TPTP Problem File: SWW477_1.p
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%------------------------------------------------------------------------------
% File : SWW477_1 : TPTP v8.2.0. Released v5.3.0.
% Domain : Software Verification
% Problem : Java type soundness line 346, 100 axioms selected
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla11]
% Names : jinja_100_tff_l346 [Bla11]
% Status : Theorem
% Rating : 1.00 v5.3.0
% Syntax : Number of formulae : 255 ( 59 unt; 92 typ; 0 def)
% Number of atoms : 418 ( 110 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 357 ( 102 ~; 0 |; 16 &)
% ( 35 <=>; 204 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 31 ( 30 usr)
% Number of type conns : 93 ( 46 >; 47 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 61 ( 61 usr; 16 con; 0-5 aty)
% Number of variables : 738 ( 720 !; 18 ?; 738 :)
% SPC : TF0_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 15:34:13
%------------------------------------------------------------------------------
%----Should-be-implicit typings (30)
tff(ty_ty_tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
exp_list_char: $tType ).
tff(ty_ty_tc__HOL__Obool,type,
bool: $tType ).
tff(ty_ty_tc__List__Olist_Itc__String__Ochar_J,type,
list_char: $tType ).
tff(ty_ty_tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_,type,
list_P1999446415t_char: $tType ).
tff(ty_ty_tc__Type__Oty,type,
ty: $tType ).
tff(ty_ty_tc__Value__Oval,type,
val: $tType ).
tff(ty_ty_tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc__fun_I,type,
fun_ex1201926843l_bool: $tType ).
tff(ty_ty_tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption_Itc__Ty,type,
fun_li688206603ion_ty: $tType ).
tff(ty_ty_tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption_Itc__Va,type,
fun_li1432931796on_val: $tType ).
tff(ty_ty_tc__fun_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_M,type,
fun_li318226104r_bool: $tType ).
tff(ty_ty_tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc,type,
fun_na939144002on_val: $tType ).
tff(ty_ty_tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooptio,type,
fun_fu1693644106l_bool: $tType ).
tff(ty_ty_tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__,type,
fun_fu100249073l_bool: $tType ).
tff(ty_ty_tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_,type,
fun_Pr680585871l_bool: $tType ).
tff(ty_ty_tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J__001,type,
fun_Pr633696065l_bool: $tType ).
tff(ty_ty_tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I,type,
fun_Pr1696029455l_bool: $tType ).
tff(ty_ty_tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I_002,type,
fun_Pr598845249l_bool: $tType ).
tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__,type,
fun_Pr691271849l_bool: $tType ).
tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String___003,type,
fun_Pr220980979l_bool: $tType ).
tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_I,type,
fun_Pr693020585l_bool: $tType ).
tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc,type,
fun_Pr903661919l_bool: $tType ).
tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option_,type,
fun_Pr27327839l_bool: $tType ).
tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List_,type,
fun_Pr111684683l_bool: $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 ).
tff(ty_ty_tc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_,type,
produc409205479on_val: $tType ).
tff(ty_ty_tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String_,type,
produc231486621on_val: $tType ).
tff(ty_ty_tc__prod_Itc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_,type,
produc1454067869on_val: $tType ).
tff(ty_ty_tc__prod_Itc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_It,type,
produc1464201097on_val: $tType ).
%----Explicit typings (62)
tff(sy_c_Conform_Ohconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O,type,
hconf_97414254t_char: ( list_P1999446415t_char * fun_na939144002on_val ) > 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_na939144002on_val * fun_li1432931796on_val * fun_li688206603ion_ty ) > bool ).
tff(sy_c_Expr_Oexp_OFAcc_000tc__List__Olist_Itc__String__Ochar_J,type,
fAcc_list_char: ( exp_list_char * list_char * list_char ) > exp_list_char ).
tff(sy_c_Expr_Oexp_OFAss_000tc__List__Olist_Itc__String__Ochar_J,type,
fAss_list_char: ( exp_list_char * list_char * list_char * exp_list_char ) > exp_list_char ).
tff(sy_c_Expr_Oexp_OTryCatch_000tc__List__Olist_Itc__String__Ochar_J,type,
tryCatch_list_char: ( exp_list_char * list_char * 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_Expr_Oexp_Othrow_000tc__List__Olist_Itc__String__Ochar_J,type,
throw_list_char: exp_list_char > exp_list_char ).
tff(sy_c_JWellForm_Owf__J__mdecl,type,
wf_J_mdecl: fun_li318226104r_bool ).
tff(sy_c_Map_Omap__add_000tc__List__Olist_Itc__String__Ochar_J_000tc__Value__Oval,type,
map_ad325961431ar_val: ( fun_li1432931796on_val * fun_li1432931796on_val ) > fun_li1432931796on_val ).
tff(sy_c_Objects_Ohext,type,
hext: ( fun_na939144002on_val * fun_na939144002on_val ) > bool ).
tff(sy_c_Product__Type_OPair_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J,type,
produc1259058957on_val: ( exp_list_char * produc12694297on_val ) > produc124828825on_val ).
tff(sy_c_Product__Type_OPair_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__pro,type,
produc899768717on_val: ( fun_na939144002on_val * fun_li1432931796on_val ) > produc12694297on_val ).
tff(sy_c_Product__Type_OPair_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Strin,type,
produc1441475159on_val: ( produc124828825on_val * produc124828825on_val ) > produc1102272487on_val ).
tff(sy_c_Product__Type_OPair_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooptio,type,
produc870913623on_val: ( produc12694297on_val * produc12694297on_val ) > produc409205479on_val ).
tff(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_,type,
produc1564932627on_val: ( produc1102272487on_val * produc1102272487on_val ) > produc231486621on_val ).
tff(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Opti,type,
produc935654419on_val: ( produc409205479on_val * produc409205479on_val ) > produc1454067869on_val ).
tff(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__Li,type,
produc1729053055on_val: ( produc231486621on_val * produc231486621on_val ) > produc1464201097on_val ).
tff(sy_c_SmallStep_Ored,type,
red: list_P1999446415t_char > fun_Pr691271849l_bool ).
tff(sy_c_State_Ohp,type,
hp: produc12694297on_val > fun_na939144002on_val ).
tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_I,type,
transi2024712006on_val: fun_Pr691271849l_bool > fun_Pr691271849l_bool ).
tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Optio,type,
transi921647814on_val: fun_Pr693020585l_bool > fun_Pr693020585l_bool ).
tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__Lis,type,
transi910771962on_val: fun_Pr903661919l_bool > fun_Pr903661919l_bool ).
tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_,type,
transi594096122on_val: fun_Pr27327839l_bool > fun_Pr27327839l_bool ).
tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oex,type,
transi678815536on_val: fun_Pr111684683l_bool > fun_Pr111684683l_bool ).
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_Type_Oty_OBoolean,type,
boolean: ty ).
tff(sy_c_Type_Oty_ONT,type,
nt: ty ).
tff(sy_c_Type_Oty_OVoid,type,
void: ty ).
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_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__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption_,type,
hAPP_f1033709212l_bool: ( fun_fu1693644106l_bool * fun_li1432931796on_val ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol,type,
hAPP_f1175813647l_bool: ( fun_fu100249073l_bool * fun_na939144002on_val ) > fun_fu1693644106l_bool ).
tff(sy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt,type,
hAPP_P1708370145l_bool: ( fun_Pr680585871l_bool * produc124828825on_val ) > bool ).
tff(sy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_004,type,
hAPP_P1116729363l_bool: ( fun_Pr633696065l_bool * produc124828825on_val ) > fun_Pr680585871l_bool ).
tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc,type,
hAPP_P159683425l_bool: ( fun_Pr1696029455l_bool * produc12694297on_val ) > bool ).
tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_005,type,
hAPP_P1988153107l_bool: ( fun_Pr598845249l_bool * produc12694297on_val ) > fun_Pr1696029455l_bool ).
tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc,type,
hAPP_P282169671l_bool: ( fun_Pr691271849l_bool * produc1102272487on_val ) > bool ).
tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_006,type,
hAPP_P2062527807l_bool: ( fun_Pr220980979l_bool * produc1102272487on_val ) > fun_Pr691271849l_bool ).
tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc,type,
hAPP_P1221872711l_bool: ( fun_Pr693020585l_bool * produc409205479on_val ) > bool ).
tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__,type,
hAPP_P378063101l_bool: ( fun_Pr903661919l_bool * produc231486621on_val ) > bool ).
tff(sy_c_hBOOL,type,
hBOOL: bool > $o ).
tff(sy_c_member_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_,type,
member840932460on_val: ( produc124828825on_val * fun_Pr680585871l_bool ) > bool ).
tff(sy_c_member_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I,type,
member763590124on_val: ( produc12694297on_val * fun_Pr1696029455l_bool ) > bool ).
tff(sy_c_member_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__,type,
member773094996on_val: ( produc1102272487on_val * fun_Pr691271849l_bool ) > bool ).
tff(sy_c_member_000tc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_I,type,
member563141460on_val: ( produc409205479on_val * fun_Pr693020585l_bool ) > bool ).
tff(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc,type,
member808015754on_val: ( produc231486621on_val * fun_Pr903661919l_bool ) > bool ).
tff(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option_,type,
member2032527242on_val: ( produc1454067869on_val * fun_Pr27327839l_bool ) > bool ).
tff(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List_,type,
member712690550on_val: ( produc1464201097on_val * fun_Pr111684683l_bool ) > bool ).
tff(sy_v_D____,type,
d: list_char ).
tff(sy_v_E____,type,
e: fun_li688206603ion_ty ).
tff(sy_v_F____,type,
f: list_char ).
tff(sy_v_P,type,
p: list_P1999446415t_char ).
tff(sy_v_T____,type,
t: ty ).
tff(sy_v_e_092_060_094isub_0622____,type,
e_2: exp_list_char ).
tff(sy_v_e_Ha____,type,
e_a: exp_list_char ).
tff(sy_v_ea____,type,
ea: exp_list_char ).
tff(sy_v_h_Ha____,type,
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 ).
