TPTP Problem File: SWW477^2.p
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%------------------------------------------------------------------------------
% File : SWW477^2 : TPTP v8.2.0. Released v5.3.0.
% Domain : Software Verification
% Problem : Java type soundness line 346, 500 axioms selected
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla11]
% Names : jinja_500_thf_l346 [Bla11]
% Status : Theorem
% Rating : 1.00 v5.3.0
% Syntax : Number of formulae : 895 ( 285 unt; 194 typ; 0 def)
% Number of atoms : 1783 ( 363 equ; 11 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 8923 ( 305 ~; 2 |; 51 &;7650 @)
% ( 182 <=>; 697 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 11 avg)
% Number of types : 34 ( 33 usr)
% Number of type conns : 1370 (1370 >; 0 *; 0 +; 0 <<)
% Number of symbols : 167 ( 161 usr; 19 con; 0-5 aty)
% ( 18 !!; 18 ??; 0 @@+; 0 @@-)
% Number of variables : 3164 ( 78 ^;3047 !; 39 ?;3164 :)
% SPC : TH1_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 19:36:21
%------------------------------------------------------------------------------
%----Should-be-implicit typings (33)
thf(ty_ty_tc__Expr__Obop,type,
bop: $tType ).
thf(ty_ty_tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
exp_list_char: $tType ).
thf(ty_ty_tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_J,type,
list_exp_list_char: $tType ).
thf(ty_ty_tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J,type,
list_list_char: $tType ).
thf(ty_ty_tc__List__Olist_Itc__String__Ochar_J,type,
list_char: $tType ).
thf(ty_ty_tc__List__Olist_Itc__Type__Oty_J,type,
list_ty: $tType ).
thf(ty_ty_tc__List__Olist_Itc__Value__Oval_J,type,
list_val: $tType ).
thf(ty_ty_tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_,type,
list_P1999446415t_char: $tType ).
thf(ty_ty_tc__Nat__Onat,type,
nat: $tType ).
thf(ty_ty_tc__Option__Ooption_Itc__Type__Oty_J,type,
option_ty: $tType ).
thf(ty_ty_tc__Option__Ooption_Itc__Value__Oval_J,type,
option_val: $tType ).
thf(ty_ty_tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062_,type,
option1728594148on_val: $tType ).
thf(ty_ty_tc__Type__Oty,type,
ty: $tType ).
thf(ty_ty_tc__Value__Oval,type,
val: $tType ).
thf(ty_ty_tc__prod_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol,type,
produc2090907612on_val: $tType ).
thf(ty_ty_tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc__prod,type,
produc1282892786on_val: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc,type,
produc1180562163on_val: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc__pro,type,
produc1285161482t_char: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062_Itc__prod_Itc__List__,type,
produc2088785539on_val: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_Itc__Strin,type,
produc1278157519t_char: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List__Olist_,type,
produc1013743697t_char: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__Olist_Itc_,type,
produc220283002t_char: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc__List__Ol,type,
produc662261637t_char: $tType ).
thf(ty_ty_tc__prod_Itc__prod_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc,type,
produc1581780743on_val: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
produc1746408499on_val: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__,type,
produc618524391on_val: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_,type,
produc349695911t_char: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062_Itc__prod_I,type,
produc1368416213on_val: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_,type,
produc1350825965t_char: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__,type,
produc1406897475t_char: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc,type,
produc1826280281t_char: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String_,type,
produc652964533on_val: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__O,type,
produc1250491293on_val: $tType ).
%----Explicit typings (197)
thf(sy_c_BigStep_Oeval,type,
eval: list_P1999446415t_char > exp_list_char > produc2090907612on_val > exp_list_char > produc2090907612on_val > $o ).
thf(sy_c_BigStep_Oevals,type,
evals: list_P1999446415t_char > list_exp_list_char > produc2090907612on_val > list_exp_list_char > produc2090907612on_val > $o ).
thf(sy_c_BigStep_Ofinal_000tc__List__Olist_Itc__String__Ochar_J,type,
final_list_char: exp_list_char > $o ).
thf(sy_c_BigStep_Ofinals_000tc__List__Olist_Itc__String__Ochar_J,type,
finals_list_char: list_exp_list_char > $o ).
thf(sy_c_Conform_Ohconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O,type,
hconf_97414254t_char: list_P1999446415t_char > ( nat > option1728594148on_val ) > $o ).
thf(sy_c_Conform_Olconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O,type,
lconf_496643946t_char: list_P1999446415t_char > ( nat > option1728594148on_val ) > ( list_char > option_val ) > ( list_char > option_ty ) > $o ).
thf(sy_c_Exceptions_ONullPointer,type,
nullPointer: list_char ).
thf(sy_c_Exceptions_Oaddr__of__sys__xcpt,type,
addr_of_sys_xcpt: list_char > nat ).
thf(sy_c_Expr_Obop_OEq,type,
c_Expr_Obop_OEq: bop ).
thf(sy_c_Expr_Oexp_OBinOp_000tc__List__Olist_Itc__String__Ochar_J,type,
binOp_list_char: exp_list_char > bop > exp_list_char > exp_list_char ).
thf(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 ).
thf(sy_c_Expr_Oexp_OCall_000tc__List__Olist_Itc__String__Ochar_J,type,
call_list_char: exp_list_char > list_char > list_exp_list_char > exp_list_char ).
thf(sy_c_Expr_Oexp_OCast_000tc__List__Olist_Itc__String__Ochar_J,type,
cast_list_char: list_char > exp_list_char > exp_list_char ).
thf(sy_c_Expr_Oexp_OCond_000tc__List__Olist_Itc__String__Ochar_J,type,
cond_list_char: exp_list_char > exp_list_char > exp_list_char > exp_list_char ).
thf(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 ).
thf(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 ).
thf(sy_c_Expr_Oexp_OLAss_000tc__List__Olist_Itc__String__Ochar_J,type,
lAss_list_char: list_char > exp_list_char > exp_list_char ).
thf(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 ).
thf(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 ).
thf(sy_c_Expr_Oexp_OVal_000tc__List__Olist_Itc__String__Ochar_J,type,
val_list_char: val > exp_list_char ).
thf(sy_c_Expr_Oexp_OWhile_000tc__List__Olist_Itc__String__Ochar_J,type,
while_list_char: exp_list_char > exp_list_char > exp_list_char ).
thf(sy_c_Expr_Oexp_Othrow_000tc__List__Olist_Itc__String__Ochar_J,type,
throw_list_char: exp_list_char > exp_list_char ).
thf(sy_c_JWellForm_Owf__J__mdecl,type,
wf_J_mdecl: list_P1999446415t_char > list_char > produc1013743697t_char > $o ).
thf(sy_c_List_Oappend_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
append_exp_list_char: list_exp_list_char > list_exp_list_char > list_exp_list_char ).
thf(sy_c_List_Olist_OCons_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
cons_exp_list_char: exp_list_char > list_exp_list_char > list_exp_list_char ).
thf(sy_c_List_Olist_OCons_000tc__List__Olist_Itc__String__Ochar_J,type,
cons_list_char: list_char > list_list_char > list_list_char ).
thf(sy_c_List_Olist_OCons_000tc__Type__Oty,type,
cons_ty: ty > list_ty > list_ty ).
thf(sy_c_List_Olist_OCons_000tc__Value__Oval,type,
cons_val: val > list_val > list_val ).
thf(sy_c_List_Omap_000tc__Value__Oval_000tc__Expr__Oexp_Itc__List__Olist_Itc__String,type,
map_va1934808527t_char: ( val > exp_list_char ) > list_val > list_exp_list_char ).
thf(sy_c_Map_Omap__add_000tc__List__Olist_Itc__String__Ochar_J_000tc__Value__Oval,type,
map_ad325961431ar_val: ( list_char > option_val ) > ( list_char > option_val ) > list_char > option_val ).
thf(sy_c_Objects_Ohext,type,
hext: ( nat > option1728594148on_val ) > ( nat > option1728594148on_val ) > $o ).
thf(sy_c_Option_Ooption_OSome_000tc__Type__Oty,type,
some_ty: ty > option_ty ).
thf(sy_c_Option_Ooption_OSome_000tc__Value__Oval,type,
some_val: val > option_val ).
thf(sy_c_Option_Ooption_OSome_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_06,type,
some_P451527732on_val: produc2088785539on_val > option1728594148on_val ).
thf(sy_c_Product__Type_OPair_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I,type,
produc755559506on_val: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc2090907612on_val ).
thf(sy_c_Product__Type_OPair_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J,type,
produc235638504on_val: exp_list_char > produc2090907612on_val > produc1282892786on_val ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc,type,
produc1302104557on_val: list_exp_list_char > produc2090907612on_val > produc1180562163on_val ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_,type,
produc921874948t_char: list_list_char > produc220283002t_char > produc1285161482t_char ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__String__Ochar_J_000_062_Itc__pr,type,
produc926070009on_val: list_char > ( produc1278157519t_char > option_val ) > produc2088785539on_val ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__String__Ochar_J_000tc__List__Ol,type,
produc5062597t_char: list_char > list_char > produc1278157519t_char ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Type__Oty_J_000tc__prod_Itc__Li,type,
produc1909267824t_char: list_ty > produc662261637t_char > produc220283002t_char ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Value__Oval_J_000tc__Expr__Oexp,type,
produc1916172923t_char: list_val > exp_list_char > produc662261637t_char ).
thf(sy_c_Product__Type_OPair_000tc__prod_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_I,type,
produc259392253on_val: produc2090907612on_val > produc2090907612on_val > produc1581780743on_val ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Strin,type,
produc833389609on_val: produc1282892786on_val > produc1282892786on_val > produc1746408499on_val ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List_,type,
produc747700183on_val: produc1180562163on_val > produc1180562163on_val > produc618524391on_val ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Stri,type,
produc24551831t_char: produc1285161482t_char > produc1285161482t_char > produc349695911t_char ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062,type,
produc1773146955on_val: produc2088785539on_val > produc2088785539on_val > produc1368416213on_val ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__,type,
produc2080520419t_char: produc1278157519t_char > produc1278157519t_char > produc1350825965t_char ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod,type,
produc57279289t_char: produc220283002t_char > produc220283002t_char > produc1406897475t_char ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Ex,type,
produc1299387215t_char: produc662261637t_char > produc662261637t_char > produc1826280281t_char ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_,type,
produc345758123on_val: produc1746408499on_val > produc1746408499on_val > produc652964533on_val ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_,type,
produc1347028499on_val: produc618524391on_val > produc618524391on_val > produc1250491293on_val ).
thf(sy_c_Product__Type_Ointernal__split_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_,type,
produc575577405_val_o: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o ) > produc2090907612on_val > $o ).
thf(sy_c_Product__Type_Ointernal__split_000tc__Expr__Oexp_Itc__List__Olist_Itc__Stri,type,
produc900512295_val_o: ( exp_list_char > produc2090907612on_val > $o ) > produc1282892786on_val > $o ).
thf(sy_c_Product__Type_Ointernal__split_000tc__List__Olist_Itc__Expr__Oexp_Itc__List,type,
produc317060852_val_o: ( list_exp_list_char > produc2090907612on_val > $o ) > produc1180562163on_val > $o ).
thf(sy_c_Product__Type_Ointernal__split_000tc__List__Olist_Itc__List__Olist_Itc__Str,type,
produc96699549char_o: ( list_list_char > produc220283002t_char > $o ) > produc1285161482t_char > $o ).
thf(sy_c_Product__Type_Ointernal__split_000tc__List__Olist_Itc__String__Ochar_J_000_,type,
produc473466070_val_o: ( list_char > ( produc1278157519t_char > option_val ) > $o ) > produc2088785539on_val > $o ).
thf(sy_c_Product__Type_Ointernal__split_000tc__List__Olist_Itc__String__Ochar_J_000t,type,
produc1140826762char_o: ( list_char > list_char > $o ) > produc1278157519t_char > $o ).
thf(sy_c_Product__Type_Ointernal__split_000tc__List__Olist_Itc__Type__Oty_J_000tc__p,type,
produc853142431char_o: ( list_ty > produc662261637t_char > $o ) > produc220283002t_char > $o ).
thf(sy_c_Product__Type_Ointernal__split_000tc__List__Olist_Itc__Value__Oval_J_000tc_,type,
produc1217817172char_o: ( list_val > exp_list_char > $o ) > produc662261637t_char > $o ).
thf(sy_c_Product__Type_Ointernal__split_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist,type,
produc2006262054_val_o: ( produc1282892786on_val > produc1282892786on_val > $o ) > produc1746408499on_val > $o ).
thf(sy_c_Product__Type_Ointernal__split_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp,type,
produc1133783928_val_o: ( produc1180562163on_val > produc1180562163on_val > $o ) > produc618524391on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000_062_Itc__Nat__Onat_Mtc__Option__Ooption,type,
produc252486962_val_o: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o ) > produc2090907612on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_001,type,
produc1016489647on_val: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1282892786on_val ) > produc2090907612on_val > produc1282892786on_val ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_002,type,
produc1650655734on_val: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1180562163on_val ) > produc2090907612on_val > produc1180562163on_val ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_003,type,
produc2056656269t_char: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1285161482t_char ) > produc2090907612on_val > produc1285161482t_char ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_004,type,
produc2039683648on_val: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc2088785539on_val ) > produc2090907612on_val > produc2088785539on_val ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_005,type,
produc562949388t_char: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1278157519t_char ) > produc2090907612on_val > produc1278157519t_char ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_006,type,
produc97831223t_char: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc220283002t_char ) > produc2090907612on_val > produc220283002t_char ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_007,type,
produc753444290t_char: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc662261637t_char ) > produc2090907612on_val > produc662261637t_char ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_008,type,
produc1186953840on_val: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1746408499on_val ) > produc2090907612on_val > produc1746408499on_val ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_009,type,
produc808731044on_val: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc618524391on_val ) > produc2090907612on_val > produc618524391on_val ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Expr__Oexp_Itc__List__Olist_Itc__Str,type,
produc1835097372_val_o: ( exp_list_char > produc2090907612on_val > $o ) > produc1282892786on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Expr__Oexp_Itc__List__Olist_Itc__Str_010,type,
produc69760047on_val: ( exp_list_char > produc2090907612on_val > produc2090907612on_val ) > produc1282892786on_val > produc2090907612on_val ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Expr__Oexp_Itc__Lis,type,
produc1841295295_val_o: ( list_exp_list_char > produc2090907612on_val > $o ) > produc1180562163on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Expr__Oexp_Itc__Lis_011,type,
produc1128742220on_val: ( list_exp_list_char > produc2090907612on_val > produc2090907612on_val ) > produc1180562163on_val > produc2090907612on_val ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__List__Olist_Itc__St,type,
produc1530867176char_o: ( list_list_char > produc220283002t_char > $o ) > produc1285161482t_char > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__List__Olist_Itc__St_012,type,
produc762569315on_val: ( list_list_char > produc220283002t_char > produc2090907612on_val ) > produc1285161482t_char > produc2090907612on_val ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000,type,
produc765165771_val_o: ( list_char > ( produc1278157519t_char > option_val ) > $o ) > produc2088785539on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_013,type,
produc1349598016on_val: ( list_char > ( produc1278157519t_char > option_val ) > produc2090907612on_val ) > produc2088785539on_val > produc2090907612on_val ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_014,type,
produc282231039char_o: ( list_char > list_char > $o ) > produc1278157519t_char > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_015,type,
produc835075084on_val: ( list_char > list_char > produc2090907612on_val ) > produc1278157519t_char > produc2090907612on_val ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Type__Oty_J_000tc__,type,
produc861054100char_o: ( list_ty > produc662261637t_char > $o ) > produc220283002t_char > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Type__Oty_J_000tc___016,type,
produc1533215415on_val: ( list_ty > produc662261637t_char > produc2090907612on_val ) > produc220283002t_char > produc2090907612on_val ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Value__Oval_J_000tc,type,
produc525137097char_o: ( list_val > exp_list_char > $o ) > produc662261637t_char > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Value__Oval_J_000tc_017,type,
produc371942594on_val: ( list_val > exp_list_char > produc2090907612on_val ) > produc662261637t_char > produc2090907612on_val ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_I_062_Itc__Nat__Onat_Mtc__Optio,type,
produc1377568711_val_o: ( produc2090907612on_val > produc2090907612on_val > $o ) > produc1581780743on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__Expr__Oexp_Itc__List__Olis,type,
produc1624062875_val_o: ( produc1282892786on_val > produc1282892786on_val > $o ) > produc1746408499on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__Expr__Oexp_Itc__List__Olis_018,type,
produc511181936on_val: ( produc1282892786on_val > produc1282892786on_val > produc2090907612on_val ) > produc1746408499on_val > produc2090907612on_val ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__List__Olist_Itc__Expr__Oex,type,
produc2136448621_val_o: ( produc1180562163on_val > produc1180562163on_val > $o ) > produc618524391on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__List__Olist_Itc__Expr__Oex_019,type,
produc27101214on_val: ( produc1180562163on_val > produc1180562163on_val > produc2090907612on_val ) > produc618524391on_val > produc2090907612on_val ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__List__Olist_Itc__List__Oli,type,
produc865480877char_o: ( produc1285161482t_char > produc1285161482t_char > $o ) > produc349695911t_char > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__List__Olist_Itc__String__O,type,
produc791773177_val_o: ( produc2088785539on_val > produc2088785539on_val > $o ) > produc1368416213on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__List__Olist_Itc__String__O_020,type,
produc2056220769char_o: ( produc1278157519t_char > produc1278157519t_char > $o ) > produc1350825965t_char > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__List__Olist_Itc__Type__Oty,type,
produc510191755char_o: ( produc220283002t_char > produc220283002t_char > $o ) > produc1406897475t_char > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__List__Olist_Itc__Value__Ov,type,
produc1537651445char_o: ( produc662261637t_char > produc662261637t_char > $o ) > produc1826280281t_char > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__,type,
produc154389913_val_o: ( produc1746408499on_val > produc1746408499on_val > $o ) > produc652964533on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__prod_Itc__List__Olist_Itc_,type,
produc382956337_val_o: ( produc618524391on_val > produc618524391on_val > $o ) > produc1250491293on_val > $o ).
