth @ SV82 @ SV900 @ SV712 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2591]) ).
thf(2750,plain,
! [SV1012: $i,SV83: $i,SV901: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV901 @ SV83 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV1012 @ SV83 ) )
= $true )
| ( ( SV901 = SV1012 )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2592]) ).
thf(2751,plain,
! [SV435: $i,SV902: $i,SV713: $i,SV86: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV86 @ SV713 ) @ SV902 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV86 @ SV435 ) @ SV713 ) @ SV902 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2593]) ).
thf(2752,plain,
! [SV94: $i,SV440: $i,SV903: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV903 @ SV440 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV94 @ SV903 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV94 ) @ SV440 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2597]) ).
thf(2753,plain,
! [SV717: $i,SV905: $i,SV1062: $i,SV448: $i,SV104: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV104 @ SV448 ) @ SV1062 ) @ SV905 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV104 @ SV717 ) @ SV1062 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV104 @ SV448 ) @ SV717 ) @ SV905 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2598]) ).
thf(2754,plain,
! [SV718: $i,SV449: $i,SV906: $i,SV1063: $i,SV105: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV105 @ SV1063 ) @ SV906 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV105 @ SV449 ) @ SV718 ) @ SV1063 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV105 @ SV449 ) @ SV718 ) @ SV906 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2599]) ).
thf(2755,plain,
! [SV719: $i,SV1013: $i,SV450: $i,SV106: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV106 @ SV450 ) @ SV1013 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV106 @ SV1013 @ SV719 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV106 @ SV450 @ SV719 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2600]) ).
thf(2756,plain,
! [SV720: $i,SV1014: $i,SV451: $i,SV107: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV107 @ SV451 ) @ SV1014 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV107 @ SV1014 @ SV720 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV107 @ SV451 @ SV720 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2601]) ).
thf(2757,plain,
! [SV1015: $i,SV113: $i,SV908: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV908 @ SV113 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1015 @ SV113 ) @ SV113 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV908 @ SV1015 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2604]) ).
thf(2758,plain,
! [SV114: $i,SV1016: $i,SV909: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV909 @ SV1016 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV909 @ SV114 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1016 @ SV114 ) @ SV114 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV114 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2605]) ).
thf(2759,plain,
! [SV724: $i,SV122: $i,SV910: $i,SV456: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV456 ) @ SV910 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV122 ) @ SV724 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV122 ) @ SV456 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV724 ) @ SV910 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2606]) ).
thf(2760,plain,
! [SV729: $i,SV462: $i,SV128: $i,SV912: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV912 @ SV128 @ tc_nat )
= $false )
| ( ( ( c_List_Onth @ ( c_List_Otake @ SV128 @ SV462 @ SV729 ) @ SV912 @ SV729 )
= ( c_List_Onth @ SV462 @ SV912 @ SV729 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2610]) ).
thf(2761,plain,
! [SV730: $i,SV129: $i,SV913: $i,SV463: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV463 ) @ SV913 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV129 @ SV463 @ SV730 ) ) @ ( c_Lambda_Osubst @ SV129 @ SV913 @ SV730 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2611]) ).
thf(2762,plain,
! [SV731: $i,SV464: $i,SV914: $i,SV130: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV130 ) @ SV914 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV130 @ SV464 @ SV731 ) ) @ ( c_Lambda_Osubst @ SV914 @ SV464 @ SV731 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2612]) ).
thf(2763,plain,
! [SV732: $i,SV131: $i,SV915: $i,SV465: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV465 ) @ SV915 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV131 @ SV465 @ SV732 ) ) @ ( c_Lambda_Osubst @ SV131 @ SV915 @ SV732 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2613]) ).
thf(2764,plain,
! [SV736: $i,SV469: $i,SV135: $i,SV916: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV916 @ SV135 @ tc_nat )
= $false )
| ( ( ( c_List_Onth @ ( c_List_Oreplicate @ SV135 @ SV469 @ SV736 ) @ SV916 @ SV736 )
= SV469 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2615]) ).
thf(2765,plain,
! [SV470: $i,SV737: $i,SV1017: $i,SV136: $i] :
( ( ( ~ ( c_Type_Otyping @ SV136 @ SV1017 @ SV737 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV1017 ) @ SV470 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV136 @ SV470 @ SV737 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2616]) ).
thf(2766,plain,
! [SV1064: $i,SV1018: $i,SV479: $i,SV146: $i] :
( ( ( ( c_List_Otake @ ( c_Int_Onumber__class_Onumber__of @ SV146 @ tc_nat ) @ ( c_List_Olist_OCons @ SV479 @ SV1018 @ SV1064 ) @ SV1064 )
= ( c_List_Olist_ONil @ SV1064 ) )
= $true )
| ( ( ( c_Int_Onumber__class_Onumber__of @ SV146 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2619]) ).
thf(2767,plain,
! [SV918: $i,SV147: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV918 @ SV147 ) @ SV147 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV918 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2620]) ).
thf(2768,plain,
! [SV148: $i,SV919: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV919 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV148 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV919 @ SV148 ) @ SV148 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2621]) ).
thf(2769,plain,
! [SV749: $i,SV154: $i,SV485: $i] :
( ( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV485 @ 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 @ SV154 ) ) @ SV485 ) @ SV749 @ 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 @ SV154 @ SV485 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV749 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2625]) ).
thf(2770,plain,
! [SV751: $i,SV488: $i,SV920: $i,SV158: $i] :
( ( ( c_Type_Otypings @ SV158 @ ( c_List_Oappend @ SV920 @ ( c_List_Olist_OCons @ SV488 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SV751 )
= $false )
| ( ( c_Type_Otyping @ SV158 @ SV488 @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ SV751 @ SV158 @ SV488 @ SV920 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2626]) ).
thf(2771,plain,
! [SV1019: $i,SV921: $i,SV752: $i,SV489: $i,SV159: $i] :
( ( ( ( c_List_Oappend @ SV159 @ SV489 @ SV752 )
!= ( c_List_Olist_OCons @ SV921 @ SV1019 @ SV752 ) )
= $true )
| ( ( ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV921 @ SV1019 @ SV159 @ SV489 @ SV752 ) @ SV489 @ SV752 )
= SV1019 )
| ( SV489
= ( c_List_Olist_OCons @ SV921 @ SV1019 @ SV752 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2627]) ).
thf(2772,plain,
! [SV1020: $i,SV922: $i,SV753: $i,SV490: $i,SV160: $i] :
( ( ( ( c_List_Olist_OCons @ SV160 @ SV490 @ SV753 )
!= ( c_List_Oappend @ SV922 @ SV1020 @ SV753 ) )
= $true )
| ( ( ( ( c_List_Olist_OCons @ SV160 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV160 @ SV490 @ SV922 @ SV1020 @ SV753 ) @ SV753 )
= SV922 )
| ( ( c_List_Olist_OCons @ SV160 @ SV490 @ SV753 )
= SV1020 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2628]) ).
thf(2773,plain,
! [SV1021: $i,SV923: $i,SV754: $i,SV491: $i,SV161: $i] :
( ( ( ( c_List_Oappend @ SV161 @ SV491 @ SV754 )
!= ( c_List_Olist_OCons @ SV923 @ SV1021 @ SV754 ) )
= $true )
| ( ( ( SV161
= ( c_List_Olist_OCons @ SV923 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV923 @ SV1021 @ SV161 @ SV491 @ SV754 ) @ SV754 ) )
| ( SV491
= ( c_List_Olist_OCons @ SV923 @ SV1021 @ SV754 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2629]) ).
thf(2774,plain,
! [SV1022: $i,SV924: $i,SV755: $i,SV492: $i,SV162: $i] :
( ( ( ( c_List_Olist_OCons @ SV162 @ SV492 @ SV755 )
!= ( c_List_Oappend @ SV924 @ SV1022 @ SV755 ) )
= $true )
| ( ( ( SV492
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV162 @ SV492 @ SV924 @ SV1022 @ SV755 ) @ SV1022 @ SV755 ) )
| ( ( c_List_Olist_OCons @ SV162 @ SV492 @ SV755 )
= SV1022 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2630]) ).
thf(2775,plain,
! [SV173: $i,SV761: $i,SV503: $i] :
( ( ( SV503
= ( c_List_Olist_ONil @ SV761 ) )
= $true )
| ( ( SV173
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_List_Otake @ SV173 @ SV503 @ SV761 )
= ( c_List_Olist_ONil @ SV761 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2633]) ).
thf(2776,plain,
! [SV764: $i,SV514: $i,SV928: $i,SV186: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV186 ) @ SV928 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV186 @ SV514 @ SV764 ) ) @ ( c_Lambda_Osubst @ SV928 @ SV514 @ SV764 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2637]) ).
thf(2777,plain,
! [SV929: $i,SV766: $i,SV516: $i,SV188: $i] :
( ( ( c_ListOrder_Ostep1 @ SV188 @ SV516 @ SV766 @ SV929 )
= $false )
| ( ( ! [SY2426: $i] : ( c_ListOrder_Ostep1 @ SV188 @ ( c_List_Oappend @ SV516 @ SY2426 @ SV929 ) @ ( c_List_Oappend @ SV766 @ SY2426 @ SV929 ) @ SV929 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2638]) ).
thf(2778,plain,
! [SV1023: $i,SV930: $i,SV767: $i,SV517: $i,SV189: $i] :
( ( ( c_ListOrder_Ostep1 @ SV189 @ ( c_List_Oappend @ SV517 @ SV767 @ SV930 ) @ ( c_List_Oappend @ SV517 @ SV1023 @ SV930 ) @ SV930 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV189 @ SV767 @ SV1023 @ SV930 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2639]) ).
thf(2779,plain,
! [SV768: $i,SV1024: $i,SV518: $i,SV190: $i] :
( ( ( c_List_Olistsp @ SV190 @ ( c_List_Oappend @ SV518 @ SV1024 @ SV768 ) @ SV768 )
= $false )
| ( ( c_List_Olistsp @ SV190 @ SV518 @ SV768 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2640]) ).
thf(2780,plain,
! [SV769: $i,SV519: $i,SV1025: $i,SV191: $i] :
( ( ( c_List_Olistsp @ SV191 @ ( c_List_Oappend @ SV1025 @ SV519 @ SV769 ) @ SV769 )
= $false )
| ( ( c_List_Olistsp @ SV191 @ SV519 @ SV769 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2641]) ).
thf(2781,plain,
! [SV521: $i,SV932: $i,SV771: $i,SV193: $i] :
( ( ( ~ ( c_List_Olistsp @ SV193 @ SV771 @ SV932 ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV193 @ SV521 @ SV932 ) )
= $true )
| ( ( c_List_Olistsp @ SV193 @ ( c_List_Oappend @ SV521 @ SV771 @ SV932 ) @ SV932 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2642]) ).
thf(2782,plain,
! [SV934: $i,SV212: $i,SV535: $i,SV779: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV779 @ SV535 ) @ SV212 ) )
= $true )
| ( ( ! [SY2428: $i,SY2429: $i] :
~ ( c_ListOrder_Ostep1 @ SV779 @ ( c_List_Olist_OCons @ SV535 @ SV934 @ SY2428 ) @ ( c_List_Olist_OCons @ SV212 @ SY2429 @ SY2428 ) @ SY2428 ) )
= $true )
| ( ( SV212 = SV535 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2645]) ).
thf(2783,plain,
! [SV213: $i,SV536: $i,SV935: $i,SV780: $i] :
( ( ( SV780 = SV935 )
= $true )
| ( ( ! [SY2430: $i,SY2431: $i] :
~ ( c_ListOrder_Ostep1 @ SY2430 @ ( c_List_Olist_OCons @ SV536 @ SV935 @ SY2431 ) @ ( c_List_Olist_OCons @ SV213 @ SV780 @ SY2431 ) @ SY2431 ) )
= $true )
| ( ( SV213 = SV536 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2646]) ).