%----Relevant facts (162)
tff(fact_0__096P_ME_Mh_A_092_060turnstile_062_Ae_A_058_ANT_096,axiom,
hBOOL(wTrt(p,ha,e,ea,nt)) ).
tff(fact_1__096_B_BT_O_AP_ME_Mh_A_092_060turnstile_062_Ae_A_058_AT_A_061_061_062_AEX,axiom,
! [Ta: ty] :
( hBOOL(wTrt(p,ha,e,ea,Ta))
=> ? [U_1: ty] :
( hBOOL(wTrt(p,h_a,e,e_a,U_1))
& hBOOL(widen_2090681816t_char(p,U_1,Ta)) ) ) ).
tff(fact_2_assms,axiom,
hBOOL(wf_pro755087577t_char(wf_J_mdecl,p)) ).
tff(fact_3_IH,axiom,
! [Ta: ty,Ea: fun_li688206603ion_ty] :
( hBOOL(hAPP_P159683425l_bool(typeSa1844245082_sconf(p,Ea),produc899768717on_val(ha,la)))
=> ( hBOOL(wTrt(p,ha,Ea,ea,Ta))
=> ? [U_1: ty] :
( hBOOL(wTrt(p,h_a,Ea,e_a,U_1))
& hBOOL(widen_2090681816t_char(p,U_1,Ta)) ) ) ) ).
tff(fact_4_conf,axiom,
hBOOL(hAPP_P159683425l_bool(typeSa1844245082_sconf(p,e),produc899768717on_val(ha,la))) ).
tff(fact_5_wt,axiom,
hBOOL(wTrt(p,ha,e,fAss_list_char(ea,f,d,e_2),t)) ).
tff(fact_6_WTrtFAccNT,axiom,
! [Fa: list_char,Da: list_char,Ta: ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char] :
( hBOOL(wTrt(Pa,Hb,Ea,Eb,nt))
=> hBOOL(wTrt(Pa,Hb,Ea,fAcc_list_char(Eb,Fa,Da),Ta)) ) ).
tff(fact_7_FAssRed1_I2_J,axiom,
! [Ta: ty,Ea: fun_li688206603ion_ty] :
( hBOOL(hAPP_P159683425l_bool(typeSa1844245082_sconf(p,Ea),produc899768717on_val(ha,la)))
=> ( hBOOL(wTrt(p,ha,Ea,ea,Ta))
=> ? [T_3: ty] :
( hBOOL(wTrt(p,h_a,Ea,e_a,T_3))
& hBOOL(widen_2090681816t_char(p,T_3,Ta)) ) ) ) ).
tff(fact_8_red,axiom,
hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(ea,produc899768717on_val(ha,la)),produc1259058957on_val(e_a,produc899768717on_val(h_a,l_a))),red(p))) ).
tff(fact_9_FAssRed1_I4_J,axiom,
hBOOL(wTrt(p,ha,e,fAss_list_char(ea,f,d,e_2),t)) ).
tff(fact_10_FAssRed1_I3_J,axiom,
hBOOL(hAPP_P159683425l_bool(typeSa1844245082_sconf(p,e),produc899768717on_val(ha,la))) ).
tff(fact_11_ty_Osimps_I13_J,axiom,
nt != boolean ).
tff(fact_12_ty_Osimps_I12_J,axiom,
boolean != nt ).
tff(fact_13_red__reds_OFAccRed,axiom,
! [Fa: list_char,Da: list_char,Eb: exp_list_char,S_1: produc12694297on_val,E_b: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Eb,S_1),produc1259058957on_val(E_b,S)),red(Pa)))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAcc_list_char(Eb,Fa,Da),S_1),produc1259058957on_val(fAcc_list_char(E_b,Fa,Da),S)),red(Pa))) ) ).
tff(fact_14_red__reds_OFAssRed1,axiom,
! [Fa: list_char,Da: list_char,E_2: exp_list_char,Eb: exp_list_char,S_1: produc12694297on_val,E_b: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Eb,S_1),produc1259058957on_val(E_b,S)),red(Pa)))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAss_list_char(Eb,Fa,Da,E_2),S_1),produc1259058957on_val(fAss_list_char(E_b,Fa,Da,E_2),S)),red(Pa))) ) ).
tff(fact_15_void,axiom,
t = void ).
tff(fact_16_widen__refl,axiom,
! [P_2: list_P1999446415t_char,T_1: ty] : hBOOL(widen_2090681816t_char(P_2,T_1,T_1)) ).
tff(fact_17_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(produc1441475159on_val(produc1259058957on_val(Eb,produc899768717on_val(Hb,Lb)),produc1259058957on_val(E_b,produc899768717on_val(H_b,L_b))),red(Pa)))
=> ( hBOOL(wTrt(Pa,Hb,Ea,Eb,Ta))
=> ( hBOOL(hconf_97414254t_char(Pa,Hb))
=> hBOOL(hconf_97414254t_char(Pa,H_b)) ) ) ) ).
tff(fact_18_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(produc1441475159on_val(produc1259058957on_val(Eb,produc899768717on_val(Hb,Lb)),produc1259058957on_val(E_b,produc899768717on_val(H_b,L_b))),red(Pa)))
=> ( hBOOL(wTrt(Pa,Hb,Ea,Eb,Ta))
=> ( hBOOL(lconf_496643946t_char(Pa,Hb,Lb,Ea))
=> hBOOL(lconf_496643946t_char(Pa,H_b,L_b,Ea)) ) ) ) ).
tff(fact_19_exp_Osimps_I154_J,axiom,
! [Exp_16: exp_list_char,List1_17: list_char,List2_17: list_char,Exp1_16: exp_list_char,List1_16: list_char,List2_16: list_char,Exp2_16: exp_list_char] : fAcc_list_char(Exp_16,List1_17,List2_17) != fAss_list_char(Exp1_16,List1_16,List2_16,Exp2_16) ).
tff(fact_20_exp_Osimps_I155_J,axiom,
! [Exp1_15: exp_list_char,List1_15: list_char,List2_15: list_char,Exp2_15: exp_list_char,Exp_15: exp_list_char,List1_14: list_char,List2_14: list_char] : fAss_list_char(Exp1_15,List1_15,List2_15,Exp2_15) != fAcc_list_char(Exp_15,List1_14,List2_14) ).
tff(fact_21_red__preserves__sconf,axiom,
! [Ea: fun_li688206603ion_ty,Ta: ty,Eb: exp_list_char,S_1: produc12694297on_val,E_b: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Eb,S_1),produc1259058957on_val(E_b,S)),red(Pa)))
=> ( hBOOL(wTrt(Pa,hp(S_1),Ea,Eb,Ta))
=> ( hBOOL(hAPP_P159683425l_bool(typeSa1844245082_sconf(Pa,Ea),S_1))
=> hBOOL(hAPP_P159683425l_bool(typeSa1844245082_sconf(Pa,Ea),S)) ) ) ) ).
tff(fact_22_ty_Osimps_I7_J,axiom,
nt != void ).
tff(fact_23_ty_Osimps_I6_J,axiom,
void != nt ).
tff(fact_24_ty_Osimps_I3_J,axiom,
boolean != void ).
tff(fact_25_ty_Osimps_I2_J,axiom,
void != boolean ).
tff(fact_26_widen__trans,axiom,
! [T: ty,P_1: list_P1999446415t_char,S_4: ty,U: ty] :
( hBOOL(widen_2090681816t_char(P_1,S_4,U))
=> ( hBOOL(widen_2090681816t_char(P_1,U,T))
=> hBOOL(widen_2090681816t_char(P_1,S_4,T)) ) ) ).
tff(fact_27_exp_Osimps_I8_J,axiom,
! [Exp1_2: exp_list_char,List1_13: list_char,List2_13: list_char,Exp2_2: exp_list_char,Exp1_1: exp_list_char,List1_12: list_char,List2_12: list_char,Exp2_1: exp_list_char] :
( ( fAss_list_char(Exp1_2,List1_13,List2_13,Exp2_2) = fAss_list_char(Exp1_1,List1_12,List2_12,Exp2_1) )
<=> ( ( Exp1_2 = Exp1_1 )
& ( List1_13 = List1_12 )
& ( List2_13 = List2_12 )
& ( Exp2_2 = Exp2_1 ) ) ) ).
tff(fact_28_exp_Osimps_I7_J,axiom,
! [Exp_2: exp_list_char,List1_13: list_char,List2_13: list_char,Exp_1: exp_list_char,List1_12: list_char,List2_12: list_char] :
( ( fAcc_list_char(Exp_2,List1_13,List2_13) = fAcc_list_char(Exp_1,List1_12,List2_12) )
<=> ( ( Exp_2 = Exp_1 )
& ( List1_13 = List1_12 )
& ( List2_13 = List2_12 ) ) ) ).
tff(fact_29_WTrtFAssNT,axiom,
! [Fa: list_char,Da: list_char,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] :
( hBOOL(wTrt(Pa,Hb,Ea,E_1,nt))
=> ( hBOOL(wTrt(Pa,Hb,Ea,E_2,T_2))
=> hBOOL(wTrt(Pa,Hb,Ea,fAss_list_char(E_1,Fa,Da,E_2),void)) ) ) ).
tff(fact_30_red__hext__incr,axiom,
! [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(produc1441475159on_val(produc1259058957on_val(Eb,produc899768717on_val(Hb,Lb)),produc1259058957on_val(E_b,produc899768717on_val(H_b,L_b))),red(Pa)))
=> hBOOL(hext(Hb,H_b)) ) ).
tff(fact_31_prod__cases4,axiom,
! [Y_1: produc1102272487on_val] :
~ ! [A_10: produc124828825on_val,B_1: exp_list_char,C_2: fun_na939144002on_val,D: fun_li1432931796on_val] : Y_1 != produc1441475159on_val(A_10,produc1259058957on_val(B_1,produc899768717on_val(C_2,D))) ).
