TPTP Problem File: SWW478_10.p
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%------------------------------------------------------------------------------
% File : SWW478_10 : TPTP v9.0.0. Released v8.2.0.
% Domain : Software Verification
% Problem : Java type soundness line 479, 100 axioms selected
% Version : SWW478_1 with the conjecture removed
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [TPTP]
% Names :
% Status : Satisfiable
% Rating : 1.00 v8.2.0
% Syntax : Number of formulae : 518 ( 78 unt; 320 typ; 0 def)
% Number of atoms : 394 ( 181 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 275 ( 79 ~; 6 |; 19 &)
% ( 48 <=>; 123 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 124 ( 123 usr)
% Number of type conns : 268 ( 135 >; 133 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 196 ( 196 usr; 62 con; 0-5 aty)
% Number of variables : 749 ( 739 !; 10 ?; 749 :)
% SPC : TF0_SAT_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 15:40:10
%------------------------------------------------------------------------------
%----Should-be-implicit typings (123)
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tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String___087,type,
fun_Pr1404764635l_bool: $tType ).
tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String___088,type,
fun_Pr1727285475on_val: $tType ).
tff(ty_ty_tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc__prod,type,
produc124828825on_val: $tType ).
tff(ty_ty_tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List_,type,
produc12694297on_val: $tType ).
tff(ty_ty_tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
produc1102272487on_val: $tType ).
%----Explicit typings (197)
tff(sy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__List__Olist_Itc__,type,
cOMBB_383678192on_val: fun_fu114905943l_bool ).
tff(sy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__prod_Itc__Expr__Oexp_Itc__,type,
cOMBB_672625589on_val: fun_fu2003389793l_bool ).
tff(sy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__prod_Itc__fun_Itc__Nat__On,type,
cOMBB_338347573on_val: fun_fu1485943649l_bool ).
tff(sy_c_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc_,type,
cOMBB_1303934920on_val: fun_fu781882819l_bool ).
tff(sy_c_COMBB_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc_,type,
cOMBB_1718333400on_val: fun_fu48585473l_bool ).
tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option,type,
cOMBB_1522540928on_val: fun_fu816125185l_bool ).
tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option_089,type,
cOMBB_1518282696on_val: fun_fu938561337l_bool ).
tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option_090,type,
cOMBB_1466889536on_val: fun_fu626845499l_bool ).
tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option_091,type,
cOMBB_1153617344on_val: fun_fu698854459l_bool ).
tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option_092,type,
cOMBB_1259202826on_val: fun_fu1755700589l_bool ).
tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc,type,
cOMBB_466903633on_val: fun_fu1506313313l_bool ).
tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_093,type,
cOMBB_635947099on_val: fun_fu1452544581l_bool ).
tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_094,type,
cOMBB_364363975on_val: fun_fu470662369l_bool ).
tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc,type,
cOMBB_740252943t_char: fun_fu2023535095l_bool ).
tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc_095,type,
cOMBB_1027621637t_char: fun_fu610694927l_bool ).
tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc_096,type,
cOMBB_819439237t_char: fun_fu1104572687l_bool ).
tff(sy_c_COMBB_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_M,type,
cOMBB_171276332on_val: fun_fu369322201l_bool ).
tff(sy_c_COMBB_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_M_097,type,
cOMBB_1759207793on_val: fun_fu1002878233l_bool ).
tff(sy_c_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It,type,
cOMBB_1750801836on_val: fun_fu121169625l_bool ).
tff(sy_c_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It_098,type,
cOMBB_1083177073on_val: fun_fu1929656089l_bool ).
tff(sy_c_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It_099,type,
cOMBB_877741809on_val: fun_fu1802993177l_bool ).
tff(sy_c_COMBB_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O,type,
cOMBB_1292453606on_val: fun_fu169292119l_bool ).
tff(sy_c_COMBB_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O_100,type,
cOMBB_1466662571on_val: fun_fu1003774433l_bool ).
tff(sy_c_COMBC_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption,type,
cOMBC_832625297y_bool: fun_fu2083094209l_bool ).
tff(sy_c_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__O,type,
cOMBC_2027949654l_bool: fun_fu1680591819l_bool ).
tff(sy_c_COMBK_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__List__Olist_Itc__Strin,type,
cOMBK_1294242658t_char: option_ty > fun_li688206603ion_ty ).
tff(sy_c_COMBK_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__List__Olist_Itc__Str,type,
cOMBK_1097134891t_char: option_val > fun_li1432931796on_val ).
tff(sy_c_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__O,type,
cOMBS_570216337l_bool: ( fun_fu1806184744l_bool * fun_fu100249073l_bool ) > fun_fu100249073l_bool ).
tff(sy_c_Conform_Ohconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O,type,
hconf_97414254t_char: list_P1999446415t_char > fun_fu1246919812l_bool ).
tff(sy_c_Conform_Olconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O,type,
lconf_496643946t_char: list_P1999446415t_char > fun_fu2141444501y_bool ).
tff(sy_c_Expr_Oexp_OBlock_000tc__List__Olist_Itc__String__Ochar_J,type,
block_list_char: ( list_char * ty * exp_list_char ) > exp_list_char ).
tff(sy_c_Expr_Oexp_OLAss_000tc__List__Olist_Itc__String__Ochar_J,type,
lAss_list_char: ( list_char * exp_list_char ) > exp_list_char ).
tff(sy_c_Expr_Oexp_OSeq_000tc__List__Olist_Itc__String__Ochar_J,type,
seq_list_char: ( exp_list_char * exp_list_char ) > exp_list_char ).
tff(sy_c_Expr_Oexp_OVal_000tc__List__Olist_Itc__String__Ochar_J,type,
val_list_char: val > exp_list_char ).
tff(sy_c_Fun_Ofun__upd_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Ooptio,type,
fun_up424764369ion_ty: ( fun_li688206603ion_ty * list_char * option_ty ) > fun_li688206603ion_ty ).
tff(sy_c_Fun_Ofun__upd_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Ooptio_101,type,
fun_up1149430426on_val: ( fun_li1432931796on_val * list_char * option_val ) > fun_li1432931796on_val ).
tff(sy_c_JWellForm_Owf__J__mdecl,type,
wf_J_mdecl: fun_li318226104r_bool ).
tff(sy_c_Option_Ooption_ONone_000tc__Type__Oty,type,
none_ty: option_ty ).
tff(sy_c_Option_Ooption_ONone_000tc__Value__Oval,type,
none_val: option_val ).
tff(sy_c_Option_Ooption_OSome_000tc__Type__Oty,type,
some_ty: ty > option_ty ).
tff(sy_c_Option_Ooption_OSome_000tc__Value__Oval,type,
some_val: val > option_val ).
tff(sy_c_Product__Type_OPair_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J,type,
produc1259058957on_val: fun_ex977868519on_val ).
tff(sy_c_Product__Type_OPair_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__pro,type,
produc899768717on_val: fun_fu1639641777on_val ).
tff(sy_c_Product__Type_OPair_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Strin,type,
produc1441475159on_val: fun_Pr1391347915on_val ).
tff(sy_c_Product__Type_Ointernal__split_000tc__Expr__Oexp_Itc__List__Olist_Itc__Stri,type,
produc399384568l_bool: fun_fu254083683l_bool ).
tff(sy_c_Product__Type_Ointernal__split_000tc__fun_Itc__Nat__Onat_Mtc__Option__Oopti,type,
produc2128769400l_bool: fun_fu947198233l_bool ).
tff(sy_c_Product__Type_Ointernal__split_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist,type,
produc1988544340l_bool: fun_fu371764249l_bool ).
tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__Expr__Oexp_Itc__List__Olist_Itc__Str,type,
produc1815960045l_bool: fun_fu254083683l_bool ).
tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__Expr__Oexp_Itc__List__Olist_Itc__Str_102,type,
produc1275132703l_bool: fun_fu1162814663l_bool ).
tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__Expr__Oexp_Itc__List__Olist_Itc__Str_103,type,
produc2036005791l_bool: fun_fu1913539015l_bool ).
tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__Expr__Oexp_Itc__List__Olist_Itc__Str_104,type,
produc1174947465on_val: fun_fu1924376903on_val ).
tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__fun_Itc__Nat__Onat_Mtc__Option__Oopt,type,
produc1958875245l_bool: fun_fu947198233l_bool ).
tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__fun_Itc__Nat__Onat_Mtc__Option__Oopt_105,type,
produc334393759l_bool: fun_fu1343174525l_bool ).
tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__fun_Itc__Nat__Onat_Mtc__Option__Oopt_106,type,
produc121041439l_bool: fun_fu1871906941l_bool ).
tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__fun_Itc__Nat__Onat_Mtc__Option__Oopt_107,type,
produc901351817on_val: fun_fu192331261on_val ).
tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__fun_Itc__Nat__Onat_Mtc__Option__Oopt_108,type,
produc1148763895on_val: fun_fu442091053on_val ).
tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__Expr__Oexp_Itc__List__Olis,type,
produc1911463199l_bool: fun_fu371764249l_bool ).
tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__Expr__Oexp_Itc__List__Olis_109,type,
produc20018513l_bool: fun_fu1562135449l_bool ).
tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__Expr__Oexp_Itc__List__Olis_110,type,
produc376702929l_bool: fun_fu2138074009l_bool ).
tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__Expr__Oexp_Itc__List__Olis_111,type,
produc1003071703on_val: fun_fu1753546205on_val ).
tff(sy_c_SmallStep_Oassigned,type,
assigned: ( list_char * exp_list_char ) > bool ).
tff(sy_c_SmallStep_Ored,type,
red: list_P1999446415t_char > fun_Pr691271849l_bool ).
tff(sy_c_SmallStep_Oredp,type,
redp: ( list_P1999446415t_char * exp_list_char * produc12694297on_val ) > fun_ex1201926843l_bool ).
tff(sy_c_State_Ohp,type,
hp: produc12694297on_val > fun_na939144002on_val ).
tff(sy_c_TypeRel_Owiden_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O,type,
widen_2090681816t_char: ( list_P1999446415t_char * ty * ty ) > bool ).
tff(sy_c_TypeSafe__Mirabelle__hhsfbkxijv_Osconf,type,
typeSa1844245082_sconf: ( list_P1999446415t_char * fun_li688206603ion_ty ) > fun_Pr1696029455l_bool ).
tff(sy_c_Value_Oval_OUnit,type,
unit: val ).
tff(sy_c_WellForm_Owf__prog_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Strin,type,
wf_pro755087577t_char: ( fun_li318226104r_bool * list_P1999446415t_char ) > bool ).
tff(sy_c_WellTypeRT_OWTrt,type,
wTrt: ( list_P1999446415t_char * fun_na939144002on_val * fun_li688206603ion_ty * exp_list_char * ty ) > bool ).
tff(sy_c_fconj,type,
fconj: fun_bo1549164019l_bool ).