thf(sy_c_SmallStep_Oblocks,type,
blocks: produc1285161482t_char > exp_list_char ).
thf(sy_c_SmallStep_Ored,type,
red: list_P1999446415t_char > produc1746408499on_val > $o ).
thf(sy_c_SmallStep_Oredp,type,
redp: list_P1999446415t_char > exp_list_char > produc2090907612on_val > exp_list_char > produc2090907612on_val > $o ).
thf(sy_c_SmallStep_Oreds,type,
reds: list_P1999446415t_char > produc618524391on_val > $o ).
thf(sy_c_SmallStep_Oredsp,type,
redsp: list_P1999446415t_char > list_exp_list_char > produc2090907612on_val > list_exp_list_char > produc2090907612on_val > $o ).
thf(sy_c_State_Ohp,type,
hp: produc2090907612on_val > nat > option1728594148on_val ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__List__Olist_Itc__String__Ochar_J,type,
transi1395422419t_char: ( produc1278157519t_char > $o ) > produc1278157519t_char > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_I_062_Itc__Nat__Onat_Mtc__Option__,type,
transi466770671on_val: ( produc1581780743on_val > $o ) > produc1581780743on_val > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_I,type,
transi2118771717on_val: ( produc1746408499on_val > $o ) > produc1746408499on_val > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_I,type,
transi808828192on_val: ( produc618524391on_val > $o ) > produc618524391on_val > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__List__Olist_,type,
transi122195895t_char: ( produc349695911t_char > $o ) > produc349695911t_char > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__String__Ocha,type,
transi1669211542on_val: ( produc1368416213on_val > $o ) > produc1368416213on_val > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__String__Ocha_021,type,
transi1095029602t_char: ( produc1350825965t_char > $o ) > produc1350825965t_char > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_,type,
transi1257872013t_char: ( produc1406897475t_char > $o ) > produc1406897475t_char > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__Value__Oval_,type,
transi1789604888t_char: ( produc1826280281t_char > $o ) > produc1826280281t_char > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__Lis,type,
transi130214086on_val: ( produc652964533on_val > $o ) > produc652964533on_val > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Ex,type,
transi1457397498on_val: ( produc1250491293on_val > $o ) > produc1250491293on_val > $o ).
thf(sy_c_TypeRel_Owiden_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O,type,
widen_2090681816t_char: list_P1999446415t_char > ty > ty > $o ).
thf(sy_c_TypeSafe__Mirabelle__xxsvwfzwam_Osconf,type,
typeSa1102574168_sconf: list_P1999446415t_char > ( list_char > option_ty ) > produc2090907612on_val > $o ).
thf(sy_c_Type_Ois__refT,type,
is_refT: ty > $o ).
thf(sy_c_Type_Oty_OBoolean,type,
boolean: ty ).
thf(sy_c_Type_Oty_ONT,type,
nt: ty ).
thf(sy_c_Type_Oty_OVoid,type,
void: ty ).
thf(sy_c_Value_Odefault__val,type,
default_val: ty > val ).
thf(sy_c_Value_Othe__Addr,type,
the_Addr: val > nat ).
thf(sy_c_Value_Oval_OAddr,type,
addr: nat > val ).
thf(sy_c_Value_Oval_OBool,type,
bool: $o > val ).
thf(sy_c_Value_Oval_ONull,type,
null: val ).
thf(sy_c_Value_Oval_OUnit,type,
unit: val ).
thf(sy_c_WWellForm_Owwf__J__mdecl,type,
wwf_J_mdecl: list_P1999446415t_char > list_char > produc1013743697t_char > $o ).
thf(sy_c_WellForm_Owf__prog_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Strin,type,
wf_pro755087577t_char: ( list_P1999446415t_char > list_char > produc1013743697t_char > $o ) > list_P1999446415t_char > $o ).
thf(sy_c_WellTypeRT_OWTrt,type,
wTrt: list_P1999446415t_char > ( nat > option1728594148on_val ) > ( list_char > option_ty ) > exp_list_char > ty > $o ).
thf(sy_c_WellTypeRT_OWTrts,type,
wTrts: list_P1999446415t_char > ( nat > option1728594148on_val ) > ( list_char > option_ty ) > list_exp_list_char > list_ty > $o ).
thf(sy_c_member_000tc__prod_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_,type,
member1846553161on_val: produc2090907612on_val > ( produc2090907612on_val > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_,type,
member1072200031on_val: produc1282892786on_val > ( produc1282892786on_val > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__S,type,
member1224782662on_val: produc1180562163on_val > ( produc1180562163on_val > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J,type,
member133545693t_char: produc1285161482t_char > ( produc1285161482t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062_Itc__prod_It,type,
member1374264560on_val: produc2088785539on_val > ( produc2088785539on_val > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_I,type,
member1251428284t_char: produc1278157519t_char > ( produc1278157519t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__O,type,
member140606439t_char: produc220283002t_char > ( produc220283002t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc_,type,
member699351154t_char: produc662261637t_char > ( produc662261637t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc_,type,
member565037556on_val: produc1581780743on_val > ( produc1581780743on_val > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__,type,
member1913460000on_val: produc1746408499on_val > ( produc1746408499on_val > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Ol,type,
member2042188884on_val: produc618524391on_val > ( produc618524391on_val > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String_,type,
member1420286996t_char: produc349695911t_char > ( produc349695911t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062_It,type,
member1235075778on_val: produc1368416213on_val > ( produc1368416213on_val > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis,type,
member794220506t_char: produc1350825965t_char > ( produc1350825965t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_It,type,
member125098544t_char: produc1406897475t_char > ( produc1406897475t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr_,type,
member1161907014t_char: produc1826280281t_char > ( produc1826280281t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc,type,
member1714424482on_val: produc652964533on_val > ( produc652964533on_val > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc,type,
member1145216138on_val: produc1250491293on_val > ( produc1250491293on_val > $o ) > $o ).
thf(sy_v_D____,type,
d: list_char ).
thf(sy_v_E____,type,
e: list_char > option_ty ).
thf(sy_v_F____,type,
f: list_char ).
thf(sy_v_P,type,
p: list_P1999446415t_char ).
thf(sy_v_T____,type,
t: ty ).
thf(sy_v_e_092_060_094isub_0622____,type,
e_2: exp_list_char ).
thf(sy_v_e_Ha____,type,
e_a: exp_list_char ).
thf(sy_v_ea____,type,
ea: exp_list_char ).
thf(sy_v_h_Ha____,type,
h_a: nat > option1728594148on_val ).
thf(sy_v_ha____,type,
ha: nat > option1728594148on_val ).
thf(sy_v_l_Ha____,type,
l_a: list_char > option_val ).
thf(sy_v_la____,type,
la: list_char > option_val ).
%----Relevant facts (700)
thf(fact_0__096P_ME_Mh_A_092_060turnstile_062_Ae_A_058_ANT_096,axiom,
wTrt @ p @ ha @ e @ ea @ nt ).
thf(fact_1__096_B_BT_O_AP_ME_Mh_A_092_060turnstile_062_Ae_A_058_AT_A_061_061_062_AEX,axiom,
! [T: ty] :
( ( wTrt @ p @ ha @ e @ ea @ T )
=> ? [U_2: ty] :
( ( wTrt @ p @ h_a @ e @ e_a @ U_2 )
& ( widen_2090681816t_char @ p @ U_2 @ T ) ) ) ).
thf(fact_2_assms,axiom,
wf_pro755087577t_char @ wf_J_mdecl @ p ).
thf(fact_3_IH,axiom,
! [T: ty,E_1: list_char > option_ty] :
( ( typeSa1102574168_sconf @ p @ E_1 @ ( produc755559506on_val @ ha @ la ) )
=> ( ( wTrt @ p @ ha @ E_1 @ ea @ T )
=> ? [U_2: ty] :
( ( wTrt @ p @ h_a @ E_1 @ e_a @ U_2 )
& ( widen_2090681816t_char @ p @ U_2 @ T ) ) ) ) ).
thf(fact_4_conf,axiom,
typeSa1102574168_sconf @ p @ e @ ( produc755559506on_val @ ha @ la ) ).
thf(fact_5_wt,axiom,
wTrt @ p @ ha @ e @ ( fAss_list_char @ ea @ f @ d @ e_2 ) @ t ).
thf(fact_6_WTrtFAccNT,axiom,
! [F: list_char,D: list_char,T: ty,P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: list_char > option_ty,E: exp_list_char] :
( ( wTrt @ P @ H @ E_1 @ E @ nt )
=> ( wTrt @ P @ H @ E_1 @ ( fAcc_list_char @ E @ F @ D ) @ T ) ) ).
thf(fact_7_FAssRed1_I2_J,axiom,
! [T: ty,E_1: list_char > option_ty] :
( ( typeSa1102574168_sconf @ p @ E_1 @ ( produc755559506on_val @ ha @ la ) )
=> ( ( wTrt @ p @ ha @ E_1 @ ea @ T )
=> ? [T_2: ty] :
( ( wTrt @ p @ h_a @ E_1 @ e_a @ T_2 )
& ( widen_2090681816t_char @ p @ T_2 @ T ) ) ) ) ).
thf(fact_8_red,axiom,
member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ea @ ( produc755559506on_val @ ha @ la ) ) @ ( produc235638504on_val @ e_a @ ( produc755559506on_val @ h_a @ l_a ) ) ) @ ( red @ p ) ).
thf(fact_9_FAssRed1_I4_J,axiom,
wTrt @ p @ ha @ e @ ( fAss_list_char @ ea @ f @ d @ e_2 ) @ t ).
thf(fact_10_FAssRed1_I3_J,axiom,
typeSa1102574168_sconf @ p @ e @ ( produc755559506on_val @ ha @ la ) ).
thf(fact_11_ty_Osimps_I13_J,axiom,
nt != boolean ).
thf(fact_12_ty_Osimps_I12_J,axiom,
boolean != nt ).
thf(fact_13_red__reds_OFAccRed,axiom,
! [F: list_char,D: list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAcc_list_char @ E @ F @ D ) @ S ) @ ( produc235638504on_val @ ( fAcc_list_char @ E_2 @ F @ D ) @ S_1 ) ) @ ( red @ P ) ) ) ).
thf(fact_14_red__reds_OFAssRed1,axiom,
! [F: list_char,D: list_char,E_2_1: exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ E @ F @ D @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( fAss_list_char @ E_2 @ F @ D @ E_2_1 ) @ S_1 ) ) @ ( red @ P ) ) ) ).
thf(fact_15_void,axiom,
t = void ).
thf(fact_16_widen__refl,axiom,
! [P_20: list_P1999446415t_char,T_8: ty] : ( widen_2090681816t_char @ P_20 @ T_8 @ T_8 ) ).
thf(fact_17_red__preserves__hconf,axiom,
! [E_1: list_char > option_ty,T: ty,E: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,E_2: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ L ) ) @ ( produc235638504on_val @ E_2 @ ( produc755559506on_val @ H_1 @ L_1 ) ) ) @ ( red @ P ) )
=> ( ( wTrt @ P @ H @ E_1 @ E @ T )
=> ( ( hconf_97414254t_char @ P @ H )
=> ( hconf_97414254t_char @ P @ H_1 ) ) ) ) ).
thf(fact_18_red__preserves__lconf,axiom,
! [E_1: list_char > option_ty,T: ty,E: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,E_2: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ L ) ) @ ( produc235638504on_val @ E_2 @ ( produc755559506on_val @ H_1 @ L_1 ) ) ) @ ( red @ P ) )
=> ( ( wTrt @ P @ H @ E_1 @ E @ T )
=> ( ( lconf_496643946t_char @ P @ H @ L @ E_1 )
=> ( lconf_496643946t_char @ P @ H_1 @ L_1 @ E_1 ) ) ) ) ).
thf(fact_19_exp_Osimps_I154_J,axiom,
! [Exp_11: exp_list_char,List1_17: list_char,List2_17: list_char,Exp1_25: exp_list_char,List1_16: list_char,List2_16: list_char,Exp2_25: exp_list_char] :
( ( fAcc_list_char @ Exp_11 @ List1_17 @ List2_17 )
!= ( fAss_list_char @ Exp1_25 @ List1_16 @ List2_16 @ Exp2_25 ) ) ).
thf(fact_20_exp_Osimps_I155_J,axiom,
! [Exp1_24: exp_list_char,List1_15: list_char,List2_15: list_char,Exp2_24: exp_list_char,Exp_10: exp_list_char,List1_14: list_char,List2_14: list_char] :
( ( fAss_list_char @ Exp1_24 @ List1_15 @ List2_15 @ Exp2_24 )
!= ( fAcc_list_char @ Exp_10 @ List1_14 @ List2_14 ) ) ).
thf(fact_21_red__preserves__sconf,axiom,
! [E_1: list_char > option_ty,T: ty,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( red @ P ) )
=> ( ( wTrt @ P @ ( hp @ S ) @ E_1 @ E @ T )
=> ( ( typeSa1102574168_sconf @ P @ E_1 @ S )
=> ( typeSa1102574168_sconf @ P @ E_1 @ S_1 ) ) ) ) ).
thf(fact_22_ty_Osimps_I7_J,axiom,
nt != void ).
thf(fact_23_ty_Osimps_I6_J,axiom,
void != nt ).
thf(fact_24_ty_Osimps_I3_J,axiom,
boolean != void ).