tff(fact_32_prod__cases4,axiom,
! [Y_1: produc231486621on_val] :
~ ! [A_10: produc1102272487on_val,B_1: produc124828825on_val,C_2: exp_list_char,D: produc12694297on_val] : Y_1 != produc1564932627on_val(A_10,produc1441475159on_val(B_1,produc1259058957on_val(C_2,D))) ).
tff(fact_33_prod__induct4,axiom,
! [X: produc1102272487on_val,Pa: fun_Pr691271849l_bool] :
( ! [A_10: produc124828825on_val,B_1: exp_list_char,C_2: fun_na939144002on_val,D: fun_li1432931796on_val] : hBOOL(hAPP_P282169671l_bool(Pa,produc1441475159on_val(A_10,produc1259058957on_val(B_1,produc899768717on_val(C_2,D)))))
=> hBOOL(hAPP_P282169671l_bool(Pa,X)) ) ).
tff(fact_34_prod__induct4,axiom,
! [X: produc231486621on_val,Pa: fun_Pr903661919l_bool] :
( ! [A_10: produc1102272487on_val,B_1: produc124828825on_val,C_2: exp_list_char,D: produc12694297on_val] : hBOOL(hAPP_P378063101l_bool(Pa,produc1564932627on_val(A_10,produc1441475159on_val(B_1,produc1259058957on_val(C_2,D)))))
=> hBOOL(hAPP_P378063101l_bool(Pa,X)) ) ).
tff(fact_35_prod__cases5,axiom,
! [Y_1: produc231486621on_val] :
~ ! [A_10: produc1102272487on_val,B_1: produc124828825on_val,C_2: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val] : Y_1 != produc1564932627on_val(A_10,produc1441475159on_val(B_1,produc1259058957on_val(C_2,produc899768717on_val(D,E)))) ).
tff(fact_36_prod__induct5,axiom,
! [X: produc231486621on_val,Pa: fun_Pr903661919l_bool] :
( ! [A_10: produc1102272487on_val,B_1: produc124828825on_val,C_2: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val] : hBOOL(hAPP_P378063101l_bool(Pa,produc1564932627on_val(A_10,produc1441475159on_val(B_1,produc1259058957on_val(C_2,produc899768717on_val(D,E))))))
=> hBOOL(hAPP_P378063101l_bool(Pa,X)) ) ).
tff(fact_37_WTrt__hext__mono,axiom,
! [H_b: fun_na939144002on_val,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,Ta: ty] :
( hBOOL(wTrt(Pa,Hb,Ea,Eb,Ta))
=> ( hBOOL(hext(Hb,H_b))
=> hBOOL(wTrt(Pa,H_b,Ea,Eb,Ta)) ) ) ).
tff(fact_38_split__paired__All,axiom,
! [Pa: fun_Pr903661919l_bool] :
( ! [X1: produc231486621on_val] : hBOOL(hAPP_P378063101l_bool(Pa,X1))
<=> ! [A_10: produc1102272487on_val,B_1: produc1102272487on_val] : hBOOL(hAPP_P378063101l_bool(Pa,produc1564932627on_val(A_10,B_1))) ) ).
tff(fact_39_split__paired__All,axiom,
! [Pa: fun_Pr693020585l_bool] :
( ! [X1: produc409205479on_val] : hBOOL(hAPP_P1221872711l_bool(Pa,X1))
<=> ! [A_10: produc12694297on_val,B_1: produc12694297on_val] : hBOOL(hAPP_P1221872711l_bool(Pa,produc870913623on_val(A_10,B_1))) ) ).
tff(fact_40_split__paired__All,axiom,
! [Pa: fun_Pr1696029455l_bool] :
( ! [X1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(Pa,X1))
<=> ! [A_10: fun_na939144002on_val,B_1: fun_li1432931796on_val] : hBOOL(hAPP_P159683425l_bool(Pa,produc899768717on_val(A_10,B_1))) ) ).
tff(fact_41_split__paired__All,axiom,
! [Pa: fun_Pr691271849l_bool] :
( ! [X1: produc1102272487on_val] : hBOOL(hAPP_P282169671l_bool(Pa,X1))
<=> ! [A_10: produc124828825on_val,B_1: produc124828825on_val] : hBOOL(hAPP_P282169671l_bool(Pa,produc1441475159on_val(A_10,B_1))) ) ).
tff(fact_42_split__paired__All,axiom,
! [Pa: fun_Pr680585871l_bool] :
( ! [X1: produc124828825on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,X1))
<=> ! [A_10: exp_list_char,B_1: produc12694297on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,produc1259058957on_val(A_10,B_1))) ) ).
tff(fact_43_Pair__eq,axiom,
! [A_2: produc1102272487on_val,B: produc1102272487on_val,A_1: produc1102272487on_val,B_2: produc1102272487on_val] :
( ( produc1564932627on_val(A_2,B) = produc1564932627on_val(A_1,B_2) )
<=> ( ( A_2 = A_1 )
& ( B = B_2 ) ) ) ).
tff(fact_44_Pair__eq,axiom,
! [A_2: produc12694297on_val,B: produc12694297on_val,A_1: produc12694297on_val,B_2: produc12694297on_val] :
( ( produc870913623on_val(A_2,B) = produc870913623on_val(A_1,B_2) )
<=> ( ( A_2 = A_1 )
& ( B = B_2 ) ) ) ).
tff(fact_45_Pair__eq,axiom,
! [A_2: fun_na939144002on_val,B: fun_li1432931796on_val,A_1: fun_na939144002on_val,B_2: fun_li1432931796on_val] :
( ( produc899768717on_val(A_2,B) = produc899768717on_val(A_1,B_2) )
<=> ( ( A_2 = A_1 )
& ( B = B_2 ) ) ) ).
tff(fact_46_Pair__eq,axiom,
! [A_2: produc124828825on_val,B: produc124828825on_val,A_1: produc124828825on_val,B_2: produc124828825on_val] :
( ( produc1441475159on_val(A_2,B) = produc1441475159on_val(A_1,B_2) )
<=> ( ( A_2 = A_1 )
& ( B = B_2 ) ) ) ).
tff(fact_47_Pair__eq,axiom,
! [A_2: exp_list_char,B: produc12694297on_val,A_1: exp_list_char,B_2: produc12694297on_val] :
( ( produc1259058957on_val(A_2,B) = produc1259058957on_val(A_1,B_2) )
<=> ( ( A_2 = A_1 )
& ( B = B_2 ) ) ) ).
tff(fact_48_Pair__inject,axiom,
! [A_2: produc1102272487on_val,B: produc1102272487on_val,A_1: produc1102272487on_val,B_2: produc1102272487on_val] :
( ( produc1564932627on_val(A_2,B) = produc1564932627on_val(A_1,B_2) )
=> ~ ( ( A_2 = A_1 )
=> ( B != B_2 ) ) ) ).
tff(fact_49_Pair__inject,axiom,
! [A_2: produc12694297on_val,B: produc12694297on_val,A_1: produc12694297on_val,B_2: produc12694297on_val] :
( ( produc870913623on_val(A_2,B) = produc870913623on_val(A_1,B_2) )
=> ~ ( ( A_2 = A_1 )
=> ( B != B_2 ) ) ) ).
tff(fact_50_Pair__inject,axiom,
! [A_2: fun_na939144002on_val,B: fun_li1432931796on_val,A_1: fun_na939144002on_val,B_2: fun_li1432931796on_val] :
( ( produc899768717on_val(A_2,B) = produc899768717on_val(A_1,B_2) )
=> ~ ( ( A_2 = A_1 )
=> ( B != B_2 ) ) ) ).
tff(fact_51_Pair__inject,axiom,
! [A_2: produc124828825on_val,B: produc124828825on_val,A_1: produc124828825on_val,B_2: produc124828825on_val] :
( ( produc1441475159on_val(A_2,B) = produc1441475159on_val(A_1,B_2) )
=> ~ ( ( A_2 = A_1 )
=> ( B != B_2 ) ) ) ).
tff(fact_52_Pair__inject,axiom,
! [A_2: exp_list_char,B: produc12694297on_val,A_1: exp_list_char,B_2: produc12694297on_val] :
( ( produc1259058957on_val(A_2,B) = produc1259058957on_val(A_1,B_2) )
=> ~ ( ( A_2 = A_1 )
=> ( B != B_2 ) ) ) ).
tff(fact_53_hext__refl,axiom,
! [Hb: fun_na939144002on_val] : hBOOL(hext(Hb,Hb)) ).
tff(fact_54_lconf__hext,axiom,
! [H_b: fun_na939144002on_val,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,Ea: fun_li688206603ion_ty] :
( hBOOL(lconf_496643946t_char(Pa,Hb,Lb,Ea))
=> ( hBOOL(hext(Hb,H_b))
=> hBOOL(lconf_496643946t_char(Pa,H_b,Lb,Ea)) ) ) ).
tff(fact_55_prod__induct3,axiom,
! [X: produc1102272487on_val,Pa: fun_Pr691271849l_bool] :
( ! [A_10: produc124828825on_val,B_1: exp_list_char,C_2: produc12694297on_val] : hBOOL(hAPP_P282169671l_bool(Pa,produc1441475159on_val(A_10,produc1259058957on_val(B_1,C_2))))
=> hBOOL(hAPP_P282169671l_bool(Pa,X)) ) ).
tff(fact_56_prod__induct3,axiom,
! [X: produc124828825on_val,Pa: fun_Pr680585871l_bool] :
( ! [A_10: exp_list_char,B_1: fun_na939144002on_val,C_2: fun_li1432931796on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,produc1259058957on_val(A_10,produc899768717on_val(B_1,C_2))))
=> hBOOL(hAPP_P1708370145l_bool(Pa,X)) ) ).