thf(2784,plain,
! [SV781: $i,SV1065: $i,SV537: $i,SV214: $i] :
( ( ( ! [SY2482: $i] : ( c_ListOrder_Ostep1 @ SV214 @ ( c_List_Olist_OCons @ SV537 @ SV1065 @ SY2482 ) @ ( c_List_Olist_OCons @ SV781 @ SV1065 @ SY2482 ) @ SY2482 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV214 @ SV537 ) @ SV781 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2647]) ).
thf(2785,plain,
! [SV936: $i,SV215: $i,SV538: $i,SV782: $i] :
( ( ( SV782 = SV538 )
= $true )
| ( ( ! [SY2432: $i,SY2433: $i] :
~ ( c_ListOrder_Ostep1 @ SV215 @ ( c_List_Olist_OCons @ SY2432 @ SV538 @ SV936 ) @ ( c_List_Olist_OCons @ SY2433 @ SV782 @ SV936 ) @ SV936 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV215 @ SV538 @ SV782 @ SV936 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2648]) ).
thf(2786,plain,
! [SV784: $i,SV937: $i,SV540: $i,SV1066: $i,SV217: $i] :
( ( ( ! [SY2483: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV217 @ SV1066 ) @ SY2483 ) )
| ~ ( c_ListOrder_Ostep1 @ SV217 @ ( c_List_Olist_OCons @ SV1066 @ SV540 @ SV937 ) @ ( c_List_Olist_OCons @ SY2483 @ SV784 @ SV937 ) @ SV937 ) ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV217 @ SV540 @ SV784 @ SV937 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2649]) ).
thf(2787,plain,
! [SV1026: $i,SV938: $i,SV785: $i,SV541: $i,SV218: $i] :
( ( ( c_ListOrder_Ostep1 @ SV218 @ ( c_List_Olist_OCons @ SV541 @ SV785 @ SV938 ) @ ( c_List_Olist_OCons @ SV541 @ SV1026 @ SV938 ) @ SV938 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV218 @ SV785 @ SV1026 @ SV938 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2650]) ).
thf(2788,plain,
! [SV1027: $i,SV939: $i,SV787: $i,SV543: $i,SV220: $i] :
( ( ( ( c_List_Oreplicate @ SV220 @ SV543 @ SV787 )
!= ( c_List_Oreplicate @ SV939 @ SV1027 @ SV787 ) )
= $true )
| ( ( ( SV543 = SV1027 )
| ( SV220
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2651]) ).
thf(2789,plain,
! [SV227: $i,SV1028: $i,SV546: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV546 @ SV1028 @ SV227 )
= $true )
| ( ( ! [SY2476: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV546 @ SY2476 @ SV227 )
| ~ ( c_HOL_Oord__class_Oless @ SY2476 @ SV1028 @ SV227 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV227 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2652]) ).
thf(2790,plain,
! [SV228: $i,SV1029: $i,SV547: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV547 @ SV1029 @ SV228 )
= $true )
| ( ( ! [SY2477: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY2477 @ SV1029 @ SV228 )
| ~ ( c_HOL_Oord__class_Oless @ SV547 @ SY2477 @ SV228 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV228 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2653]) ).
thf(2791,plain,
! [SV1067: $i,SV941: $i,SV790: $i,SV549: $i,SV230: $i] :
( ( ( ( c_List_Oreplicate @ SV230 @ SV549 @ SV790 )
!= ( c_List_Oreplicate @ SV941 @ SV1067 @ SV790 ) )
= $true )
| ( ( SV230 = SV941 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2654]) ).
thf(2792,plain,
! [SV244: $i,SV1030: $i,SV946: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV946 @ SV1030 @ SV244 )
= $true )
| ( ( ( SV1030 = SV946 )
| ( c_HOL_Oord__class_Oless @ SV1030 @ SV946 @ SV244 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV244 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2659]) ).
thf(2793,plain,
! [SV245: $i,SV1031: $i,SV947: $i] :
( ( ( SV947 = SV1031 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1031 @ SV947 @ SV245 )
| ( c_HOL_Oord__class_Oless @ SV947 @ SV1031 @ SV245 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV245 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2660]) ).
thf(2794,plain,
! [SV247: $i,SV558: $i,SV794: $i] :
( ( ( SV794 = SV558 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV794 @ SV558 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV558 @ SV794 @ tc_nat )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV247 @ SV558 ) @ SV794 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2661]) ).
thf(2795,plain,
! [SV249: $i,SV1032: $i,SV948: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV948 @ SV1032 @ SV249 )
= $true )
| ( ( ( SV1032 = SV948 )
| ( c_HOL_Oord__class_Oless @ SV1032 @ SV948 @ SV249 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV249 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2662]) ).
thf(2796,plain,
! [SV250: $i,SV1033: $i,SV949: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV949 @ SV1033 @ SV250 )
= $true )
| ( ( ( SV1033 = SV949 )
| ( c_HOL_Oord__class_Oless @ SV1033 @ SV949 @ SV250 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV250 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2663]) ).
thf(2797,plain,
! [SV251: $i,SV1034: $i,SV950: $i] :
( ( ( SV950 = SV1034 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV950 @ SV1034 @ SV251 )
| ( c_HOL_Oord__class_Oless @ SV1034 @ SV950 @ SV251 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV251 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2664]) ).
thf(2798,plain,
! [SV796: $i,SV253: $i,SV561: $i,SV1035: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV1035 ) @ SV561 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV253 @ SV1035 @ SV796 ) )
= $true )
| ( ( c_Type_Otyping @ SV253 @ SV561 @ SV796 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2666]) ).
thf(2799,plain,
! [SV254: $i,SV1036: $i,SV951: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV951 @ SV1036 @ SV254 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1036 @ SV951 @ SV254 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV254 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2667]) ).
thf(2800,plain,
! [SV255: $i,SV1037: $i,SV952: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV952 @ SV1037 @ SV255 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1037 @ SV952 @ SV255 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV255 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2668]) ).
thf(2801,plain,
! [SV256: $i,SV1038: $i,SV953: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV953 @ SV1038 @ SV256 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1038 @ SV953 @ SV256 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV256 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2669]) ).
thf(2802,plain,
! [SV257: $i,SV1039: $i,SV954: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV954 @ SV1039 @ SV257 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1039 @ SV954 @ SV257 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV257 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2670]) ).
thf(2803,plain,
! [SV1040: $i,SV800: $i,SV567: $i,SV265: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV265 ) @ SV567 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV800 ) @ SV1040 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV265 = SV800 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2672]) ).
thf(2804,plain,
! [SV955: $i,SV801: $i,SV568: $i,SV266: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV266 ) @ SV568 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV801 ) @ SV955 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV568 = SV955 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2673]) ).
thf(2805,plain,
! [SV1041: $i,SV957: $i,SV807: $i,SV574: $i,SV273: $i] :
( ( ( ( c_List_Olist_OCons @ SV273 @ SV574 @ SV807 )
!= ( c_List_Oappend @ SV957 @ SV1041 @ SV807 ) )
= $true )
| ( ( ( SV574
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV273 @ SV574 @ SV957 @ SV1041 @ SV807 ) @ SV1041 @ SV807 ) )
| ( SV957
= ( c_List_Olist_ONil @ SV807 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2678]) ).
thf(2806,plain,
! [SV1042: $i,SV958: $i,SV808: $i,SV575: $i,SV274: $i] :
( ( ( ( c_List_Oappend @ SV274 @ SV575 @ SV808 )
!= ( c_List_Olist_OCons @ SV958 @ SV1042 @ SV808 ) )
= $true )
| ( ( ( SV274
= ( c_List_Olist_OCons @ SV958 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV958 @ SV1042 @ SV274 @ SV575 @ SV808 ) @ SV808 ) )
| ( SV274
= ( c_List_Olist_ONil @ SV808 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2679]) ).
thf(2807,plain,
! [SV578: $i,SV277: $i,SV959: $i,SV811: $i] :
( ( ( SV811 = SV959 )
= $true )
| ( ( ! [SY2450: $i,SY2451: $i] :
~ ( c_ListOrder_Ostep1 @ SY2450 @ ( c_List_Oappend @ SV277 @ ( c_List_Olist_OCons @ SV811 @ ( c_List_Olist_ONil @ SY2451 ) @ SY2451 ) @ SY2451 ) @ ( c_List_Oappend @ SV578 @ ( c_List_Olist_OCons @ SV959 @ ( c_List_Olist_ONil @ SY2451 ) @ SY2451 ) @ SY2451 ) @ SY2451 ) )
= $true )
| ( ( SV277 = SV578 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2680]) ).
thf(2808,plain,
! [SV960: $i,SV278: $i,SV812: $i,SV579: $i] :
( ( ( SV579 = SV812 )
= $true )
| ( ( ! [SY2452: $i,SY2453: $i] :
~ ( c_ListOrder_Ostep1 @ SV278 @ ( c_List_Oappend @ SV960 @ ( c_List_Olist_OCons @ SV579 @ ( c_List_Olist_ONil @ SY2452 ) @ SY2452 ) @ SY2452 ) @ ( c_List_Oappend @ SY2453 @ ( c_List_Olist_OCons @ SV812 @ ( c_List_Olist_ONil @ SY2452 ) @ SY2452 ) @ SY2452 ) @ SY2452 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV278 @ SV579 ) @ SV812 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2681]) ).
thf(2809,plain,
! [SV1043: $i,SV961: $i,SV813: $i,SV580: $i,SV279: $i] :
( ( ( ( c_List_Oappend @ SV279 @ SV580 @ SV813 )
!= ( c_List_Olist_OCons @ SV961 @ SV1043 @ SV813 ) )
= $true )
| ( ( ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV961 @ SV1043 @ SV279 @ SV580 @ SV813 ) @ SV580 @ SV813 )
= SV1043 )
| ( SV279
= ( c_List_Olist_ONil @ SV813 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2682]) ).
thf(2810,plain,
! [SV1044: $i,SV962: $i,SV814: $i,SV581: $i,SV280: $i] :
( ( ( ( c_List_Olist_OCons @ SV280 @ SV581 @ SV814 )
!= ( c_List_Oappend @ SV962 @ SV1044 @ SV814 ) )
= $true )
| ( ( ( ( c_List_Olist_OCons @ SV280 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV280 @ SV581 @ SV962 @ SV1044 @ SV814 ) @ SV814 )
= SV962 )
| ( SV962
= ( c_List_Olist_ONil @ SV814 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2683]) ).
thf(2811,plain,
! [SV816: $i,SV583: $i,SV1068: $i,SV963: $i,SV282: $i] :
( ( ( ! [SY2484: $i] :
( ( c_ListOrder_Ostep1 @ SV282 @ SV963 @ SV1068 @ SY2484 )
| ~ ( c_ListOrder_Ostep1 @ SV282 @ ( c_List_Oappend @ SV963 @ ( c_List_Olist_OCons @ SV583 @ ( c_List_Olist_ONil @ SY2484 ) @ SY2484 ) @ SY2484 ) @ ( c_List_Oappend @ SV1068 @ ( c_List_Olist_OCons @ SV816 @ ( c_List_Olist_ONil @ SY2484 ) @ SY2484 ) @ SY2484 ) @ SY2484 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV282 @ SV583 ) @ SV816 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2684]) ).
thf(2812,plain,
! [SV964: $i,SV817: $i,SV584: $i,SV283: $i] :
( ( ( ( c_List_Orev @ SV283 @ SV584 )
= ( c_List_Olist_OCons @ SV817 @ SV964 @ SV584 ) )
= $false )
| ( ( SV283
= ( c_List_Oappend @ ( c_List_Orev @ SV964 @ SV584 ) @ ( c_List_Olist_OCons @ SV817 @ ( c_List_Olist_ONil @ SV584 ) @ SV584 ) @ SV584 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2685]) ).