tff(sy_c_hAPP_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun_I,type,
hAPP_e1833980889l_bool: ( fun_ex1201926843l_bool * exp_list_char ) > fun_Pr1696029455l_bool ).
tff(sy_c_hAPP_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun_I_112,type,
hAPP_e592495499l_bool: ( fun_ex1732109805l_bool * exp_list_char ) > fun_Pr1793564609l_bool ).
tff(sy_c_hAPP_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun_I_113,type,
hAPP_e500528395l_bool: ( fun_ex1123147373l_bool * exp_list_char ) > fun_Pr598845249l_bool ).
tff(sy_c_hAPP_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun_I_114,type,
hAPP_e1659493427on_val: ( fun_ex977868519on_val * exp_list_char ) > fun_Pr231134077on_val ).
tff(sy_c_hAPP_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun_I_115,type,
hAPP_e108155315on_val: ( fun_ex1005552999on_val * exp_list_char ) > fun_Pr1833267965on_val ).
tff(sy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool,type,
hAPP_bool_bool: ( fun_bool_bool * bool ) > bool ).
tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J,type,
hAPP_b589554111l_bool: ( fun_bo1549164019l_bool * bool ) > fun_bool_bool ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Ooption_Itc__Ty,type,
hAPP_l512744617ion_ty: ( fun_li688206603ion_ty * list_char ) > option_ty ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Ooption_Itc__Va,type,
hAPP_l207779698on_val: ( fun_li1432931796on_val * list_char ) > option_val ).
tff(sy_c_hAPP_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc,type,
hAPP_f546724245l_bool: ( fun_fu2122484477l_bool * fun_ex1201926843l_bool ) > fun_ex1201926843l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc_116,type,
hAPP_f1930574389l_bool: ( fun_fu254083683l_bool * fun_ex1201926843l_bool ) > fun_Pr680585871l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc_117,type,
hAPP_f1760682521l_bool: ( fun_fu1162814663l_bool * fun_ex1732109805l_bool ) > fun_Pr633696065l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc_118,type,
hAPP_f468299289l_bool: ( fun_fu1913539015l_bool * fun_ex1123147373l_bool ) > fun_Pr134674113l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc_119,type,
hAPP_f439412817l_bool: ( fun_fu1241242885l_bool * fun_ex977868519on_val ) > fun_ex1201926843l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc_120,type,
hAPP_f653692369l_bool: ( fun_fu676595845l_bool * fun_ex1005552999on_val ) > fun_ex1201926843l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc_121,type,
hAPP_f1520199827on_val: ( fun_fu1924376903on_val * fun_ex1005552999on_val ) > fun_Pr2087158653on_val ).
tff(sy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc__,type,
hAPP_f1863694447l_bool: ( fun_fu114905943l_bool * fun_bool_bool ) > fun_fu1590192889l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc___122,type,
hAPP_f1560238713l_bool: ( fun_fu2003389793l_bool * fun_bool_bool ) > fun_fu983865091l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc___123,type,
hAPP_f1308714617l_bool: ( fun_fu1485943649l_bool * fun_bool_bool ) > fun_fu1319073539l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_,type,
hAPP_f1977633121l_bool: ( fun_fu781882819l_bool * fun_bo1549164019l_bool ) > fun_fu1457514859l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption_,type,
hAPP_f1001225811y_bool: ( fun_fu964075521y_bool * fun_li688206603ion_ty ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__124,type,
hAPP_f603925568l_bool: ( fun_fu2075294830l_bool * fun_li688206603ion_ty ) > fun_fu1693644106l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__125,type,
hAPP_f550652027l_bool: ( fun_fu863769827l_bool * fun_li688206603ion_ty ) > fun_fu100249073l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__126,type,
hAPP_f1033709212l_bool: ( fun_fu1693644106l_bool * fun_li1432931796on_val ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__127,type,
hAPP_f2060496320y_bool: ( fun_fu1670877422y_bool * fun_li1432931796on_val ) > fun_fu964075521y_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__128,type,
hAPP_f2011777102l_bool: ( fun_fu1677251708l_bool * fun_li1432931796on_val ) > fun_Pr680585871l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__129,type,
hAPP_f396019662l_bool: ( fun_fu905586428l_bool * fun_li1432931796on_val ) > fun_Pr1696029455l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__130,type,
hAPP_f1926378906on_val: ( fun_fu277794946on_val * fun_li1432931796on_val ) > produc124828825on_val ).
tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__131,type,
hAPP_f1727192346on_val: ( fun_fu1690035458on_val * fun_li1432931796on_val ) > produc12694297on_val ).
tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__132,type,
hAPP_f602593190on_val: ( fun_fu1622757844on_val * fun_li1432931796on_val ) > produc1102272487on_val ).
tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol,type,
hAPP_f61040418l_bool: ( fun_fu1246919812l_bool * fun_na939144002on_val ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_133,type,
hAPP_f1145256474l_bool: ( fun_fu250820942l_bool * fun_na939144002on_val ) > fun_bool_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_134,type,
hAPP_f1617787571l_bool: ( fun_fu570492181l_bool * fun_na939144002on_val ) > fun_fu2075294830l_bool ).
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h_a: fun_na939144002on_val ).
tff(sy_v_ha____,type,
ha: fun_na939144002on_val ).
tff(sy_v_l_Ha____,type,
l_a: fun_li1432931796on_val ).
tff(sy_v_la____,type,
la: fun_li1432931796on_val ).
tff(sy_v_v_H____,type,
v_2: val ).
tff(sy_v_v____,type,
v: val ).
%----Relevant facts (167)
tff(fact_0_InitBlockRed_I3_J,axiom,
hAPP_l207779698on_val(l_a,v_1) = some_val(v_2) ).
tff(fact_1_InitBlockRed_I1_J,axiom,
hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,ha),fun_up1149430426on_val(la,v_1,some_val(v))))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,e_a),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,h_a),l_a))),red(p))) ).
tff(fact_2_fun__upd__triv,axiom,
! [F: fun_li1432931796on_val,X_1: list_char] : ( fun_up1149430426on_val(F,X_1,hAPP_l207779698on_val(F,X_1)) = F ) ).
tff(fact_3_fun__upd__triv,axiom,
! [F: fun_li688206603ion_ty,X_1: list_char] : ( fun_up424764369ion_ty(F,X_1,hAPP_l512744617ion_ty(F,X_1)) = F ) ).
tff(fact_4_assms,axiom,
hBOOL(wf_pro755087577t_char(wf_J_mdecl,p)) ).
tff(fact_5_map__upd__Some__unfold,axiom,
! [M: fun_li1432931796on_val,A_10: list_char,B_1: val,X_1: list_char,Y_1: val] :
( ( hAPP_l207779698on_val(fun_up1149430426on_val(M,A_10,some_val(B_1)),X_1) = some_val(Y_1) )
<=> ( ( ( X_1 = A_10 )
& ( B_1 = Y_1 ) )
| ( ( X_1 != A_10 )
& ( hAPP_l207779698on_val(M,X_1) = some_val(Y_1) ) ) ) ) ).
tff(fact_6_map__upd__Some__unfold,axiom,
! [M: fun_li688206603ion_ty,A_10: list_char,B_1: ty,X_1: list_char,Y_1: ty] :
( ( hAPP_l512744617ion_ty(fun_up424764369ion_ty(M,A_10,some_ty(B_1)),X_1) = some_ty(Y_1) )
<=> ( ( ( X_1 = A_10 )
& ( B_1 = Y_1 ) )
| ( ( X_1 != A_10 )
& ( hAPP_l512744617ion_ty(M,X_1) = some_ty(Y_1) ) ) ) ) ).
tff(fact_7_map__upd__triv,axiom,
! [T: fun_li1432931796on_val,K: list_char,X_1: val] :
( ( hAPP_l207779698on_val(T,K) = some_val(X_1) )
=> ( fun_up1149430426on_val(T,K,some_val(X_1)) = T ) ) ).
tff(fact_8_map__upd__triv,axiom,
! [T: fun_li688206603ion_ty,K: list_char,X_1: ty] :
( ( hAPP_l512744617ion_ty(T,K) = some_ty(X_1) )
=> ( fun_up424764369ion_ty(T,K,some_ty(X_1)) = T ) ) ).
tff(fact_9_map__upd__eqD1,axiom,
! [M: fun_li1432931796on_val,A_10: list_char,X_1: val,N: fun_li1432931796on_val,Y_1: val] :
( ( fun_up1149430426on_val(M,A_10,some_val(X_1)) = fun_up1149430426on_val(N,A_10,some_val(Y_1)) )
=> ( X_1 = Y_1 ) ) ).
tff(fact_10_map__upd__eqD1,axiom,
! [M: fun_li688206603ion_ty,A_10: list_char,X_1: ty,N: fun_li688206603ion_ty,Y_1: ty] :
( ( fun_up424764369ion_ty(M,A_10,some_ty(X_1)) = fun_up424764369ion_ty(N,A_10,some_ty(Y_1)) )
=> ( X_1 = Y_1 ) ) ).
tff(fact_11_InitBlockRed_I2_J,axiom,
! [Ta: ty,Ea: fun_li688206603ion_ty] :
( hBOOL(hAPP_P159683425l_bool(typeSa1844245082_sconf(p,Ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,ha),fun_up1149430426on_val(la,v_1,some_val(v)))))
=> ( hBOOL(wTrt(p,ha,Ea,ea,Ta))
=> ? [T_5: ty] :
( hBOOL(wTrt(p,h_a,Ea,e_a,T_5))
& hBOOL(widen_2090681816t_char(p,T_5,Ta)) ) ) ) ).
tff(fact_12_prod__induct4,axiom,
! [X_1: produc1102272487on_val,Pa: fun_Pr691271849l_bool] :
( ! [A_15: produc124828825on_val,B: exp_list_char,C_1: fun_na939144002on_val,D_1: fun_li1432931796on_val] : hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,C_1),D_1)))))
=> hBOOL(hAPP_P282169671l_bool(Pa,X_1)) ) ).
tff(fact_13_prod__cases4,axiom,
! [Y_1: produc1102272487on_val] :
~ ! [A_15: produc124828825on_val,B: exp_list_char,C_1: fun_na939144002on_val,D_1: fun_li1432931796on_val] : ( Y_1 != hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,C_1),D_1))) ) ).
tff(fact_14_InitBlockRed_I4_J,axiom,
hBOOL(hAPP_P159683425l_bool(typeSa1844245082_sconf(p,e),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,ha),la))) ).
tff(fact_15_Pair__inject,axiom,
! [A_10: produc124828825on_val,B_1: produc124828825on_val,A_9: produc124828825on_val,B_2: produc124828825on_val] :
( ( hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_10),B_1) = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_9),B_2) )
=> ~ ( ( A_10 = A_9 )
=> ( B_1 != B_2 ) ) ) ).
tff(fact_16_Pair__inject,axiom,
! [A_10: exp_list_char,B_1: produc12694297on_val,A_9: exp_list_char,B_2: produc12694297on_val] :
( ( hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_10),B_1) = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_9),B_2) )
=> ~ ( ( A_10 = A_9 )
=> ( B_1 != B_2 ) ) ) ).