tff(fact_57_prod__induct3,axiom,
! [X: produc409205479on_val,Pa: fun_Pr693020585l_bool] :
( ! [A_10: produc12694297on_val,B_1: fun_na939144002on_val,C_2: fun_li1432931796on_val] : hBOOL(hAPP_P1221872711l_bool(Pa,produc870913623on_val(A_10,produc899768717on_val(B_1,C_2))))
=> hBOOL(hAPP_P1221872711l_bool(Pa,X)) ) ).
tff(fact_58_prod__induct3,axiom,
! [X: produc231486621on_val,Pa: fun_Pr903661919l_bool] :
( ! [A_10: produc1102272487on_val,B_1: produc124828825on_val,C_2: produc124828825on_val] : hBOOL(hAPP_P378063101l_bool(Pa,produc1564932627on_val(A_10,produc1441475159on_val(B_1,C_2))))
=> hBOOL(hAPP_P378063101l_bool(Pa,X)) ) ).
tff(fact_59_prod__cases3,axiom,
! [Y_1: produc1102272487on_val] :
~ ! [A_10: produc124828825on_val,B_1: exp_list_char,C_2: produc12694297on_val] : Y_1 != produc1441475159on_val(A_10,produc1259058957on_val(B_1,C_2)) ).
tff(fact_60_prod__cases3,axiom,
! [Y_1: produc124828825on_val] :
~ ! [A_10: exp_list_char,B_1: fun_na939144002on_val,C_2: fun_li1432931796on_val] : Y_1 != produc1259058957on_val(A_10,produc899768717on_val(B_1,C_2)) ).
tff(fact_61_prod__cases3,axiom,
! [Y_1: produc409205479on_val] :
~ ! [A_10: produc12694297on_val,B_1: fun_na939144002on_val,C_2: fun_li1432931796on_val] : Y_1 != produc870913623on_val(A_10,produc899768717on_val(B_1,C_2)) ).
tff(fact_62_prod__cases3,axiom,
! [Y_1: produc231486621on_val] :
~ ! [A_10: produc1102272487on_val,B_1: produc124828825on_val,C_2: produc124828825on_val] : Y_1 != produc1564932627on_val(A_10,produc1441475159on_val(B_1,C_2)) ).
tff(fact_63_hext__trans,axiom,
! [H: fun_na939144002on_val,Hb: fun_na939144002on_val,H_b: fun_na939144002on_val] :
( hBOOL(hext(Hb,H_b))
=> ( hBOOL(hext(H_b,H))
=> hBOOL(hext(Hb,H)) ) ) ).
tff(fact_64_red__lcl__add,axiom,
! [L_0: fun_li1432931796on_val,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(produc1441475159on_val(produc1259058957on_val(Eb,produc899768717on_val(Hb,Lb)),produc1259058957on_val(E_b,produc899768717on_val(H_b,L_b))),red(Pa)))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Eb,produc899768717on_val(Hb,map_ad325961431ar_val(L_0,Lb))),produc1259058957on_val(E_b,produc899768717on_val(H_b,map_ad325961431ar_val(L_0,L_b)))),red(Pa))) ) ).
tff(fact_65_pred__equals__eq2,axiom,
! [S_3: fun_Pr903661919l_bool,R_1: fun_Pr903661919l_bool] :
( ! [X_1: produc1102272487on_val,Xa_1: produc1102272487on_val] :
( hBOOL(member808015754on_val(produc1564932627on_val(X_1,Xa_1),R_1))
<=> hBOOL(member808015754on_val(produc1564932627on_val(X_1,Xa_1),S_3)) )
<=> ( R_1 = S_3 ) ) ).
tff(fact_66_pred__equals__eq2,axiom,
! [S_3: fun_Pr693020585l_bool,R_1: fun_Pr693020585l_bool] :
( ! [X_1: produc12694297on_val,Xa_1: produc12694297on_val] :
( hBOOL(member563141460on_val(produc870913623on_val(X_1,Xa_1),R_1))
<=> hBOOL(member563141460on_val(produc870913623on_val(X_1,Xa_1),S_3)) )
<=> ( R_1 = S_3 ) ) ).
tff(fact_67_pred__equals__eq2,axiom,
! [S_3: fun_Pr1696029455l_bool,R_1: fun_Pr1696029455l_bool] :
( ! [X_1: fun_na939144002on_val,Xa_1: fun_li1432931796on_val] :
( hBOOL(member763590124on_val(produc899768717on_val(X_1,Xa_1),R_1))
<=> hBOOL(member763590124on_val(produc899768717on_val(X_1,Xa_1),S_3)) )
<=> ( R_1 = S_3 ) ) ).
tff(fact_68_pred__equals__eq2,axiom,
! [S_3: fun_Pr680585871l_bool,R_1: fun_Pr680585871l_bool] :
( ! [X_1: exp_list_char,Xa_1: produc12694297on_val] :
( hBOOL(member840932460on_val(produc1259058957on_val(X_1,Xa_1),R_1))
<=> hBOOL(member840932460on_val(produc1259058957on_val(X_1,Xa_1),S_3)) )
<=> ( R_1 = S_3 ) ) ).
tff(fact_69_pred__equals__eq2,axiom,
! [S_3: fun_Pr691271849l_bool,R_1: fun_Pr691271849l_bool] :
( ! [X_1: produc124828825on_val,Xa_1: produc124828825on_val] :
( hBOOL(member773094996on_val(produc1441475159on_val(X_1,Xa_1),R_1))
<=> hBOOL(member773094996on_val(produc1441475159on_val(X_1,Xa_1),S_3)) )
<=> ( R_1 = S_3 ) ) ).
tff(fact_70_prod_Oexhaust,axiom,
! [Y_1: produc231486621on_val] :
~ ! [A_10: produc1102272487on_val,B_1: produc1102272487on_val] : Y_1 != produc1564932627on_val(A_10,B_1) ).
tff(fact_71_prod_Oexhaust,axiom,
! [Y_1: produc409205479on_val] :
~ ! [A_10: produc12694297on_val,B_1: produc12694297on_val] : Y_1 != produc870913623on_val(A_10,B_1) ).
tff(fact_72_prod_Oexhaust,axiom,
! [Y_1: produc12694297on_val] :
~ ! [A_10: fun_na939144002on_val,B_1: fun_li1432931796on_val] : Y_1 != produc899768717on_val(A_10,B_1) ).
tff(fact_73_prod_Oexhaust,axiom,
! [Y_1: produc1102272487on_val] :
~ ! [A_10: produc124828825on_val,B_1: produc124828825on_val] : Y_1 != produc1441475159on_val(A_10,B_1) ).
tff(fact_74_prod_Oexhaust,axiom,
! [Y_1: produc124828825on_val] :
~ ! [A_10: exp_list_char,B_1: produc12694297on_val] : Y_1 != produc1259058957on_val(A_10,B_1) ).
tff(fact_75_PairE,axiom,
! [P: produc231486621on_val] :
~ ! [X_1: produc1102272487on_val,Y: produc1102272487on_val] : P != produc1564932627on_val(X_1,Y) ).
tff(fact_76_PairE,axiom,
! [P: produc409205479on_val] :
~ ! [X_1: produc12694297on_val,Y: produc12694297on_val] : P != produc870913623on_val(X_1,Y) ).
tff(fact_77_PairE,axiom,
! [P: produc12694297on_val] :
~ ! [X_1: fun_na939144002on_val,Y: fun_li1432931796on_val] : P != produc899768717on_val(X_1,Y) ).
tff(fact_78_PairE,axiom,
! [P: produc1102272487on_val] :
~ ! [X_1: produc124828825on_val,Y: produc124828825on_val] : P != produc1441475159on_val(X_1,Y) ).
tff(fact_79_PairE,axiom,
! [P: produc124828825on_val] :
~ ! [X_1: exp_list_char,Y: produc12694297on_val] : P != produc1259058957on_val(X_1,Y) ).
tff(fact_80_Red__lcl__add,axiom,
! [L_0: fun_li1432931796on_val,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(produc1441475159on_val(produc1259058957on_val(Eb,produc899768717on_val(Hb,Lb)),produc1259058957on_val(E_b,produc899768717on_val(H_b,L_b))),transi2024712006on_val(red(Pa))))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Eb,produc899768717on_val(Hb,map_ad325961431ar_val(L_0,Lb))),produc1259058957on_val(E_b,produc899768717on_val(H_b,map_ad325961431ar_val(L_0,L_b)))),transi2024712006on_val(red(Pa)))) ) ).
tff(fact_81_split__paired__Ex,axiom,
! [Pa: fun_Pr903661919l_bool] :
( ? [X1: produc231486621on_val] : hBOOL(hAPP_P378063101l_bool(Pa,X1))
<=> ? [A_10: produc1102272487on_val,B_1: produc1102272487on_val] : hBOOL(hAPP_P378063101l_bool(Pa,produc1564932627on_val(A_10,B_1))) ) ).
tff(fact_82_split__paired__Ex,axiom,
! [Pa: fun_Pr693020585l_bool] :
( ? [X1: produc409205479on_val] : hBOOL(hAPP_P1221872711l_bool(Pa,X1))
<=> ? [A_10: produc12694297on_val,B_1: produc12694297on_val] : hBOOL(hAPP_P1221872711l_bool(Pa,produc870913623on_val(A_10,B_1))) ) ).
tff(fact_83_split__paired__Ex,axiom,
! [Pa: fun_Pr1696029455l_bool] :
( ? [X1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(Pa,X1))
<=> ? [A_10: fun_na939144002on_val,B_1: fun_li1432931796on_val] : hBOOL(hAPP_P159683425l_bool(Pa,produc899768717on_val(A_10,B_1))) ) ).
tff(fact_84_split__paired__Ex,axiom,
! [Pa: fun_Pr691271849l_bool] :
( ? [X1: produc1102272487on_val] : hBOOL(hAPP_P282169671l_bool(Pa,X1))
<=> ? [A_10: produc124828825on_val,B_1: produc124828825on_val] : hBOOL(hAPP_P282169671l_bool(Pa,produc1441475159on_val(A_10,B_1))) ) ).