thf(2813,plain,
! [SV965: $i,SV587: $i,SV286: $i,SV820: $i] :
( ( ( c_ListOrder_Ostep1 @ SV820 @ SV286 @ SV587 @ SV965 )
= $true )
| ( ( ! [SY2458: $i,SY2459: $i] :
~ ( c_ListOrder_Ostep1 @ SV820 @ ( c_List_Oappend @ SV286 @ ( c_List_Olist_OCons @ SY2458 @ ( c_List_Olist_ONil @ SV965 ) @ SV965 ) @ SV965 ) @ ( c_List_Oappend @ SV587 @ ( c_List_Olist_OCons @ SY2459 @ ( c_List_Olist_ONil @ SV965 ) @ SV965 ) @ SV965 ) @ SV965 ) )
= $true )
| ( ( SV286 = SV587 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2686]) ).
thf(2814,plain,
! [SV288: $i,SV589: $i,SV1069: $i,SV1045: $i,SV822: $i] :
( ( ( ~ ( c_Type_Otyping @ SV822 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1045 ) @ SV1069 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV589 )
| ~ ( c_Type_Otyping @ SV822 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1045 ) @ SV1069 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV288 ) )
= $true )
| ( ( SV288 = SV589 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2687]) ).
thf(2815,plain,
! [SV968: $i,SV826: $i,SV593: $i,SV293: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV293 ) @ SV593 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV826 @ SV968 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( SV293
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV826 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV293 @ SV593 @ SV826 @ SV968 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV968
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2691]) ).
thf(2816,plain,
! [SV827: $i,SV297: $i,SV596: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV596 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV297 @ SV596 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV827 @ 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 @ SV297 ) ) @ SV596 ) @ SV827 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2693]) ).
thf(2817,plain,
! [SV970: $i,SV828: $i,SV597: $i,SV298: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV298 ) @ SV597 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV828 @ SV970 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( SV970
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV298 @ SV597 @ SV828 @ SV970 ) @ ( c_List_Olist_OCons @ SV597 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( SV970
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2694]) ).
thf(2818,plain,
! [SV1046: $i,SV976: $i,SV833: $i,SV604: $i,SV306: $i] :
( ( ( ( c_List_Oappend @ SV306 @ ( c_List_Olist_OCons @ SV604 @ ( c_List_Olist_ONil @ SV833 ) @ SV833 ) @ SV833 )
!= ( c_List_Oappend @ SV976 @ ( c_List_Olist_OCons @ SV1046 @ ( c_List_Olist_ONil @ SV833 ) @ SV833 ) @ SV833 ) )
= $true )
| ( ( SV604 = SV1046 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2695]) ).
thf(2819,plain,
! [SV1070: $i,SV977: $i,SV834: $i,SV605: $i,SV307: $i] :
( ( ( ( c_List_Oappend @ SV307 @ ( c_List_Olist_OCons @ SV605 @ ( c_List_Olist_ONil @ SV834 ) @ SV834 ) @ SV834 )
!= ( c_List_Oappend @ SV977 @ ( c_List_Olist_OCons @ SV1070 @ ( c_List_Olist_ONil @ SV834 ) @ SV834 ) @ SV834 ) )
= $true )
| ( ( SV307 = SV977 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2696]) ).
thf(2820,plain,
! [SV1047: $i,SV837: $i,SV609: $i,SV311: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV311 ) @ SV609 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV837 ) @ SV1047 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV311 = SV837 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2697]) ).
thf(2821,plain,
! [SV979: $i,SV838: $i,SV610: $i,SV312: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV312 ) @ SV610 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV838 ) @ SV979 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV610 = SV979 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2698]) ).
thf(2822,plain,
! [SV1048: $i,SV980: $i,SV839: $i,SV611: $i,SV313: $i] :
( ( ( ( c_List_Olist_OCons @ SV313 @ SV611 @ SV839 )
!= ( c_List_Olist_OCons @ SV980 @ SV1048 @ SV839 ) )
= $true )
| ( ( SV611 = SV1048 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2699]) ).
thf(2823,plain,
! [SV1071: $i,SV981: $i,SV840: $i,SV612: $i,SV314: $i] :
( ( ( ( c_List_Olist_OCons @ SV314 @ SV612 @ SV840 )
!= ( c_List_Olist_OCons @ SV981 @ SV1071 @ SV840 ) )
= $true )
| ( ( SV314 = SV981 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2700]) ).
thf(2824,plain,
! [SV1049: $i,SV849: $i,SV621: $i,SV324: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV324 ) @ SV621 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV849 ) @ SV1049 ) )
= $false )
| ( ( SV324 = SV849 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2707]) ).
thf(2825,plain,
! [SV983: $i,SV850: $i,SV622: $i,SV325: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV325 ) @ SV622 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV850 ) @ SV983 ) )
= $false )
| ( ( SV622 = SV983 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2708]) ).
thf(2826,plain,
! [SV987: $i,SV857: $i,SV636: $i,SV340: $i] :
( ( ( ( c_List_Oappend @ SV340 @ SV636 @ SV857 )
= ( c_List_Oappend @ SV340 @ SV987 @ SV857 ) )
= $false )
| ( ( SV636 = SV987 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2715]) ).
thf(2827,plain,
! [SV988: $i,SV858: $i,SV637: $i,SV341: $i] :
( ( ( ( c_List_Oappend @ SV341 @ SV637 @ SV858 )
= ( c_List_Oappend @ SV988 @ SV637 @ SV858 ) )
= $false )
| ( ( SV341 = SV988 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2716]) ).
thf(2828,plain,
! [SV1072: $i,SV1050: $i,SV989: $i,SV859: $i,SV638: $i,SV343: $i] :
( ( ( c_List_Ofoldl @ SV343 @ SV638 @ ( c_List_Olist_OCons @ SV859 @ SV989 @ SV1050 ) @ SV1072 @ SV1050 )
= ( c_List_Ofoldl @ SV343 @ ( hAPP @ ( hAPP @ SV343 @ SV638 ) @ SV859 ) @ SV989 @ SV1072 @ SV1050 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2717]) ).
thf(2829,plain,
! [SV1073: $i,SV1051: $i,SV994: $i,SV871: $i,SV650: $i,SV356: $i] :
( ( ( c_List_Ofoldl @ SV356 @ SV650 @ ( c_List_Oappend @ SV871 @ SV994 @ SV1051 ) @ SV1073 @ SV1051 )
= ( c_List_Ofoldl @ SV356 @ ( c_List_Ofoldl @ SV356 @ SV650 @ SV871 @ SV1073 @ SV1051 ) @ SV994 @ SV1073 @ SV1051 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2720]) ).
thf(2830,plain,
! [SV661: $i,SV875: $i,SV6: $i,SV367: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV367 @ ( c_Nat_Osize__class_Osize @ SV6 @ ( tc_List_Olist @ SV875 ) ) @ tc_nat ) )
= $true )
| ( ( ( c_List_Onth @ SV6 @ SV367 @ SV875 )
= SV661 )
= $true )
| ( ( ( c_List_Olist__update @ SV6 @ SV367 @ SV661 @ SV875 )
= SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2723]) ).
thf(2831,plain,
! [SV1053: $i,SV373: $i,SV667: $i,SV12: $i,SV879: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV879 @ ( c_Nat_Osize__class_Osize @ SV12 @ ( tc_List_Olist @ SV667 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV12 @ SV373 @ SV667 ) @ SV879 @ SV1053 @ SV667 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV12 @ SV879 @ SV1053 @ SV667 ) @ SV373 @ SV667 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2727]) ).
thf(2832,plain,
! [SV1054: $i,SV374: $i,SV668: $i,SV13: $i,SV880: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV880 @ ( c_Nat_Osize__class_Osize @ SV13 @ ( tc_List_Olist @ SV668 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV13 @ SV374 @ SV668 ) @ SV880 @ SV1054 @ SV668 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV13 @ SV880 @ SV1054 @ SV668 ) @ SV374 @ SV668 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2728]) ).
thf(2833,plain,
! [SV1074: $i,SV998: $i,SV881: $i,SV670: $i,SV376: $i,SV15: $i] :
( ( ( ( c_List_Olist__update @ ( c_List_Olist__update @ SV15 @ SV376 @ SV670 @ SV881 ) @ SV998 @ SV1074 @ SV881 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV15 @ SV998 @ SV1074 @ SV881 ) @ SV376 @ SV670 @ SV881 ) )
= $true )
| ( ( SV376 = SV998 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2729]) ).
thf(2834,plain,
! [SV672: $i,SV883: $i,SV17: $i,SV1000: $i,SV378: $i] :
( ( ( SV378 = SV1000 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV378 @ ( c_Nat_Osize__class_Osize @ SV17 @ ( tc_List_Olist @ SV883 ) ) @ tc_nat ) )
= $true )
| ( ( ( c_List_Onth @ ( c_List_Olist__update @ SV17 @ SV378 @ SV672 @ SV883 ) @ SV1000 @ SV883 )
= ( c_List_Onth @ SV17 @ SV1000 @ SV883 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2730]) ).
thf(2835,plain,
! [SV886: $i,SV679: $i,SV385: $i,SV24: $i] :
( ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SV385 ) ) @ SV679 @ SV385 )
!= SV24 )
= $true )
| ( ( ( SV679
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV679 @ ( tc_List_Olist @ SV385 ) ) @ SV24 @ SV385 ) )
| ( ( c_List_Oappend @ SV679 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV679 @ ( tc_List_Olist @ SV385 ) ) @ SV24 @ SV385 ) @ SV886 @ SV385 ) @ SV385 )
= ( c_List_Oappend @ SV24 @ SV886 @ SV385 ) ) )
= $true )
| ( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SV385 ) ) @ SV679 @ SV385 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV679 @ ( tc_List_Olist @ SV385 ) ) @ SV24 @ SV385 ) @ SV886 @ SV385 ) @ SV385 )
= SV886 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2732]) ).
thf(2836,plain,
! [SV1055: $i,SV887: $i,SV680: $i,SV386: $i,SV25: $i] :
( ( ( ( c_List_Odrop @ SV25 @ SV386 @ SV680 )
= ( c_List_Olist_OCons @ SV887 @ SV1055 @ SV680 ) )
= $false )
| ( ( ( c_List_Onth @ SV386 @ SV25 @ SV680 )
= SV887 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2733]) ).
thf(2837,plain,
! [SV692: $i,SV401: $i,SV890: $i,SV1075: $i,SV1003: $i,SV40: $i] :
( ( ( ~ ( c_Type_Otyping @ SV40 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1003 ) @ SV1075 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV890 )
| ! [SY2485: $i] :
~ ( c_Type_Otypings @ SV40 @ SV1075 @ SY2485 )
| ~ ( c_Type_Otyping @ SV40 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1003 ) @ SV1075 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV401 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV692 ) )
= $true )
| ( ( c_Type_Otypings @ SV40 @ SV401 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV692 @ SV890 @ SV40 @ SV401 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2736]) ).
thf(2838,plain,
! [SV1076: $i,SV65: $i,SV1058: $i] :
( ( ( ( ( c_Int_Onumber__class_Onumber__of @ SV1058 @ SV65 )
!= ( c_Int_Onumber__class_Onumber__of @ SV1076 @ SV65 ) )
| ( SV1058 = SV1076 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV65 )
= $false )
| ( ( class_Int_Oring__char__0 @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2739]) ).
thf(2839,plain,
! [SV421: $i,SV701: $i,SV1059: $i,SV1006: $i,SV69: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV69 @ SV1006 @ SV1059 ) @ SV701 ) @ SV421 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV69 @ SV421 ) @ SV701 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2742]) ).
thf(2840,plain,
! [SV702: $i,SV422: $i,SV897: $i,SV1007: $i,SV70: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV1007 ) @ SV897 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV70 @ SV422 @ SV702 ) @ SV897 ) @ SV1007 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2743]) ).