tff(fact_17_Pair__inject,axiom,
! [A_10: fun_na939144002on_val,B_1: fun_li1432931796on_val,A_9: fun_na939144002on_val,B_2: fun_li1432931796on_val] :
( ( hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1) = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_9),B_2) )
=> ~ ( ( A_10 = A_9 )
=> ( B_1 != B_2 ) ) ) ).
tff(fact_18_Pair__eq,axiom,
! [A_10: produc124828825on_val,B_1: produc124828825on_val,A_9: produc124828825on_val,B_2: produc124828825on_val] :
( ( hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_10),B_1) = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_9),B_2) )
<=> ( ( A_10 = A_9 )
& ( B_1 = B_2 ) ) ) ).
tff(fact_19_Pair__eq,axiom,
! [A_10: exp_list_char,B_1: produc12694297on_val,A_9: exp_list_char,B_2: produc12694297on_val] :
( ( hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_10),B_1) = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_9),B_2) )
<=> ( ( A_10 = A_9 )
& ( B_1 = B_2 ) ) ) ).
tff(fact_20_Pair__eq,axiom,
! [A_10: fun_na939144002on_val,B_1: fun_li1432931796on_val,A_9: fun_na939144002on_val,B_2: fun_li1432931796on_val] :
( ( hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1) = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_9),B_2) )
<=> ( ( A_10 = A_9 )
& ( B_1 = B_2 ) ) ) ).
tff(fact_21_split__paired__All,axiom,
! [Pa: fun_Pr691271849l_bool] :
( ! [X1: produc1102272487on_val] : hBOOL(hAPP_P282169671l_bool(Pa,X1))
<=> ! [A_15: produc124828825on_val,B: produc124828825on_val] : hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),B))) ) ).
tff(fact_22_split__paired__All,axiom,
! [Pa: fun_Pr680585871l_bool] :
( ! [X1: produc124828825on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,X1))
<=> ! [A_15: exp_list_char,B: produc12694297on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_15),B))) ) ).
tff(fact_23_split__paired__All,axiom,
! [Pa: fun_Pr1696029455l_bool] :
( ! [X1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(Pa,X1))
<=> ! [A_15: fun_na939144002on_val,B: fun_li1432931796on_val] : hBOOL(hAPP_P159683425l_bool(Pa,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_15),B))) ) ).
tff(fact_24_fun__upd__def,axiom,
! [F: fun_li1432931796on_val,B_1: option_val,A_10: list_char,X: list_char] :
( ( ( X = A_10 )
=> ( hAPP_l207779698on_val(fun_up1149430426on_val(F,A_10,B_1),X) = B_1 ) )
& ( ( X != A_10 )
=> ( hAPP_l207779698on_val(fun_up1149430426on_val(F,A_10,B_1),X) = hAPP_l207779698on_val(F,X) ) ) ) ).
tff(fact_25_fun__upd__def,axiom,
! [F: fun_li688206603ion_ty,B_1: option_ty,A_10: list_char,X: list_char] :
( ( ( X = A_10 )
=> ( hAPP_l512744617ion_ty(fun_up424764369ion_ty(F,A_10,B_1),X) = B_1 ) )
& ( ( X != A_10 )
=> ( hAPP_l512744617ion_ty(fun_up424764369ion_ty(F,A_10,B_1),X) = hAPP_l512744617ion_ty(F,X) ) ) ) ).
tff(fact_26_fun__upd__idem,axiom,
! [F: fun_li1432931796on_val,X_1: list_char,Y_1: option_val] :
( ( hAPP_l207779698on_val(F,X_1) = Y_1 )
=> ( fun_up1149430426on_val(F,X_1,Y_1) = F ) ) ).
tff(fact_27_fun__upd__idem,axiom,
! [F: fun_li688206603ion_ty,X_1: list_char,Y_1: option_ty] :
( ( hAPP_l512744617ion_ty(F,X_1) = Y_1 )
=> ( fun_up424764369ion_ty(F,X_1,Y_1) = F ) ) ).
tff(fact_28_fun__upd__other,axiom,
! [F: fun_li1432931796on_val,Y_1: option_val,Z: list_char,X_1: list_char] :
( ( Z != X_1 )
=> ( hAPP_l207779698on_val(fun_up1149430426on_val(F,X_1,Y_1),Z) = hAPP_l207779698on_val(F,Z) ) ) ).
tff(fact_29_fun__upd__other,axiom,
! [F: fun_li688206603ion_ty,Y_1: option_ty,Z: list_char,X_1: list_char] :
( ( Z != X_1 )
=> ( hAPP_l512744617ion_ty(fun_up424764369ion_ty(F,X_1,Y_1),Z) = hAPP_l512744617ion_ty(F,Z) ) ) ).
tff(fact_30_fun__upd__twist,axiom,
! [M: fun_li1432931796on_val,B_1: option_val,D: option_val,A_10: list_char,C: list_char] :
( ( A_10 != C )
=> ( fun_up1149430426on_val(fun_up1149430426on_val(M,A_10,B_1),C,D) = fun_up1149430426on_val(fun_up1149430426on_val(M,C,D),A_10,B_1) ) ) ).
tff(fact_31_fun__upd__twist,axiom,
! [M: fun_li688206603ion_ty,B_1: option_ty,D: option_ty,A_10: list_char,C: list_char] :
( ( A_10 != C )
=> ( fun_up424764369ion_ty(fun_up424764369ion_ty(M,A_10,B_1),C,D) = fun_up424764369ion_ty(fun_up424764369ion_ty(M,C,D),A_10,B_1) ) ) ).
tff(fact_32_fun__upd__apply,axiom,
! [F: fun_li1432931796on_val,Y_1: option_val,Z: list_char,X_1: list_char] :
( ( ( Z = X_1 )
=> ( hAPP_l207779698on_val(fun_up1149430426on_val(F,X_1,Y_1),Z) = Y_1 ) )
& ( ( Z != X_1 )
=> ( hAPP_l207779698on_val(fun_up1149430426on_val(F,X_1,Y_1),Z) = hAPP_l207779698on_val(F,Z) ) ) ) ).
tff(fact_33_fun__upd__apply,axiom,
! [F: fun_li688206603ion_ty,Y_1: option_ty,Z: list_char,X_1: list_char] :
( ( ( Z = X_1 )
=> ( hAPP_l512744617ion_ty(fun_up424764369ion_ty(F,X_1,Y_1),Z) = Y_1 ) )
& ( ( Z != X_1 )
=> ( hAPP_l512744617ion_ty(fun_up424764369ion_ty(F,X_1,Y_1),Z) = hAPP_l512744617ion_ty(F,Z) ) ) ) ).
tff(fact_34_fun__upd__same,axiom,
! [F: fun_li1432931796on_val,X_1: list_char,Y_1: option_val] : ( hAPP_l207779698on_val(fun_up1149430426on_val(F,X_1,Y_1),X_1) = Y_1 ) ).
tff(fact_35_fun__upd__same,axiom,
! [F: fun_li688206603ion_ty,X_1: list_char,Y_1: option_ty] : ( hAPP_l512744617ion_ty(fun_up424764369ion_ty(F,X_1,Y_1),X_1) = Y_1 ) ).
tff(fact_36_fun__upd__upd,axiom,
! [F: fun_li1432931796on_val,X_1: list_char,Y_1: option_val,Z: option_val] : ( fun_up1149430426on_val(fun_up1149430426on_val(F,X_1,Y_1),X_1,Z) = fun_up1149430426on_val(F,X_1,Z) ) ).
tff(fact_37_fun__upd__upd,axiom,
! [F: fun_li688206603ion_ty,X_1: list_char,Y_1: option_ty,Z: option_ty] : ( fun_up424764369ion_ty(fun_up424764369ion_ty(F,X_1,Y_1),X_1,Z) = fun_up424764369ion_ty(F,X_1,Z) ) ).
tff(fact_38_fun__upd__idem__iff,axiom,
! [F: fun_li1432931796on_val,X_1: list_char,Y_1: option_val] :
( ( fun_up1149430426on_val(F,X_1,Y_1) = F )
<=> ( hAPP_l207779698on_val(F,X_1) = Y_1 ) ) ).
tff(fact_39_fun__upd__idem__iff,axiom,
! [F: fun_li688206603ion_ty,X_1: list_char,Y_1: option_ty] :
( ( fun_up424764369ion_ty(F,X_1,Y_1) = F )
<=> ( hAPP_l512744617ion_ty(F,X_1) = Y_1 ) ) ).
tff(fact_40_widen__refl,axiom,
! [P_3: list_P1999446415t_char,T_4: ty] : hBOOL(widen_2090681816t_char(P_3,T_4,T_4)) ).
tff(fact_41_red__preserves__hconf,axiom,
! [Ea: fun_li688206603ion_ty,Ta: ty,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))),red(Pa)))
=> ( hBOOL(wTrt(Pa,Hb,Ea,Eb,Ta))
=> ( hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),Hb))
=> hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),H_b)) ) ) ) ).
tff(fact_42_red__preserves__lconf,axiom,
! [Ea: fun_li688206603ion_ty,Ta: ty,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))),red(Pa)))
=> ( hBOOL(wTrt(Pa,Hb,Ea,Eb,Ta))
=> ( hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),Hb),Lb),Ea))
=> hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),H_b),L_b),Ea)) ) ) ) ).
tff(fact_43_prod__cases3,axiom,
! [Y_1: produc1102272487on_val] :
~ ! [A_15: produc124828825on_val,B: exp_list_char,C_1: produc12694297on_val] : ( Y_1 != hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B),C_1)) ) ).
tff(fact_44_prod__cases3,axiom,
! [Y_1: produc124828825on_val] :
~ ! [A_15: exp_list_char,B: fun_na939144002on_val,C_1: fun_li1432931796on_val] : ( Y_1 != hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_15),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,B),C_1)) ) ).
tff(fact_45_prod__induct3,axiom,
! [X_1: produc1102272487on_val,Pa: fun_Pr691271849l_bool] :
( ! [A_15: produc124828825on_val,B: exp_list_char,C_1: produc12694297on_val] : hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B),C_1))))
=> hBOOL(hAPP_P282169671l_bool(Pa,X_1)) ) ).
tff(fact_46_prod__induct3,axiom,
! [X_1: produc124828825on_val,Pa: fun_Pr680585871l_bool] :
( ! [A_15: exp_list_char,B: fun_na939144002on_val,C_1: fun_li1432931796on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_15),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,B),C_1))))
=> hBOOL(hAPP_P1708370145l_bool(Pa,X_1)) ) ).
tff(fact_47_red__preserves__sconf,axiom,
! [Ea: fun_li688206603ion_ty,Ta: ty,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_1)),red(Pa)))
=> ( hBOOL(wTrt(Pa,hp(S),Ea,Eb,Ta))
=> ( hBOOL(hAPP_P159683425l_bool(typeSa1844245082_sconf(Pa,Ea),S))
=> hBOOL(hAPP_P159683425l_bool(typeSa1844245082_sconf(Pa,Ea),S_1)) ) ) ) ).