tff(fact_85_split__paired__Ex,axiom,
! [Pa: fun_Pr680585871l_bool] :
( ? [X1: produc124828825on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,X1))
<=> ? [A_10: exp_list_char,B_1: produc12694297on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,produc1259058957on_val(A_10,B_1))) ) ).
tff(fact_86_FAccReds,axiom,
! [Fa: list_char,Da: list_char,Eb: exp_list_char,S_1: produc12694297on_val,E_b: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Eb,S_1),produc1259058957on_val(E_b,S)),transi2024712006on_val(red(Pa))))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAcc_list_char(Eb,Fa,Da),S_1),produc1259058957on_val(fAcc_list_char(E_b,Fa,Da),S)),transi2024712006on_val(red(Pa)))) ) ).
tff(fact_87_FAssReds1,axiom,
! [Fa: list_char,Da: list_char,E_2: exp_list_char,Eb: exp_list_char,S_1: produc12694297on_val,E_b: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Eb,S_1),produc1259058957on_val(E_b,S)),transi2024712006on_val(red(Pa))))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAss_list_char(Eb,Fa,Da,E_2),S_1),produc1259058957on_val(fAss_list_char(E_b,Fa,Da,E_2),S)),transi2024712006on_val(red(Pa)))) ) ).
tff(fact_88_rtrancl_Ortrancl__refl,axiom,
! [A_2: produc1102272487on_val,R: fun_Pr903661919l_bool] : hBOOL(member808015754on_val(produc1564932627on_val(A_2,A_2),transi910771962on_val(R))) ).
tff(fact_89_rtrancl_Ortrancl__refl,axiom,
! [A_2: produc12694297on_val,R: fun_Pr693020585l_bool] : hBOOL(member563141460on_val(produc870913623on_val(A_2,A_2),transi921647814on_val(R))) ).
tff(fact_90_rtrancl_Ortrancl__refl,axiom,
! [A_2: produc124828825on_val,R: fun_Pr691271849l_bool] : hBOOL(member773094996on_val(produc1441475159on_val(A_2,A_2),transi2024712006on_val(R))) ).
tff(fact_91_r__into__rtrancl,axiom,
! [P: produc231486621on_val,R: fun_Pr903661919l_bool] :
( hBOOL(member808015754on_val(P,R))
=> hBOOL(member808015754on_val(P,transi910771962on_val(R))) ) ).
tff(fact_92_r__into__rtrancl,axiom,
! [P: produc409205479on_val,R: fun_Pr693020585l_bool] :
( hBOOL(member563141460on_val(P,R))
=> hBOOL(member563141460on_val(P,transi921647814on_val(R))) ) ).
tff(fact_93_r__into__rtrancl,axiom,
! [P: produc1102272487on_val,R: fun_Pr691271849l_bool] :
( hBOOL(member773094996on_val(P,R))
=> hBOOL(member773094996on_val(P,transi2024712006on_val(R))) ) ).
tff(fact_94_rtrancl__idemp,axiom,
! [R: fun_Pr903661919l_bool] : transi910771962on_val(transi910771962on_val(R)) = transi910771962on_val(R) ).
tff(fact_95_rtrancl__idemp,axiom,
! [R: fun_Pr693020585l_bool] : transi921647814on_val(transi921647814on_val(R)) = transi921647814on_val(R) ).
tff(fact_96_rtrancl__idemp,axiom,
! [R: fun_Pr691271849l_bool] : transi2024712006on_val(transi2024712006on_val(R)) = transi2024712006on_val(R) ).
tff(fact_97_converse__rtrancl__into__rtrancl,axiom,
! [C_1: produc1102272487on_val,A_2: produc1102272487on_val,B: produc1102272487on_val,R: fun_Pr903661919l_bool] :
( hBOOL(member808015754on_val(produc1564932627on_val(A_2,B),R))
=> ( hBOOL(member808015754on_val(produc1564932627on_val(B,C_1),transi910771962on_val(R)))
=> hBOOL(member808015754on_val(produc1564932627on_val(A_2,C_1),transi910771962on_val(R))) ) ) ).
tff(fact_98_converse__rtrancl__into__rtrancl,axiom,
! [C_1: produc12694297on_val,A_2: produc12694297on_val,B: produc12694297on_val,R: fun_Pr693020585l_bool] :
( hBOOL(member563141460on_val(produc870913623on_val(A_2,B),R))
=> ( hBOOL(member563141460on_val(produc870913623on_val(B,C_1),transi921647814on_val(R)))
=> hBOOL(member563141460on_val(produc870913623on_val(A_2,C_1),transi921647814on_val(R))) ) ) ).
tff(fact_99_converse__rtrancl__into__rtrancl,axiom,
! [C_1: produc124828825on_val,A_2: produc124828825on_val,B: produc124828825on_val,R: fun_Pr691271849l_bool] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_2,B),R))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(B,C_1),transi2024712006on_val(R)))
=> hBOOL(member773094996on_val(produc1441475159on_val(A_2,C_1),transi2024712006on_val(R))) ) ) ).
tff(fact_100_rtrancl_Ortrancl__into__rtrancl,axiom,
! [C_1: produc1102272487on_val,A_2: produc1102272487on_val,B: produc1102272487on_val,R: fun_Pr903661919l_bool] :
( hBOOL(member808015754on_val(produc1564932627on_val(A_2,B),transi910771962on_val(R)))
=> ( hBOOL(member808015754on_val(produc1564932627on_val(B,C_1),R))
=> hBOOL(member808015754on_val(produc1564932627on_val(A_2,C_1),transi910771962on_val(R))) ) ) ).
tff(fact_101_rtrancl_Ortrancl__into__rtrancl,axiom,
! [C_1: produc12694297on_val,A_2: produc12694297on_val,B: produc12694297on_val,R: fun_Pr693020585l_bool] :
( hBOOL(member563141460on_val(produc870913623on_val(A_2,B),transi921647814on_val(R)))
=> ( hBOOL(member563141460on_val(produc870913623on_val(B,C_1),R))
=> hBOOL(member563141460on_val(produc870913623on_val(A_2,C_1),transi921647814on_val(R))) ) ) ).
tff(fact_102_rtrancl_Ortrancl__into__rtrancl,axiom,
! [C_1: produc124828825on_val,A_2: produc124828825on_val,B: produc124828825on_val,R: fun_Pr691271849l_bool] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_2,B),transi2024712006on_val(R)))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(B,C_1),R))
=> hBOOL(member773094996on_val(produc1441475159on_val(A_2,C_1),transi2024712006on_val(R))) ) ) ).
tff(fact_103_rtrancl__trans,axiom,
! [C_1: produc1102272487on_val,A_2: produc1102272487on_val,B: produc1102272487on_val,R: fun_Pr903661919l_bool] :
( hBOOL(member808015754on_val(produc1564932627on_val(A_2,B),transi910771962on_val(R)))
=> ( hBOOL(member808015754on_val(produc1564932627on_val(B,C_1),transi910771962on_val(R)))
=> hBOOL(member808015754on_val(produc1564932627on_val(A_2,C_1),transi910771962on_val(R))) ) ) ).
tff(fact_104_rtrancl__trans,axiom,
! [C_1: produc12694297on_val,A_2: produc12694297on_val,B: produc12694297on_val,R: fun_Pr693020585l_bool] :
( hBOOL(member563141460on_val(produc870913623on_val(A_2,B),transi921647814on_val(R)))
=> ( hBOOL(member563141460on_val(produc870913623on_val(B,C_1),transi921647814on_val(R)))
=> hBOOL(member563141460on_val(produc870913623on_val(A_2,C_1),transi921647814on_val(R))) ) ) ).
tff(fact_105_rtrancl__trans,axiom,
! [C_1: produc124828825on_val,A_2: produc124828825on_val,B: produc124828825on_val,R: fun_Pr691271849l_bool] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_2,B),transi2024712006on_val(R)))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(B,C_1),transi2024712006on_val(R)))
=> hBOOL(member773094996on_val(produc1441475159on_val(A_2,C_1),transi2024712006on_val(R))) ) ) ).
tff(fact_106_converse__rtranclE2,axiom,
! [Xa: produc1102272487on_val,Xb: produc1102272487on_val,Za: produc1102272487on_val,Zb: produc1102272487on_val,R: fun_Pr111684683l_bool] :
( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(Xa,Xb),produc1564932627on_val(Za,Zb)),transi678815536on_val(R)))
=> ( ( produc1564932627on_val(Xa,Xb) != produc1564932627on_val(Za,Zb) )
=> ~ ! [A_10: produc1102272487on_val,B_1: produc1102272487on_val] :
( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(Xa,Xb),produc1564932627on_val(A_10,B_1)),R))
=> ~ hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(A_10,B_1),produc1564932627on_val(Za,Zb)),transi678815536on_val(R))) ) ) ) ).
tff(fact_107_converse__rtranclE2,axiom,
! [Xa: produc12694297on_val,Xb: produc12694297on_val,Za: produc12694297on_val,Zb: produc12694297on_val,R: fun_Pr27327839l_bool] :
( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(Xa,Xb),produc870913623on_val(Za,Zb)),transi594096122on_val(R)))
=> ( ( produc870913623on_val(Xa,Xb) != produc870913623on_val(Za,Zb) )
=> ~ ! [A_10: produc12694297on_val,B_1: produc12694297on_val] :
( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(Xa,Xb),produc870913623on_val(A_10,B_1)),R))
=> ~ hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(A_10,B_1),produc870913623on_val(Za,Zb)),transi594096122on_val(R))) ) ) ) ).
tff(fact_108_converse__rtranclE2,axiom,
! [Xa: fun_na939144002on_val,Xb: fun_li1432931796on_val,Za: fun_na939144002on_val,Zb: fun_li1432931796on_val,R: fun_Pr693020585l_bool] :
( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Xa,Xb),produc899768717on_val(Za,Zb)),transi921647814on_val(R)))
=> ( ( produc899768717on_val(Xa,Xb) != produc899768717on_val(Za,Zb) )
=> ~ ! [A_10: fun_na939144002on_val,B_1: fun_li1432931796on_val] :
( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Xa,Xb),produc899768717on_val(A_10,B_1)),R))
=> ~ hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(A_10,B_1),produc899768717on_val(Za,Zb)),transi921647814on_val(R))) ) ) ) ).