thf(2841,plain,
! [SV423: $i,SV703: $i,SV1060: $i,SV1008: $i,SV71: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV71 @ SV1008 @ SV1060 ) @ SV703 ) @ SV423 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV71 @ SV423 ) @ SV703 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2744]) ).
thf(2842,plain,
! [SV704: $i,SV424: $i,SV898: $i,SV1009: $i,SV72: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV72 @ SV1009 ) @ SV898 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV72 @ SV424 @ SV704 ) @ SV898 ) @ SV1009 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2745]) ).
thf(2843,plain,
! [SV1010: $i,SV429: $i,SV709: $i,SV77: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV77 @ SV709 ) @ SV429 ) @ SV1010 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV77 @ SV1010 @ SV709 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV77 @ SV429 @ SV709 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2746]) ).
thf(2844,plain,
! [SV430: $i,SV710: $i,SV1011: $i,SV78: $i] :
( ( ( c_Wellfounded_Oaccp @ SV78 @ SV1011 @ SV710 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV78 @ SV710 ) @ SV430 ) @ SV1011 ) ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV78 @ SV430 @ SV710 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2747]) ).
thf(2845,plain,
! [SV711: $i,SV899: $i,SV1061: $i,SV431: $i,SV79: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV79 @ SV431 ) @ SV1061 ) @ SV899 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV79 @ SV431 ) @ SV711 ) @ SV1061 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV79 @ SV431 ) @ SV711 ) @ SV899 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2748]) ).
thf(2846,plain,
! [SV1012: $i,SV83: $i,SV901: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV901 @ SV83 )
= ( c_Nat_Osemiring__1__class_Oof__nat @ SV1012 @ SV83 ) )
= $false )
| ( ( SV901 = SV1012 )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2750]) ).
thf(2847,plain,
! [SV440: $i,SV903: $i,SV94: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV94 @ SV903 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV903 @ SV440 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV94 ) @ SV440 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2752]) ).
thf(2848,plain,
! [SV717: $i,SV905: $i,SV1062: $i,SV448: $i,SV104: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV104 @ SV448 ) @ SV1062 ) @ SV905 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV104 @ SV717 ) @ SV1062 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV104 @ SV448 ) @ SV717 ) @ SV905 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2753]) ).
thf(2849,plain,
! [SV718: $i,SV449: $i,SV906: $i,SV1063: $i,SV105: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV105 @ SV1063 ) @ SV906 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV105 @ SV449 ) @ SV718 ) @ SV1063 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV105 @ SV449 ) @ SV718 ) @ SV906 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2754]) ).
thf(2850,plain,
! [SV719: $i,SV1013: $i,SV450: $i,SV106: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV106 @ SV450 ) @ SV1013 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV106 @ SV1013 @ SV719 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV106 @ SV450 @ SV719 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2755]) ).
thf(2851,plain,
! [SV720: $i,SV1014: $i,SV451: $i,SV107: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV107 @ SV451 ) @ SV1014 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV107 @ SV1014 @ SV720 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV107 @ SV451 @ SV720 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2756]) ).
thf(2852,plain,
! [SV113: $i,SV1015: $i,SV908: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV908 @ SV1015 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV908 @ SV113 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1015 @ SV113 ) @ SV113 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2757]) ).
thf(2853,plain,
! [SV1016: $i,SV114: $i,SV909: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV909 @ SV114 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1016 @ SV114 ) @ SV114 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV909 @ SV1016 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2758]) ).
thf(2854,plain,
! [SV724: $i,SV122: $i,SV910: $i,SV456: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV456 ) @ SV910 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV122 ) @ SV724 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV122 ) @ SV456 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV724 ) @ SV910 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2759]) ).
thf(2855,plain,
! [SV470: $i,SV737: $i,SV1017: $i,SV136: $i] :
( ( ( c_Type_Otyping @ SV136 @ SV1017 @ SV737 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV1017 ) @ SV470 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV136 @ SV470 @ SV737 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2765]) ).
thf(2856,plain,
! [SV749: $i,SV154: $i,SV485: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV485 @ 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 @ SV154 ) ) @ SV485 ) @ SV749 @ 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 @ SV154 @ SV485 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV749 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2769]) ).
thf(2857,plain,
! [SV1019: $i,SV921: $i,SV752: $i,SV489: $i,SV159: $i] :
( ( ( ( c_List_Oappend @ SV159 @ SV489 @ SV752 )
= ( c_List_Olist_OCons @ SV921 @ SV1019 @ SV752 ) )
= $false )
| ( ( ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV921 @ SV1019 @ SV159 @ SV489 @ SV752 ) @ SV489 @ SV752 )
= SV1019 )
| ( SV489
= ( c_List_Olist_OCons @ SV921 @ SV1019 @ SV752 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2771]) ).
thf(2858,plain,
! [SV1020: $i,SV922: $i,SV753: $i,SV490: $i,SV160: $i] :
( ( ( ( c_List_Olist_OCons @ SV160 @ SV490 @ SV753 )
= ( c_List_Oappend @ SV922 @ SV1020 @ SV753 ) )
= $false )
| ( ( ( ( c_List_Olist_OCons @ SV160 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV160 @ SV490 @ SV922 @ SV1020 @ SV753 ) @ SV753 )
= SV922 )
| ( ( c_List_Olist_OCons @ SV160 @ SV490 @ SV753 )
= SV1020 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2772]) ).
thf(2859,plain,
! [SV1021: $i,SV923: $i,SV754: $i,SV491: $i,SV161: $i] :
( ( ( ( c_List_Oappend @ SV161 @ SV491 @ SV754 )
= ( c_List_Olist_OCons @ SV923 @ SV1021 @ SV754 ) )
= $false )
| ( ( ( SV161
= ( c_List_Olist_OCons @ SV923 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV923 @ SV1021 @ SV161 @ SV491 @ SV754 ) @ SV754 ) )
| ( SV491
= ( c_List_Olist_OCons @ SV923 @ SV1021 @ SV754 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2773]) ).
thf(2860,plain,
! [SV1022: $i,SV924: $i,SV755: $i,SV492: $i,SV162: $i] :
( ( ( ( c_List_Olist_OCons @ SV162 @ SV492 @ SV755 )
= ( c_List_Oappend @ SV924 @ SV1022 @ SV755 ) )
= $false )
| ( ( ( SV492
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV162 @ SV492 @ SV924 @ SV1022 @ SV755 ) @ SV1022 @ SV755 ) )
| ( ( c_List_Olist_OCons @ SV162 @ SV492 @ SV755 )
= SV1022 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2774]) ).
thf(2861,plain,
! [SV766: $i,SV929: $i,SV1077: $i,SV516: $i,SV188: $i] :
( ( ( c_ListOrder_Ostep1 @ SV188 @ ( c_List_Oappend @ SV516 @ SV1077 @ SV929 ) @ ( c_List_Oappend @ SV766 @ SV1077 @ SV929 ) @ SV929 )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV188 @ SV516 @ SV766 @ SV929 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2777]) ).
thf(2862,plain,
! [SV517: $i,SV930: $i,SV1023: $i,SV767: $i,SV189: $i] :
( ( ( c_ListOrder_Ostep1 @ SV189 @ SV767 @ SV1023 @ SV930 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV189 @ ( c_List_Oappend @ SV517 @ SV767 @ SV930 ) @ ( c_List_Oappend @ SV517 @ SV1023 @ SV930 ) @ SV930 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2778]) ).
thf(2863,plain,
! [SV521: $i,SV932: $i,SV771: $i,SV193: $i] :
( ( ( c_List_Olistsp @ SV193 @ SV771 @ SV932 )
= $false )
| ( ( ~ ( c_List_Olistsp @ SV193 @ SV521 @ SV932 ) )
= $true )
| ( ( c_List_Olistsp @ SV193 @ ( c_List_Oappend @ SV521 @ SV771 @ SV932 ) @ SV932 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2781]) ).
thf(2864,plain,
! [SV212: $i,SV1078: $i,SV934: $i,SV535: $i,SV779: $i] :
( ( ( ! [SY2486: $i] :
~ ( c_ListOrder_Ostep1 @ SV779 @ ( c_List_Olist_OCons @ SV535 @ SV934 @ SV1078 ) @ ( c_List_Olist_OCons @ SV212 @ SY2486 @ SV1078 ) @ SV1078 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV779 @ SV535 ) @ SV212 ) )
= $true )
| ( ( SV212 = SV535 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2782]) ).
thf(2865,plain,
! [SV780: $i,SV213: $i,SV935: $i,SV536: $i,SV1079: $i] :
( ( ( ! [SY2487: $i] :
~ ( c_ListOrder_Ostep1 @ SV1079 @ ( c_List_Olist_OCons @ SV536 @ SV935 @ SY2487 ) @ ( c_List_Olist_OCons @ SV213 @ SV780 @ SY2487 ) @ SY2487 ) )
= $true )
| ( ( SV780 = SV935 )
= $true )
| ( ( SV213 = SV536 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2783]) ).
thf(2866,plain,
! [SV781: $i,SV1080: $i,SV1065: $i,SV537: $i,SV214: $i] :
( ( ( c_ListOrder_Ostep1 @ SV214 @ ( c_List_Olist_OCons @ SV537 @ SV1065 @ SV1080 ) @ ( c_List_Olist_OCons @ SV781 @ SV1065 @ SV1080 ) @ SV1080 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV214 @ SV537 ) @ SV781 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2784]) ).
thf(2867,plain,
! [SV782: $i,SV936: $i,SV538: $i,SV1081: $i,SV215: $i] :
( ( ( ! [SY2488: $i] :
~ ( c_ListOrder_Ostep1 @ SV215 @ ( c_List_Olist_OCons @ SV1081 @ SV538 @ SV936 ) @ ( c_List_Olist_OCons @ SY2488 @ SV782 @ SV936 ) @ SV936 ) )
= $true )
| ( ( SV782 = SV538 )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV215 @ SV538 @ SV782 @ SV936 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2785]) ).
thf(2868,plain,
! [SV784: $i,SV937: $i,SV540: $i,SV1082: $i,SV1066: $i,SV217: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV217 @ SV1066 ) @ SV1082 ) )
| ~ ( c_ListOrder_Ostep1 @ SV217 @ ( c_List_Olist_OCons @ SV1066 @ SV540 @ SV937 ) @ ( c_List_Olist_OCons @ SV1082 @ SV784 @ SV937 ) @ SV937 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV217 @ SV540 @ SV784 @ SV937 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2786]) ).
thf(2869,plain,
! [SV541: $i,SV938: $i,SV1026: $i,SV785: $i,SV218: $i] :
( ( ( c_ListOrder_Ostep1 @ SV218 @ SV785 @ SV1026 @ SV938 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV218 @ ( c_List_Olist_OCons @ SV541 @ SV785 @ SV938 ) @ ( c_List_Olist_OCons @ SV541 @ SV1026 @ SV938 ) @ SV938 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2787]) ).
thf(2870,plain,
! [SV1027: $i,SV939: $i,SV787: $i,SV543: $i,SV220: $i] :
( ( ( ( c_List_Oreplicate @ SV220 @ SV543 @ SV787 )
= ( c_List_Oreplicate @ SV939 @ SV1027 @ SV787 ) )
= $false )
| ( ( ( SV543 = SV1027 )
| ( SV220
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2788]) ).
thf(2871,plain,
! [SV1028: $i,SV227: $i,SV1083: $i,SV546: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV546 @ SV1083 @ SV227 )
| ~ ( c_HOL_Oord__class_Oless @ SV1083 @ SV1028 @ SV227 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV546 @ SV1028 @ SV227 )
= $true )
| ( ( class_Orderings_Oorder @ SV227 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2789]) ).