thf(fact_25_ty_Osimps_I2_J,axiom,
void != boolean ).
thf(fact_26_Pair__inject,axiom,
! [A_19: produc1278157519t_char,B_17: produc1278157519t_char,A_18: produc1278157519t_char,B_16: produc1278157519t_char] :
( ( ( produc2080520419t_char @ A_19 @ B_17 )
= ( produc2080520419t_char @ A_18 @ B_16 ) )
=> ~ ( ( A_19 = A_18 )
=> ( B_17 != B_16 ) ) ) ).
thf(fact_27_Pair__inject,axiom,
! [A_19: produc2088785539on_val,B_17: produc2088785539on_val,A_18: produc2088785539on_val,B_16: produc2088785539on_val] :
( ( ( produc1773146955on_val @ A_19 @ B_17 )
= ( produc1773146955on_val @ A_18 @ B_16 ) )
=> ~ ( ( A_19 = A_18 )
=> ( B_17 != B_16 ) ) ) ).
thf(fact_28_Pair__inject,axiom,
! [A_19: produc662261637t_char,B_17: produc662261637t_char,A_18: produc662261637t_char,B_16: produc662261637t_char] :
( ( ( produc1299387215t_char @ A_19 @ B_17 )
= ( produc1299387215t_char @ A_18 @ B_16 ) )
=> ~ ( ( A_19 = A_18 )
=> ( B_17 != B_16 ) ) ) ).
thf(fact_29_Pair__inject,axiom,
! [A_19: produc220283002t_char,B_17: produc220283002t_char,A_18: produc220283002t_char,B_16: produc220283002t_char] :
( ( ( produc57279289t_char @ A_19 @ B_17 )
= ( produc57279289t_char @ A_18 @ B_16 ) )
=> ~ ( ( A_19 = A_18 )
=> ( B_17 != B_16 ) ) ) ).
thf(fact_30_Pair__inject,axiom,
! [A_19: produc1285161482t_char,B_17: produc1285161482t_char,A_18: produc1285161482t_char,B_16: produc1285161482t_char] :
( ( ( produc24551831t_char @ A_19 @ B_17 )
= ( produc24551831t_char @ A_18 @ B_16 ) )
=> ~ ( ( A_19 = A_18 )
=> ( B_17 != B_16 ) ) ) ).
thf(fact_31_Pair__inject,axiom,
! [A_19: produc618524391on_val,B_17: produc618524391on_val,A_18: produc618524391on_val,B_16: produc618524391on_val] :
( ( ( produc1347028499on_val @ A_19 @ B_17 )
= ( produc1347028499on_val @ A_18 @ B_16 ) )
=> ~ ( ( A_19 = A_18 )
=> ( B_17 != B_16 ) ) ) ).
thf(fact_32_Pair__inject,axiom,
! [A_19: produc1746408499on_val,B_17: produc1746408499on_val,A_18: produc1746408499on_val,B_16: produc1746408499on_val] :
( ( ( produc345758123on_val @ A_19 @ B_17 )
= ( produc345758123on_val @ A_18 @ B_16 ) )
=> ~ ( ( A_19 = A_18 )
=> ( B_17 != B_16 ) ) ) ).
thf(fact_33_Pair__inject,axiom,
! [A_19: produc2090907612on_val,B_17: produc2090907612on_val,A_18: produc2090907612on_val,B_16: produc2090907612on_val] :
( ( ( produc259392253on_val @ A_19 @ B_17 )
= ( produc259392253on_val @ A_18 @ B_16 ) )
=> ~ ( ( A_19 = A_18 )
=> ( B_17 != B_16 ) ) ) ).
thf(fact_34_Pair__inject,axiom,
! [A_19: nat > option1728594148on_val,B_17: list_char > option_val,A_18: nat > option1728594148on_val,B_16: list_char > option_val] :
( ( ( produc755559506on_val @ A_19 @ B_17 )
= ( produc755559506on_val @ A_18 @ B_16 ) )
=> ~ ( ( A_19 = A_18 )
=> ( B_17 != B_16 ) ) ) ).
thf(fact_35_Pair__inject,axiom,
! [A_19: produc1282892786on_val,B_17: produc1282892786on_val,A_18: produc1282892786on_val,B_16: produc1282892786on_val] :
( ( ( produc833389609on_val @ A_19 @ B_17 )
= ( produc833389609on_val @ A_18 @ B_16 ) )
=> ~ ( ( A_19 = A_18 )
=> ( B_17 != B_16 ) ) ) ).
thf(fact_36_Pair__inject,axiom,
! [A_19: exp_list_char,B_17: produc2090907612on_val,A_18: exp_list_char,B_16: produc2090907612on_val] :
( ( ( produc235638504on_val @ A_19 @ B_17 )
= ( produc235638504on_val @ A_18 @ B_16 ) )
=> ~ ( ( A_19 = A_18 )
=> ( B_17 != B_16 ) ) ) ).
thf(fact_37_Pair__inject,axiom,
! [A_19: produc1180562163on_val,B_17: produc1180562163on_val,A_18: produc1180562163on_val,B_16: produc1180562163on_val] :
( ( ( produc747700183on_val @ A_19 @ B_17 )
= ( produc747700183on_val @ A_18 @ B_16 ) )
=> ~ ( ( A_19 = A_18 )
=> ( B_17 != B_16 ) ) ) ).
thf(fact_38_Pair__inject,axiom,
! [A_19: list_exp_list_char,B_17: produc2090907612on_val,A_18: list_exp_list_char,B_16: produc2090907612on_val] :
( ( ( produc1302104557on_val @ A_19 @ B_17 )
= ( produc1302104557on_val @ A_18 @ B_16 ) )
=> ~ ( ( A_19 = A_18 )
=> ( B_17 != B_16 ) ) ) ).
thf(fact_39_Pair__inject,axiom,
! [A_19: list_list_char,B_17: produc220283002t_char,A_18: list_list_char,B_16: produc220283002t_char] :
( ( ( produc921874948t_char @ A_19 @ B_17 )
= ( produc921874948t_char @ A_18 @ B_16 ) )
=> ~ ( ( A_19 = A_18 )
=> ( B_17 != B_16 ) ) ) ).
thf(fact_40_Pair__inject,axiom,
! [A_19: list_ty,B_17: produc662261637t_char,A_18: list_ty,B_16: produc662261637t_char] :
( ( ( produc1909267824t_char @ A_19 @ B_17 )
= ( produc1909267824t_char @ A_18 @ B_16 ) )
=> ~ ( ( A_19 = A_18 )
=> ( B_17 != B_16 ) ) ) ).
thf(fact_41_Pair__inject,axiom,
! [A_19: list_val,B_17: exp_list_char,A_18: list_val,B_16: exp_list_char] :
( ( ( produc1916172923t_char @ A_19 @ B_17 )
= ( produc1916172923t_char @ A_18 @ B_16 ) )
=> ~ ( ( A_19 = A_18 )
=> ( B_17 != B_16 ) ) ) ).
thf(fact_42_Pair__inject,axiom,
! [A_19: list_char,B_17: produc1278157519t_char > option_val,A_18: list_char,B_16: produc1278157519t_char > option_val] :
( ( ( produc926070009on_val @ A_19 @ B_17 )
= ( produc926070009on_val @ A_18 @ B_16 ) )
=> ~ ( ( A_19 = A_18 )
=> ( B_17 != B_16 ) ) ) ).
thf(fact_43_Pair__inject,axiom,
! [A_19: list_char,B_17: list_char,A_18: list_char,B_16: list_char] :
( ( ( produc5062597t_char @ A_19 @ B_17 )
= ( produc5062597t_char @ A_18 @ B_16 ) )
=> ~ ( ( A_19 = A_18 )
=> ( B_17 != B_16 ) ) ) ).
thf(fact_44_Pair__eq,axiom,
! [A_17: produc1278157519t_char,B_15: produc1278157519t_char,A_16: produc1278157519t_char,B_14: produc1278157519t_char] :
( ( ( produc2080520419t_char @ A_17 @ B_15 )
= ( produc2080520419t_char @ A_16 @ B_14 ) )
<=> ( ( A_17 = A_16 )
& ( B_15 = B_14 ) ) ) ).
thf(fact_45_Pair__eq,axiom,
! [A_17: produc2088785539on_val,B_15: produc2088785539on_val,A_16: produc2088785539on_val,B_14: produc2088785539on_val] :
( ( ( produc1773146955on_val @ A_17 @ B_15 )
= ( produc1773146955on_val @ A_16 @ B_14 ) )
<=> ( ( A_17 = A_16 )
& ( B_15 = B_14 ) ) ) ).
thf(fact_46_Pair__eq,axiom,
! [A_17: produc662261637t_char,B_15: produc662261637t_char,A_16: produc662261637t_char,B_14: produc662261637t_char] :
( ( ( produc1299387215t_char @ A_17 @ B_15 )
= ( produc1299387215t_char @ A_16 @ B_14 ) )
<=> ( ( A_17 = A_16 )
& ( B_15 = B_14 ) ) ) ).
thf(fact_47_Pair__eq,axiom,
! [A_17: produc220283002t_char,B_15: produc220283002t_char,A_16: produc220283002t_char,B_14: produc220283002t_char] :
( ( ( produc57279289t_char @ A_17 @ B_15 )
= ( produc57279289t_char @ A_16 @ B_14 ) )
<=> ( ( A_17 = A_16 )
& ( B_15 = B_14 ) ) ) ).
thf(fact_48_Pair__eq,axiom,
! [A_17: produc1285161482t_char,B_15: produc1285161482t_char,A_16: produc1285161482t_char,B_14: produc1285161482t_char] :
( ( ( produc24551831t_char @ A_17 @ B_15 )
= ( produc24551831t_char @ A_16 @ B_14 ) )
<=> ( ( A_17 = A_16 )
& ( B_15 = B_14 ) ) ) ).
thf(fact_49_Pair__eq,axiom,
! [A_17: produc618524391on_val,B_15: produc618524391on_val,A_16: produc618524391on_val,B_14: produc618524391on_val] :
( ( ( produc1347028499on_val @ A_17 @ B_15 )
= ( produc1347028499on_val @ A_16 @ B_14 ) )
<=> ( ( A_17 = A_16 )
& ( B_15 = B_14 ) ) ) ).
thf(fact_50_Pair__eq,axiom,
! [A_17: produc1746408499on_val,B_15: produc1746408499on_val,A_16: produc1746408499on_val,B_14: produc1746408499on_val] :
( ( ( produc345758123on_val @ A_17 @ B_15 )
= ( produc345758123on_val @ A_16 @ B_14 ) )
<=> ( ( A_17 = A_16 )
& ( B_15 = B_14 ) ) ) ).
thf(fact_51_Pair__eq,axiom,
! [A_17: produc2090907612on_val,B_15: produc2090907612on_val,A_16: produc2090907612on_val,B_14: produc2090907612on_val] :
( ( ( produc259392253on_val @ A_17 @ B_15 )
= ( produc259392253on_val @ A_16 @ B_14 ) )
<=> ( ( A_17 = A_16 )
& ( B_15 = B_14 ) ) ) ).
thf(fact_52_Pair__eq,axiom,
! [A_17: nat > option1728594148on_val,B_15: list_char > option_val,A_16: nat > option1728594148on_val,B_14: list_char > option_val] :
( ( ( produc755559506on_val @ A_17 @ B_15 )
= ( produc755559506on_val @ A_16 @ B_14 ) )
<=> ( ( A_17 = A_16 )
& ( B_15 = B_14 ) ) ) ).
thf(fact_53_Pair__eq,axiom,
! [A_17: produc1282892786on_val,B_15: produc1282892786on_val,A_16: produc1282892786on_val,B_14: produc1282892786on_val] :
( ( ( produc833389609on_val @ A_17 @ B_15 )
= ( produc833389609on_val @ A_16 @ B_14 ) )
<=> ( ( A_17 = A_16 )
& ( B_15 = B_14 ) ) ) ).
thf(fact_54_Pair__eq,axiom,
! [A_17: exp_list_char,B_15: produc2090907612on_val,A_16: exp_list_char,B_14: produc2090907612on_val] :
( ( ( produc235638504on_val @ A_17 @ B_15 )
= ( produc235638504on_val @ A_16 @ B_14 ) )
<=> ( ( A_17 = A_16 )
& ( B_15 = B_14 ) ) ) ).
thf(fact_55_Pair__eq,axiom,
! [A_17: produc1180562163on_val,B_15: produc1180562163on_val,A_16: produc1180562163on_val,B_14: produc1180562163on_val] :
( ( ( produc747700183on_val @ A_17 @ B_15 )
= ( produc747700183on_val @ A_16 @ B_14 ) )
<=> ( ( A_17 = A_16 )
& ( B_15 = B_14 ) ) ) ).
thf(fact_56_Pair__eq,axiom,
! [A_17: list_exp_list_char,B_15: produc2090907612on_val,A_16: list_exp_list_char,B_14: produc2090907612on_val] :
( ( ( produc1302104557on_val @ A_17 @ B_15 )
= ( produc1302104557on_val @ A_16 @ B_14 ) )
<=> ( ( A_17 = A_16 )
& ( B_15 = B_14 ) ) ) ).
thf(fact_57_Pair__eq,axiom,
! [A_17: list_list_char,B_15: produc220283002t_char,A_16: list_list_char,B_14: produc220283002t_char] :
( ( ( produc921874948t_char @ A_17 @ B_15 )
= ( produc921874948t_char @ A_16 @ B_14 ) )
<=> ( ( A_17 = A_16 )
& ( B_15 = B_14 ) ) ) ).
thf(fact_58_Pair__eq,axiom,
! [A_17: list_ty,B_15: produc662261637t_char,A_16: list_ty,B_14: produc662261637t_char] :
( ( ( produc1909267824t_char @ A_17 @ B_15 )
= ( produc1909267824t_char @ A_16 @ B_14 ) )
<=> ( ( A_17 = A_16 )
& ( B_15 = B_14 ) ) ) ).
thf(fact_59_Pair__eq,axiom,
! [A_17: list_val,B_15: exp_list_char,A_16: list_val,B_14: exp_list_char] :
( ( ( produc1916172923t_char @ A_17 @ B_15 )
= ( produc1916172923t_char @ A_16 @ B_14 ) )
<=> ( ( A_17 = A_16 )
& ( B_15 = B_14 ) ) ) ).
thf(fact_60_Pair__eq,axiom,
! [A_17: list_char,B_15: produc1278157519t_char > option_val,A_16: list_char,B_14: produc1278157519t_char > option_val] :
( ( ( produc926070009on_val @ A_17 @ B_15 )
= ( produc926070009on_val @ A_16 @ B_14 ) )
<=> ( ( A_17 = A_16 )
& ( B_15 = B_14 ) ) ) ).
thf(fact_61_Pair__eq,axiom,
! [A_17: list_char,B_15: list_char,A_16: list_char,B_14: list_char] :
( ( ( produc5062597t_char @ A_17 @ B_15 )
= ( produc5062597t_char @ A_16 @ B_14 ) )
<=> ( ( A_17 = A_16 )
& ( B_15 = B_14 ) ) ) ).