tff(fact_109_converse__rtranclE2,axiom,
! [Xa: produc124828825on_val,Xb: produc124828825on_val,Za: produc124828825on_val,Zb: produc124828825on_val,R: fun_Pr903661919l_bool] :
( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Xa,Xb),produc1441475159on_val(Za,Zb)),transi910771962on_val(R)))
=> ( ( produc1441475159on_val(Xa,Xb) != produc1441475159on_val(Za,Zb) )
=> ~ ! [A_10: produc124828825on_val,B_1: produc124828825on_val] :
( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Xa,Xb),produc1441475159on_val(A_10,B_1)),R))
=> ~ hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(A_10,B_1),produc1441475159on_val(Za,Zb)),transi910771962on_val(R))) ) ) ) ).
tff(fact_110_converse__rtranclE2,axiom,
! [Xa: exp_list_char,Xb: produc12694297on_val,Za: exp_list_char,Zb: produc12694297on_val,R: fun_Pr691271849l_bool] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Xa,Xb),produc1259058957on_val(Za,Zb)),transi2024712006on_val(R)))
=> ( ( produc1259058957on_val(Xa,Xb) != produc1259058957on_val(Za,Zb) )
=> ~ ! [A_10: exp_list_char,B_1: produc12694297on_val] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Xa,Xb),produc1259058957on_val(A_10,B_1)),R))
=> ~ hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(A_10,B_1),produc1259058957on_val(Za,Zb)),transi2024712006on_val(R))) ) ) ) ).
tff(fact_111_converse__rtrancl__induct2,axiom,
! [Pa: fun_Pr220980979l_bool,Ax: produc1102272487on_val,Ay: produc1102272487on_val,Bx: produc1102272487on_val,By: produc1102272487on_val,R: fun_Pr111684683l_bool] :
( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(Ax,Ay),produc1564932627on_val(Bx,By)),transi678815536on_val(R)))
=> ( hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,Bx),By))
=> ( ! [A_10: produc1102272487on_val,B_1: produc1102272487on_val,Aa: produc1102272487on_val,Ba: produc1102272487on_val] :
( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(A_10,B_1),produc1564932627on_val(Aa,Ba)),R))
=> ( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(Aa,Ba),produc1564932627on_val(Bx,By)),transi678815536on_val(R)))
=> ( hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,Aa),Ba))
=> hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,A_10),B_1)) ) ) )
=> hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,Ax),Ay)) ) ) ) ).
tff(fact_112_converse__rtrancl__induct2,axiom,
! [Pa: fun_Pr598845249l_bool,Ax: produc12694297on_val,Ay: produc12694297on_val,Bx: produc12694297on_val,By: produc12694297on_val,R: fun_Pr27327839l_bool] :
( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(Ax,Ay),produc870913623on_val(Bx,By)),transi594096122on_val(R)))
=> ( hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,Bx),By))
=> ( ! [A_10: produc12694297on_val,B_1: produc12694297on_val,Aa: produc12694297on_val,Ba: produc12694297on_val] :
( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(A_10,B_1),produc870913623on_val(Aa,Ba)),R))
=> ( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(Aa,Ba),produc870913623on_val(Bx,By)),transi594096122on_val(R)))
=> ( hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,Aa),Ba))
=> hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,A_10),B_1)) ) ) )
=> hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,Ax),Ay)) ) ) ) ).
tff(fact_113_converse__rtrancl__induct2,axiom,
! [Pa: fun_fu100249073l_bool,Ax: fun_na939144002on_val,Ay: fun_li1432931796on_val,Bx: fun_na939144002on_val,By: fun_li1432931796on_val,R: fun_Pr693020585l_bool] :
( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Ax,Ay),produc899768717on_val(Bx,By)),transi921647814on_val(R)))
=> ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Bx),By))
=> ( ! [A_10: fun_na939144002on_val,B_1: fun_li1432931796on_val,Aa: fun_na939144002on_val,Ba: fun_li1432931796on_val] :
( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(A_10,B_1),produc899768717on_val(Aa,Ba)),R))
=> ( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Aa,Ba),produc899768717on_val(Bx,By)),transi921647814on_val(R)))
=> ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Aa),Ba))
=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,A_10),B_1)) ) ) )
=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Ax),Ay)) ) ) ) ).
tff(fact_114_converse__rtrancl__induct2,axiom,
! [Pa: fun_Pr633696065l_bool,Ax: produc124828825on_val,Ay: produc124828825on_val,Bx: produc124828825on_val,By: produc124828825on_val,R: fun_Pr903661919l_bool] :
( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Ax,Ay),produc1441475159on_val(Bx,By)),transi910771962on_val(R)))
=> ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Bx),By))
=> ( ! [A_10: produc124828825on_val,B_1: produc124828825on_val,Aa: produc124828825on_val,Ba: produc124828825on_val] :
( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(A_10,B_1),produc1441475159on_val(Aa,Ba)),R))
=> ( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Aa,Ba),produc1441475159on_val(Bx,By)),transi910771962on_val(R)))
=> ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Aa),Ba))
=> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,A_10),B_1)) ) ) )
=> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Ax),Ay)) ) ) ) ).
tff(fact_115_converse__rtrancl__induct2,axiom,
! [Pa: fun_ex1201926843l_bool,Ax: exp_list_char,Ay: produc12694297on_val,Bx: exp_list_char,By: produc12694297on_val,R: fun_Pr691271849l_bool] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ax,Ay),produc1259058957on_val(Bx,By)),transi2024712006on_val(R)))
=> ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Bx),By))
=> ( ! [A_10: exp_list_char,B_1: produc12694297on_val,Aa: exp_list_char,Ba: produc12694297on_val] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(A_10,B_1),produc1259058957on_val(Aa,Ba)),R))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Aa,Ba),produc1259058957on_val(Bx,By)),transi2024712006on_val(R)))
=> ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Aa),Ba))
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,A_10),B_1)) ) ) )
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Ax),Ay)) ) ) ) ).
tff(fact_116_rtrancl__induct2,axiom,
! [Pa: fun_Pr220980979l_bool,Ax: produc1102272487on_val,Ay: produc1102272487on_val,Bx: produc1102272487on_val,By: produc1102272487on_val,R: fun_Pr111684683l_bool] :
( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(Ax,Ay),produc1564932627on_val(Bx,By)),transi678815536on_val(R)))
=> ( hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,Ax),Ay))
=> ( ! [A_10: produc1102272487on_val,B_1: produc1102272487on_val,Aa: produc1102272487on_val,Ba: produc1102272487on_val] :
( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(Ax,Ay),produc1564932627on_val(A_10,B_1)),transi678815536on_val(R)))
=> ( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(A_10,B_1),produc1564932627on_val(Aa,Ba)),R))
=> ( hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,A_10),B_1))
=> hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,Aa),Ba)) ) ) )
=> hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,Bx),By)) ) ) ) ).
tff(fact_117_rtrancl__induct2,axiom,
! [Pa: fun_Pr598845249l_bool,Ax: produc12694297on_val,Ay: produc12694297on_val,Bx: produc12694297on_val,By: produc12694297on_val,R: fun_Pr27327839l_bool] :
( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(Ax,Ay),produc870913623on_val(Bx,By)),transi594096122on_val(R)))
=> ( hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,Ax),Ay))
=> ( ! [A_10: produc12694297on_val,B_1: produc12694297on_val,Aa: produc12694297on_val,Ba: produc12694297on_val] :
( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(Ax,Ay),produc870913623on_val(A_10,B_1)),transi594096122on_val(R)))
=> ( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(A_10,B_1),produc870913623on_val(Aa,Ba)),R))
=> ( hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,A_10),B_1))
=> hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,Aa),Ba)) ) ) )
=> hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,Bx),By)) ) ) ) ).
tff(fact_118_rtrancl__induct2,axiom,
! [Pa: fun_fu100249073l_bool,Ax: fun_na939144002on_val,Ay: fun_li1432931796on_val,Bx: fun_na939144002on_val,By: fun_li1432931796on_val,R: fun_Pr693020585l_bool] :
( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Ax,Ay),produc899768717on_val(Bx,By)),transi921647814on_val(R)))
=> ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Ax),Ay))
=> ( ! [A_10: fun_na939144002on_val,B_1: fun_li1432931796on_val,Aa: fun_na939144002on_val,Ba: fun_li1432931796on_val] :
( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Ax,Ay),produc899768717on_val(A_10,B_1)),transi921647814on_val(R)))
=> ( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(A_10,B_1),produc899768717on_val(Aa,Ba)),R))
=> ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,A_10),B_1))
=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Aa),Ba)) ) ) )
=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Bx),By)) ) ) ) ).
tff(fact_119_rtrancl__induct2,axiom,
! [Pa: fun_Pr633696065l_bool,Ax: produc124828825on_val,Ay: produc124828825on_val,Bx: produc124828825on_val,By: produc124828825on_val,R: fun_Pr903661919l_bool] :
( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Ax,Ay),produc1441475159on_val(Bx,By)),transi910771962on_val(R)))
=> ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Ax),Ay))
=> ( ! [A_10: produc124828825on_val,B_1: produc124828825on_val,Aa: produc124828825on_val,Ba: produc124828825on_val] :
( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Ax,Ay),produc1441475159on_val(A_10,B_1)),transi910771962on_val(R)))
=> ( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(A_10,B_1),produc1441475159on_val(Aa,Ba)),R))
=> ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,A_10),B_1))
=> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Aa),Ba)) ) ) )
=> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Bx),By)) ) ) ) ).