thf(2872,plain,
! [SV547: $i,SV228: $i,SV1029: $i,SV1084: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1084 @ SV1029 @ SV228 )
| ~ ( c_HOL_Oord__class_Oless @ SV547 @ SV1084 @ SV228 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV547 @ SV1029 @ SV228 )
= $true )
| ( ( class_Orderings_Opreorder @ SV228 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2790]) ).
thf(2873,plain,
! [SV1067: $i,SV941: $i,SV790: $i,SV549: $i,SV230: $i] :
( ( ( ( c_List_Oreplicate @ SV230 @ SV549 @ SV790 )
= ( c_List_Oreplicate @ SV941 @ SV1067 @ SV790 ) )
= $false )
| ( ( SV230 = SV941 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2791]) ).
thf(2874,plain,
! [SV244: $i,SV946: $i,SV1030: $i] :
( ( ( SV1030 = SV946 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1030 @ SV946 @ SV244 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV946 @ SV1030 @ SV244 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV244 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2792]) ).
thf(2875,plain,
! [SV245: $i,SV947: $i,SV1031: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1031 @ SV947 @ SV245 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV947 @ SV1031 @ SV245 )
= $true )
| ( ( SV947 = SV1031 )
= $true )
| ( ( class_Orderings_Olinorder @ SV245 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2793]) ).
thf(2876,plain,
! [SV249: $i,SV948: $i,SV1032: $i] :
( ( ( SV1032 = SV948 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1032 @ SV948 @ SV249 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV948 @ SV1032 @ SV249 )
= $true )
| ( ( class_Orderings_Olinorder @ SV249 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2795]) ).
thf(2877,plain,
! [SV250: $i,SV949: $i,SV1033: $i] :
( ( ( SV1033 = SV949 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1033 @ SV949 @ SV250 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV949 @ SV1033 @ SV250 )
= $true )
| ( ( class_Orderings_Olinorder @ SV250 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2796]) ).
thf(2878,plain,
! [SV251: $i,SV1034: $i,SV950: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV950 @ SV1034 @ SV251 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1034 @ SV950 @ SV251 )
= $true )
| ( ( SV950 = SV1034 )
= $true )
| ( ( class_Orderings_Olinorder @ SV251 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2797]) ).
thf(2879,plain,
! [SV796: $i,SV253: $i,SV561: $i,SV1035: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV1035 ) @ SV561 ) )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV253 @ SV1035 @ SV796 ) )
= $true )
| ( ( c_Type_Otyping @ SV253 @ SV561 @ SV796 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2798]) ).
thf(2880,plain,
! [SV254: $i,SV1036: $i,SV951: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV951 @ SV1036 @ SV254 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1036 @ SV951 @ SV254 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV254 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2799]) ).
thf(2881,plain,
! [SV255: $i,SV1037: $i,SV952: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV952 @ SV1037 @ SV255 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1037 @ SV952 @ SV255 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV255 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2800]) ).
thf(2882,plain,
! [SV256: $i,SV1038: $i,SV953: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV953 @ SV1038 @ SV256 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1038 @ SV953 @ SV256 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV256 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2801]) ).
thf(2883,plain,
! [SV257: $i,SV1039: $i,SV954: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV954 @ SV1039 @ SV257 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1039 @ SV954 @ SV257 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV257 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2802]) ).
thf(2884,plain,
! [SV1041: $i,SV957: $i,SV807: $i,SV574: $i,SV273: $i] :
( ( ( ( c_List_Olist_OCons @ SV273 @ SV574 @ SV807 )
= ( c_List_Oappend @ SV957 @ SV1041 @ SV807 ) )
= $false )
| ( ( ( SV574
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV273 @ SV574 @ SV957 @ SV1041 @ SV807 ) @ SV1041 @ SV807 ) )
| ( SV957
= ( c_List_Olist_ONil @ SV807 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2805]) ).
thf(2885,plain,
! [SV1042: $i,SV958: $i,SV808: $i,SV575: $i,SV274: $i] :
( ( ( ( c_List_Oappend @ SV274 @ SV575 @ SV808 )
= ( c_List_Olist_OCons @ SV958 @ SV1042 @ SV808 ) )
= $false )
| ( ( ( SV274
= ( c_List_Olist_OCons @ SV958 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV958 @ SV1042 @ SV274 @ SV575 @ SV808 ) @ SV808 ) )
| ( SV274
= ( c_List_Olist_ONil @ SV808 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2806]) ).
thf(2886,plain,
! [SV959: $i,SV578: $i,SV811: $i,SV277: $i,SV1085: $i] :
( ( ( ! [SY2489: $i] :
~ ( c_ListOrder_Ostep1 @ SV1085 @ ( c_List_Oappend @ SV277 @ ( c_List_Olist_OCons @ SV811 @ ( c_List_Olist_ONil @ SY2489 ) @ SY2489 ) @ SY2489 ) @ ( c_List_Oappend @ SV578 @ ( c_List_Olist_OCons @ SV959 @ ( c_List_Olist_ONil @ SY2489 ) @ SY2489 ) @ SY2489 ) @ SY2489 ) )
= $true )
| ( ( SV811 = SV959 )
= $true )
| ( ( SV277 = SV578 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2807]) ).
thf(2887,plain,
! [SV812: $i,SV1086: $i,SV579: $i,SV960: $i,SV278: $i] :
( ( ( ! [SY2490: $i] :
~ ( c_ListOrder_Ostep1 @ SV278 @ ( c_List_Oappend @ SV960 @ ( c_List_Olist_OCons @ SV579 @ ( c_List_Olist_ONil @ SV1086 ) @ SV1086 ) @ SV1086 ) @ ( c_List_Oappend @ SY2490 @ ( c_List_Olist_OCons @ SV812 @ ( c_List_Olist_ONil @ SV1086 ) @ SV1086 ) @ SV1086 ) @ SV1086 ) )
= $true )
| ( ( SV579 = SV812 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV278 @ SV579 ) @ SV812 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2808]) ).
thf(2888,plain,
! [SV1043: $i,SV961: $i,SV813: $i,SV580: $i,SV279: $i] :
( ( ( ( c_List_Oappend @ SV279 @ SV580 @ SV813 )
= ( c_List_Olist_OCons @ SV961 @ SV1043 @ SV813 ) )
= $false )
| ( ( ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV961 @ SV1043 @ SV279 @ SV580 @ SV813 ) @ SV580 @ SV813 )
= SV1043 )
| ( SV279
= ( c_List_Olist_ONil @ SV813 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2809]) ).
thf(2889,plain,
! [SV1044: $i,SV962: $i,SV814: $i,SV581: $i,SV280: $i] :
( ( ( ( c_List_Olist_OCons @ SV280 @ SV581 @ SV814 )
= ( c_List_Oappend @ SV962 @ SV1044 @ SV814 ) )
= $false )
| ( ( ( ( c_List_Olist_OCons @ SV280 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV280 @ SV581 @ SV962 @ SV1044 @ SV814 ) @ SV814 )
= SV962 )
| ( SV962
= ( c_List_Olist_ONil @ SV814 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2810]) ).
thf(2890,plain,
! [SV816: $i,SV583: $i,SV1087: $i,SV1068: $i,SV963: $i,SV282: $i] :
( ( ( ( c_ListOrder_Ostep1 @ SV282 @ SV963 @ SV1068 @ SV1087 )
| ~ ( c_ListOrder_Ostep1 @ SV282 @ ( c_List_Oappend @ SV963 @ ( c_List_Olist_OCons @ SV583 @ ( c_List_Olist_ONil @ SV1087 ) @ SV1087 ) @ SV1087 ) @ ( c_List_Oappend @ SV1068 @ ( c_List_Olist_OCons @ SV816 @ ( c_List_Olist_ONil @ SV1087 ) @ SV1087 ) @ SV1087 ) @ SV1087 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV282 @ SV583 ) @ SV816 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2811]) ).
thf(2891,plain,
! [SV587: $i,SV965: $i,SV1088: $i,SV286: $i,SV820: $i] :
( ( ( ! [SY2491: $i] :
~ ( c_ListOrder_Ostep1 @ SV820 @ ( c_List_Oappend @ SV286 @ ( c_List_Olist_OCons @ SV1088 @ ( c_List_Olist_ONil @ SV965 ) @ SV965 ) @ SV965 ) @ ( c_List_Oappend @ SV587 @ ( c_List_Olist_OCons @ SY2491 @ ( c_List_Olist_ONil @ SV965 ) @ SV965 ) @ SV965 ) @ SV965 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV820 @ SV286 @ SV587 @ SV965 )
= $true )
| ( ( SV286 = SV587 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2813]) ).
thf(2892,plain,
! [SV288: $i,SV589: $i,SV1069: $i,SV1045: $i,SV822: $i] :
( ( ( ~ ( c_Type_Otyping @ SV822 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1045 ) @ SV1069 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV589 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV822 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1045 ) @ SV1069 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV288 ) )
= $true )
| ( ( SV288 = SV589 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2814]) ).
thf(2893,plain,
! [SV968: $i,SV593: $i,SV826: $i,SV293: $i] :
( ( ( SV293
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV826 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV293 @ SV593 @ SV826 @ SV968 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV968
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV293 ) @ SV593 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV826 @ SV968 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2815]) ).
thf(2894,plain,
! [SV827: $i,SV596: $i,SV297: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV297 @ SV596 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV827 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV596 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV297 ) ) @ SV596 ) @ SV827 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2816]) ).
thf(2895,plain,
! [SV828: $i,SV597: $i,SV298: $i,SV970: $i] :
( ( ( SV970
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV298 @ SV597 @ SV828 @ SV970 ) @ ( c_List_Olist_OCons @ SV597 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true )
| ( ( SV970
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV298 ) @ SV597 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV828 @ SV970 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2817]) ).
thf(2896,plain,
! [SV1046: $i,SV976: $i,SV833: $i,SV604: $i,SV306: $i] :
( ( ( ( c_List_Oappend @ SV306 @ ( c_List_Olist_OCons @ SV604 @ ( c_List_Olist_ONil @ SV833 ) @ SV833 ) @ SV833 )
= ( c_List_Oappend @ SV976 @ ( c_List_Olist_OCons @ SV1046 @ ( c_List_Olist_ONil @ SV833 ) @ SV833 ) @ SV833 ) )
= $false )
| ( ( SV604 = SV1046 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2818]) ).
thf(2897,plain,
! [SV1070: $i,SV977: $i,SV834: $i,SV605: $i,SV307: $i] :
( ( ( ( c_List_Oappend @ SV307 @ ( c_List_Olist_OCons @ SV605 @ ( c_List_Olist_ONil @ SV834 ) @ SV834 ) @ SV834 )
= ( c_List_Oappend @ SV977 @ ( c_List_Olist_OCons @ SV1070 @ ( c_List_Olist_ONil @ SV834 ) @ SV834 ) @ SV834 ) )
= $false )
| ( ( SV307 = SV977 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2819]) ).
thf(2898,plain,
! [SV1048: $i,SV980: $i,SV839: $i,SV611: $i,SV313: $i] :
( ( ( ( c_List_Olist_OCons @ SV313 @ SV611 @ SV839 )
= ( c_List_Olist_OCons @ SV980 @ SV1048 @ SV839 ) )
= $false )
| ( ( SV611 = SV1048 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2822]) ).
thf(2899,plain,
! [SV1071: $i,SV981: $i,SV840: $i,SV612: $i,SV314: $i] :
( ( ( ( c_List_Olist_OCons @ SV314 @ SV612 @ SV840 )
= ( c_List_Olist_OCons @ SV981 @ SV1071 @ SV840 ) )
= $false )
| ( ( SV314 = SV981 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2823]) ).