tff(fact_48_pred__equals__eq2,axiom,
! [S_3: fun_Pr680585871l_bool,R_1: fun_Pr680585871l_bool] :
( ! [X: exp_list_char,Xa: produc12694297on_val] :
( hBOOL(member840932460on_val(hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X),Xa),R_1))
<=> hBOOL(member840932460on_val(hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X),Xa),S_3)) )
<=> ( R_1 = S_3 ) ) ).
tff(fact_49_pred__equals__eq2,axiom,
! [S_3: fun_Pr1696029455l_bool,R_1: fun_Pr1696029455l_bool] :
( ! [X: fun_na939144002on_val,Xa: fun_li1432931796on_val] :
( hBOOL(member763590124on_val(hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X),Xa),R_1))
<=> hBOOL(member763590124on_val(hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X),Xa),S_3)) )
<=> ( R_1 = S_3 ) ) ).
tff(fact_50_pred__equals__eq2,axiom,
! [S_3: fun_Pr691271849l_bool,R_1: fun_Pr691271849l_bool] :
( ! [X: produc124828825on_val,Xa: produc124828825on_val] :
( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X),Xa),R_1))
<=> hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X),Xa),S_3)) )
<=> ( R_1 = S_3 ) ) ).
tff(fact_51_prod_Oexhaust,axiom,
! [Y_1: produc1102272487on_val] :
~ ! [A_15: produc124828825on_val,B: produc124828825on_val] : ( Y_1 != hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),B) ) ).
tff(fact_52_prod_Oexhaust,axiom,
! [Y_1: produc124828825on_val] :
~ ! [A_15: exp_list_char,B: produc12694297on_val] : ( Y_1 != hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_15),B) ) ).
tff(fact_53_prod_Oexhaust,axiom,
! [Y_1: produc12694297on_val] :
~ ! [A_15: fun_na939144002on_val,B: fun_li1432931796on_val] : ( Y_1 != hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_15),B) ) ).
tff(fact_54_widen__trans,axiom,
! [T_3: ty,P_2: list_P1999446415t_char,S_2: ty,U_1: ty] :
( hBOOL(widen_2090681816t_char(P_2,S_2,U_1))
=> ( hBOOL(widen_2090681816t_char(P_2,U_1,T_3))
=> hBOOL(widen_2090681816t_char(P_2,S_2,T_3)) ) ) ).
tff(fact_55_InitBlockRed_I5_J,axiom,
hBOOL(wTrt(p,ha,e,block_list_char(v_1,t_1,seq_list_char(lAss_list_char(v_1,val_list_char(v)),ea)),t)) ).
tff(fact_56_split__paired__Ex,axiom,
! [Pa: fun_Pr691271849l_bool] :
( ? [X1: produc1102272487on_val] : hBOOL(hAPP_P282169671l_bool(Pa,X1))
<=> ? [A_15: produc124828825on_val,B: produc124828825on_val] : hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),B))) ) ).
tff(fact_57_split__paired__Ex,axiom,
! [Pa: fun_Pr680585871l_bool] :
( ? [X1: produc124828825on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,X1))
<=> ? [A_15: exp_list_char,B: produc12694297on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_15),B))) ) ).
tff(fact_58_split__paired__Ex,axiom,
! [Pa: fun_Pr1696029455l_bool] :
( ? [X1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(Pa,X1))
<=> ? [A_15: fun_na939144002on_val,B: fun_li1432931796on_val] : hBOOL(hAPP_P159683425l_bool(Pa,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_15),B))) ) ).
tff(fact_59_PairE,axiom,
! [P_1: produc1102272487on_val] :
~ ! [X: produc124828825on_val,Y: produc124828825on_val] : ( P_1 != hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X),Y) ) ).
tff(fact_60_PairE,axiom,
! [P_1: produc124828825on_val] :
~ ! [X: exp_list_char,Y: produc12694297on_val] : ( P_1 != hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X),Y) ) ).
tff(fact_61_PairE,axiom,
! [P_1: produc12694297on_val] :
~ ! [X: fun_na939144002on_val,Y: fun_li1432931796on_val] : ( P_1 != hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X),Y) ) ).
tff(fact_62_internal__split__conv,axiom,
! [C: fun_fu100249073l_bool,A_10: fun_na939144002on_val,B_1: fun_li1432931796on_val] :
( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc2128769400l_bool,C),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1)))
<=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(C,A_10),B_1)) ) ).
tff(fact_63_sconf__def,axiom,
! [Pa: list_P1999446415t_char,Ea: fun_li688206603ion_ty,S: produc12694297on_val] :
( hBOOL(hAPP_P159683425l_bool(typeSa1844245082_sconf(Pa,Ea),S))
<=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,cOMBS_570216337l_bool(hAPP_f1523875321l_bool(hAPP_f592397849l_bool(cOMBB_1718333400on_val,cOMBB_383678192on_val),hAPP_f1452292669l_bool(hAPP_f1977633121l_bool(cOMBB_1303934920on_val,fconj),hconf_97414254t_char(Pa))),hAPP_f550652027l_bool(hAPP_f838396643l_bool(cOMBC_2027949654l_bool,hAPP_f857351829l_bool(hAPP_f348318673l_bool(cOMBB_1518282696on_val,cOMBC_832625297y_bool),lconf_496643946t_char(Pa))),Ea))),S)) ) ).
tff(fact_64_prod__caseI,axiom,
! [F1: fun_Pr633696065l_bool,A_10: produc124828825on_val,B_1: produc124828825on_val] :
( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(F1,A_10),B_1))
=> hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,F1),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_10),B_1))) ) ).
tff(fact_65_prod__caseI,axiom,
! [F1: fun_ex1201926843l_bool,A_10: exp_list_char,B_1: produc12694297on_val] :
( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(F1,A_10),B_1))
=> hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,F1),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_10),B_1))) ) ).
tff(fact_66_prod__caseI,axiom,
! [F1: fun_fu100249073l_bool,A_10: fun_na939144002on_val,B_1: fun_li1432931796on_val] :
( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F1,A_10),B_1))
=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1))) ) ).
tff(fact_67_splitI,axiom,
! [F: fun_Pr633696065l_bool,A_10: produc124828825on_val,B_1: produc124828825on_val] :
( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(F,A_10),B_1))
=> hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,F),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_10),B_1))) ) ).
tff(fact_68_splitI,axiom,
! [F: fun_ex1201926843l_bool,A_10: exp_list_char,B_1: produc12694297on_val] :
( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(F,A_10),B_1))
=> hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,F),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_10),B_1))) ) ).
tff(fact_69_splitI,axiom,
! [F: fun_fu100249073l_bool,A_10: fun_na939144002on_val,B_1: fun_li1432931796on_val] :
( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F,A_10),B_1))
=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1))) ) ).
tff(fact_70_splitD,axiom,
! [F: fun_Pr633696065l_bool,A_10: produc124828825on_val,B_1: produc124828825on_val] :
( hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,F),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_10),B_1)))
=> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(F,A_10),B_1)) ) ).
tff(fact_71_splitD,axiom,
! [F: fun_ex1201926843l_bool,A_10: exp_list_char,B_1: produc12694297on_val] :
( hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,F),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_10),B_1)))
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(F,A_10),B_1)) ) ).
tff(fact_72_splitD,axiom,
! [F: fun_fu100249073l_bool,A_10: fun_na939144002on_val,B_1: fun_li1432931796on_val] :
( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1)))
=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F,A_10),B_1)) ) ).
tff(fact_73_split__weak__cong,axiom,
! [C: fun_ex1201926843l_bool,P_1: produc124828825on_val,Q_2: produc124828825on_val] :
( ( P_1 = Q_2 )
=> ( hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,C),P_1))
<=> hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,C),Q_2)) ) ) ).
tff(fact_74_split__weak__cong,axiom,
! [C: fun_Pr633696065l_bool,P_1: produc1102272487on_val,Q_2: produc1102272487on_val] :
( ( P_1 = Q_2 )
=> ( hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,C),P_1))
<=> hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,C),Q_2)) ) ) ).
tff(fact_75_split__weak__cong,axiom,
! [C: fun_fu100249073l_bool,P_1: produc12694297on_val,Q_2: produc12694297on_val] :
( ( P_1 = Q_2 )
=> ( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,C),P_1))
<=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,C),Q_2)) ) ) ).
tff(fact_76_internal__split__def,axiom,
produc399384568l_bool = produc1815960045l_bool ).
tff(fact_77_internal__split__def,axiom,
produc1988544340l_bool = produc1911463199l_bool ).
tff(fact_78_internal__split__def,axiom,
produc2128769400l_bool = produc1958875245l_bool ).
tff(fact_79_split__twice,axiom,
! [F: fun_fu100249073l_bool,G: fun_ex1005552999on_val,P_1: produc124828825on_val] :
( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F),hAPP_P789556885on_val(hAPP_f1520199827on_val(produc1174947465on_val,G),P_1)))
<=> hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,hAPP_f653692369l_bool(hAPP_f516738477l_bool(cOMBB_819439237t_char,hAPP_f1825030711l_bool(cOMBB_877741809on_val,hAPP_f2121594859l_bool(produc1958875245l_bool,F))),G)),P_1)) ) ).
tff(fact_80_split__twice,axiom,
! [F: fun_fu100249073l_bool,G: fun_Pr1719283041on_val,P_1: produc1102272487on_val] :
( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F),hAPP_P1760219823on_val(hAPP_f394183983on_val(produc1003071703on_val,G),P_1)))
<=> hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,hAPP_f1241216909l_bool(hAPP_f1438732387l_bool(cOMBB_635947099on_val,hAPP_f881985847l_bool(cOMBB_1083177073on_val,hAPP_f2121594859l_bool(produc1958875245l_bool,F))),G)),P_1)) ) ).
tff(fact_81_split__twice,axiom,
! [F: fun_ex1201926843l_bool,G: fun_fu2073188913on_val,P_1: produc12694297on_val] :
( hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,F),hAPP_P604205461on_val(hAPP_f1309113673on_val(produc901351817on_val,G),P_1)))
<=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f850751421l_bool(hAPP_f399538905l_bool(cOMBB_1466889536on_val,hAPP_f1233687287l_bool(cOMBB_171276332on_val,hAPP_f1930574389l_bool(produc1815960045l_bool,F))),G)),P_1)) ) ).
tff(fact_82_split__twice,axiom,
! [F: fun_Pr633696065l_bool,G: fun_fu1133203323on_val,P_1: produc12694297on_val] :
( hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,F),hAPP_P2024243179on_val(hAPP_f204556415on_val(produc1148763895on_val,G),P_1)))
<=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f927043595l_bool(hAPP_f1043869573l_bool(cOMBB_1259202826on_val,hAPP_f2052660463l_bool(cOMBB_1292453606on_val,hAPP_f635218277l_bool(produc1911463199l_bool,F))),G)),P_1)) ) ).