tff(fact_120_rtrancl__induct2,axiom,
! [Pa: fun_ex1201926843l_bool,Ax: exp_list_char,Ay: produc12694297on_val,Bx: exp_list_char,By: produc12694297on_val,R: fun_Pr691271849l_bool] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ax,Ay),produc1259058957on_val(Bx,By)),transi2024712006on_val(R)))
=> ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Ax),Ay))
=> ( ! [A_10: exp_list_char,B_1: produc12694297on_val,Aa: exp_list_char,Ba: produc12694297on_val] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ax,Ay),produc1259058957on_val(A_10,B_1)),transi2024712006on_val(R)))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(A_10,B_1),produc1259058957on_val(Aa,Ba)),R))
=> ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,A_10),B_1))
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Aa),Ba)) ) ) )
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Bx),By)) ) ) ) ).
tff(fact_121_rtranclE,axiom,
! [A_2: produc1102272487on_val,B: produc1102272487on_val,R: fun_Pr903661919l_bool] :
( hBOOL(member808015754on_val(produc1564932627on_val(A_2,B),transi910771962on_val(R)))
=> ( ( A_2 != B )
=> ~ ! [Y: produc1102272487on_val] :
( hBOOL(member808015754on_val(produc1564932627on_val(A_2,Y),transi910771962on_val(R)))
=> ~ hBOOL(member808015754on_val(produc1564932627on_val(Y,B),R)) ) ) ) ).
tff(fact_122_rtranclE,axiom,
! [A_2: produc12694297on_val,B: produc12694297on_val,R: fun_Pr693020585l_bool] :
( hBOOL(member563141460on_val(produc870913623on_val(A_2,B),transi921647814on_val(R)))
=> ( ( A_2 != B )
=> ~ ! [Y: produc12694297on_val] :
( hBOOL(member563141460on_val(produc870913623on_val(A_2,Y),transi921647814on_val(R)))
=> ~ hBOOL(member563141460on_val(produc870913623on_val(Y,B),R)) ) ) ) ).
tff(fact_123_rtranclE,axiom,
! [A_2: produc124828825on_val,B: produc124828825on_val,R: fun_Pr691271849l_bool] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_2,B),transi2024712006on_val(R)))
=> ( ( A_2 != B )
=> ~ ! [Y: produc124828825on_val] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_2,Y),transi2024712006on_val(R)))
=> ~ hBOOL(member773094996on_val(produc1441475159on_val(Y,B),R)) ) ) ) ).
tff(fact_124_converse__rtranclE,axiom,
! [X: produc1102272487on_val,Z_1: produc1102272487on_val,R: fun_Pr903661919l_bool] :
( hBOOL(member808015754on_val(produc1564932627on_val(X,Z_1),transi910771962on_val(R)))
=> ( ( X != Z_1 )
=> ~ ! [Y: produc1102272487on_val] :
( hBOOL(member808015754on_val(produc1564932627on_val(X,Y),R))
=> ~ hBOOL(member808015754on_val(produc1564932627on_val(Y,Z_1),transi910771962on_val(R))) ) ) ) ).
tff(fact_125_converse__rtranclE,axiom,
! [X: produc12694297on_val,Z_1: produc12694297on_val,R: fun_Pr693020585l_bool] :
( hBOOL(member563141460on_val(produc870913623on_val(X,Z_1),transi921647814on_val(R)))
=> ( ( X != Z_1 )
=> ~ ! [Y: produc12694297on_val] :
( hBOOL(member563141460on_val(produc870913623on_val(X,Y),R))
=> ~ hBOOL(member563141460on_val(produc870913623on_val(Y,Z_1),transi921647814on_val(R))) ) ) ) ).
tff(fact_126_converse__rtranclE,axiom,
! [X: produc124828825on_val,Z_1: produc124828825on_val,R: fun_Pr691271849l_bool] :
( hBOOL(member773094996on_val(produc1441475159on_val(X,Z_1),transi2024712006on_val(R)))
=> ( ( X != Z_1 )
=> ~ ! [Y: produc124828825on_val] :
( hBOOL(member773094996on_val(produc1441475159on_val(X,Y),R))
=> ~ hBOOL(member773094996on_val(produc1441475159on_val(Y,Z_1),transi2024712006on_val(R))) ) ) ) ).
tff(fact_127_converse__rtrancl__induct,axiom,
! [Pa: fun_Pr691271849l_bool,A_2: produc1102272487on_val,B: produc1102272487on_val,R: fun_Pr903661919l_bool] :
( hBOOL(member808015754on_val(produc1564932627on_val(A_2,B),transi910771962on_val(R)))
=> ( hBOOL(hAPP_P282169671l_bool(Pa,B))
=> ( ! [Y: produc1102272487on_val,Z: produc1102272487on_val] :
( hBOOL(member808015754on_val(produc1564932627on_val(Y,Z),R))
=> ( hBOOL(member808015754on_val(produc1564932627on_val(Z,B),transi910771962on_val(R)))
=> ( hBOOL(hAPP_P282169671l_bool(Pa,Z))
=> hBOOL(hAPP_P282169671l_bool(Pa,Y)) ) ) )
=> hBOOL(hAPP_P282169671l_bool(Pa,A_2)) ) ) ) ).
tff(fact_128_converse__rtrancl__induct,axiom,
! [Pa: fun_Pr1696029455l_bool,A_2: produc12694297on_val,B: produc12694297on_val,R: fun_Pr693020585l_bool] :
( hBOOL(member563141460on_val(produc870913623on_val(A_2,B),transi921647814on_val(R)))
=> ( hBOOL(hAPP_P159683425l_bool(Pa,B))
=> ( ! [Y: produc12694297on_val,Z: produc12694297on_val] :
( hBOOL(member563141460on_val(produc870913623on_val(Y,Z),R))
=> ( hBOOL(member563141460on_val(produc870913623on_val(Z,B),transi921647814on_val(R)))
=> ( hBOOL(hAPP_P159683425l_bool(Pa,Z))
=> hBOOL(hAPP_P159683425l_bool(Pa,Y)) ) ) )
=> hBOOL(hAPP_P159683425l_bool(Pa,A_2)) ) ) ) ).
tff(fact_129_converse__rtrancl__induct,axiom,
! [Pa: fun_Pr680585871l_bool,A_2: produc124828825on_val,B: produc124828825on_val,R: fun_Pr691271849l_bool] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_2,B),transi2024712006on_val(R)))
=> ( hBOOL(hAPP_P1708370145l_bool(Pa,B))
=> ( ! [Y: produc124828825on_val,Z: produc124828825on_val] :
( hBOOL(member773094996on_val(produc1441475159on_val(Y,Z),R))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(Z,B),transi2024712006on_val(R)))
=> ( hBOOL(hAPP_P1708370145l_bool(Pa,Z))
=> hBOOL(hAPP_P1708370145l_bool(Pa,Y)) ) ) )
=> hBOOL(hAPP_P1708370145l_bool(Pa,A_2)) ) ) ) ).
tff(fact_130_rtrancl__induct,axiom,
! [Pa: fun_Pr691271849l_bool,A_2: produc1102272487on_val,B: produc1102272487on_val,R: fun_Pr903661919l_bool] :
( hBOOL(member808015754on_val(produc1564932627on_val(A_2,B),transi910771962on_val(R)))
=> ( hBOOL(hAPP_P282169671l_bool(Pa,A_2))
=> ( ! [Y: produc1102272487on_val,Z: produc1102272487on_val] :
( hBOOL(member808015754on_val(produc1564932627on_val(A_2,Y),transi910771962on_val(R)))
=> ( hBOOL(member808015754on_val(produc1564932627on_val(Y,Z),R))
=> ( hBOOL(hAPP_P282169671l_bool(Pa,Y))
=> hBOOL(hAPP_P282169671l_bool(Pa,Z)) ) ) )
=> hBOOL(hAPP_P282169671l_bool(Pa,B)) ) ) ) ).
tff(fact_131_rtrancl__induct,axiom,
! [Pa: fun_Pr1696029455l_bool,A_2: produc12694297on_val,B: produc12694297on_val,R: fun_Pr693020585l_bool] :
( hBOOL(member563141460on_val(produc870913623on_val(A_2,B),transi921647814on_val(R)))
=> ( hBOOL(hAPP_P159683425l_bool(Pa,A_2))
=> ( ! [Y: produc12694297on_val,Z: produc12694297on_val] :
( hBOOL(member563141460on_val(produc870913623on_val(A_2,Y),transi921647814on_val(R)))
=> ( hBOOL(member563141460on_val(produc870913623on_val(Y,Z),R))
=> ( hBOOL(hAPP_P159683425l_bool(Pa,Y))
=> hBOOL(hAPP_P159683425l_bool(Pa,Z)) ) ) )
=> hBOOL(hAPP_P159683425l_bool(Pa,B)) ) ) ) ).
tff(fact_132_rtrancl__induct,axiom,
! [Pa: fun_Pr680585871l_bool,A_2: produc124828825on_val,B: produc124828825on_val,R: fun_Pr691271849l_bool] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_2,B),transi2024712006on_val(R)))
=> ( hBOOL(hAPP_P1708370145l_bool(Pa,A_2))
=> ( ! [Y: produc124828825on_val,Z: produc124828825on_val] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_2,Y),transi2024712006on_val(R)))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(Y,Z),R))
=> ( hBOOL(hAPP_P1708370145l_bool(Pa,Y))
=> hBOOL(hAPP_P1708370145l_bool(Pa,Z)) ) ) )
=> hBOOL(hAPP_P1708370145l_bool(Pa,B)) ) ) ) ).
tff(fact_133_mem__def,axiom,
! [X: produc231486621on_val,A_9: fun_Pr903661919l_bool] :
( hBOOL(member808015754on_val(X,A_9))
<=> hBOOL(hAPP_P378063101l_bool(A_9,X)) ) ).
tff(fact_134_mem__def,axiom,
! [X: produc409205479on_val,A_9: fun_Pr693020585l_bool] :
( hBOOL(member563141460on_val(X,A_9))
<=> hBOOL(hAPP_P1221872711l_bool(A_9,X)) ) ).