thf(fact_62_split__paired__All,axiom,
! [P_19: produc1350825965t_char > $o] :
( ( !! @ produc1350825965t_char @ P_19 )
<=> ! [A_1: produc1278157519t_char,B_4: produc1278157519t_char] : ( P_19 @ ( produc2080520419t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_63_split__paired__All,axiom,
! [P_19: produc1368416213on_val > $o] :
( ( !! @ produc1368416213on_val @ P_19 )
<=> ! [A_1: produc2088785539on_val,B_4: produc2088785539on_val] : ( P_19 @ ( produc1773146955on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_64_split__paired__All,axiom,
! [P_19: produc1826280281t_char > $o] :
( ( !! @ produc1826280281t_char @ P_19 )
<=> ! [A_1: produc662261637t_char,B_4: produc662261637t_char] : ( P_19 @ ( produc1299387215t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_65_split__paired__All,axiom,
! [P_19: produc1406897475t_char > $o] :
( ( !! @ produc1406897475t_char @ P_19 )
<=> ! [A_1: produc220283002t_char,B_4: produc220283002t_char] : ( P_19 @ ( produc57279289t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_66_split__paired__All,axiom,
! [P_19: produc349695911t_char > $o] :
( ( !! @ produc349695911t_char @ P_19 )
<=> ! [A_1: produc1285161482t_char,B_4: produc1285161482t_char] : ( P_19 @ ( produc24551831t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_67_split__paired__All,axiom,
! [P_19: produc1250491293on_val > $o] :
( ( !! @ produc1250491293on_val @ P_19 )
<=> ! [A_1: produc618524391on_val,B_4: produc618524391on_val] : ( P_19 @ ( produc1347028499on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_68_split__paired__All,axiom,
! [P_19: produc652964533on_val > $o] :
( ( !! @ produc652964533on_val @ P_19 )
<=> ! [A_1: produc1746408499on_val,B_4: produc1746408499on_val] : ( P_19 @ ( produc345758123on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_69_split__paired__All,axiom,
! [P_19: produc1581780743on_val > $o] :
( ( !! @ produc1581780743on_val @ P_19 )
<=> ! [A_1: produc2090907612on_val,B_4: produc2090907612on_val] : ( P_19 @ ( produc259392253on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_70_split__paired__All,axiom,
! [P_19: produc2090907612on_val > $o] :
( ( !! @ produc2090907612on_val @ P_19 )
<=> ! [A_1: nat > option1728594148on_val,B_4: list_char > option_val] : ( P_19 @ ( produc755559506on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_71_split__paired__All,axiom,
! [P_19: produc1746408499on_val > $o] :
( ( !! @ produc1746408499on_val @ P_19 )
<=> ! [A_1: produc1282892786on_val,B_4: produc1282892786on_val] : ( P_19 @ ( produc833389609on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_72_split__paired__All,axiom,
! [P_19: produc1282892786on_val > $o] :
( ( !! @ produc1282892786on_val @ P_19 )
<=> ! [A_1: exp_list_char,B_4: produc2090907612on_val] : ( P_19 @ ( produc235638504on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_73_split__paired__All,axiom,
! [P_19: produc618524391on_val > $o] :
( ( !! @ produc618524391on_val @ P_19 )
<=> ! [A_1: produc1180562163on_val,B_4: produc1180562163on_val] : ( P_19 @ ( produc747700183on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_74_split__paired__All,axiom,
! [P_19: produc1180562163on_val > $o] :
( ( !! @ produc1180562163on_val @ P_19 )
<=> ! [A_1: list_exp_list_char,B_4: produc2090907612on_val] : ( P_19 @ ( produc1302104557on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_75_split__paired__All,axiom,
! [P_19: produc1285161482t_char > $o] :
( ( !! @ produc1285161482t_char @ P_19 )
<=> ! [A_1: list_list_char,B_4: produc220283002t_char] : ( P_19 @ ( produc921874948t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_76_split__paired__All,axiom,
! [P_19: produc220283002t_char > $o] :
( ( !! @ produc220283002t_char @ P_19 )
<=> ! [A_1: list_ty,B_4: produc662261637t_char] : ( P_19 @ ( produc1909267824t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_77_split__paired__All,axiom,
! [P_19: produc662261637t_char > $o] :
( ( !! @ produc662261637t_char @ P_19 )
<=> ! [A_1: list_val,B_4: exp_list_char] : ( P_19 @ ( produc1916172923t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_78_split__paired__All,axiom,
! [P_19: produc2088785539on_val > $o] :
( ( !! @ produc2088785539on_val @ P_19 )
<=> ! [A_1: list_char,B_4: produc1278157519t_char > option_val] : ( P_19 @ ( produc926070009on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_79_split__paired__All,axiom,
! [P_19: produc1278157519t_char > $o] :
( ( !! @ produc1278157519t_char @ P_19 )
<=> ! [A_1: list_char,B_4: list_char] : ( P_19 @ ( produc5062597t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_80_widen__trans,axiom,
! [T_7: ty,P_18: list_P1999446415t_char,S_5: ty,U_1: ty] :
( ( widen_2090681816t_char @ P_18 @ S_5 @ U_1 )
=> ( ( widen_2090681816t_char @ P_18 @ U_1 @ T_7 )
=> ( widen_2090681816t_char @ P_18 @ S_5 @ T_7 ) ) ) ).
thf(fact_81_exp_Osimps_I8_J,axiom,
! [Exp1_23: exp_list_char,List1_13: list_char,List2_13: list_char,Exp2_23: exp_list_char,Exp1_22: exp_list_char,List1_12: list_char,List2_12: list_char,Exp2_22: exp_list_char] :
( ( ( fAss_list_char @ Exp1_23 @ List1_13 @ List2_13 @ Exp2_23 )
= ( fAss_list_char @ Exp1_22 @ List1_12 @ List2_12 @ Exp2_22 ) )
<=> ( ( Exp1_23 = Exp1_22 )
& ( List1_13 = List1_12 )
& ( List2_13 = List2_12 )
& ( Exp2_23 = Exp2_22 ) ) ) ).
thf(fact_82_exp_Osimps_I7_J,axiom,
! [Exp_9: exp_list_char,List1_11: list_char,List2_11: list_char,Exp_8: exp_list_char,List1_10: list_char,List2_10: list_char] :
( ( ( fAcc_list_char @ Exp_9 @ List1_11 @ List2_11 )
= ( fAcc_list_char @ Exp_8 @ List1_10 @ List2_10 ) )
<=> ( ( Exp_9 = Exp_8 )
& ( List1_11 = List1_10 )
& ( List2_11 = List2_10 ) ) ) ).
thf(fact_83_WTrtFAssNT,axiom,
! [F: list_char,D: list_char,E_2_1: exp_list_char,T_2_1: ty,P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: list_char > option_ty,E_1_1: exp_list_char] :
( ( wTrt @ P @ H @ E_1 @ E_1_1 @ nt )
=> ( ( wTrt @ P @ H @ E_1 @ E_2_1 @ T_2_1 )
=> ( wTrt @ P @ H @ E_1 @ ( fAss_list_char @ E_1_1 @ F @ D @ E_2_1 ) @ void ) ) ) ).
thf(fact_84_prod__cases5,axiom,
! [Y_4: produc1250491293on_val] :
~ ! [A_1: produc618524391on_val,B_4: produc1180562163on_val,C_9: list_exp_list_char,D_1: nat > option1728594148on_val,E_4: list_char > option_val] :
( Y_4
!= ( produc1347028499on_val @ A_1 @ ( produc747700183on_val @ B_4 @ ( produc1302104557on_val @ C_9 @ ( produc755559506on_val @ D_1 @ E_4 ) ) ) ) ) ).
thf(fact_85_prod__cases5,axiom,
! [Y_4: produc652964533on_val] :
~ ! [A_1: produc1746408499on_val,B_4: produc1282892786on_val,C_9: exp_list_char,D_1: nat > option1728594148on_val,E_4: list_char > option_val] :
( Y_4
!= ( produc345758123on_val @ A_1 @ ( produc833389609on_val @ B_4 @ ( produc235638504on_val @ C_9 @ ( produc755559506on_val @ D_1 @ E_4 ) ) ) ) ) ).
thf(fact_86_prod__cases5,axiom,
! [Y_4: produc349695911t_char] :
~ ! [A_1: produc1285161482t_char,B_4: list_list_char,C_9: list_ty,D_1: list_val,E_4: exp_list_char] :
( Y_4
!= ( produc24551831t_char @ A_1 @ ( produc921874948t_char @ B_4 @ ( produc1909267824t_char @ C_9 @ ( produc1916172923t_char @ D_1 @ E_4 ) ) ) ) ) ).
thf(fact_87_prod__induct5,axiom,
! [X_6: produc1250491293on_val,P_17: produc1250491293on_val > $o] :
( ! [A_1: produc618524391on_val,B_4: produc1180562163on_val,C_9: list_exp_list_char,D_1: nat > option1728594148on_val,E_4: list_char > option_val] : ( P_17 @ ( produc1347028499on_val @ A_1 @ ( produc747700183on_val @ B_4 @ ( produc1302104557on_val @ C_9 @ ( produc755559506on_val @ D_1 @ E_4 ) ) ) ) )
=> ( P_17 @ X_6 ) ) ).
thf(fact_88_prod__induct5,axiom,
! [X_6: produc652964533on_val,P_17: produc652964533on_val > $o] :
( ! [A_1: produc1746408499on_val,B_4: produc1282892786on_val,C_9: exp_list_char,D_1: nat > option1728594148on_val,E_4: list_char > option_val] : ( P_17 @ ( produc345758123on_val @ A_1 @ ( produc833389609on_val @ B_4 @ ( produc235638504on_val @ C_9 @ ( produc755559506on_val @ D_1 @ E_4 ) ) ) ) )
=> ( P_17 @ X_6 ) ) ).
thf(fact_89_prod__induct5,axiom,
! [X_6: produc349695911t_char,P_17: produc349695911t_char > $o] :
( ! [A_1: produc1285161482t_char,B_4: list_list_char,C_9: list_ty,D_1: list_val,E_4: exp_list_char] : ( P_17 @ ( produc24551831t_char @ A_1 @ ( produc921874948t_char @ B_4 @ ( produc1909267824t_char @ C_9 @ ( produc1916172923t_char @ D_1 @ E_4 ) ) ) ) )
=> ( P_17 @ X_6 ) ) ).
thf(fact_90_prod__cases4,axiom,
! [Y_3: produc1746408499on_val] :
~ ! [A_1: produc1282892786on_val,B_4: exp_list_char,C_9: nat > option1728594148on_val,D_1: list_char > option_val] :
( Y_3
!= ( produc833389609on_val @ A_1 @ ( produc235638504on_val @ B_4 @ ( produc755559506on_val @ C_9 @ D_1 ) ) ) ) ).
thf(fact_91_prod__cases4,axiom,
! [Y_3: produc618524391on_val] :
~ ! [A_1: produc1180562163on_val,B_4: list_exp_list_char,C_9: nat > option1728594148on_val,D_1: list_char > option_val] :
( Y_3
!= ( produc747700183on_val @ A_1 @ ( produc1302104557on_val @ B_4 @ ( produc755559506on_val @ C_9 @ D_1 ) ) ) ) ).
thf(fact_92_prod__cases4,axiom,
! [Y_3: produc1285161482t_char] :
~ ! [A_1: list_list_char,B_4: list_ty,C_9: list_val,D_1: exp_list_char] :
( Y_3
!= ( produc921874948t_char @ A_1 @ ( produc1909267824t_char @ B_4 @ ( produc1916172923t_char @ C_9 @ D_1 ) ) ) ) ).
thf(fact_93_prod__cases4,axiom,
! [Y_3: produc652964533on_val] :
~ ! [A_1: produc1746408499on_val,B_4: produc1282892786on_val,C_9: exp_list_char,D_1: produc2090907612on_val] :
( Y_3
!= ( produc345758123on_val @ A_1 @ ( produc833389609on_val @ B_4 @ ( produc235638504on_val @ C_9 @ D_1 ) ) ) ) ).
thf(fact_94_prod__cases4,axiom,
! [Y_3: produc1250491293on_val] :
~ ! [A_1: produc618524391on_val,B_4: produc1180562163on_val,C_9: list_exp_list_char,D_1: produc2090907612on_val] :
( Y_3
!= ( produc1347028499on_val @ A_1 @ ( produc747700183on_val @ B_4 @ ( produc1302104557on_val @ C_9 @ D_1 ) ) ) ) ).
thf(fact_95_prod__cases4,axiom,
! [Y_3: produc349695911t_char] :
~ ! [A_1: produc1285161482t_char,B_4: list_list_char,C_9: list_ty,D_1: produc662261637t_char] :
( Y_3
!= ( produc24551831t_char @ A_1 @ ( produc921874948t_char @ B_4 @ ( produc1909267824t_char @ C_9 @ D_1 ) ) ) ) ).
thf(fact_96_prod__cases4,axiom,
! [Y_3: produc1406897475t_char] :
~ ! [A_1: produc220283002t_char,B_4: list_ty,C_9: list_val,D_1: exp_list_char] :
( Y_3
!= ( produc57279289t_char @ A_1 @ ( produc1909267824t_char @ B_4 @ ( produc1916172923t_char @ C_9 @ D_1 ) ) ) ) ).
thf(fact_97_prod__induct4,axiom,
! [X_5: produc1746408499on_val,P_16: produc1746408499on_val > $o] :
( ! [A_1: produc1282892786on_val,B_4: exp_list_char,C_9: nat > option1728594148on_val,D_1: list_char > option_val] : ( P_16 @ ( produc833389609on_val @ A_1 @ ( produc235638504on_val @ B_4 @ ( produc755559506on_val @ C_9 @ D_1 ) ) ) )
=> ( P_16 @ X_5 ) ) ).
thf(fact_98_prod__induct4,axiom,
! [X_5: produc618524391on_val,P_16: produc618524391on_val > $o] :
( ! [A_1: produc1180562163on_val,B_4: list_exp_list_char,C_9: nat > option1728594148on_val,D_1: list_char > option_val] : ( P_16 @ ( produc747700183on_val @ A_1 @ ( produc1302104557on_val @ B_4 @ ( produc755559506on_val @ C_9 @ D_1 ) ) ) )
=> ( P_16 @ X_5 ) ) ).
thf(fact_99_prod__induct4,axiom,
! [X_5: produc1285161482t_char,P_16: produc1285161482t_char > $o] :
( ! [A_1: list_list_char,B_4: list_ty,C_9: list_val,D_1: exp_list_char] : ( P_16 @ ( produc921874948t_char @ A_1 @ ( produc1909267824t_char @ B_4 @ ( produc1916172923t_char @ C_9 @ D_1 ) ) ) )
=> ( P_16 @ X_5 ) ) ).
thf(fact_100_prod__induct4,axiom,
! [X_5: produc652964533on_val,P_16: produc652964533on_val > $o] :
( ! [A_1: produc1746408499on_val,B_4: produc1282892786on_val,C_9: exp_list_char,D_1: produc2090907612on_val] : ( P_16 @ ( produc345758123on_val @ A_1 @ ( produc833389609on_val @ B_4 @ ( produc235638504on_val @ C_9 @ D_1 ) ) ) )
=> ( P_16 @ X_5 ) ) ).
thf(fact_101_prod__induct4,axiom,
! [X_5: produc1250491293on_val,P_16: produc1250491293on_val > $o] :
( ! [A_1: produc618524391on_val,B_4: produc1180562163on_val,C_9: list_exp_list_char,D_1: produc2090907612on_val] : ( P_16 @ ( produc1347028499on_val @ A_1 @ ( produc747700183on_val @ B_4 @ ( produc1302104557on_val @ C_9 @ D_1 ) ) ) )
=> ( P_16 @ X_5 ) ) ).
thf(fact_102_prod__induct4,axiom,
! [X_5: produc349695911t_char,P_16: produc349695911t_char > $o] :
( ! [A_1: produc1285161482t_char,B_4: list_list_char,C_9: list_ty,D_1: produc662261637t_char] : ( P_16 @ ( produc24551831t_char @ A_1 @ ( produc921874948t_char @ B_4 @ ( produc1909267824t_char @ C_9 @ D_1 ) ) ) )
=> ( P_16 @ X_5 ) ) ).