tff(fact_83_split__part,axiom,
! [Pa: bool,Q_1: fun_ex1201926843l_bool,X: produc124828825on_val] :
( hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,hAPP_f546724245l_bool(hAPP_f917296015l_bool(cOMBB_740252943t_char,hAPP_f1308714617l_bool(cOMBB_338347573on_val,hAPP_b589554111l_bool(fconj,Pa))),Q_1)),X))
<=> ( hBOOL(Pa)
& hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,Q_1),X)) ) ) ).
tff(fact_84_split__part,axiom,
! [Pa: bool,Q_1: fun_Pr633696065l_bool,X: produc1102272487on_val] :
( hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,hAPP_f641257349l_bool(hAPP_f2032347769l_bool(cOMBB_466903633on_val,hAPP_f1560238713l_bool(cOMBB_672625589on_val,hAPP_b589554111l_bool(fconj,Pa))),Q_1)),X))
<=> ( hBOOL(Pa)
& hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,Q_1),X)) ) ) ).
tff(fact_85_split__part,axiom,
! [Pa: bool,Q_1: fun_fu100249073l_bool,X: produc12694297on_val] :
( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f555424277l_bool(hAPP_f1734879897l_bool(cOMBB_1522540928on_val,hAPP_f1863694447l_bool(cOMBB_383678192on_val,hAPP_b589554111l_bool(fconj,Pa))),Q_1)),X))
<=> ( hBOOL(Pa)
& hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,Q_1),X)) ) ) ).
tff(fact_86_prod_Osimps_I2_J,axiom,
! [F1: fun_fu100249073l_bool,A_10: fun_na939144002on_val,B_1: fun_li1432931796on_val] :
( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1)))
<=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F1,A_10),B_1)) ) ).
tff(fact_87_prod_Osimps_I2_J,axiom,
! [F1: fun_Pr633696065l_bool,A_10: produc124828825on_val,B_1: produc124828825on_val] :
( hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,F1),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_10),B_1)))
<=> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(F1,A_10),B_1)) ) ).
tff(fact_88_prod_Osimps_I2_J,axiom,
! [F1: fun_ex1201926843l_bool,A_10: exp_list_char,B_1: produc12694297on_val] :
( hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,F1),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_10),B_1)))
<=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(F1,A_10),B_1)) ) ).
tff(fact_89_split__conv,axiom,
! [F: fun_fu100249073l_bool,A_10: fun_na939144002on_val,B_1: fun_li1432931796on_val] :
( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1)))
<=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F,A_10),B_1)) ) ).
tff(fact_90_split__conv,axiom,
! [F: fun_Pr633696065l_bool,A_10: produc124828825on_val,B_1: produc124828825on_val] :
( hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,F),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_10),B_1)))
<=> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(F,A_10),B_1)) ) ).
tff(fact_91_split__conv,axiom,
! [F: fun_ex1201926843l_bool,A_10: exp_list_char,B_1: produc12694297on_val] :
( hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,F),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_10),B_1)))
<=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(F,A_10),B_1)) ) ).
tff(fact_92_split__eta,axiom,
! [F: fun_Pr1696029455l_bool] : ( hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f1363667773l_bool(hAPP_f1050935001l_bool(cOMBB_1153617344on_val,hAPP_f2057883639l_bool(cOMBB_1750801836on_val,F)),produc899768717on_val)) = F ) ).
tff(fact_93_split__eta,axiom,
! [F: fun_Pr691271849l_bool] : ( hAPP_f635218277l_bool(produc1911463199l_bool,hAPP_f1342895119l_bool(hAPP_f639265145l_bool(cOMBB_364363975on_val,hAPP_f365540729l_bool(cOMBB_1466662571on_val,F)),produc1441475159on_val)) = F ) ).
tff(fact_94_split__eta,axiom,
! [F: fun_Pr680585871l_bool] : ( hAPP_f1930574389l_bool(produc1815960045l_bool,hAPP_f439412817l_bool(hAPP_f1725502637l_bool(cOMBB_1027621637t_char,hAPP_f10074679l_bool(cOMBB_1759207793on_val,F)),produc1259058957on_val)) = F ) ).
tff(fact_95_red__reds_OInitBlockRed,axiom,
! [Ta: ty,V_a: val,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,Va_1: list_char,Va: val,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,Va_1,some_val(Va))))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))),red(Pa)))
=> ( ( hAPP_l207779698on_val(L_b,Va_1) = some_val(V_a) )
=> hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,val_list_char(Va)),Eb))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,val_list_char(V_a)),E_b))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1))))),red(Pa))) ) ) ).
tff(fact_96_red__reds_ORedInitBlock,axiom,
! [Va_1: list_char,Ta: ty,Va: val,U: val,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,val_list_char(Va)),val_list_char(U)))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,val_list_char(U)),S)),red(Pa))) ).
tff(fact_97_splitI2,axiom,
! [C: fun_Pr633696065l_bool,P_1: produc1102272487on_val] :
( ! [A_15: produc124828825on_val,B: produc124828825on_val] :
( ( P_1 = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),B) )
=> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(C,A_15),B)) )
=> hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,C),P_1)) ) ).
tff(fact_98_splitI2,axiom,
! [C: fun_ex1201926843l_bool,P_1: produc124828825on_val] :
( ! [A_15: exp_list_char,B: produc12694297on_val] :
( ( P_1 = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_15),B) )
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(C,A_15),B)) )
=> hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,C),P_1)) ) ).
tff(fact_99_splitI2,axiom,
! [C: fun_fu100249073l_bool,P_1: produc12694297on_val] :
( ! [A_15: fun_na939144002on_val,B: fun_li1432931796on_val] :
( ( P_1 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_15),B) )
=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(C,A_15),B)) )
=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,C),P_1)) ) ).
tff(fact_100_splitE,axiom,
! [C: fun_Pr633696065l_bool,P_1: produc1102272487on_val] :
( hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,C),P_1))
=> ~ ! [X: produc124828825on_val,Y: produc124828825on_val] :
( ( P_1 = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X),Y) )
=> ~ hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(C,X),Y)) ) ) ).
tff(fact_101_splitE,axiom,
! [C: fun_ex1201926843l_bool,P_1: produc124828825on_val] :
( hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,C),P_1))
=> ~ ! [X: exp_list_char,Y: produc12694297on_val] :
( ( P_1 = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X),Y) )
=> ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(C,X),Y)) ) ) ).
tff(fact_102_splitE,axiom,
! [C: fun_fu100249073l_bool,P_1: produc12694297on_val] :
( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,C),P_1))
=> ~ ! [X: fun_na939144002on_val,Y: fun_li1432931796on_val] :
( ( P_1 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X),Y) )
=> ~ hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(C,X),Y)) ) ) ).
tff(fact_103_WTrtBlock,axiom,
! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Va_1: list_char,Ta: ty,Eb: exp_list_char,T_a: ty] :
( hBOOL(wTrt(Pa,Hb,fun_up424764369ion_ty(Ea,Va_1,some_ty(Ta)),Eb,T_a))
=> hBOOL(wTrt(Pa,Hb,Ea,block_list_char(Va_1,Ta,Eb),T_a)) ) ).
tff(fact_104_mem__splitI,axiom,
! [Z: produc12694297on_val,C: fun_Pr293514739l_bool,A_10: produc124828825on_val,B_1: produc124828825on_val] :
( hBOOL(member763590124on_val(Z,hAPP_P595502227l_bool(hAPP_P1134042693l_bool(C,A_10),B_1)))
=> hBOOL(member763590124on_val(Z,hAPP_P1826803705l_bool(hAPP_f444383845l_bool(produc376702929l_bool,C),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_10),B_1)))) ) ).
tff(fact_105_mem__splitI,axiom,
! [Z: produc124828825on_val,C: fun_Pr741412723l_bool,A_10: produc124828825on_val,B_1: produc124828825on_val] :
( hBOOL(member840932460on_val(Z,hAPP_P1116729363l_bool(hAPP_P1953518277l_bool(C,A_10),B_1)))
=> hBOOL(member840932460on_val(Z,hAPP_P678729081l_bool(hAPP_f1591648613l_bool(produc20018513l_bool,C),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_10),B_1)))) ) ).
tff(fact_106_mem__splitI,axiom,
! [Z: produc12694297on_val,C: fun_ex1123147373l_bool,A_10: exp_list_char,B_1: produc12694297on_val] :
( hBOOL(member763590124on_val(Z,hAPP_P1988153107l_bool(hAPP_e500528395l_bool(C,A_10),B_1)))
=> hBOOL(member763590124on_val(Z,hAPP_P595502227l_bool(hAPP_f468299289l_bool(produc2036005791l_bool,C),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_10),B_1)))) ) ).
tff(fact_107_mem__splitI,axiom,
! [Z: produc124828825on_val,C: fun_ex1732109805l_bool,A_10: exp_list_char,B_1: produc12694297on_val] :
( hBOOL(member840932460on_val(Z,hAPP_P1638898323l_bool(hAPP_e592495499l_bool(C,A_10),B_1)))
=> hBOOL(member840932460on_val(Z,hAPP_P1116729363l_bool(hAPP_f1760682521l_bool(produc1275132703l_bool,C),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_10),B_1)))) ) ).
tff(fact_108_mem__splitI,axiom,
! [Z: produc12694297on_val,C: fun_fu110544035l_bool,A_10: fun_na939144002on_val,B_1: fun_li1432931796on_val] :
( hBOOL(member763590124on_val(Z,hAPP_f396019662l_bool(hAPP_f2135509569l_bool(C,A_10),B_1)))
=> hBOOL(member763590124on_val(Z,hAPP_P1988153107l_bool(hAPP_f1276548047l_bool(produc121041439l_bool,C),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1)))) ) ).
tff(fact_109_mem__splitI,axiom,
! [Z: produc124828825on_val,C: fun_fu606696995l_bool,A_10: fun_na939144002on_val,B_1: fun_li1432931796on_val] :
( hBOOL(member840932460on_val(Z,hAPP_f2011777102l_bool(hAPP_f2144092865l_bool(C,A_10),B_1)))
=> hBOOL(member840932460on_val(Z,hAPP_P1638898323l_bool(hAPP_f833559503l_bool(produc334393759l_bool,C),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1)))) ) ).
tff(fact_110_WTrtSeq,axiom,
! [E_2: exp_list_char,T_2: ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,E_1: exp_list_char,T_1: ty] :
( hBOOL(wTrt(Pa,Hb,Ea,E_1,T_1))
=> ( hBOOL(wTrt(Pa,Hb,Ea,E_2,T_2))
=> hBOOL(wTrt(Pa,Hb,Ea,seq_list_char(E_1,E_2),T_2)) ) ) ).
tff(fact_111_red__reds_OSeqRed,axiom,
! [E_2: exp_list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_1)),red(Pa)))
=> hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,seq_list_char(Eb,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,seq_list_char(E_b,E_2)),S_1)),red(Pa))) ) ).