tff(fact_135_mem__def,axiom,
! [X: produc124828825on_val,A_9: fun_Pr680585871l_bool] :
( hBOOL(member840932460on_val(X,A_9))
<=> hBOOL(hAPP_P1708370145l_bool(A_9,X)) ) ).
tff(fact_136_mem__def,axiom,
! [X: produc12694297on_val,A_9: fun_Pr1696029455l_bool] :
( hBOOL(member763590124on_val(X,A_9))
<=> hBOOL(hAPP_P159683425l_bool(A_9,X)) ) ).
tff(fact_137_mem__def,axiom,
! [X: produc1102272487on_val,A_9: fun_Pr691271849l_bool] :
( hBOOL(member773094996on_val(X,A_9))
<=> hBOOL(hAPP_P282169671l_bool(A_9,X)) ) ).
tff(fact_138_FAssReds2,axiom,
! [V: val,Fa: list_char,Da: list_char,Eb: exp_list_char,S_1: produc12694297on_val,E_b: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Eb,S_1),produc1259058957on_val(E_b,S)),transi2024712006on_val(red(Pa))))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAss_list_char(val_list_char(V),Fa,Da,Eb),S_1),produc1259058957on_val(fAss_list_char(val_list_char(V),Fa,Da,E_b),S)),transi2024712006on_val(red(Pa)))) ) ).
tff(fact_139_exp_Osimps_I3_J,axiom,
! [Val_9: val,Val_8: val] :
( ( val_list_char(Val_9) = val_list_char(Val_8) )
<=> ( Val_9 = Val_8 ) ) ).
tff(fact_140_exp_Osimps_I76_J,axiom,
! [Val_7: val,Exp_14: exp_list_char,List1_11: list_char,List2_11: list_char] : val_list_char(Val_7) != fAcc_list_char(Exp_14,List1_11,List2_11) ).
tff(fact_141_exp_Osimps_I77_J,axiom,
! [Exp_13: exp_list_char,List1_10: list_char,List2_10: list_char,Val_6: val] : fAcc_list_char(Exp_13,List1_10,List2_10) != val_list_char(Val_6) ).
tff(fact_142_exp_Osimps_I78_J,axiom,
! [Val_5: val,Exp1_14: exp_list_char,List1_9: list_char,List2_9: list_char,Exp2_14: exp_list_char] : val_list_char(Val_5) != fAss_list_char(Exp1_14,List1_9,List2_9,Exp2_14) ).
tff(fact_143_exp_Osimps_I79_J,axiom,
! [Exp1_13: exp_list_char,List1_8: list_char,List2_8: list_char,Exp2_13: exp_list_char,Val_4: val] : fAss_list_char(Exp1_13,List1_8,List2_8,Exp2_13) != val_list_char(Val_4) ).
tff(fact_144_red__reds_OFAssRed2,axiom,
! [V: val,Fa: list_char,Da: list_char,Eb: exp_list_char,S_1: produc12694297on_val,E_b: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Eb,S_1),produc1259058957on_val(E_b,S)),red(Pa)))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAss_list_char(val_list_char(V),Fa,Da,Eb),S_1),produc1259058957on_val(fAss_list_char(val_list_char(V),Fa,Da,E_b),S)),red(Pa))) ) ).
tff(fact_145_FAssRedsThrow2,axiom,
! [Fa: list_char,Da: list_char,E_2: exp_list_char,Eb: exp_list_char,S_2: produc12694297on_val,E_1: exp_list_char,S_0: produc12694297on_val,V: val,S_1_1: produc12694297on_val,Pa: list_P1999446415t_char] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(E_1,S_0),produc1259058957on_val(val_list_char(V),S_1_1)),transi2024712006on_val(red(Pa))))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(E_2,S_1_1),produc1259058957on_val(throw_list_char(Eb),S_2)),transi2024712006on_val(red(Pa))))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAss_list_char(E_1,Fa,Da,E_2),S_0),produc1259058957on_val(throw_list_char(Eb),S_2)),transi2024712006on_val(red(Pa)))) ) ) ).
tff(fact_146_TryRedsVal,axiom,
! [C: list_char,V_1: list_char,E_2: exp_list_char,Eb: exp_list_char,S_1: produc12694297on_val,V: val,S: produc12694297on_val,Pa: list_P1999446415t_char] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Eb,S_1),produc1259058957on_val(val_list_char(V),S)),transi2024712006on_val(red(Pa))))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(tryCatch_list_char(Eb,C,V_1,E_2),S_1),produc1259058957on_val(val_list_char(V),S)),transi2024712006on_val(red(Pa)))) ) ).
tff(fact_147_exp_Osimps_I90_J,axiom,
! [Val_3: val,Exp_12: exp_list_char] : val_list_char(Val_3) != throw_list_char(Exp_12) ).
tff(fact_148_exp_Osimps_I91_J,axiom,
! [Exp_11: exp_list_char,Val_2: val] : throw_list_char(Exp_11) != val_list_char(Val_2) ).
tff(fact_149_exp_Osimps_I92_J,axiom,
! [Val_1: val,Exp1_12: exp_list_char,List_8: list_char,A_8: list_char,Exp2_12: exp_list_char] : val_list_char(Val_1) != tryCatch_list_char(Exp1_12,List_8,A_8,Exp2_12) ).
tff(fact_150_exp_Osimps_I93_J,axiom,
! [Exp1_11: exp_list_char,List_7: list_char,A_7: list_char,Exp2_11: exp_list_char,Val: val] : tryCatch_list_char(Exp1_11,List_7,A_7,Exp2_11) != val_list_char(Val) ).
tff(fact_151_exp_Osimps_I180_J,axiom,
! [Exp1_10: exp_list_char,List1_7: list_char,List2_7: list_char,Exp2_10: exp_list_char,Exp_10: exp_list_char] : fAss_list_char(Exp1_10,List1_7,List2_7,Exp2_10) != throw_list_char(Exp_10) ).
tff(fact_152_exp_Osimps_I181_J,axiom,
! [Exp_9: exp_list_char,Exp1_9: exp_list_char,List1_6: list_char,List2_6: list_char,Exp2_9: exp_list_char] : throw_list_char(Exp_9) != fAss_list_char(Exp1_9,List1_6,List2_6,Exp2_9) ).
tff(fact_153_exp_Osimps_I166_J,axiom,
! [Exp_8: exp_list_char,List1_5: list_char,List2_5: list_char,Exp_7: exp_list_char] : fAcc_list_char(Exp_8,List1_5,List2_5) != throw_list_char(Exp_7) ).
tff(fact_154_exp_Osimps_I167_J,axiom,
! [Exp_6: exp_list_char,Exp_5: exp_list_char,List1_4: list_char,List2_4: list_char] : throw_list_char(Exp_6) != fAcc_list_char(Exp_5,List1_4,List2_4) ).
tff(fact_155_exp_Osimps_I183_J,axiom,
! [Exp1_8: exp_list_char,List_6: list_char,A_6: list_char,Exp2_8: exp_list_char,Exp1_7: exp_list_char,List1_3: list_char,List2_3: list_char,Exp2_7: exp_list_char] : tryCatch_list_char(Exp1_8,List_6,A_6,Exp2_8) != fAss_list_char(Exp1_7,List1_3,List2_3,Exp2_7) ).
tff(fact_156_exp_Osimps_I182_J,axiom,
! [Exp1_6: exp_list_char,List1_2: list_char,List2_2: list_char,Exp2_6: exp_list_char,Exp1_5: exp_list_char,List_5: list_char,A_5: list_char,Exp2_5: exp_list_char] : fAss_list_char(Exp1_6,List1_2,List2_2,Exp2_6) != tryCatch_list_char(Exp1_5,List_5,A_5,Exp2_5) ).
tff(fact_157_exp_Osimps_I169_J,axiom,
! [Exp1_4: exp_list_char,List_4: list_char,A_4: list_char,Exp2_4: exp_list_char,Exp_4: exp_list_char,List1_1: list_char,List2_1: list_char] : tryCatch_list_char(Exp1_4,List_4,A_4,Exp2_4) != fAcc_list_char(Exp_4,List1_1,List2_1) ).
tff(fact_158_exp_Osimps_I168_J,axiom,
! [Exp_3: exp_list_char,List1: list_char,List2: list_char,Exp1_3: exp_list_char,List_3: list_char,A_3: list_char,Exp2_3: exp_list_char] : fAcc_list_char(Exp_3,List1,List2) != tryCatch_list_char(Exp1_3,List_3,A_3,Exp2_3) ).
tff(fact_159_exp_Osimps_I15_J,axiom,
! [Exp1_2: exp_list_char,List_2: list_char,A_2: list_char,Exp2_2: exp_list_char,Exp1_1: exp_list_char,List_1: list_char,A_1: list_char,Exp2_1: exp_list_char] :
( ( tryCatch_list_char(Exp1_2,List_2,A_2,Exp2_2) = tryCatch_list_char(Exp1_1,List_1,A_1,Exp2_1) )
<=> ( ( Exp1_2 = Exp1_1 )
& ( List_2 = List_1 )
& ( A_2 = A_1 )
& ( Exp2_2 = Exp2_1 ) ) ) ).
tff(fact_160_exp_Osimps_I14_J,axiom,
! [Exp_2: exp_list_char,Exp_1: exp_list_char] :
( ( throw_list_char(Exp_2) = throw_list_char(Exp_1) )
<=> ( Exp_2 = Exp_1 ) ) ).
tff(fact_161_exp_Osimps_I225_J,axiom,
! [Exp1: exp_list_char,List: list_char,A: list_char,Exp2: exp_list_char,Exp: exp_list_char] : tryCatch_list_char(Exp1,List,A,Exp2) != throw_list_char(Exp) ).
%----Conjectures (1)
tff(conj_0,conjecture,
hBOOL(wTrt(p,h_a,e,e_a,nt)) ).
%------------------------------------------------------------------------------