thf(fact_103_prod__induct4,axiom,
! [X_5: produc1406897475t_char,P_16: produc1406897475t_char > $o] :
( ! [A_1: produc220283002t_char,B_4: list_ty,C_9: list_val,D_1: exp_list_char] : ( P_16 @ ( produc57279289t_char @ A_1 @ ( produc1909267824t_char @ B_4 @ ( produc1916172923t_char @ C_9 @ D_1 ) ) ) )
=> ( P_16 @ X_5 ) ) ).
thf(fact_104_prod__cases3,axiom,
! [Y_2: produc1746408499on_val] :
~ ! [A_1: produc1282892786on_val,B_4: exp_list_char,C_9: produc2090907612on_val] :
( Y_2
!= ( produc833389609on_val @ A_1 @ ( produc235638504on_val @ B_4 @ C_9 ) ) ) ).
thf(fact_105_prod__cases3,axiom,
! [Y_2: produc1282892786on_val] :
~ ! [A_1: exp_list_char,B_4: nat > option1728594148on_val,C_9: list_char > option_val] :
( Y_2
!= ( produc235638504on_val @ A_1 @ ( produc755559506on_val @ B_4 @ C_9 ) ) ) ).
thf(fact_106_prod__cases3,axiom,
! [Y_2: produc618524391on_val] :
~ ! [A_1: produc1180562163on_val,B_4: list_exp_list_char,C_9: produc2090907612on_val] :
( Y_2
!= ( produc747700183on_val @ A_1 @ ( produc1302104557on_val @ B_4 @ C_9 ) ) ) ).
thf(fact_107_prod__cases3,axiom,
! [Y_2: produc1180562163on_val] :
~ ! [A_1: list_exp_list_char,B_4: nat > option1728594148on_val,C_9: list_char > option_val] :
( Y_2
!= ( produc1302104557on_val @ A_1 @ ( produc755559506on_val @ B_4 @ C_9 ) ) ) ).
thf(fact_108_prod__cases3,axiom,
! [Y_2: produc1285161482t_char] :
~ ! [A_1: list_list_char,B_4: list_ty,C_9: produc662261637t_char] :
( Y_2
!= ( produc921874948t_char @ A_1 @ ( produc1909267824t_char @ B_4 @ C_9 ) ) ) ).
thf(fact_109_prod__cases3,axiom,
! [Y_2: produc220283002t_char] :
~ ! [A_1: list_ty,B_4: list_val,C_9: exp_list_char] :
( Y_2
!= ( produc1909267824t_char @ A_1 @ ( produc1916172923t_char @ B_4 @ C_9 ) ) ) ).
thf(fact_110_prod__cases3,axiom,
! [Y_2: produc1581780743on_val] :
~ ! [A_1: produc2090907612on_val,B_4: nat > option1728594148on_val,C_9: list_char > option_val] :
( Y_2
!= ( produc259392253on_val @ A_1 @ ( produc755559506on_val @ B_4 @ C_9 ) ) ) ).
thf(fact_111_prod__cases3,axiom,
! [Y_2: produc652964533on_val] :
~ ! [A_1: produc1746408499on_val,B_4: produc1282892786on_val,C_9: produc1282892786on_val] :
( Y_2
!= ( produc345758123on_val @ A_1 @ ( produc833389609on_val @ B_4 @ C_9 ) ) ) ).
thf(fact_112_prod__cases3,axiom,
! [Y_2: produc1250491293on_val] :
~ ! [A_1: produc618524391on_val,B_4: produc1180562163on_val,C_9: produc1180562163on_val] :
( Y_2
!= ( produc1347028499on_val @ A_1 @ ( produc747700183on_val @ B_4 @ C_9 ) ) ) ).
thf(fact_113_prod__cases3,axiom,
! [Y_2: produc349695911t_char] :
~ ! [A_1: produc1285161482t_char,B_4: list_list_char,C_9: produc220283002t_char] :
( Y_2
!= ( produc24551831t_char @ A_1 @ ( produc921874948t_char @ B_4 @ C_9 ) ) ) ).
thf(fact_114_prod__cases3,axiom,
! [Y_2: produc1406897475t_char] :
~ ! [A_1: produc220283002t_char,B_4: list_ty,C_9: produc662261637t_char] :
( Y_2
!= ( produc57279289t_char @ A_1 @ ( produc1909267824t_char @ B_4 @ C_9 ) ) ) ).
thf(fact_115_prod__cases3,axiom,
! [Y_2: produc1826280281t_char] :
~ ! [A_1: produc662261637t_char,B_4: list_val,C_9: exp_list_char] :
( Y_2
!= ( produc1299387215t_char @ A_1 @ ( produc1916172923t_char @ B_4 @ C_9 ) ) ) ).
thf(fact_116_prod__cases3,axiom,
! [Y_2: produc1368416213on_val] :
~ ! [A_1: produc2088785539on_val,B_4: list_char,C_9: produc1278157519t_char > option_val] :
( Y_2
!= ( produc1773146955on_val @ A_1 @ ( produc926070009on_val @ B_4 @ C_9 ) ) ) ).
thf(fact_117_prod__cases3,axiom,
! [Y_2: produc1350825965t_char] :
~ ! [A_1: produc1278157519t_char,B_4: list_char,C_9: list_char] :
( Y_2
!= ( produc2080520419t_char @ A_1 @ ( produc5062597t_char @ B_4 @ C_9 ) ) ) ).
thf(fact_118_prod__induct3,axiom,
! [X_4: produc1746408499on_val,P_15: produc1746408499on_val > $o] :
( ! [A_1: produc1282892786on_val,B_4: exp_list_char,C_9: produc2090907612on_val] : ( P_15 @ ( produc833389609on_val @ A_1 @ ( produc235638504on_val @ B_4 @ C_9 ) ) )
=> ( P_15 @ X_4 ) ) ).
thf(fact_119_prod__induct3,axiom,
! [X_4: produc1282892786on_val,P_15: produc1282892786on_val > $o] :
( ! [A_1: exp_list_char,B_4: nat > option1728594148on_val,C_9: list_char > option_val] : ( P_15 @ ( produc235638504on_val @ A_1 @ ( produc755559506on_val @ B_4 @ C_9 ) ) )
=> ( P_15 @ X_4 ) ) ).
thf(fact_120_prod__induct3,axiom,
! [X_4: produc618524391on_val,P_15: produc618524391on_val > $o] :
( ! [A_1: produc1180562163on_val,B_4: list_exp_list_char,C_9: produc2090907612on_val] : ( P_15 @ ( produc747700183on_val @ A_1 @ ( produc1302104557on_val @ B_4 @ C_9 ) ) )
=> ( P_15 @ X_4 ) ) ).
thf(fact_121_prod__induct3,axiom,
! [X_4: produc1180562163on_val,P_15: produc1180562163on_val > $o] :
( ! [A_1: list_exp_list_char,B_4: nat > option1728594148on_val,C_9: list_char > option_val] : ( P_15 @ ( produc1302104557on_val @ A_1 @ ( produc755559506on_val @ B_4 @ C_9 ) ) )
=> ( P_15 @ X_4 ) ) ).
thf(fact_122_prod__induct3,axiom,
! [X_4: produc1285161482t_char,P_15: produc1285161482t_char > $o] :
( ! [A_1: list_list_char,B_4: list_ty,C_9: produc662261637t_char] : ( P_15 @ ( produc921874948t_char @ A_1 @ ( produc1909267824t_char @ B_4 @ C_9 ) ) )
=> ( P_15 @ X_4 ) ) ).
thf(fact_123_prod__induct3,axiom,
! [X_4: produc220283002t_char,P_15: produc220283002t_char > $o] :
( ! [A_1: list_ty,B_4: list_val,C_9: exp_list_char] : ( P_15 @ ( produc1909267824t_char @ A_1 @ ( produc1916172923t_char @ B_4 @ C_9 ) ) )
=> ( P_15 @ X_4 ) ) ).
thf(fact_124_prod__induct3,axiom,
! [X_4: produc1581780743on_val,P_15: produc1581780743on_val > $o] :
( ! [A_1: produc2090907612on_val,B_4: nat > option1728594148on_val,C_9: list_char > option_val] : ( P_15 @ ( produc259392253on_val @ A_1 @ ( produc755559506on_val @ B_4 @ C_9 ) ) )
=> ( P_15 @ X_4 ) ) ).
thf(fact_125_prod__induct3,axiom,
! [X_4: produc652964533on_val,P_15: produc652964533on_val > $o] :
( ! [A_1: produc1746408499on_val,B_4: produc1282892786on_val,C_9: produc1282892786on_val] : ( P_15 @ ( produc345758123on_val @ A_1 @ ( produc833389609on_val @ B_4 @ C_9 ) ) )
=> ( P_15 @ X_4 ) ) ).
thf(fact_126_prod__induct3,axiom,
! [X_4: produc1250491293on_val,P_15: produc1250491293on_val > $o] :
( ! [A_1: produc618524391on_val,B_4: produc1180562163on_val,C_9: produc1180562163on_val] : ( P_15 @ ( produc1347028499on_val @ A_1 @ ( produc747700183on_val @ B_4 @ C_9 ) ) )
=> ( P_15 @ X_4 ) ) ).
thf(fact_127_prod__induct3,axiom,
! [X_4: produc349695911t_char,P_15: produc349695911t_char > $o] :
( ! [A_1: produc1285161482t_char,B_4: list_list_char,C_9: produc220283002t_char] : ( P_15 @ ( produc24551831t_char @ A_1 @ ( produc921874948t_char @ B_4 @ C_9 ) ) )
=> ( P_15 @ X_4 ) ) ).
thf(fact_128_prod__induct3,axiom,
! [X_4: produc1406897475t_char,P_15: produc1406897475t_char > $o] :
( ! [A_1: produc220283002t_char,B_4: list_ty,C_9: produc662261637t_char] : ( P_15 @ ( produc57279289t_char @ A_1 @ ( produc1909267824t_char @ B_4 @ C_9 ) ) )
=> ( P_15 @ X_4 ) ) ).
thf(fact_129_prod__induct3,axiom,
! [X_4: produc1826280281t_char,P_15: produc1826280281t_char > $o] :
( ! [A_1: produc662261637t_char,B_4: list_val,C_9: exp_list_char] : ( P_15 @ ( produc1299387215t_char @ A_1 @ ( produc1916172923t_char @ B_4 @ C_9 ) ) )
=> ( P_15 @ X_4 ) ) ).
thf(fact_130_prod__induct3,axiom,
! [X_4: produc1368416213on_val,P_15: produc1368416213on_val > $o] :
( ! [A_1: produc2088785539on_val,B_4: list_char,C_9: produc1278157519t_char > option_val] : ( P_15 @ ( produc1773146955on_val @ A_1 @ ( produc926070009on_val @ B_4 @ C_9 ) ) )
=> ( P_15 @ X_4 ) ) ).
thf(fact_131_prod__induct3,axiom,
! [X_4: produc1350825965t_char,P_15: produc1350825965t_char > $o] :
( ! [A_1: produc1278157519t_char,B_4: list_char,C_9: list_char] : ( P_15 @ ( produc2080520419t_char @ A_1 @ ( produc5062597t_char @ B_4 @ C_9 ) ) )
=> ( P_15 @ X_4 ) ) ).
thf(fact_132_red__hext__incr,axiom,
! [E: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,E_2: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ L ) ) @ ( produc235638504on_val @ E_2 @ ( produc755559506on_val @ H_1 @ L_1 ) ) ) @ ( red @ P ) )
=> ( hext @ H @ H_1 ) ) ).
thf(fact_133_red__lcl__add,axiom,
! [L_0: list_char > option_val,E: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,E_2: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ L ) ) @ ( produc235638504on_val @ E_2 @ ( produc755559506on_val @ H_1 @ L_1 ) ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ ( map_ad325961431ar_val @ L_0 @ L ) ) ) @ ( produc235638504on_val @ E_2 @ ( produc755559506on_val @ H_1 @ ( map_ad325961431ar_val @ L_0 @ L_1 ) ) ) ) @ ( red @ P ) ) ) ).
thf(fact_134_prod_Oexhaust,axiom,
! [Y_1: produc1350825965t_char] :
~ ! [A_1: produc1278157519t_char,B_4: produc1278157519t_char] :
( Y_1
!= ( produc2080520419t_char @ A_1 @ B_4 ) ) ).
thf(fact_135_prod_Oexhaust,axiom,
! [Y_1: produc1368416213on_val] :
~ ! [A_1: produc2088785539on_val,B_4: produc2088785539on_val] :
( Y_1
!= ( produc1773146955on_val @ A_1 @ B_4 ) ) ).
thf(fact_136_prod_Oexhaust,axiom,
! [Y_1: produc1826280281t_char] :
~ ! [A_1: produc662261637t_char,B_4: produc662261637t_char] :
( Y_1
!= ( produc1299387215t_char @ A_1 @ B_4 ) ) ).
thf(fact_137_prod_Oexhaust,axiom,
! [Y_1: produc1406897475t_char] :
~ ! [A_1: produc220283002t_char,B_4: produc220283002t_char] :
( Y_1
!= ( produc57279289t_char @ A_1 @ B_4 ) ) ).
thf(fact_138_prod_Oexhaust,axiom,
! [Y_1: produc349695911t_char] :
~ ! [A_1: produc1285161482t_char,B_4: produc1285161482t_char] :
( Y_1
!= ( produc24551831t_char @ A_1 @ B_4 ) ) ).
thf(fact_139_prod_Oexhaust,axiom,
! [Y_1: produc1250491293on_val] :
~ ! [A_1: produc618524391on_val,B_4: produc618524391on_val] :
( Y_1
!= ( produc1347028499on_val @ A_1 @ B_4 ) ) ).
thf(fact_140_prod_Oexhaust,axiom,
! [Y_1: produc652964533on_val] :
~ ! [A_1: produc1746408499on_val,B_4: produc1746408499on_val] :
( Y_1
!= ( produc345758123on_val @ A_1 @ B_4 ) ) ).
thf(fact_141_prod_Oexhaust,axiom,
! [Y_1: produc1581780743on_val] :
~ ! [A_1: produc2090907612on_val,B_4: produc2090907612on_val] :
( Y_1
!= ( produc259392253on_val @ A_1 @ B_4 ) ) ).
thf(fact_142_prod_Oexhaust,axiom,
! [Y_1: produc2090907612on_val] :
~ ! [A_1: nat > option1728594148on_val,B_4: list_char > option_val] :
( Y_1
!= ( produc755559506on_val @ A_1 @ B_4 ) ) ).
thf(fact_143_prod_Oexhaust,axiom,
! [Y_1: produc1746408499on_val] :
~ ! [A_1: produc1282892786on_val,B_4: produc1282892786on_val] :
( Y_1
!= ( produc833389609on_val @ A_1 @ B_4 ) ) ).
thf(fact_144_prod_Oexhaust,axiom,
! [Y_1: produc1282892786on_val] :
~ ! [A_1: exp_list_char,B_4: produc2090907612on_val] :
( Y_1
!= ( produc235638504on_val @ A_1 @ B_4 ) ) ).
thf(fact_145_prod_Oexhaust,axiom,
! [Y_1: produc618524391on_val] :
~ ! [A_1: produc1180562163on_val,B_4: produc1180562163on_val] :
( Y_1
!= ( produc747700183on_val @ A_1 @ B_4 ) ) ).
thf(fact_146_prod_Oexhaust,axiom,
! [Y_1: produc1180562163on_val] :
~ ! [A_1: list_exp_list_char,B_4: produc2090907612on_val] :
( Y_1
!= ( produc1302104557on_val @ A_1 @ B_4 ) ) ).
thf(fact_147_prod_Oexhaust,axiom,
! [Y_1: produc1285161482t_char] :
~ ! [A_1: list_list_char,B_4: produc220283002t_char] :
( Y_1
!= ( produc921874948t_char @ A_1 @ B_4 ) ) ).