thf(2900,plain,
! [SV661: $i,SV875: $i,SV6: $i,SV367: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV367 @ ( c_Nat_Osize__class_Osize @ SV6 @ ( tc_List_Olist @ SV875 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Onth @ SV6 @ SV367 @ SV875 )
= SV661 )
= $true )
| ( ( ( c_List_Olist__update @ SV6 @ SV367 @ SV661 @ SV875 )
= SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2830]) ).
thf(2901,plain,
! [SV672: $i,SV1000: $i,SV883: $i,SV17: $i,SV378: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV378 @ ( c_Nat_Osize__class_Osize @ SV17 @ ( tc_List_Olist @ SV883 ) ) @ tc_nat )
= $false )
| ( ( SV378 = SV1000 )
= $true )
| ( ( ( c_List_Onth @ ( c_List_Olist__update @ SV17 @ SV378 @ SV672 @ SV883 ) @ SV1000 @ SV883 )
= ( c_List_Onth @ SV17 @ SV1000 @ SV883 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2834]) ).
thf(2902,plain,
! [SV886: $i,SV679: $i,SV385: $i,SV24: $i] :
( ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SV385 ) ) @ SV679 @ SV385 )
= SV24 )
= $false )
| ( ( ( SV679
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV679 @ ( tc_List_Olist @ SV385 ) ) @ SV24 @ SV385 ) )
| ( ( c_List_Oappend @ SV679 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV679 @ ( tc_List_Olist @ SV385 ) ) @ SV24 @ SV385 ) @ SV886 @ SV385 ) @ SV385 )
= ( c_List_Oappend @ SV24 @ SV886 @ SV385 ) ) )
= $true )
| ( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SV385 ) ) @ SV679 @ SV385 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV679 @ ( tc_List_Olist @ SV385 ) ) @ SV24 @ SV385 ) @ SV886 @ SV385 ) @ SV385 )
= SV886 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2835]) ).
thf(2903,plain,
! [SV692: $i,SV401: $i,SV890: $i,SV1075: $i,SV1003: $i,SV40: $i] :
( ( ( ~ ( c_Type_Otyping @ SV40 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1003 ) @ SV1075 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV890 ) )
= $true )
| ( ( ! [SY2485: $i] :
~ ( c_Type_Otypings @ SV40 @ SV1075 @ SY2485 )
| ~ ( c_Type_Otyping @ SV40 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1003 ) @ SV1075 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV401 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV692 ) )
= $true )
| ( ( c_Type_Otypings @ SV40 @ SV401 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV692 @ SV890 @ SV40 @ SV401 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2837]) ).
thf(2904,plain,
! [SV1076: $i,SV65: $i,SV1058: $i] :
( ( ( ( c_Int_Onumber__class_Onumber__of @ SV1058 @ SV65 )
!= ( c_Int_Onumber__class_Onumber__of @ SV1076 @ SV65 ) )
= $true )
| ( ( SV1058 = SV1076 )
= $true )
| ( ( class_Int_Onumber__ring @ SV65 )
= $false )
| ( ( class_Int_Oring__char__0 @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2838]) ).
thf(2905,plain,
! [SV429: $i,SV709: $i,SV1010: $i,SV77: $i] :
( ( ( c_Wellfounded_Oaccp @ SV77 @ SV1010 @ SV709 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV77 @ SV709 ) @ SV429 ) @ SV1010 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV77 @ SV429 @ SV709 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2843]) ).
thf(2906,plain,
! [SV1011: $i,SV430: $i,SV710: $i,SV78: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV78 @ SV710 ) @ SV430 ) @ SV1011 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV78 @ SV1011 @ SV710 )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV78 @ SV430 @ SV710 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2844]) ).
thf(2907,plain,
! [SV711: $i,SV899: $i,SV1061: $i,SV431: $i,SV79: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV79 @ SV431 ) @ SV1061 ) @ SV899 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV79 @ SV431 ) @ SV711 ) @ SV1061 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV79 @ SV431 ) @ SV711 ) @ SV899 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2845]) ).
thf(2908,plain,
! [SV717: $i,SV905: $i,SV1062: $i,SV448: $i,SV104: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV104 @ SV448 ) @ SV1062 ) @ SV905 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV104 @ SV717 ) @ SV1062 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV104 @ SV448 ) @ SV717 ) @ SV905 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2848]) ).
thf(2909,plain,
! [SV718: $i,SV449: $i,SV906: $i,SV1063: $i,SV105: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV105 @ SV1063 ) @ SV906 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV105 @ SV449 ) @ SV718 ) @ SV1063 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV105 @ SV449 ) @ SV718 ) @ SV906 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2849]) ).
thf(2910,plain,
! [SV450: $i,SV719: $i,SV1013: $i,SV106: $i] :
( ( ( c_Wellfounded_Oaccp @ SV106 @ SV1013 @ SV719 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV106 @ SV450 ) @ SV1013 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV106 @ SV450 @ SV719 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2850]) ).
thf(2911,plain,
! [SV451: $i,SV720: $i,SV1014: $i,SV107: $i] :
( ( ( c_Wellfounded_Oaccp @ SV107 @ SV1014 @ SV720 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV107 @ SV451 ) @ SV1014 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV107 @ SV451 @ SV720 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2851]) ).
thf(2912,plain,
! [SV910: $i,SV456: $i,SV724: $i,SV122: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV122 ) @ SV724 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV456 ) @ SV910 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV122 ) @ SV456 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV724 ) @ SV910 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2854]) ).
thf(2913,plain,
! [SV737: $i,SV136: $i,SV470: $i,SV1017: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV1017 ) @ SV470 ) )
= $false )
| ( ( c_Type_Otyping @ SV136 @ SV1017 @ SV737 )
= $false )
| ( ( c_Type_Otyping @ SV136 @ SV470 @ SV737 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2855]) ).
thf(2914,plain,
! [SV752: $i,SV489: $i,SV159: $i,SV1019: $i,SV921: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV921 @ SV1019 @ SV159 @ SV489 @ SV752 ) @ SV489 @ SV752 )
= SV1019 )
= $true )
| ( ( SV489
= ( c_List_Olist_OCons @ SV921 @ SV1019 @ SV752 ) )
= $true )
| ( ( ( c_List_Oappend @ SV159 @ SV489 @ SV752 )
= ( c_List_Olist_OCons @ SV921 @ SV1019 @ SV752 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2857]) ).
thf(2915,plain,
! [SV753: $i,SV1020: $i,SV922: $i,SV490: $i,SV160: $i] :
( ( ( ( c_List_Olist_OCons @ SV160 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV160 @ SV490 @ SV922 @ SV1020 @ SV753 ) @ SV753 )
= SV922 )
= $true )
| ( ( ( c_List_Olist_OCons @ SV160 @ SV490 @ SV753 )
= SV1020 )
= $true )
| ( ( ( c_List_Olist_OCons @ SV160 @ SV490 @ SV753 )
= ( c_List_Oappend @ SV922 @ SV1020 @ SV753 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2858]) ).
thf(2916,plain,
! [SV754: $i,SV491: $i,SV1021: $i,SV923: $i,SV161: $i] :
( ( ( SV161
= ( c_List_Olist_OCons @ SV923 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV923 @ SV1021 @ SV161 @ SV491 @ SV754 ) @ SV754 ) )
= $true )
| ( ( SV491
= ( c_List_Olist_OCons @ SV923 @ SV1021 @ SV754 ) )
= $true )
| ( ( ( c_List_Oappend @ SV161 @ SV491 @ SV754 )
= ( c_List_Olist_OCons @ SV923 @ SV1021 @ SV754 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2859]) ).
thf(2917,plain,
! [SV755: $i,SV1022: $i,SV924: $i,SV162: $i,SV492: $i] :
( ( ( SV492
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV162 @ SV492 @ SV924 @ SV1022 @ SV755 ) @ SV1022 @ SV755 ) )
= $true )
| ( ( ( c_List_Olist_OCons @ SV162 @ SV492 @ SV755 )
= SV1022 )
= $true )
| ( ( ( c_List_Olist_OCons @ SV162 @ SV492 @ SV755 )
= ( c_List_Oappend @ SV924 @ SV1022 @ SV755 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2860]) ).
thf(2918,plain,
! [SV771: $i,SV932: $i,SV521: $i,SV193: $i] :
( ( ( c_List_Olistsp @ SV193 @ SV521 @ SV932 )
= $false )
| ( ( c_List_Olistsp @ SV193 @ SV771 @ SV932 )
= $false )
| ( ( c_List_Olistsp @ SV193 @ ( c_List_Oappend @ SV521 @ SV771 @ SV932 ) @ SV932 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2863]) ).
thf(2919,plain,
! [SV1089: $i,SV212: $i,SV1078: $i,SV934: $i,SV535: $i,SV779: $i] :
( ( ( ~ ( c_ListOrder_Ostep1 @ SV779 @ ( c_List_Olist_OCons @ SV535 @ SV934 @ SV1078 ) @ ( c_List_Olist_OCons @ SV212 @ SV1089 @ SV1078 ) @ SV1078 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV779 @ SV535 ) @ SV212 ) )
= $true )
| ( ( SV212 = SV535 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2864]) ).
thf(2920,plain,
! [SV780: $i,SV213: $i,SV1090: $i,SV935: $i,SV536: $i,SV1079: $i] :
( ( ( ~ ( c_ListOrder_Ostep1 @ SV1079 @ ( c_List_Olist_OCons @ SV536 @ SV935 @ SV1090 ) @ ( c_List_Olist_OCons @ SV213 @ SV780 @ SV1090 ) @ SV1090 ) )
= $true )
| ( ( SV780 = SV935 )
= $true )
| ( ( SV213 = SV536 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2865]) ).
thf(2921,plain,
! [SV782: $i,SV1091: $i,SV936: $i,SV538: $i,SV1081: $i,SV215: $i] :
( ( ( ~ ( c_ListOrder_Ostep1 @ SV215 @ ( c_List_Olist_OCons @ SV1081 @ SV538 @ SV936 ) @ ( c_List_Olist_OCons @ SV1091 @ SV782 @ SV936 ) @ SV936 ) )
= $true )
| ( ( SV782 = SV538 )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV215 @ SV538 @ SV782 @ SV936 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2867]) ).
thf(2922,plain,
! [SV784: $i,SV937: $i,SV540: $i,SV1082: $i,SV1066: $i,SV217: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV217 @ SV1066 ) @ SV1082 ) )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV217 @ ( c_List_Olist_OCons @ SV1066 @ SV540 @ SV937 ) @ ( c_List_Olist_OCons @ SV1082 @ SV784 @ SV937 ) @ SV937 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV217 @ SV540 @ SV784 @ SV937 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2868]) ).
thf(2923,plain,
! [SV939: $i,SV787: $i,SV220: $i,SV1027: $i,SV543: $i] :
( ( ( SV543 = SV1027 )
= $true )
| ( ( SV220
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_List_Oreplicate @ SV220 @ SV543 @ SV787 )
= ( c_List_Oreplicate @ SV939 @ SV1027 @ SV787 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2870]) ).
thf(2924,plain,
! [SV1028: $i,SV227: $i,SV1083: $i,SV546: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV546 @ SV1083 @ SV227 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1083 @ SV1028 @ SV227 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV546 @ SV1028 @ SV227 )
= $true )
| ( ( class_Orderings_Oorder @ SV227 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2871]) ).
thf(2925,plain,
! [SV547: $i,SV228: $i,SV1029: $i,SV1084: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1084 @ SV1029 @ SV228 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV547 @ SV1084 @ SV228 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV547 @ SV1029 @ SV228 )
= $true )
| ( ( class_Orderings_Opreorder @ SV228 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2872]) ).
thf(2926,plain,
! [SV561: $i,SV796: $i,SV1035: $i,SV253: $i] :
( ( ( c_Type_Otyping @ SV253 @ SV1035 @ SV796 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV1035 ) @ SV561 ) )
= $false )
| ( ( c_Type_Otyping @ SV253 @ SV561 @ SV796 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2879]) ).