tff(fact_112_red__reds_OLAssRed,axiom,
! [Va_1: list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_1)),red(Pa)))
=> hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(Va_1,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(Va_1,E_b)),S_1)),red(Pa))) ) ).
tff(fact_113_red__reds_ORedSeq,axiom,
! [Va: val,E_2: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,seq_list_char(val_list_char(Va),E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),S)),red(Pa))) ).
tff(fact_114_red__reds_ORedBlock,axiom,
! [Va_1: list_char,Ta: ty,U: val,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,val_list_char(U))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,val_list_char(U)),S)),red(Pa))) ).
tff(fact_115_mem__splitE,axiom,
! [Z: produc12694297on_val,C: fun_Pr293514739l_bool,P_1: produc1102272487on_val] :
( hBOOL(member763590124on_val(Z,hAPP_P1826803705l_bool(hAPP_f444383845l_bool(produc376702929l_bool,C),P_1)))
=> ~ ! [X: produc124828825on_val,Y: produc124828825on_val] :
( ( P_1 = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X),Y) )
=> ~ hBOOL(member763590124on_val(Z,hAPP_P595502227l_bool(hAPP_P1134042693l_bool(C,X),Y))) ) ) ).
tff(fact_116_mem__splitE,axiom,
! [Z: produc124828825on_val,C: fun_Pr741412723l_bool,P_1: produc1102272487on_val] :
( hBOOL(member840932460on_val(Z,hAPP_P678729081l_bool(hAPP_f1591648613l_bool(produc20018513l_bool,C),P_1)))
=> ~ ! [X: produc124828825on_val,Y: produc124828825on_val] :
( ( P_1 = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X),Y) )
=> ~ hBOOL(member840932460on_val(Z,hAPP_P1116729363l_bool(hAPP_P1953518277l_bool(C,X),Y))) ) ) ).
tff(fact_117_mem__splitE,axiom,
! [Z: produc12694297on_val,C: fun_ex1123147373l_bool,P_1: produc124828825on_val] :
( hBOOL(member763590124on_val(Z,hAPP_P595502227l_bool(hAPP_f468299289l_bool(produc2036005791l_bool,C),P_1)))
=> ~ ! [X: exp_list_char,Y: produc12694297on_val] :
( ( P_1 = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X),Y) )
=> ~ hBOOL(member763590124on_val(Z,hAPP_P1988153107l_bool(hAPP_e500528395l_bool(C,X),Y))) ) ) ).
tff(fact_118_mem__splitE,axiom,
! [Z: produc124828825on_val,C: fun_ex1732109805l_bool,P_1: produc124828825on_val] :
( hBOOL(member840932460on_val(Z,hAPP_P1116729363l_bool(hAPP_f1760682521l_bool(produc1275132703l_bool,C),P_1)))
=> ~ ! [X: exp_list_char,Y: produc12694297on_val] :
( ( P_1 = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X),Y) )
=> ~ hBOOL(member840932460on_val(Z,hAPP_P1638898323l_bool(hAPP_e592495499l_bool(C,X),Y))) ) ) ).
tff(fact_119_mem__splitE,axiom,
! [Z: produc12694297on_val,C: fun_fu110544035l_bool,P_1: produc12694297on_val] :
( hBOOL(member763590124on_val(Z,hAPP_P1988153107l_bool(hAPP_f1276548047l_bool(produc121041439l_bool,C),P_1)))
=> ~ ! [X: fun_na939144002on_val,Y: fun_li1432931796on_val] :
( ( P_1 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X),Y) )
=> ~ hBOOL(member763590124on_val(Z,hAPP_f396019662l_bool(hAPP_f2135509569l_bool(C,X),Y))) ) ) ).
tff(fact_120_mem__splitE,axiom,
! [Z: produc124828825on_val,C: fun_fu606696995l_bool,P_1: produc12694297on_val] :
( hBOOL(member840932460on_val(Z,hAPP_P1638898323l_bool(hAPP_f833559503l_bool(produc334393759l_bool,C),P_1)))
=> ~ ! [X: fun_na939144002on_val,Y: fun_li1432931796on_val] :
( ( P_1 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X),Y) )
=> ~ hBOOL(member840932460on_val(Z,hAPP_f2011777102l_bool(hAPP_f2144092865l_bool(C,X),Y))) ) ) ).
tff(fact_121_mem__splitI2,axiom,
! [Z: produc12694297on_val,C: fun_Pr293514739l_bool,P_1: produc1102272487on_val] :
( ! [A_15: produc124828825on_val,B: produc124828825on_val] :
( ( P_1 = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),B) )
=> hBOOL(member763590124on_val(Z,hAPP_P595502227l_bool(hAPP_P1134042693l_bool(C,A_15),B))) )
=> hBOOL(member763590124on_val(Z,hAPP_P1826803705l_bool(hAPP_f444383845l_bool(produc376702929l_bool,C),P_1))) ) ).
tff(fact_122_mem__splitI2,axiom,
! [Z: produc124828825on_val,C: fun_Pr741412723l_bool,P_1: produc1102272487on_val] :
( ! [A_15: produc124828825on_val,B: produc124828825on_val] :
( ( P_1 = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),B) )
=> hBOOL(member840932460on_val(Z,hAPP_P1116729363l_bool(hAPP_P1953518277l_bool(C,A_15),B))) )
=> hBOOL(member840932460on_val(Z,hAPP_P678729081l_bool(hAPP_f1591648613l_bool(produc20018513l_bool,C),P_1))) ) ).
tff(fact_123_mem__splitI2,axiom,
! [Z: produc12694297on_val,C: fun_ex1123147373l_bool,P_1: produc124828825on_val] :
( ! [A_15: exp_list_char,B: produc12694297on_val] :
( ( P_1 = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_15),B) )
=> hBOOL(member763590124on_val(Z,hAPP_P1988153107l_bool(hAPP_e500528395l_bool(C,A_15),B))) )
=> hBOOL(member763590124on_val(Z,hAPP_P595502227l_bool(hAPP_f468299289l_bool(produc2036005791l_bool,C),P_1))) ) ).
tff(fact_124_mem__splitI2,axiom,
! [Z: produc124828825on_val,C: fun_ex1732109805l_bool,P_1: produc124828825on_val] :
( ! [A_15: exp_list_char,B: produc12694297on_val] :
( ( P_1 = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_15),B) )
=> hBOOL(member840932460on_val(Z,hAPP_P1638898323l_bool(hAPP_e592495499l_bool(C,A_15),B))) )
=> hBOOL(member840932460on_val(Z,hAPP_P1116729363l_bool(hAPP_f1760682521l_bool(produc1275132703l_bool,C),P_1))) ) ).
tff(fact_125_mem__splitI2,axiom,
! [Z: produc12694297on_val,C: fun_fu110544035l_bool,P_1: produc12694297on_val] :
( ! [A_15: fun_na939144002on_val,B: fun_li1432931796on_val] :
( ( P_1 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_15),B) )
=> hBOOL(member763590124on_val(Z,hAPP_f396019662l_bool(hAPP_f2135509569l_bool(C,A_15),B))) )
=> hBOOL(member763590124on_val(Z,hAPP_P1988153107l_bool(hAPP_f1276548047l_bool(produc121041439l_bool,C),P_1))) ) ).
tff(fact_126_mem__splitI2,axiom,
! [Z: produc124828825on_val,C: fun_fu606696995l_bool,P_1: produc12694297on_val] :
( ! [A_15: fun_na939144002on_val,B: fun_li1432931796on_val] :
( ( P_1 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_15),B) )
=> hBOOL(member840932460on_val(Z,hAPP_f2011777102l_bool(hAPP_f2144092865l_bool(C,A_15),B))) )
=> hBOOL(member840932460on_val(Z,hAPP_P1638898323l_bool(hAPP_f833559503l_bool(produc334393759l_bool,C),P_1))) ) ).
tff(fact_127_red__reds_ORedLAss,axiom,
! [Va_1: list_char,Va: val,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(Va_1,val_list_char(Va))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,val_list_char(unit)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,Va_1,some_val(Va))))),red(Pa))) ).
tff(fact_128_cond__split__eta,axiom,
! [G: fun_Pr1696029455l_bool,F: fun_fu100249073l_bool] :
( ! [X: fun_na939144002on_val,Y: fun_li1432931796on_val] :
( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F,X),Y))
<=> hBOOL(hAPP_P159683425l_bool(G,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X),Y))) )
=> ( hAPP_f2121594859l_bool(produc1958875245l_bool,F) = G ) ) ).
tff(fact_129_cond__split__eta,axiom,
! [G: fun_Pr691271849l_bool,F: fun_Pr633696065l_bool] :
( ! [X: produc124828825on_val,Y: produc124828825on_val] :
( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(F,X),Y))
<=> hBOOL(hAPP_P282169671l_bool(G,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X),Y))) )
=> ( hAPP_f635218277l_bool(produc1911463199l_bool,F) = G ) ) ).
tff(fact_130_cond__split__eta,axiom,
! [G: fun_Pr680585871l_bool,F: fun_ex1201926843l_bool] :
( ! [X: exp_list_char,Y: produc12694297on_val] :
( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(F,X),Y))
<=> hBOOL(hAPP_P1708370145l_bool(G,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X),Y))) )
=> ( hAPP_f1930574389l_bool(produc1815960045l_bool,F) = G ) ) ).
tff(fact_131_splitE2,axiom,
! [Q_1: fun_bool_bool,Pa: fun_fu100249073l_bool,Z: produc12694297on_val] :
( hBOOL(hAPP_bool_bool(Q_1,hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,Pa),Z)))
=> ~ ! [X: fun_na939144002on_val,Y: fun_li1432931796on_val] :
( ( Z = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X),Y) )
=> ~ hBOOL(hAPP_bool_bool(Q_1,hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,X),Y))) ) ) ).
tff(fact_132_splitE2,axiom,
! [Q_1: fun_bool_bool,Pa: fun_Pr633696065l_bool,Z: produc1102272487on_val] :
( hBOOL(hAPP_bool_bool(Q_1,hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,Pa),Z)))
=> ~ ! [X: produc124828825on_val,Y: produc124828825on_val] :
( ( Z = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X),Y) )
=> ~ hBOOL(hAPP_bool_bool(Q_1,hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,X),Y))) ) ) ).
tff(fact_133_splitE2,axiom,
! [Q_1: fun_bool_bool,Pa: fun_ex1201926843l_bool,Z: produc124828825on_val] :
( hBOOL(hAPP_bool_bool(Q_1,hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,Pa),Z)))
=> ~ ! [X: exp_list_char,Y: produc12694297on_val] :
( ( Z = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X),Y) )
=> ~ hBOOL(hAPP_bool_bool(Q_1,hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,X),Y))) ) ) ).
tff(fact_134_exp_Osimps_I143_J,axiom,
! [A_14: list_char,Ty_7: ty,Exp_13: exp_list_char,A_13: list_char,Exp_12: exp_list_char] : ( block_list_char(A_14,Ty_7,Exp_13) != lAss_list_char(A_13,Exp_12) ) ).