thf(fact_148_prod_Oexhaust,axiom,
! [Y_1: produc220283002t_char] :
~ ! [A_1: list_ty,B_4: produc662261637t_char] :
( Y_1
!= ( produc1909267824t_char @ A_1 @ B_4 ) ) ).
thf(fact_149_prod_Oexhaust,axiom,
! [Y_1: produc662261637t_char] :
~ ! [A_1: list_val,B_4: exp_list_char] :
( Y_1
!= ( produc1916172923t_char @ A_1 @ B_4 ) ) ).
thf(fact_150_prod_Oexhaust,axiom,
! [Y_1: produc2088785539on_val] :
~ ! [A_1: list_char,B_4: produc1278157519t_char > option_val] :
( Y_1
!= ( produc926070009on_val @ A_1 @ B_4 ) ) ).
thf(fact_151_prod_Oexhaust,axiom,
! [Y_1: produc1278157519t_char] :
~ ! [A_1: list_char,B_4: list_char] :
( Y_1
!= ( produc5062597t_char @ A_1 @ B_4 ) ) ).
thf(fact_152_PairE,axiom,
! [P_14: produc1350825965t_char] :
~ ! [X_1: produc1278157519t_char,Y: produc1278157519t_char] :
( P_14
!= ( produc2080520419t_char @ X_1 @ Y ) ) ).
thf(fact_153_PairE,axiom,
! [P_14: produc1368416213on_val] :
~ ! [X_1: produc2088785539on_val,Y: produc2088785539on_val] :
( P_14
!= ( produc1773146955on_val @ X_1 @ Y ) ) ).
thf(fact_154_PairE,axiom,
! [P_14: produc1826280281t_char] :
~ ! [X_1: produc662261637t_char,Y: produc662261637t_char] :
( P_14
!= ( produc1299387215t_char @ X_1 @ Y ) ) ).
thf(fact_155_PairE,axiom,
! [P_14: produc1406897475t_char] :
~ ! [X_1: produc220283002t_char,Y: produc220283002t_char] :
( P_14
!= ( produc57279289t_char @ X_1 @ Y ) ) ).
thf(fact_156_PairE,axiom,
! [P_14: produc349695911t_char] :
~ ! [X_1: produc1285161482t_char,Y: produc1285161482t_char] :
( P_14
!= ( produc24551831t_char @ X_1 @ Y ) ) ).
thf(fact_157_PairE,axiom,
! [P_14: produc1250491293on_val] :
~ ! [X_1: produc618524391on_val,Y: produc618524391on_val] :
( P_14
!= ( produc1347028499on_val @ X_1 @ Y ) ) ).
thf(fact_158_PairE,axiom,
! [P_14: produc652964533on_val] :
~ ! [X_1: produc1746408499on_val,Y: produc1746408499on_val] :
( P_14
!= ( produc345758123on_val @ X_1 @ Y ) ) ).
thf(fact_159_PairE,axiom,
! [P_14: produc1581780743on_val] :
~ ! [X_1: produc2090907612on_val,Y: produc2090907612on_val] :
( P_14
!= ( produc259392253on_val @ X_1 @ Y ) ) ).
thf(fact_160_PairE,axiom,
! [P_14: produc2090907612on_val] :
~ ! [X_1: nat > option1728594148on_val,Y: list_char > option_val] :
( P_14
!= ( produc755559506on_val @ X_1 @ Y ) ) ).
thf(fact_161_PairE,axiom,
! [P_14: produc1746408499on_val] :
~ ! [X_1: produc1282892786on_val,Y: produc1282892786on_val] :
( P_14
!= ( produc833389609on_val @ X_1 @ Y ) ) ).
thf(fact_162_PairE,axiom,
! [P_14: produc1282892786on_val] :
~ ! [X_1: exp_list_char,Y: produc2090907612on_val] :
( P_14
!= ( produc235638504on_val @ X_1 @ Y ) ) ).
thf(fact_163_PairE,axiom,
! [P_14: produc618524391on_val] :
~ ! [X_1: produc1180562163on_val,Y: produc1180562163on_val] :
( P_14
!= ( produc747700183on_val @ X_1 @ Y ) ) ).
thf(fact_164_PairE,axiom,
! [P_14: produc1180562163on_val] :
~ ! [X_1: list_exp_list_char,Y: produc2090907612on_val] :
( P_14
!= ( produc1302104557on_val @ X_1 @ Y ) ) ).
thf(fact_165_PairE,axiom,
! [P_14: produc1285161482t_char] :
~ ! [X_1: list_list_char,Y: produc220283002t_char] :
( P_14
!= ( produc921874948t_char @ X_1 @ Y ) ) ).
thf(fact_166_PairE,axiom,
! [P_14: produc220283002t_char] :
~ ! [X_1: list_ty,Y: produc662261637t_char] :
( P_14
!= ( produc1909267824t_char @ X_1 @ Y ) ) ).
thf(fact_167_PairE,axiom,
! [P_14: produc662261637t_char] :
~ ! [X_1: list_val,Y: exp_list_char] :
( P_14
!= ( produc1916172923t_char @ X_1 @ Y ) ) ).
thf(fact_168_PairE,axiom,
! [P_14: produc2088785539on_val] :
~ ! [X_1: list_char,Y: produc1278157519t_char > option_val] :
( P_14
!= ( produc926070009on_val @ X_1 @ Y ) ) ).
thf(fact_169_PairE,axiom,
! [P_14: produc1278157519t_char] :
~ ! [X_1: list_char,Y: list_char] :
( P_14
!= ( produc5062597t_char @ X_1 @ Y ) ) ).
thf(fact_170_WTrt__hext__mono,axiom,
! [H_1: nat > option1728594148on_val,P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: list_char > option_ty,E: exp_list_char,T: ty] :
( ( wTrt @ P @ H @ E_1 @ E @ T )
=> ( ( hext @ H @ H_1 )
=> ( wTrt @ P @ H_1 @ E_1 @ E @ T ) ) ) ).
thf(fact_171_hext__refl,axiom,
! [H: nat > option1728594148on_val] : ( hext @ H @ H ) ).
thf(fact_172_lconf__hext,axiom,
! [H_5: nat > option1728594148on_val,P_13: list_P1999446415t_char,H_4: nat > option1728594148on_val,L_3: list_char > option_val,E_6: list_char > option_ty] :
( ( lconf_496643946t_char @ P_13 @ H_4 @ L_3 @ E_6 )
=> ( ( hext @ H_4 @ H_5 )
=> ( lconf_496643946t_char @ P_13 @ H_5 @ L_3 @ E_6 ) ) ) ).
thf(fact_173_Red__lcl__add,axiom,
! [L_0: list_char > option_val,E: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,E_2: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ L ) ) @ ( produc235638504on_val @ E_2 @ ( produc755559506on_val @ H_1 @ L_1 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ ( map_ad325961431ar_val @ L_0 @ L ) ) ) @ ( produc235638504on_val @ E_2 @ ( produc755559506on_val @ H_1 @ ( map_ad325961431ar_val @ L_0 @ L_1 ) ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_174_pred__equals__eq2,axiom,
! [S_4: produc1350825965t_char > $o,R_13: produc1350825965t_char > $o] :
( ! [X_1: produc1278157519t_char,Xa: produc1278157519t_char] :
( ( member794220506t_char @ ( produc2080520419t_char @ X_1 @ Xa ) @ R_13 )
<=> ( member794220506t_char @ ( produc2080520419t_char @ X_1 @ Xa ) @ S_4 ) )
<=> ( R_13 = S_4 ) ) ).
thf(fact_175_pred__equals__eq2,axiom,
! [S_4: produc1368416213on_val > $o,R_13: produc1368416213on_val > $o] :
( ! [X_1: produc2088785539on_val,Xa: produc2088785539on_val] :
( ( member1235075778on_val @ ( produc1773146955on_val @ X_1 @ Xa ) @ R_13 )
<=> ( member1235075778on_val @ ( produc1773146955on_val @ X_1 @ Xa ) @ S_4 ) )
<=> ( R_13 = S_4 ) ) ).
thf(fact_176_pred__equals__eq2,axiom,
! [S_4: produc1826280281t_char > $o,R_13: produc1826280281t_char > $o] :
( ! [X_1: produc662261637t_char,Xa: produc662261637t_char] :
( ( member1161907014t_char @ ( produc1299387215t_char @ X_1 @ Xa ) @ R_13 )
<=> ( member1161907014t_char @ ( produc1299387215t_char @ X_1 @ Xa ) @ S_4 ) )
<=> ( R_13 = S_4 ) ) ).
thf(fact_177_pred__equals__eq2,axiom,
! [S_4: produc1406897475t_char > $o,R_13: produc1406897475t_char > $o] :
( ! [X_1: produc220283002t_char,Xa: produc220283002t_char] :
( ( member125098544t_char @ ( produc57279289t_char @ X_1 @ Xa ) @ R_13 )
<=> ( member125098544t_char @ ( produc57279289t_char @ X_1 @ Xa ) @ S_4 ) )
<=> ( R_13 = S_4 ) ) ).
thf(fact_178_pred__equals__eq2,axiom,
! [S_4: produc349695911t_char > $o,R_13: produc349695911t_char > $o] :
( ! [X_1: produc1285161482t_char,Xa: produc1285161482t_char] :
( ( member1420286996t_char @ ( produc24551831t_char @ X_1 @ Xa ) @ R_13 )
<=> ( member1420286996t_char @ ( produc24551831t_char @ X_1 @ Xa ) @ S_4 ) )
<=> ( R_13 = S_4 ) ) ).
thf(fact_179_pred__equals__eq2,axiom,
! [S_4: produc1250491293on_val > $o,R_13: produc1250491293on_val > $o] :
( ! [X_1: produc618524391on_val,Xa: produc618524391on_val] :
( ( member1145216138on_val @ ( produc1347028499on_val @ X_1 @ Xa ) @ R_13 )
<=> ( member1145216138on_val @ ( produc1347028499on_val @ X_1 @ Xa ) @ S_4 ) )
<=> ( R_13 = S_4 ) ) ).
thf(fact_180_pred__equals__eq2,axiom,
! [S_4: produc652964533on_val > $o,R_13: produc652964533on_val > $o] :
( ! [X_1: produc1746408499on_val,Xa: produc1746408499on_val] :
( ( member1714424482on_val @ ( produc345758123on_val @ X_1 @ Xa ) @ R_13 )
<=> ( member1714424482on_val @ ( produc345758123on_val @ X_1 @ Xa ) @ S_4 ) )
<=> ( R_13 = S_4 ) ) ).
thf(fact_181_pred__equals__eq2,axiom,
! [S_4: produc1581780743on_val > $o,R_13: produc1581780743on_val > $o] :
( ! [X_1: produc2090907612on_val,Xa: produc2090907612on_val] :
( ( member565037556on_val @ ( produc259392253on_val @ X_1 @ Xa ) @ R_13 )
<=> ( member565037556on_val @ ( produc259392253on_val @ X_1 @ Xa ) @ S_4 ) )
<=> ( R_13 = S_4 ) ) ).
thf(fact_182_pred__equals__eq2,axiom,
! [S_4: produc2090907612on_val > $o,R_13: produc2090907612on_val > $o] :
( ! [X_1: nat > option1728594148on_val,Xa: list_char > option_val] :
( ( member1846553161on_val @ ( produc755559506on_val @ X_1 @ Xa ) @ R_13 )
<=> ( member1846553161on_val @ ( produc755559506on_val @ X_1 @ Xa ) @ S_4 ) )
<=> ( R_13 = S_4 ) ) ).
thf(fact_183_pred__equals__eq2,axiom,
! [S_4: produc1282892786on_val > $o,R_13: produc1282892786on_val > $o] :
( ! [X_1: exp_list_char,Xa: produc2090907612on_val] :
( ( member1072200031on_val @ ( produc235638504on_val @ X_1 @ Xa ) @ R_13 )
<=> ( member1072200031on_val @ ( produc235638504on_val @ X_1 @ Xa ) @ S_4 ) )
<=> ( R_13 = S_4 ) ) ).
thf(fact_184_pred__equals__eq2,axiom,
! [S_4: produc1180562163on_val > $o,R_13: produc1180562163on_val > $o] :
( ! [X_1: list_exp_list_char,Xa: produc2090907612on_val] :
( ( member1224782662on_val @ ( produc1302104557on_val @ X_1 @ Xa ) @ R_13 )
<=> ( member1224782662on_val @ ( produc1302104557on_val @ X_1 @ Xa ) @ S_4 ) )
<=> ( R_13 = S_4 ) ) ).
thf(fact_185_pred__equals__eq2,axiom,
! [S_4: produc1285161482t_char > $o,R_13: produc1285161482t_char > $o] :
( ! [X_1: list_list_char,Xa: produc220283002t_char] :
( ( member133545693t_char @ ( produc921874948t_char @ X_1 @ Xa ) @ R_13 )
<=> ( member133545693t_char @ ( produc921874948t_char @ X_1 @ Xa ) @ S_4 ) )
<=> ( R_13 = S_4 ) ) ).
thf(fact_186_pred__equals__eq2,axiom,
! [S_4: produc220283002t_char > $o,R_13: produc220283002t_char > $o] :
( ! [X_1: list_ty,Xa: produc662261637t_char] :
( ( member140606439t_char @ ( produc1909267824t_char @ X_1 @ Xa ) @ R_13 )
<=> ( member140606439t_char @ ( produc1909267824t_char @ X_1 @ Xa ) @ S_4 ) )
<=> ( R_13 = S_4 ) ) ).
thf(fact_187_pred__equals__eq2,axiom,
! [S_4: produc662261637t_char > $o,R_13: produc662261637t_char > $o] :
( ! [X_1: list_val,Xa: exp_list_char] :
( ( member699351154t_char @ ( produc1916172923t_char @ X_1 @ Xa ) @ R_13 )
<=> ( member699351154t_char @ ( produc1916172923t_char @ X_1 @ Xa ) @ S_4 ) )
<=> ( R_13 = S_4 ) ) ).
thf(fact_188_pred__equals__eq2,axiom,
! [S_4: produc2088785539on_val > $o,R_13: produc2088785539on_val > $o] :
( ! [X_1: list_char,Xa: produc1278157519t_char > option_val] :
( ( member1374264560on_val @ ( produc926070009on_val @ X_1 @ Xa ) @ R_13 )
<=> ( member1374264560on_val @ ( produc926070009on_val @ X_1 @ Xa ) @ S_4 ) )
<=> ( R_13 = S_4 ) ) ).
thf(fact_189_pred__equals__eq2,axiom,
! [S_4: produc1278157519t_char > $o,R_13: produc1278157519t_char > $o] :
( ! [X_1: list_char,Xa: list_char] :
( ( member1251428284t_char @ ( produc5062597t_char @ X_1 @ Xa ) @ R_13 )
<=> ( member1251428284t_char @ ( produc5062597t_char @ X_1 @ Xa ) @ S_4 ) )
<=> ( R_13 = S_4 ) ) ).
thf(fact_190_pred__equals__eq2,axiom,
! [S_4: produc1746408499on_val > $o,R_13: produc1746408499on_val > $o] :
( ! [X_1: produc1282892786on_val,Xa: produc1282892786on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ X_1 @ Xa ) @ R_13 )
<=> ( member1913460000on_val @ ( produc833389609on_val @ X_1 @ Xa ) @ S_4 ) )
<=> ( R_13 = S_4 ) ) ).
thf(fact_191_pred__equals__eq2,axiom,
! [S_4: produc618524391on_val > $o,R_13: produc618524391on_val > $o] :
( ! [X_1: produc1180562163on_val,Xa: produc1180562163on_val] :
( ( member2042188884on_val @ ( produc747700183on_val @ X_1 @ Xa ) @ R_13 )
<=> ( member2042188884on_val @ ( produc747700183on_val @ X_1 @ Xa ) @ S_4 ) )
<=> ( R_13 = S_4 ) ) ).