thf(2927,plain,
! [SV254: $i,SV951: $i,SV1036: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1036 @ SV951 @ SV254 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV951 @ SV1036 @ SV254 )
= $false )
| ( ( class_Orderings_Oorder @ SV254 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2880]) ).
thf(2928,plain,
! [SV255: $i,SV952: $i,SV1037: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1037 @ SV952 @ SV255 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV952 @ SV1037 @ SV255 )
= $false )
| ( ( class_Orderings_Olinorder @ SV255 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2881]) ).
thf(2929,plain,
! [SV256: $i,SV953: $i,SV1038: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1038 @ SV953 @ SV256 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV953 @ SV1038 @ SV256 )
= $false )
| ( ( class_Orderings_Opreorder @ SV256 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2882]) ).
thf(2930,plain,
! [SV257: $i,SV954: $i,SV1039: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1039 @ SV954 @ SV257 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV954 @ SV1039 @ SV257 )
= $false )
| ( ( class_Orderings_Opreorder @ SV257 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2883]) ).
thf(2931,plain,
! [SV807: $i,SV1041: $i,SV957: $i,SV273: $i,SV574: $i] :
( ( ( SV574
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV273 @ SV574 @ SV957 @ SV1041 @ SV807 ) @ SV1041 @ SV807 ) )
= $true )
| ( ( SV957
= ( c_List_Olist_ONil @ SV807 ) )
= $true )
| ( ( ( c_List_Olist_OCons @ SV273 @ SV574 @ SV807 )
= ( c_List_Oappend @ SV957 @ SV1041 @ SV807 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2884]) ).
thf(2932,plain,
! [SV808: $i,SV575: $i,SV1042: $i,SV958: $i,SV274: $i] :
( ( ( SV274
= ( c_List_Olist_OCons @ SV958 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV958 @ SV1042 @ SV274 @ SV575 @ SV808 ) @ SV808 ) )
= $true )
| ( ( SV274
= ( c_List_Olist_ONil @ SV808 ) )
= $true )
| ( ( ( c_List_Oappend @ SV274 @ SV575 @ SV808 )
= ( c_List_Olist_OCons @ SV958 @ SV1042 @ SV808 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2885]) ).
thf(2933,plain,
! [SV959: $i,SV578: $i,SV1092: $i,SV811: $i,SV277: $i,SV1085: $i] :
( ( ( ~ ( c_ListOrder_Ostep1 @ SV1085 @ ( c_List_Oappend @ SV277 @ ( c_List_Olist_OCons @ SV811 @ ( c_List_Olist_ONil @ SV1092 ) @ SV1092 ) @ SV1092 ) @ ( c_List_Oappend @ SV578 @ ( c_List_Olist_OCons @ SV959 @ ( c_List_Olist_ONil @ SV1092 ) @ SV1092 ) @ SV1092 ) @ SV1092 ) )
= $true )
| ( ( SV811 = SV959 )
= $true )
| ( ( SV277 = SV578 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2886]) ).
thf(2934,plain,
! [SV812: $i,SV1093: $i,SV1086: $i,SV579: $i,SV960: $i,SV278: $i] :
( ( ( ~ ( c_ListOrder_Ostep1 @ SV278 @ ( c_List_Oappend @ SV960 @ ( c_List_Olist_OCons @ SV579 @ ( c_List_Olist_ONil @ SV1086 ) @ SV1086 ) @ SV1086 ) @ ( c_List_Oappend @ SV1093 @ ( c_List_Olist_OCons @ SV812 @ ( c_List_Olist_ONil @ SV1086 ) @ SV1086 ) @ SV1086 ) @ SV1086 ) )
= $true )
| ( ( SV579 = SV812 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV278 @ SV579 ) @ SV812 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2887]) ).
thf(2935,plain,
! [SV813: $i,SV580: $i,SV279: $i,SV1043: $i,SV961: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV961 @ SV1043 @ SV279 @ SV580 @ SV813 ) @ SV580 @ SV813 )
= SV1043 )
= $true )
| ( ( SV279
= ( c_List_Olist_ONil @ SV813 ) )
= $true )
| ( ( ( c_List_Oappend @ SV279 @ SV580 @ SV813 )
= ( c_List_Olist_OCons @ SV961 @ SV1043 @ SV813 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2888]) ).
thf(2936,plain,
! [SV814: $i,SV1044: $i,SV962: $i,SV581: $i,SV280: $i] :
( ( ( ( c_List_Olist_OCons @ SV280 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV280 @ SV581 @ SV962 @ SV1044 @ SV814 ) @ SV814 )
= SV962 )
= $true )
| ( ( SV962
= ( c_List_Olist_ONil @ SV814 ) )
= $true )
| ( ( ( c_List_Olist_OCons @ SV280 @ SV581 @ SV814 )
= ( c_List_Oappend @ SV962 @ SV1044 @ SV814 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2889]) ).
thf(2937,plain,
! [SV816: $i,SV583: $i,SV1087: $i,SV1068: $i,SV963: $i,SV282: $i] :
( ( ( c_ListOrder_Ostep1 @ SV282 @ SV963 @ SV1068 @ SV1087 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV282 @ ( c_List_Oappend @ SV963 @ ( c_List_Olist_OCons @ SV583 @ ( c_List_Olist_ONil @ SV1087 ) @ SV1087 ) @ SV1087 ) @ ( c_List_Oappend @ SV1068 @ ( c_List_Olist_OCons @ SV816 @ ( c_List_Olist_ONil @ SV1087 ) @ SV1087 ) @ SV1087 ) @ SV1087 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV282 @ SV583 ) @ SV816 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2890]) ).
thf(2938,plain,
! [SV1094: $i,SV587: $i,SV965: $i,SV1088: $i,SV286: $i,SV820: $i] :
( ( ( ~ ( c_ListOrder_Ostep1 @ SV820 @ ( c_List_Oappend @ SV286 @ ( c_List_Olist_OCons @ SV1088 @ ( c_List_Olist_ONil @ SV965 ) @ SV965 ) @ SV965 ) @ ( c_List_Oappend @ SV587 @ ( c_List_Olist_OCons @ SV1094 @ ( c_List_Olist_ONil @ SV965 ) @ SV965 ) @ SV965 ) @ SV965 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV820 @ SV286 @ SV587 @ SV965 )
= $true )
| ( ( SV286 = SV587 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2891]) ).
thf(2939,plain,
! [SV288: $i,SV589: $i,SV1069: $i,SV1045: $i,SV822: $i] :
( ( ( c_Type_Otyping @ SV822 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1045 ) @ SV1069 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV589 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV822 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1045 ) @ SV1069 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV288 ) )
= $true )
| ( ( SV288 = SV589 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2892]) ).
thf(2940,plain,
! [SV886: $i,SV24: $i,SV385: $i,SV679: $i] :
( ( ( SV679
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV679 @ ( tc_List_Olist @ SV385 ) ) @ SV24 @ SV385 ) )
= $true )
| ( ( ( c_List_Oappend @ SV679 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV679 @ ( tc_List_Olist @ SV385 ) ) @ SV24 @ SV385 ) @ SV886 @ SV385 ) @ SV385 )
= ( c_List_Oappend @ SV24 @ SV886 @ SV385 ) )
= $true )
| ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SV385 ) ) @ SV679 @ SV385 )
= SV24 )
= $false )
| ( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SV385 ) ) @ SV679 @ SV385 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV679 @ ( tc_List_Olist @ SV385 ) ) @ SV24 @ SV385 ) @ SV886 @ SV385 ) @ SV385 )
= SV886 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2902]) ).
thf(2941,plain,
! [SV692: $i,SV401: $i,SV890: $i,SV1075: $i,SV1003: $i,SV40: $i] :
( ( ( c_Type_Otyping @ SV40 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1003 ) @ SV1075 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV890 )
= $false )
| ( ( ! [SY2485: $i] :
~ ( c_Type_Otypings @ SV40 @ SV1075 @ SY2485 )
| ~ ( c_Type_Otyping @ SV40 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1003 ) @ SV1075 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV401 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV692 ) )
= $true )
| ( ( c_Type_Otypings @ SV40 @ SV401 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV692 @ SV890 @ SV40 @ SV401 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2903]) ).
thf(2942,plain,
! [SV1076: $i,SV65: $i,SV1058: $i] :
( ( ( ( c_Int_Onumber__class_Onumber__of @ SV1058 @ SV65 )
= ( c_Int_Onumber__class_Onumber__of @ SV1076 @ SV65 ) )
= $false )
| ( ( SV1058 = SV1076 )
= $true )
| ( ( class_Int_Onumber__ring @ SV65 )
= $false )
| ( ( class_Int_Oring__char__0 @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2904]) ).
thf(2943,plain,
! [SV899: $i,SV1061: $i,SV711: $i,SV431: $i,SV79: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV79 @ SV431 ) @ SV711 ) @ SV1061 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV79 @ SV431 ) @ SV1061 ) @ SV899 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV79 @ SV431 ) @ SV711 ) @ SV899 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2907]) ).
thf(2944,plain,
! [SV905: $i,SV448: $i,SV1062: $i,SV717: $i,SV104: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV104 @ SV717 ) @ SV1062 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV104 @ SV448 ) @ SV1062 ) @ SV905 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV104 @ SV448 ) @ SV717 ) @ SV905 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2908]) ).
thf(2945,plain,
! [SV906: $i,SV1063: $i,SV718: $i,SV449: $i,SV105: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV105 @ SV449 ) @ SV718 ) @ SV1063 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV105 @ SV1063 ) @ SV906 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV105 @ SV449 ) @ SV718 ) @ SV906 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2909]) ).
thf(2946,plain,
! [SV1089: $i,SV212: $i,SV1078: $i,SV934: $i,SV535: $i,SV779: $i] :
( ( ( c_ListOrder_Ostep1 @ SV779 @ ( c_List_Olist_OCons @ SV535 @ SV934 @ SV1078 ) @ ( c_List_Olist_OCons @ SV212 @ SV1089 @ SV1078 ) @ SV1078 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV779 @ SV535 ) @ SV212 ) )
= $true )
| ( ( SV212 = SV535 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2919]) ).
thf(2947,plain,
! [SV780: $i,SV213: $i,SV1090: $i,SV935: $i,SV536: $i,SV1079: $i] :
( ( ( c_ListOrder_Ostep1 @ SV1079 @ ( c_List_Olist_OCons @ SV536 @ SV935 @ SV1090 ) @ ( c_List_Olist_OCons @ SV213 @ SV780 @ SV1090 ) @ SV1090 )
= $false )
| ( ( SV780 = SV935 )
= $true )
| ( ( SV213 = SV536 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2920]) ).
thf(2948,plain,
! [SV782: $i,SV1091: $i,SV936: $i,SV538: $i,SV1081: $i,SV215: $i] :
( ( ( c_ListOrder_Ostep1 @ SV215 @ ( c_List_Olist_OCons @ SV1081 @ SV538 @ SV936 ) @ ( c_List_Olist_OCons @ SV1091 @ SV782 @ SV936 ) @ SV936 )
= $false )
| ( ( SV782 = SV538 )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV215 @ SV538 @ SV782 @ SV936 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2921]) ).
thf(2949,plain,
! [SV784: $i,SV1082: $i,SV937: $i,SV540: $i,SV1066: $i,SV217: $i] :
( ( ( c_ListOrder_Ostep1 @ SV217 @ ( c_List_Olist_OCons @ SV1066 @ SV540 @ SV937 ) @ ( c_List_Olist_OCons @ SV1082 @ SV784 @ SV937 ) @ SV937 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV217 @ SV1066 ) @ SV1082 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV217 @ SV540 @ SV784 @ SV937 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2922]) ).