tff(fact_135_exp_Osimps_I196_J,axiom,
! [A_12: list_char,Ty_6: ty,Exp_11: exp_list_char,Exp1_7: exp_list_char,Exp2_7: exp_list_char] : ( block_list_char(A_12,Ty_6,Exp_11) != seq_list_char(Exp1_7,Exp2_7) ) ).
tff(fact_136_exp_Osimps_I3_J,axiom,
! [Val_7: val,Val_6: val] :
( ( val_list_char(Val_7) = val_list_char(Val_6) )
<=> ( Val_7 = Val_6 ) ) ).
tff(fact_137_exp_Osimps_I11_J,axiom,
! [Exp1_6: exp_list_char,Exp2_6: exp_list_char,Exp1_5: exp_list_char,Exp2_5: exp_list_char] :
( ( seq_list_char(Exp1_6,Exp2_6) = seq_list_char(Exp1_5,Exp2_5) )
<=> ( ( Exp1_6 = Exp1_5 )
& ( Exp2_6 = Exp2_5 ) ) ) ).
tff(fact_138_exp_Osimps_I6_J,axiom,
! [A_10: list_char,Exp_10: exp_list_char,A_9: list_char,Exp_9: exp_list_char] :
( ( lAss_list_char(A_10,Exp_10) = lAss_list_char(A_9,Exp_9) )
<=> ( ( A_10 = A_9 )
& ( Exp_10 = Exp_9 ) ) ) ).
tff(fact_139_mem__def,axiom,
! [X_1: produc12694297on_val,A_11: fun_Pr1696029455l_bool] :
( hBOOL(member763590124on_val(X_1,A_11))
<=> hBOOL(hAPP_P159683425l_bool(A_11,X_1)) ) ).
tff(fact_140_mem__def,axiom,
! [X_1: produc124828825on_val,A_11: fun_Pr680585871l_bool] :
( hBOOL(member840932460on_val(X_1,A_11))
<=> hBOOL(hAPP_P1708370145l_bool(A_11,X_1)) ) ).
tff(fact_141_mem__def,axiom,
! [X_1: produc1102272487on_val,A_11: fun_Pr691271849l_bool] :
( hBOOL(member773094996on_val(X_1,A_11))
<=> hBOOL(hAPP_P282169671l_bool(A_11,X_1)) ) ).
tff(fact_142_exp_Osimps_I10_J,axiom,
! [A_10: list_char,Ty_5: ty,Exp_10: exp_list_char,A_9: list_char,Ty_4: ty,Exp_9: exp_list_char] :
( ( block_list_char(A_10,Ty_5,Exp_10) = block_list_char(A_9,Ty_4,Exp_9) )
<=> ( ( A_10 = A_9 )
& ( Ty_5 = Ty_4 )
& ( Exp_10 = Exp_9 ) ) ) ).
tff(fact_143_exp_Osimps_I84_J,axiom,
! [Val_5: val,Exp1_4: exp_list_char,Exp2_4: exp_list_char] : ( val_list_char(Val_5) != seq_list_char(Exp1_4,Exp2_4) ) ).
tff(fact_144_exp_Osimps_I74_J,axiom,
! [Val_4: val,A_8: list_char,Exp_8: exp_list_char] : ( val_list_char(Val_4) != lAss_list_char(A_8,Exp_8) ) ).
tff(fact_145_exp_Osimps_I85_J,axiom,
! [Exp1_3: exp_list_char,Exp2_3: exp_list_char,Val_3: val] : ( seq_list_char(Exp1_3,Exp2_3) != val_list_char(Val_3) ) ).
tff(fact_146_exp_Osimps_I75_J,axiom,
! [A_7: list_char,Exp_7: exp_list_char,Val_2: val] : ( lAss_list_char(A_7,Exp_7) != val_list_char(Val_2) ) ).
tff(fact_147_exp_Osimps_I82_J,axiom,
! [Val_1: val,A_6: list_char,Ty_3: ty,Exp_6: exp_list_char] : ( val_list_char(Val_1) != block_list_char(A_6,Ty_3,Exp_6) ) ).
tff(fact_148_exp_Osimps_I83_J,axiom,
! [A_5: list_char,Ty_2: ty,Exp_5: exp_list_char,Val: val] : ( block_list_char(A_5,Ty_2,Exp_5) != val_list_char(Val) ) ).
tff(fact_149_exp_Osimps_I145_J,axiom,
! [Exp1_2: exp_list_char,Exp2_2: exp_list_char,A_4: list_char,Exp_4: exp_list_char] : ( seq_list_char(Exp1_2,Exp2_2) != lAss_list_char(A_4,Exp_4) ) ).
tff(fact_150_exp_Osimps_I144_J,axiom,
! [A_3: list_char,Exp_3: exp_list_char,Exp1_1: exp_list_char,Exp2_1: exp_list_char] : ( lAss_list_char(A_3,Exp_3) != seq_list_char(Exp1_1,Exp2_1) ) ).
tff(fact_151_exp_Osimps_I197_J,axiom,
! [Exp1: exp_list_char,Exp2: exp_list_char,A_2: list_char,Ty_1: ty,Exp_2: exp_list_char] : ( seq_list_char(Exp1,Exp2) != block_list_char(A_2,Ty_1,Exp_2) ) ).
tff(fact_152_exp_Osimps_I142_J,axiom,
! [A_1: list_char,Exp_1: exp_list_char,A: list_char,Ty: ty,Exp: exp_list_char] : ( lAss_list_char(A_1,Exp_1) != block_list_char(A,Ty,Exp) ) ).
tff(fact_153_redp__redsp_OInitBlockRed,axiom,
! [Ta: ty,V_a: val,Pa: list_P1999446415t_char,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,Va_1: list_char,Va: val,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: fun_li1432931796on_val] :
( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,Va_1,some_val(Va)))),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))
=> ( ( hAPP_l207779698on_val(L_b,Va_1) = some_val(V_a) )
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,val_list_char(Va)),Eb)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,val_list_char(V_a)),E_b))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1))))) ) ) ).
tff(fact_154_red__reds_OBlockRedSome,axiom,
! [Ta: ty,Va: val,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,Va_1: list_char,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,Va_1,none_val)))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))),red(Pa)))
=> ( ( hAPP_l207779698on_val(L_b,Va_1) = some_val(Va) )
=> ( ~ hBOOL(assigned(Va_1,Eb))
=> hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,Eb)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,val_list_char(Va)),E_b))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1))))),red(Pa))) ) ) ) ).
tff(fact_155_redp__redsp_OSeqRed,axiom,
! [E_2: exp_list_char,Pa: list_P1999446415t_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_1: produc12694297on_val] :
( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_1))
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,seq_list_char(Eb,E_2),S),seq_list_char(E_b,E_2)),S_1)) ) ).
tff(fact_156_redp__redsp_OLAssRed,axiom,
! [Va_1: list_char,Pa: list_P1999446415t_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_1: produc12694297on_val] :
( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_1))
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,lAss_list_char(Va_1,Eb),S),lAss_list_char(Va_1,E_b)),S_1)) ) ).
tff(fact_157_redp__redsp_OBlockRedNone,axiom,
! [Ta: ty,Pa: list_P1999446415t_char,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,Va_1: list_char,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: fun_li1432931796on_val] :
( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,Va_1,none_val))),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))
=> ( ( hAPP_l207779698on_val(L_b,Va_1) = none_val )
=> ( ~ hBOOL(assigned(Va_1,Eb))
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(Va_1,Ta,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),block_list_char(Va_1,Ta,E_b)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1))))) ) ) ) ).
tff(fact_158_redp__redsp_ORedSeq,axiom,
! [Pa: list_P1999446415t_char,Va: val,E_2: exp_list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,seq_list_char(val_list_char(Va),E_2),S),E_2),S)) ).
tff(fact_159_map__upd__nonempty,axiom,
! [T: fun_li1432931796on_val,K: list_char,X_1: val] :
~ ! [X: list_char] : ( hAPP_l207779698on_val(fun_up1149430426on_val(T,K,some_val(X_1)),X) = none_val ) ).
tff(fact_160_map__upd__nonempty,axiom,
! [T: fun_li688206603ion_ty,K: list_char,X_1: ty] :
~ ! [X: list_char] : ( hAPP_l512744617ion_ty(fun_up424764369ion_ty(T,K,some_ty(X_1)),X) = none_ty ) ).
tff(fact_161_redp__redsp_ORedBlock,axiom,
! [Pa: list_P1999446415t_char,Va_1: list_char,Ta: ty,U: val,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(Va_1,Ta,val_list_char(U)),S),val_list_char(U)),S)) ).
tff(fact_162_empty__upd__none,axiom,
! [X_1: list_char,X: list_char] : ( hAPP_l207779698on_val(fun_up1149430426on_val(cOMBK_1097134891t_char(none_val),X_1,none_val),X) = none_val ) ).
tff(fact_163_empty__upd__none,axiom,
! [X_1: list_char,X: list_char] : ( hAPP_l512744617ion_ty(fun_up424764369ion_ty(cOMBK_1294242658t_char(none_ty),X_1,none_ty),X) = none_ty ) ).
tff(fact_164_redp__redsp_OBlockRedSome,axiom,
! [Ta: ty,Va: val,Pa: list_P1999446415t_char,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,Va_1: list_char,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: fun_li1432931796on_val] :
( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,Va_1,none_val))),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))
=> ( ( hAPP_l207779698on_val(L_b,Va_1) = some_val(Va) )
=> ( ~ hBOOL(assigned(Va_1,Eb))
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(Va_1,Ta,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,val_list_char(Va)),E_b))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1))))) ) ) ) ).
tff(fact_165_redp__red__eq,axiom,
! [Pa: list_P1999446415t_char,X: exp_list_char,Xa: produc12694297on_val,Xb: exp_list_char,Xc: produc12694297on_val] :
( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,X,Xa),Xb),Xc))
<=> hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X),Xa)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Xb),Xc)),red(Pa))) ) ).
tff(fact_166_redp__redsp_ORedInitBlock,axiom,
! [Pa: list_P1999446415t_char,Va_1: list_char,Ta: ty,Va: val,U: val,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,val_list_char(Va)),val_list_char(U))),S),val_list_char(U)),S)) ).