thf(fact_192_split__paired__Ex,axiom,
! [P_12: produc1350825965t_char > $o] :
( ( ?? @ produc1350825965t_char @ P_12 )
<=> ? [A_1: produc1278157519t_char,B_4: produc1278157519t_char] : ( P_12 @ ( produc2080520419t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_193_split__paired__Ex,axiom,
! [P_12: produc1368416213on_val > $o] :
( ( ?? @ produc1368416213on_val @ P_12 )
<=> ? [A_1: produc2088785539on_val,B_4: produc2088785539on_val] : ( P_12 @ ( produc1773146955on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_194_split__paired__Ex,axiom,
! [P_12: produc1826280281t_char > $o] :
( ( ?? @ produc1826280281t_char @ P_12 )
<=> ? [A_1: produc662261637t_char,B_4: produc662261637t_char] : ( P_12 @ ( produc1299387215t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_195_split__paired__Ex,axiom,
! [P_12: produc1406897475t_char > $o] :
( ( ?? @ produc1406897475t_char @ P_12 )
<=> ? [A_1: produc220283002t_char,B_4: produc220283002t_char] : ( P_12 @ ( produc57279289t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_196_split__paired__Ex,axiom,
! [P_12: produc349695911t_char > $o] :
( ( ?? @ produc349695911t_char @ P_12 )
<=> ? [A_1: produc1285161482t_char,B_4: produc1285161482t_char] : ( P_12 @ ( produc24551831t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_197_split__paired__Ex,axiom,
! [P_12: produc1250491293on_val > $o] :
( ( ?? @ produc1250491293on_val @ P_12 )
<=> ? [A_1: produc618524391on_val,B_4: produc618524391on_val] : ( P_12 @ ( produc1347028499on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_198_split__paired__Ex,axiom,
! [P_12: produc652964533on_val > $o] :
( ( ?? @ produc652964533on_val @ P_12 )
<=> ? [A_1: produc1746408499on_val,B_4: produc1746408499on_val] : ( P_12 @ ( produc345758123on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_199_split__paired__Ex,axiom,
! [P_12: produc1581780743on_val > $o] :
( ( ?? @ produc1581780743on_val @ P_12 )
<=> ? [A_1: produc2090907612on_val,B_4: produc2090907612on_val] : ( P_12 @ ( produc259392253on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_200_split__paired__Ex,axiom,
! [P_12: produc2090907612on_val > $o] :
( ( ?? @ produc2090907612on_val @ P_12 )
<=> ? [A_1: nat > option1728594148on_val,B_4: list_char > option_val] : ( P_12 @ ( produc755559506on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_201_split__paired__Ex,axiom,
! [P_12: produc1746408499on_val > $o] :
( ( ?? @ produc1746408499on_val @ P_12 )
<=> ? [A_1: produc1282892786on_val,B_4: produc1282892786on_val] : ( P_12 @ ( produc833389609on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_202_split__paired__Ex,axiom,
! [P_12: produc1282892786on_val > $o] :
( ( ?? @ produc1282892786on_val @ P_12 )
<=> ? [A_1: exp_list_char,B_4: produc2090907612on_val] : ( P_12 @ ( produc235638504on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_203_split__paired__Ex,axiom,
! [P_12: produc618524391on_val > $o] :
( ( ?? @ produc618524391on_val @ P_12 )
<=> ? [A_1: produc1180562163on_val,B_4: produc1180562163on_val] : ( P_12 @ ( produc747700183on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_204_split__paired__Ex,axiom,
! [P_12: produc1180562163on_val > $o] :
( ( ?? @ produc1180562163on_val @ P_12 )
<=> ? [A_1: list_exp_list_char,B_4: produc2090907612on_val] : ( P_12 @ ( produc1302104557on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_205_split__paired__Ex,axiom,
! [P_12: produc1285161482t_char > $o] :
( ( ?? @ produc1285161482t_char @ P_12 )
<=> ? [A_1: list_list_char,B_4: produc220283002t_char] : ( P_12 @ ( produc921874948t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_206_split__paired__Ex,axiom,
! [P_12: produc220283002t_char > $o] :
( ( ?? @ produc220283002t_char @ P_12 )
<=> ? [A_1: list_ty,B_4: produc662261637t_char] : ( P_12 @ ( produc1909267824t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_207_split__paired__Ex,axiom,
! [P_12: produc662261637t_char > $o] :
( ( ?? @ produc662261637t_char @ P_12 )
<=> ? [A_1: list_val,B_4: exp_list_char] : ( P_12 @ ( produc1916172923t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_208_split__paired__Ex,axiom,
! [P_12: produc2088785539on_val > $o] :
( ( ?? @ produc2088785539on_val @ P_12 )
<=> ? [A_1: list_char,B_4: produc1278157519t_char > option_val] : ( P_12 @ ( produc926070009on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_209_split__paired__Ex,axiom,
! [P_12: produc1278157519t_char > $o] :
( ( ?? @ produc1278157519t_char @ P_12 )
<=> ? [A_1: list_char,B_4: list_char] : ( P_12 @ ( produc5062597t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_210_internal__split__conv,axiom,
! [C_8: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,A_15: nat > option1728594148on_val,B_13: list_char > option_val] :
( ( produc575577405_val_o @ C_8 @ ( produc755559506on_val @ A_15 @ B_13 ) )
<=> ( C_8 @ A_15 @ B_13 ) ) ).
thf(fact_211_WTrtWhile,axiom,
! [C_1: exp_list_char,T: ty,P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: list_char > option_ty,E: exp_list_char] :
( ( wTrt @ P @ H @ E_1 @ E @ boolean )
=> ( ( wTrt @ P @ H @ E_1 @ C_1 @ T )
=> ( wTrt @ P @ H @ E_1 @ ( while_list_char @ E @ C_1 ) @ void ) ) ) ).
thf(fact_212_sconf__def,axiom,
! [P: list_P1999446415t_char,E_1: list_char > option_ty,S: produc2090907612on_val] :
( ( typeSa1102574168_sconf @ P @ E_1 @ S )
<=> ( produc252486962_val_o
@ ^ [H_3: nat > option1728594148on_val,L_2: list_char > option_val] : ( (&) @ ( hconf_97414254t_char @ P @ H_3 ) @ ( lconf_496643946t_char @ P @ H_3 @ L_2 @ E_1 ) )
@ S ) ) ).
thf(fact_213_WTrtCond,axiom,
! [T: ty,E_2_1: exp_list_char,T_2_1: ty,E_1_1: exp_list_char,T_1_1: ty,P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: list_char > option_ty,E: exp_list_char] :
( ( wTrt @ P @ H @ E_1 @ E @ boolean )
=> ( ( wTrt @ P @ H @ E_1 @ E_1_1 @ T_1_1 )
=> ( ( wTrt @ P @ H @ E_1 @ E_2_1 @ T_2_1 )
=> ( ( ( widen_2090681816t_char @ P @ T_1_1 @ T_2_1 )
| ( widen_2090681816t_char @ P @ T_2_1 @ T_1_1 ) )
=> ( ( ( widen_2090681816t_char @ P @ T_1_1 @ T_2_1 )
=> ( T = T_2_1 ) )
=> ( ( ( widen_2090681816t_char @ P @ T_2_1 @ T_1_1 )
=> ( T = T_1_1 ) )
=> ( wTrt @ P @ H @ E_1 @ ( cond_list_char @ E @ E_1_1 @ E_2_1 ) @ T ) ) ) ) ) ) ) ).
thf(fact_214_prod__caseI,axiom,
! [F1_1: produc1278157519t_char > produc1278157519t_char > $o,A_14: produc1278157519t_char,B_12: produc1278157519t_char] :
( ( F1_1 @ A_14 @ B_12 )
=> ( produc2056220769char_o @ F1_1 @ ( produc2080520419t_char @ A_14 @ B_12 ) ) ) ).
thf(fact_215_prod__caseI,axiom,
! [F1_1: produc2088785539on_val > produc2088785539on_val > $o,A_14: produc2088785539on_val,B_12: produc2088785539on_val] :
( ( F1_1 @ A_14 @ B_12 )
=> ( produc791773177_val_o @ F1_1 @ ( produc1773146955on_val @ A_14 @ B_12 ) ) ) ).
thf(fact_216_prod__caseI,axiom,
! [F1_1: produc662261637t_char > produc662261637t_char > $o,A_14: produc662261637t_char,B_12: produc662261637t_char] :
( ( F1_1 @ A_14 @ B_12 )
=> ( produc1537651445char_o @ F1_1 @ ( produc1299387215t_char @ A_14 @ B_12 ) ) ) ).
thf(fact_217_prod__caseI,axiom,
! [F1_1: produc220283002t_char > produc220283002t_char > $o,A_14: produc220283002t_char,B_12: produc220283002t_char] :
( ( F1_1 @ A_14 @ B_12 )
=> ( produc510191755char_o @ F1_1 @ ( produc57279289t_char @ A_14 @ B_12 ) ) ) ).
thf(fact_218_prod__caseI,axiom,
! [F1_1: produc1285161482t_char > produc1285161482t_char > $o,A_14: produc1285161482t_char,B_12: produc1285161482t_char] :
( ( F1_1 @ A_14 @ B_12 )
=> ( produc865480877char_o @ F1_1 @ ( produc24551831t_char @ A_14 @ B_12 ) ) ) ).
thf(fact_219_prod__caseI,axiom,
! [F1_1: produc618524391on_val > produc618524391on_val > $o,A_14: produc618524391on_val,B_12: produc618524391on_val] :
( ( F1_1 @ A_14 @ B_12 )
=> ( produc382956337_val_o @ F1_1 @ ( produc1347028499on_val @ A_14 @ B_12 ) ) ) ).
thf(fact_220_prod__caseI,axiom,
! [F1_1: produc1746408499on_val > produc1746408499on_val > $o,A_14: produc1746408499on_val,B_12: produc1746408499on_val] :
( ( F1_1 @ A_14 @ B_12 )
=> ( produc154389913_val_o @ F1_1 @ ( produc345758123on_val @ A_14 @ B_12 ) ) ) ).
thf(fact_221_prod__caseI,axiom,
! [F1_1: produc2090907612on_val > produc2090907612on_val > $o,A_14: produc2090907612on_val,B_12: produc2090907612on_val] :
( ( F1_1 @ A_14 @ B_12 )
=> ( produc1377568711_val_o @ F1_1 @ ( produc259392253on_val @ A_14 @ B_12 ) ) ) ).
thf(fact_222_prod__caseI,axiom,
! [F1_1: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,A_14: nat > option1728594148on_val,B_12: list_char > option_val] :
( ( F1_1 @ A_14 @ B_12 )
=> ( produc252486962_val_o @ F1_1 @ ( produc755559506on_val @ A_14 @ B_12 ) ) ) ).
thf(fact_223_prod__caseI,axiom,
! [F1_1: produc1282892786on_val > produc1282892786on_val > $o,A_14: produc1282892786on_val,B_12: produc1282892786on_val] :
( ( F1_1 @ A_14 @ B_12 )
=> ( produc1624062875_val_o @ F1_1 @ ( produc833389609on_val @ A_14 @ B_12 ) ) ) ).
thf(fact_224_prod__caseI,axiom,
! [F1_1: exp_list_char > produc2090907612on_val > $o,A_14: exp_list_char,B_12: produc2090907612on_val] :
( ( F1_1 @ A_14 @ B_12 )
=> ( produc1835097372_val_o @ F1_1 @ ( produc235638504on_val @ A_14 @ B_12 ) ) ) ).
thf(fact_225_prod__caseI,axiom,
! [F1_1: produc1180562163on_val > produc1180562163on_val > $o,A_14: produc1180562163on_val,B_12: produc1180562163on_val] :
( ( F1_1 @ A_14 @ B_12 )
=> ( produc2136448621_val_o @ F1_1 @ ( produc747700183on_val @ A_14 @ B_12 ) ) ) ).
thf(fact_226_prod__caseI,axiom,
! [F1_1: list_exp_list_char > produc2090907612on_val > $o,A_14: list_exp_list_char,B_12: produc2090907612on_val] :
( ( F1_1 @ A_14 @ B_12 )
=> ( produc1841295295_val_o @ F1_1 @ ( produc1302104557on_val @ A_14 @ B_12 ) ) ) ).
thf(fact_227_prod__caseI,axiom,
! [F1_1: list_list_char > produc220283002t_char > $o,A_14: list_list_char,B_12: produc220283002t_char] :
( ( F1_1 @ A_14 @ B_12 )
=> ( produc1530867176char_o @ F1_1 @ ( produc921874948t_char @ A_14 @ B_12 ) ) ) ).
thf(fact_228_prod__caseI,axiom,
! [F1_1: list_ty > produc662261637t_char > $o,A_14: list_ty,B_12: produc662261637t_char] :
( ( F1_1 @ A_14 @ B_12 )
=> ( produc861054100char_o @ F1_1 @ ( produc1909267824t_char @ A_14 @ B_12 ) ) ) ).
thf(fact_229_prod__caseI,axiom,
! [F1_1: list_val > exp_list_char > $o,A_14: list_val,B_12: exp_list_char] :
( ( F1_1 @ A_14 @ B_12 )
=> ( produc525137097char_o @ F1_1 @ ( produc1916172923t_char @ A_14 @ B_12 ) ) ) ).
thf(fact_230_prod__caseI,axiom,
! [F1_1: list_char > ( produc1278157519t_char > option_val ) > $o,A_14: list_char,B_12: produc1278157519t_char > option_val] :
( ( F1_1 @ A_14 @ B_12 )
=> ( produc765165771_val_o @ F1_1 @ ( produc926070009on_val @ A_14 @ B_12 ) ) ) ).
thf(fact_231_prod__caseI,axiom,
! [F1_1: list_char > list_char > $o,A_14: list_char,B_12: list_char] :
( ( F1_1 @ A_14 @ B_12 )
=> ( produc282231039char_o @ F1_1 @ ( produc5062597t_char @ A_14 @ B_12 ) ) ) ).
thf(fact_232_splitI,axiom,
! [F_6: produc1278157519t_char > produc1278157519t_char > $o,A_13: produc1278157519t_char,B_11: produc1278157519t_char] :
( ( F_6 @ A_13 @ B_11 )
=> ( produc2056220769char_o @ F_6 @ ( produc2080520419t_char @ A_13 @ B_11 ) ) ) ).
thf(fact_233_splitI,axiom,
! [F_6: produc2088785539on_val > produc2088785539on_val > $o,A_13: produc2088785539on_val,B_11: produc2088785539on_val] :
( ( F_6 @ A_13 @ B_11 )
=> ( produc791773177_val_o @ F_6 @ ( produc1773146955on_val @ A_13 @ B_11 ) ) ) ).
thf(fact_234_splitI,axiom,
! [F_6: produc662261637t_char > produc662261637t_char > $o,A_13: produc662261637t_char,B_11: produc662261637t_char] :
( ( F_6 @ A_13 @ B_11 )
=> ( produc1537651445char_o @ F_6 @ ( produc1299387215t_char @ A_13 @ B_11 ) ) ) ).
thf(fact_235_splitI,axiom,
! [F_6: produc220283002t_char > produc220283002t_char > $o,A_13: produc220283002t_char,B_11: produc220283002t_char] :
( ( F_6 @ A_13 @ B_11 )
=> ( produc510191755char_o @ F_6 @ ( produc57279289t_char @ A_13 @ B_11 ) ) ) ).