thf(2950,plain,
! [SV1028: $i,SV227: $i,SV1083: $i,SV546: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV546 @ SV1083 @ SV227 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1083 @ SV1028 @ SV227 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV546 @ SV1028 @ SV227 )
= $true )
| ( ( class_Orderings_Oorder @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2924]) ).
thf(2951,plain,
! [SV547: $i,SV228: $i,SV1029: $i,SV1084: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1084 @ SV1029 @ SV228 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV547 @ SV1084 @ SV228 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV547 @ SV1029 @ SV228 )
= $true )
| ( ( class_Orderings_Opreorder @ SV228 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2925]) ).
thf(2952,plain,
! [SV959: $i,SV578: $i,SV1092: $i,SV811: $i,SV277: $i,SV1085: $i] :
( ( ( c_ListOrder_Ostep1 @ SV1085 @ ( c_List_Oappend @ SV277 @ ( c_List_Olist_OCons @ SV811 @ ( c_List_Olist_ONil @ SV1092 ) @ SV1092 ) @ SV1092 ) @ ( c_List_Oappend @ SV578 @ ( c_List_Olist_OCons @ SV959 @ ( c_List_Olist_ONil @ SV1092 ) @ SV1092 ) @ SV1092 ) @ SV1092 )
= $false )
| ( ( SV811 = SV959 )
= $true )
| ( ( SV277 = SV578 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2933]) ).
thf(2953,plain,
! [SV812: $i,SV1093: $i,SV1086: $i,SV579: $i,SV960: $i,SV278: $i] :
( ( ( c_ListOrder_Ostep1 @ SV278 @ ( c_List_Oappend @ SV960 @ ( c_List_Olist_OCons @ SV579 @ ( c_List_Olist_ONil @ SV1086 ) @ SV1086 ) @ SV1086 ) @ ( c_List_Oappend @ SV1093 @ ( c_List_Olist_OCons @ SV812 @ ( c_List_Olist_ONil @ SV1086 ) @ SV1086 ) @ SV1086 ) @ SV1086 )
= $false )
| ( ( SV579 = SV812 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV278 @ SV579 ) @ SV812 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2934]) ).
thf(2954,plain,
! [SV816: $i,SV1068: $i,SV1087: $i,SV583: $i,SV963: $i,SV282: $i] :
( ( ( c_ListOrder_Ostep1 @ SV282 @ ( c_List_Oappend @ SV963 @ ( c_List_Olist_OCons @ SV583 @ ( c_List_Olist_ONil @ SV1087 ) @ SV1087 ) @ SV1087 ) @ ( c_List_Oappend @ SV1068 @ ( c_List_Olist_OCons @ SV816 @ ( c_List_Olist_ONil @ SV1087 ) @ SV1087 ) @ SV1087 ) @ SV1087 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV282 @ SV963 @ SV1068 @ SV1087 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV282 @ SV583 ) @ SV816 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2937]) ).
thf(2955,plain,
! [SV1094: $i,SV587: $i,SV965: $i,SV1088: $i,SV286: $i,SV820: $i] :
( ( ( c_ListOrder_Ostep1 @ SV820 @ ( c_List_Oappend @ SV286 @ ( c_List_Olist_OCons @ SV1088 @ ( c_List_Olist_ONil @ SV965 ) @ SV965 ) @ SV965 ) @ ( c_List_Oappend @ SV587 @ ( c_List_Olist_OCons @ SV1094 @ ( c_List_Olist_ONil @ SV965 ) @ SV965 ) @ SV965 ) @ SV965 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV820 @ SV286 @ SV587 @ SV965 )
= $true )
| ( ( SV286 = SV587 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2938]) ).
thf(2956,plain,
! [SV589: $i,SV288: $i,SV1069: $i,SV1045: $i,SV822: $i] :
( ( ( c_Type_Otyping @ SV822 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1045 ) @ SV1069 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV288 )
= $false )
| ( ( c_Type_Otyping @ SV822 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1045 ) @ SV1069 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV589 )
= $false )
| ( ( SV288 = SV589 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2939]) ).
thf(2957,plain,
! [SV886: $i,SV24: $i,SV385: $i,SV679: $i] :
( ( ( SV679
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV679 @ ( tc_List_Olist @ SV385 ) ) @ SV24 @ SV385 ) )
= $false )
| ( ( ( c_List_Oappend @ SV679 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV679 @ ( tc_List_Olist @ SV385 ) ) @ SV24 @ SV385 ) @ SV886 @ SV385 ) @ SV385 )
= ( c_List_Oappend @ SV24 @ SV886 @ SV385 ) )
= $true )
| ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SV385 ) ) @ SV679 @ SV385 )
= SV24 )
= $false )
| ( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SV385 ) ) @ SV679 @ SV385 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV679 @ ( tc_List_Olist @ SV385 ) ) @ SV24 @ SV385 ) @ SV886 @ SV385 ) @ SV385 )
= SV886 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2940]) ).
thf(2958,plain,
! [SV890: $i,SV692: $i,SV401: $i,SV1003: $i,SV1075: $i,SV40: $i] :
( ( ( ! [SY2485: $i] :
~ ( c_Type_Otypings @ SV40 @ SV1075 @ SY2485 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV40 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1003 ) @ SV1075 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV401 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV692 ) )
= $true )
| ( ( c_Type_Otyping @ SV40 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1003 ) @ SV1075 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV890 )
= $false )
| ( ( c_Type_Otypings @ SV40 @ SV401 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV692 @ SV890 @ SV40 @ SV401 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2941]) ).
thf(2959,plain,
! [SV546: $i,SV227: $i,SV1028: $i,SV1083: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1083 @ SV1028 @ SV227 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV546 @ SV1083 @ SV227 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV546 @ SV1028 @ SV227 )
= $true )
| ( ( class_Orderings_Oorder @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2950]) ).
thf(2960,plain,
! [SV1029: $i,SV228: $i,SV1084: $i,SV547: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV547 @ SV1084 @ SV228 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1084 @ SV1029 @ SV228 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV547 @ SV1029 @ SV228 )
= $true )
| ( ( class_Orderings_Opreorder @ SV228 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2951]) ).
thf(2961,plain,
! [SV890: $i,SV692: $i,SV401: $i,SV1003: $i,SV1095: $i,SV1075: $i,SV40: $i] :
( ( ( ~ ( c_Type_Otypings @ SV40 @ SV1075 @ SV1095 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV40 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1003 ) @ SV1075 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV401 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV692 ) )
= $true )
| ( ( c_Type_Otyping @ SV40 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1003 ) @ SV1075 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV890 )
= $false )
| ( ( c_Type_Otypings @ SV40 @ SV401 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV692 @ SV890 @ SV40 @ SV401 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2958]) ).
thf(2962,plain,
! [SV890: $i,SV692: $i,SV401: $i,SV1003: $i,SV1095: $i,SV1075: $i,SV40: $i] :
( ( ( c_Type_Otypings @ SV40 @ SV1075 @ SV1095 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV40 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1003 ) @ SV1075 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV401 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV692 ) )
= $true )
| ( ( c_Type_Otyping @ SV40 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1003 ) @ SV1075 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV890 )
= $false )
| ( ( c_Type_Otypings @ SV40 @ SV401 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV692 @ SV890 @ SV40 @ SV401 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2961]) ).
thf(2963,plain,
! [SV890: $i,SV1095: $i,SV692: $i,SV401: $i,SV1075: $i,SV1003: $i,SV40: $i] :
( ( ( c_Type_Otyping @ SV40 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1003 ) @ SV1075 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV401 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV692 )
= $false )
| ( ( c_Type_Otypings @ SV40 @ SV1075 @ SV1095 )
= $false )
| ( ( c_Type_Otyping @ SV40 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1003 ) @ SV1075 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV890 )
= $false )
| ( ( c_Type_Otypings @ SV40 @ SV401 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV692 @ SV890 @ SV40 @ SV401 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2962]) ).
thf(2964,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[928,2963,2960,2959,2957,2956,2955,2954,2953,2952,2949,2948,2947,2946,2945,2944,2943,2942,2936,2935,2932,2931,2930,2929,2928,2927,2926,2923,2918,2917,2916,2915,2914,2913,2912,2911,2910,2906,2905,2901,2900,2899,2898,2897,2896,2895,2894,2893,2878,2877,2876,2875,2874,2873,2869,2866,2862,2861,2856,2853,2852,2847,2846,2842,2841,2840,2839,2836,2833,2832,2831,2829,2828,2827,2826,2825,2824,2821,2820,2812,2804,2803,2794,2780,2779,2776,2775,2770,2768,2767,2766,2764,2763,2762,2761,2760,2751,2749,2741,2740,2738,2737,2735,2734,2731,2726,2725,2724,2722,2721,2719,2718,2714,2713,2712,2711,2710,2709,2706,2705,2704,2703,2702,2701,2692,2690,2689,2688,2677,2676,2675,2674,2671,2665,2658,2657,2656,2655,2644,2643,2636,2635,2634,2632,2631,2624,2623,2622,2618,2617,2614,2609,2608,2607,2603,2602,2596,2595,2594,2580,2579,2577,2576,2575,2571,2570,2566,2564,2562,2556,2552,2550,2549,2548,2545,2544,2542,2541,2540,2539,2538,2537,2533,2527,2523,2512,2511,2508,2507,2506,2505,2504,2501,2478,2477,2467,2465,2459,2457,2453,2452,2444,2443,2442,2441,2440,2439,2438,2435,2433,2423,2420,2419,2404,2403,2402,2393,2392,2388,2385,2378,2377,2376,2370,2369,2354,2353,2352,2351,2350,2347,2346,2340,2332,2321,2312,2281,2276,2257,2255,2254,2251,2246,2245,2242,2241,2211,2210,2208,2203,2201,2198,2188,2176,2174,2173,2172,2170,2169,2155,2154,2150,2148,2143,2138,2135,2134,2122,2120,2119,2116,2115,2107,2103,2102,2092,2091,2087,2086,2085,2084,2079,2073,2058,2057,2056,2055,2054,2053,2051,2045,2044,2036,2027,2026,2025,2021,2002,2001,2000,1999,1998,1979,1969,1930,1928,1909,1908,1902,1901,1900,1893,1892,1891,1876,1875,1855,1852,1849,1848,1846,1844,1843,1840,1838,1831,1814,1813,1780,1776,1775,1770,1743,1740,1734,1733,1732,1731,1730,1727,1726,1719,1717,1680,1673,1660,1652,1622,1613,1610,1581,1580,1542,1528,1527,1526,1519,1517,1436,1434,1433,1410,1409,1404,1317,1313,1312,1311,1310,1309,1308,1307,1306,1305,1304,1303,1302,1301,1300,1299,1298,1297,1296,1295,1052,1018,931,930,929]) ).
thf(2965,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2964]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL777-1 : 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
% 0.09/0.17 % Computer : n004.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 12:33:39 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 58.13/10.10 ...
% 58.13/10.10
% 58.13/10.10 No.of.Axioms: 388
% 58.13/10.10
% 58.13/10.10 Length.of.Defs: 0
% 58.13/10.10
% 58.13/10.10 Contains.Choice.Funs: false
% 58.13/10.10 ....................................................................................................................................................................
% 58.13/10.10
% 58.13/10.10 ********************************
% 58.13/10.10 * All subproblems solved! *
% 58.13/10.10 ********************************
% 58.13/10.10 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:388,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:72,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2964,loop_count:0,foatp_calls:1,translation:fof_full)
% 58.13/10.10
% 58.13/10.10 %**** Beginning of derivation protocol ****
% 58.13/10.10 % SZS output start CNFRefutation
% See solution above
% 58.13/10.12
% 58.13/10.12 %**** End of derivation protocol ****
% 58.13/10.12 %**** no. of clauses in derivation: 2965 ****
% 58.13/10.12 %**** clause counter: 2964 ****
% 58.13/10.12
% 58.13/10.12 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:388,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:72,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2964,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------