%----Helper facts (31)
tff(help_fconj_1_1_U,axiom,
! [Q: bool,P: bool] :
( ~ hBOOL(P)
| ~ hBOOL(Q)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) ) ).
tff(help_fconj_2_1_U,axiom,
! [P: bool,Q: bool] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q))
| hBOOL(P) ) ).
tff(help_fconj_3_1_U,axiom,
! [P: bool,Q: bool] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q))
| hBOOL(Q) ) ).
tff(help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__List__Olist_,axiom,
! [P: option_ty,Q: list_char] : ( hAPP_l512744617ion_ty(cOMBK_1294242658t_char(P),Q) = P ) ).
tff(help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__List__Olis,axiom,
! [P: option_val,Q: list_char] : ( hAPP_l207779698on_val(cOMBK_1097134891t_char(P),Q) = P ) ).
tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__List__O,axiom,
! [P: fun_bool_bool,Q: fun_fu1693644106l_bool,R: fun_li1432931796on_val] : ( hAPP_f1033709212l_bool(hAPP_f1074020887l_bool(hAPP_f1863694447l_bool(cOMBB_383678192on_val,P),Q),R) = hAPP_bool_bool(P,hAPP_f1033709212l_bool(Q,R)) ) ).
tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Optio,axiom,
! [P: fun_fu1670877422y_bool,Q: fun_li688206603ion_ty,R: fun_li1432931796on_val] : ( hAPP_f1033709212l_bool(hAPP_f603925568l_bool(hAPP_f181262431l_bool(cOMBC_832625297y_bool,P),Q),R) = hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(P,R),Q) ) ).
tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,axiom,
! [P: fun_bo1549164019l_bool,Q: fun_fu1246919812l_bool,R: fun_na939144002on_val] : ( hAPP_f1145256474l_bool(hAPP_f1452292669l_bool(hAPP_f1977633121l_bool(cOMBB_1303934920on_val,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_f61040418l_bool(Q,R)) ) ).
tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__prod_Itc__fun_It,axiom,
! [P: fun_bool_bool,Q: fun_Pr1696029455l_bool,R: produc12694297on_val] : ( hAPP_P159683425l_bool(hAPP_f2134824737l_bool(hAPP_f1308714617l_bool(cOMBB_338347573on_val,P),Q),R) = hAPP_bool_bool(P,hAPP_P159683425l_bool(Q,R)) ) ).
tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__prod_Itc__Expr__,axiom,
! [P: fun_bool_bool,Q: fun_Pr680585871l_bool,R: produc124828825on_val] : ( hAPP_P1708370145l_bool(hAPP_f926562337l_bool(hAPP_f1560238713l_bool(cOMBB_672625589on_val,P),Q),R) = hAPP_bool_bool(P,hAPP_P1708370145l_bool(Q,R)) ) ).
tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It,axiom,
! [P: fun_fu570492181l_bool,Q: fun_li688206603ion_ty,R: fun_na939144002on_val] : ( hAPP_f1175813647l_bool(hAPP_f550652027l_bool(hAPP_f838396643l_bool(cOMBC_2027949654l_bool,P),Q),R) = hAPP_f603925568l_bool(hAPP_f1617787571l_bool(P,R),Q) ) ).
tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It,axiom,
! [P: fun_Pr1696029455l_bool,Q: fun_fu1690035458on_val,R: fun_li1432931796on_val] : ( hAPP_f1033709212l_bool(hAPP_f1008932791l_bool(hAPP_f2057883639l_bool(cOMBB_1750801836on_val,P),Q),R) = hAPP_P159683425l_bool(P,hAPP_f1727192346on_val(Q,R)) ) ).
tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M,axiom,
! [P: fun_fu1590192889l_bool,Q: fun_fu100249073l_bool,R: fun_na939144002on_val] : ( hAPP_f1175813647l_bool(hAPP_f555424277l_bool(hAPP_f1734879897l_bool(cOMBB_1522540928on_val,P),Q),R) = hAPP_f1074020887l_bool(P,hAPP_f1175813647l_bool(Q,R)) ) ).
tff(help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It,axiom,
! [P: fun_fu1806184744l_bool,Q: fun_fu100249073l_bool,R: fun_na939144002on_val] : ( hAPP_f1175813647l_bool(cOMBS_570216337l_bool(P,Q),R) = hAPP_f1074020887l_bool(hAPP_f1492320500l_bool(P,R),hAPP_f1175813647l_bool(Q,R)) ) ).
tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O,axiom,
! [P: fun_Pr680585871l_bool,Q: fun_fu277794946on_val,R: fun_li1432931796on_val] : ( hAPP_f1033709212l_bool(hAPP_f318082871l_bool(hAPP_f1233687287l_bool(cOMBB_171276332on_val,P),Q),R) = hAPP_P1708370145l_bool(P,hAPP_f1926378906on_val(Q,R)) ) ).
tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc,axiom,
! [P: fun_fu114905943l_bool,Q: fun_fu250820942l_bool,R: fun_na939144002on_val] : ( hAPP_f1492320500l_bool(hAPP_f1523875321l_bool(hAPP_f592397849l_bool(cOMBB_1718333400on_val,P),Q),R) = hAPP_f1863694447l_bool(P,hAPP_f1145256474l_bool(Q,R)) ) ).
tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_200,axiom,
! [P: fun_fu2083094209l_bool,Q: fun_fu2141444501y_bool,R: fun_na939144002on_val] : ( hAPP_f1617787571l_bool(hAPP_f857351829l_bool(hAPP_f348318673l_bool(cOMBB_1518282696on_val,P),Q),R) = hAPP_f181262431l_bool(P,hAPP_f1213370163y_bool(Q,R)) ) ).
tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_201,axiom,
! [P: fun_Pr1696029455l_bool,Q: fun_Pr1833267965on_val,R: produc12694297on_val] : ( hAPP_P159683425l_bool(hAPP_f1301559543l_bool(hAPP_f1825030711l_bool(cOMBB_877741809on_val,P),Q),R) = hAPP_P159683425l_bool(P,hAPP_P1776198677on_val(Q,R)) ) ).
tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O_202,axiom,
! [P: fun_Pr680585871l_bool,Q: fun_Pr231134077on_val,R: produc12694297on_val] : ( hAPP_P159683425l_bool(hAPP_f489055607l_bool(hAPP_f10074679l_bool(cOMBB_1759207793on_val,P),Q),R) = hAPP_P1708370145l_bool(P,hAPP_P604205461on_val(Q,R)) ) ).
tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_203,axiom,
! [P: fun_Pr1696029455l_bool,Q: fun_Pr2087158653on_val,R: produc124828825on_val] : ( hAPP_P1708370145l_bool(hAPP_f1712766199l_bool(hAPP_f881985847l_bool(cOMBB_1083177073on_val,P),Q),R) = hAPP_P159683425l_bool(P,hAPP_P789556885on_val(Q,R)) ) ).
tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O,axiom,
! [P: fun_fu1319073539l_bool,Q: fun_ex1201926843l_bool,R: exp_list_char] : ( hAPP_e1833980889l_bool(hAPP_f546724245l_bool(hAPP_f917296015l_bool(cOMBB_740252943t_char,P),Q),R) = hAPP_f2134824737l_bool(P,hAPP_e1833980889l_bool(Q,R)) ) ).
tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_204,axiom,
! [P: fun_fu1176066021l_bool,Q: fun_fu1639641777on_val,R: fun_na939144002on_val] : ( hAPP_f1175813647l_bool(hAPP_f1363667773l_bool(hAPP_f1050935001l_bool(cOMBB_1153617344on_val,P),Q),R) = hAPP_f1008932791l_bool(P,hAPP_f1849790461on_val(Q,R)) ) ).
tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_205,axiom,
! [P: fun_fu1640122725l_bool,Q: fun_fu2073188913on_val,R: fun_na939144002on_val] : ( hAPP_f1175813647l_bool(hAPP_f850751421l_bool(hAPP_f399538905l_bool(cOMBB_1466889536on_val,P),Q),R) = hAPP_f318082871l_bool(P,hAPP_f1840640125on_val(Q,R)) ) ).
tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_,axiom,
! [P: fun_Pr691271849l_bool,Q: fun_fu1622757844on_val,R: fun_li1432931796on_val] : ( hAPP_f1033709212l_bool(hAPP_f524589473l_bool(hAPP_f2052660463l_bool(cOMBB_1292453606on_val,P),Q),R) = hAPP_P282169671l_bool(P,hAPP_f602593190on_val(Q,R)) ) ).
tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_206,axiom,
! [P: fun_fu225006629l_bool,Q: fun_ex1005552999on_val,R: exp_list_char] : ( hAPP_e1833980889l_bool(hAPP_f653692369l_bool(hAPP_f516738477l_bool(cOMBB_819439237t_char,P),Q),R) = hAPP_f1301559543l_bool(P,hAPP_e108155315on_val(Q,R)) ) ).
tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_207,axiom,
! [P: fun_fu1929378469l_bool,Q: fun_ex977868519on_val,R: exp_list_char] : ( hAPP_e1833980889l_bool(hAPP_f439412817l_bool(hAPP_f1725502637l_bool(cOMBB_1027621637t_char,P),Q),R) = hAPP_f489055607l_bool(P,hAPP_e1659493427on_val(Q,R)) ) ).
tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__208,axiom,
! [P: fun_Pr691271849l_bool,Q: fun_Pr714818201on_val,R: produc124828825on_val] : ( hAPP_P1708370145l_bool(hAPP_f204771371l_bool(hAPP_f365540729l_bool(cOMBB_1466662571on_val,P),Q),R) = hAPP_P282169671l_bool(P,hAPP_P1886180715on_val(Q,R)) ) ).
tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__,axiom,
! [P: fun_fu983865091l_bool,Q: fun_Pr633696065l_bool,R: produc124828825on_val] : ( hAPP_P1116729363l_bool(hAPP_f641257349l_bool(hAPP_f2032347769l_bool(cOMBB_466903633on_val,P),Q),R) = hAPP_f926562337l_bool(P,hAPP_P1116729363l_bool(Q,R)) ) ).
tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_209,axiom,
! [P: fun_fu964448643l_bool,Q: fun_fu1133203323on_val,R: fun_na939144002on_val] : ( hAPP_f1175813647l_bool(hAPP_f927043595l_bool(hAPP_f1043869573l_bool(cOMBB_1259202826on_val,P),Q),R) = hAPP_f524589473l_bool(P,hAPP_f600512025on_val(Q,R)) ) ).
tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc___210,axiom,
! [P: fun_fu2085256997l_bool,Q: fun_Pr1719283041on_val,R: produc124828825on_val] : ( hAPP_P1116729363l_bool(hAPP_f1241216909l_bool(hAPP_f1438732387l_bool(cOMBB_635947099on_val,P),Q),R) = hAPP_f1712766199l_bool(P,hAPP_P2083594489on_val(Q,R)) ) ).
tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc___211,axiom,
! [P: fun_fu1587641869l_bool,Q: fun_Pr1391347915on_val,R: produc124828825on_val] : ( hAPP_P1116729363l_bool(hAPP_f1342895119l_bool(hAPP_f639265145l_bool(cOMBB_364363975on_val,P),Q),R) = hAPP_f204771371l_bool(P,hAPP_P1870962205on_val(Q,R)) ) ).
%----Conjectures (1)
% tff(conj_0,conjecture,
% hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,ha),fun_up1149430426on_val(la,v_1,some_val(v))))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,e_a),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,h_a),l_a))),red(p))) ).
%------------------------------------------------------------------------------