thf(fact_236_splitI,axiom,
! [F_6: produc1285161482t_char > produc1285161482t_char > $o,A_13: produc1285161482t_char,B_11: produc1285161482t_char] :
( ( F_6 @ A_13 @ B_11 )
=> ( produc865480877char_o @ F_6 @ ( produc24551831t_char @ A_13 @ B_11 ) ) ) ).
thf(fact_237_splitI,axiom,
! [F_6: produc618524391on_val > produc618524391on_val > $o,A_13: produc618524391on_val,B_11: produc618524391on_val] :
( ( F_6 @ A_13 @ B_11 )
=> ( produc382956337_val_o @ F_6 @ ( produc1347028499on_val @ A_13 @ B_11 ) ) ) ).
thf(fact_238_splitI,axiom,
! [F_6: produc1746408499on_val > produc1746408499on_val > $o,A_13: produc1746408499on_val,B_11: produc1746408499on_val] :
( ( F_6 @ A_13 @ B_11 )
=> ( produc154389913_val_o @ F_6 @ ( produc345758123on_val @ A_13 @ B_11 ) ) ) ).
thf(fact_239_splitI,axiom,
! [F_6: produc2090907612on_val > produc2090907612on_val > $o,A_13: produc2090907612on_val,B_11: produc2090907612on_val] :
( ( F_6 @ A_13 @ B_11 )
=> ( produc1377568711_val_o @ F_6 @ ( produc259392253on_val @ A_13 @ B_11 ) ) ) ).
thf(fact_240_splitI,axiom,
! [F_6: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,A_13: nat > option1728594148on_val,B_11: list_char > option_val] :
( ( F_6 @ A_13 @ B_11 )
=> ( produc252486962_val_o @ F_6 @ ( produc755559506on_val @ A_13 @ B_11 ) ) ) ).
thf(fact_241_splitI,axiom,
! [F_6: produc1282892786on_val > produc1282892786on_val > $o,A_13: produc1282892786on_val,B_11: produc1282892786on_val] :
( ( F_6 @ A_13 @ B_11 )
=> ( produc1624062875_val_o @ F_6 @ ( produc833389609on_val @ A_13 @ B_11 ) ) ) ).
thf(fact_242_splitI,axiom,
! [F_6: exp_list_char > produc2090907612on_val > $o,A_13: exp_list_char,B_11: produc2090907612on_val] :
( ( F_6 @ A_13 @ B_11 )
=> ( produc1835097372_val_o @ F_6 @ ( produc235638504on_val @ A_13 @ B_11 ) ) ) ).
thf(fact_243_splitI,axiom,
! [F_6: produc1180562163on_val > produc1180562163on_val > $o,A_13: produc1180562163on_val,B_11: produc1180562163on_val] :
( ( F_6 @ A_13 @ B_11 )
=> ( produc2136448621_val_o @ F_6 @ ( produc747700183on_val @ A_13 @ B_11 ) ) ) ).
thf(fact_244_splitI,axiom,
! [F_6: list_exp_list_char > produc2090907612on_val > $o,A_13: list_exp_list_char,B_11: produc2090907612on_val] :
( ( F_6 @ A_13 @ B_11 )
=> ( produc1841295295_val_o @ F_6 @ ( produc1302104557on_val @ A_13 @ B_11 ) ) ) ).
thf(fact_245_splitI,axiom,
! [F_6: list_list_char > produc220283002t_char > $o,A_13: list_list_char,B_11: produc220283002t_char] :
( ( F_6 @ A_13 @ B_11 )
=> ( produc1530867176char_o @ F_6 @ ( produc921874948t_char @ A_13 @ B_11 ) ) ) ).
thf(fact_246_splitI,axiom,
! [F_6: list_ty > produc662261637t_char > $o,A_13: list_ty,B_11: produc662261637t_char] :
( ( F_6 @ A_13 @ B_11 )
=> ( produc861054100char_o @ F_6 @ ( produc1909267824t_char @ A_13 @ B_11 ) ) ) ).
thf(fact_247_splitI,axiom,
! [F_6: list_val > exp_list_char > $o,A_13: list_val,B_11: exp_list_char] :
( ( F_6 @ A_13 @ B_11 )
=> ( produc525137097char_o @ F_6 @ ( produc1916172923t_char @ A_13 @ B_11 ) ) ) ).
thf(fact_248_splitI,axiom,
! [F_6: list_char > ( produc1278157519t_char > option_val ) > $o,A_13: list_char,B_11: produc1278157519t_char > option_val] :
( ( F_6 @ A_13 @ B_11 )
=> ( produc765165771_val_o @ F_6 @ ( produc926070009on_val @ A_13 @ B_11 ) ) ) ).
thf(fact_249_splitI,axiom,
! [F_6: list_char > list_char > $o,A_13: list_char,B_11: list_char] :
( ( F_6 @ A_13 @ B_11 )
=> ( produc282231039char_o @ F_6 @ ( produc5062597t_char @ A_13 @ B_11 ) ) ) ).
thf(fact_250_split__part,axiom,
! [P_11: $o,Q_2: list_char > list_char > $o,X_1: produc1278157519t_char] :
( ( produc282231039char_o
@ ^ [A_1: list_char,B_4: list_char] : ( (&) @ P_11 @ ( Q_2 @ A_1 @ B_4 ) )
@ X_1 )
<=> ( P_11
& ( produc282231039char_o @ Q_2 @ X_1 ) ) ) ).
thf(fact_251_split__part,axiom,
! [P_11: $o,Q_2: list_char > ( produc1278157519t_char > option_val ) > $o,X_1: produc2088785539on_val] :
( ( produc765165771_val_o
@ ^ [A_1: list_char,B_4: produc1278157519t_char > option_val] : ( (&) @ P_11 @ ( Q_2 @ A_1 @ B_4 ) )
@ X_1 )
<=> ( P_11
& ( produc765165771_val_o @ Q_2 @ X_1 ) ) ) ).
thf(fact_252_split__part,axiom,
! [P_11: $o,Q_2: list_val > exp_list_char > $o,X_1: produc662261637t_char] :
( ( produc525137097char_o
@ ^ [A_1: list_val,B_4: exp_list_char] : ( (&) @ P_11 @ ( Q_2 @ A_1 @ B_4 ) )
@ X_1 )
<=> ( P_11
& ( produc525137097char_o @ Q_2 @ X_1 ) ) ) ).
thf(fact_253_split__part,axiom,
! [P_11: $o,Q_2: list_ty > produc662261637t_char > $o,X_1: produc220283002t_char] :
( ( produc861054100char_o
@ ^ [A_1: list_ty,B_4: produc662261637t_char] : ( (&) @ P_11 @ ( Q_2 @ A_1 @ B_4 ) )
@ X_1 )
<=> ( P_11
& ( produc861054100char_o @ Q_2 @ X_1 ) ) ) ).
thf(fact_254_split__part,axiom,
! [P_11: $o,Q_2: list_list_char > produc220283002t_char > $o,X_1: produc1285161482t_char] :
( ( produc1530867176char_o
@ ^ [A_1: list_list_char,B_4: produc220283002t_char] : ( (&) @ P_11 @ ( Q_2 @ A_1 @ B_4 ) )
@ X_1 )
<=> ( P_11
& ( produc1530867176char_o @ Q_2 @ X_1 ) ) ) ).
thf(fact_255_split__part,axiom,
! [P_11: $o,Q_2: list_exp_list_char > produc2090907612on_val > $o,X_1: produc1180562163on_val] :
( ( produc1841295295_val_o
@ ^ [A_1: list_exp_list_char,B_4: produc2090907612on_val] : ( (&) @ P_11 @ ( Q_2 @ A_1 @ B_4 ) )
@ X_1 )
<=> ( P_11
& ( produc1841295295_val_o @ Q_2 @ X_1 ) ) ) ).
thf(fact_256_split__part,axiom,
! [P_11: $o,Q_2: produc1180562163on_val > produc1180562163on_val > $o,X_1: produc618524391on_val] :
( ( produc2136448621_val_o
@ ^ [A_1: produc1180562163on_val,B_4: produc1180562163on_val] : ( (&) @ P_11 @ ( Q_2 @ A_1 @ B_4 ) )
@ X_1 )
<=> ( P_11
& ( produc2136448621_val_o @ Q_2 @ X_1 ) ) ) ).
thf(fact_257_split__part,axiom,
! [P_11: $o,Q_2: exp_list_char > produc2090907612on_val > $o,X_1: produc1282892786on_val] :
( ( produc1835097372_val_o
@ ^ [A_1: exp_list_char,B_4: produc2090907612on_val] : ( (&) @ P_11 @ ( Q_2 @ A_1 @ B_4 ) )
@ X_1 )
<=> ( P_11
& ( produc1835097372_val_o @ Q_2 @ X_1 ) ) ) ).
thf(fact_258_split__part,axiom,
! [P_11: $o,Q_2: produc1282892786on_val > produc1282892786on_val > $o,X_1: produc1746408499on_val] :
( ( produc1624062875_val_o
@ ^ [A_1: produc1282892786on_val,B_4: produc1282892786on_val] : ( (&) @ P_11 @ ( Q_2 @ A_1 @ B_4 ) )
@ X_1 )
<=> ( P_11
& ( produc1624062875_val_o @ Q_2 @ X_1 ) ) ) ).
thf(fact_259_split__part,axiom,
! [P_11: $o,Q_2: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,X_1: produc2090907612on_val] :
( ( produc252486962_val_o
@ ^ [A_1: nat > option1728594148on_val,B_4: list_char > option_val] : ( (&) @ P_11 @ ( Q_2 @ A_1 @ B_4 ) )
@ X_1 )
<=> ( P_11
& ( produc252486962_val_o @ Q_2 @ X_1 ) ) ) ).
thf(fact_260_exp_Osimps_I215_J,axiom,
! [Exp1_21: exp_list_char,Exp2_21: exp_list_char,Exp1_20: exp_list_char,Exp2_20: exp_list_char,Exp3_7: exp_list_char] :
( ( while_list_char @ Exp1_21 @ Exp2_21 )
!= ( cond_list_char @ Exp1_20 @ Exp2_20 @ Exp3_7 ) ) ).
thf(fact_261_exp_Osimps_I214_J,axiom,
! [Exp1_19: exp_list_char,Exp2_19: exp_list_char,Exp3_6: exp_list_char,Exp1_18: exp_list_char,Exp2_18: exp_list_char] :
( ( cond_list_char @ Exp1_19 @ Exp2_19 @ Exp3_6 )
!= ( while_list_char @ Exp1_18 @ Exp2_18 ) ) ).
thf(fact_262_exp_Osimps_I13_J,axiom,
! [Exp1_17: exp_list_char,Exp2_17: exp_list_char,Exp1_16: exp_list_char,Exp2_16: exp_list_char] :
( ( ( while_list_char @ Exp1_17 @ Exp2_17 )
= ( while_list_char @ Exp1_16 @ Exp2_16 ) )
<=> ( ( Exp1_17 = Exp1_16 )
& ( Exp2_17 = Exp2_16 ) ) ) ).
thf(fact_263_exp_Osimps_I12_J,axiom,
! [Exp1_15: exp_list_char,Exp2_15: exp_list_char,Exp3_5: exp_list_char,Exp1_14: exp_list_char,Exp2_14: exp_list_char,Exp3_4: exp_list_char] :
( ( ( cond_list_char @ Exp1_15 @ Exp2_15 @ Exp3_5 )
= ( cond_list_char @ Exp1_14 @ Exp2_14 @ Exp3_4 ) )
<=> ( ( Exp1_15 = Exp1_14 )
& ( Exp2_15 = Exp2_14 )
& ( Exp3_5 = Exp3_4 ) ) ) ).
thf(fact_264_internal__split__def,axiom,
produc1140826762char_o = produc282231039char_o ).
thf(fact_265_internal__split__def,axiom,
produc473466070_val_o = produc765165771_val_o ).
thf(fact_266_internal__split__def,axiom,
produc1217817172char_o = produc525137097char_o ).
thf(fact_267_internal__split__def,axiom,
produc853142431char_o = produc861054100char_o ).
thf(fact_268_internal__split__def,axiom,
produc96699549char_o = produc1530867176char_o ).
thf(fact_269_internal__split__def,axiom,
produc317060852_val_o = produc1841295295_val_o ).
thf(fact_270_internal__split__def,axiom,
produc1133783928_val_o = produc2136448621_val_o ).
thf(fact_271_internal__split__def,axiom,
produc900512295_val_o = produc1835097372_val_o ).
thf(fact_272_internal__split__def,axiom,
produc2006262054_val_o = produc1624062875_val_o ).
thf(fact_273_internal__split__def,axiom,
produc575577405_val_o = produc252486962_val_o ).
thf(fact_274_split__weak__cong,axiom,
! [C_7: list_char > list_char > $o,P_10: produc1278157519t_char,Q_1: produc1278157519t_char] :
( ( P_10 = Q_1 )
=> ( ( produc282231039char_o @ C_7 @ P_10 )
<=> ( produc282231039char_o @ C_7 @ Q_1 ) ) ) ).
thf(fact_275_split__weak__cong,axiom,
! [C_7: list_char > ( produc1278157519t_char > option_val ) > $o,P_10: produc2088785539on_val,Q_1: produc2088785539on_val] :
( ( P_10 = Q_1 )
=> ( ( produc765165771_val_o @ C_7 @ P_10 )
<=> ( produc765165771_val_o @ C_7 @ Q_1 ) ) ) ).
thf(fact_276_split__weak__cong,axiom,
! [C_7: list_val > exp_list_char > $o,P_10: produc662261637t_char,Q_1: produc662261637t_char] :
( ( P_10 = Q_1 )
=> ( ( produc525137097char_o @ C_7 @ P_10 )
<=> ( produc525137097char_o @ C_7 @ Q_1 ) ) ) ).
thf(fact_277_split__weak__cong,axiom,
! [C_7: list_ty > produc662261637t_char > $o,P_10: produc220283002t_char,Q_1: produc220283002t_char] :
( ( P_10 = Q_1 )
=> ( ( produc861054100char_o @ C_7 @ P_10 )
<=> ( produc861054100char_o @ C_7 @ Q_1 ) ) ) ).
thf(fact_278_split__weak__cong,axiom,
! [C_7: list_list_char > produc220283002t_char > $o,P_10: produc1285161482t_char,Q_1: produc1285161482t_char] :
( ( P_10 = Q_1 )
=> ( ( produc1530867176char_o @ C_7 @ P_10 )
<=> ( produc1530867176char_o @ C_7 @ Q_1 ) ) ) ).
thf(fact_279_split__weak__cong,axiom,
! [C_7: list_exp_list_char > produc2090907612on_val > $o,P_10: produc1180562163on_val,Q_1: produc1180562163on_val] :
( ( P_10 = Q_1 )
=> ( ( produc1841295295_val_o @ C_7 @ P_10 )
<=> ( produc1841295295_val_o @ C_7 @ Q_1 ) ) ) ).
thf(fact_280_split__weak__cong,axiom,
! [C_7: produc1180562163on_val > produc1180562163on_val > $o,P_10: produc618524391on_val,Q_1: produc618524391on_val] :
( ( P_10 = Q_1 )
=> ( ( produc2136448621_val_o @ C_7 @ P_10 )
<=> ( produc2136448621_val_o @ C_7 @ Q_1 ) ) ) ).
thf(fact_281_split__weak__cong,axiom,
! [C_7: exp_list_char > produc2090907612on_val > $o,P_10: produc1282892786on_val,Q_1: produc1282892786on_val] :
( ( P_10 = Q_1 )
=> ( ( produc1835097372_val_o @ C_7 @ P_10 )
<=> ( produc1835097372_val_o @ C_7 @ Q_1 ) ) ) ).
thf(fact_282_split__weak__cong,axiom,
! [C_7: produc1282892786on_val > produc1282892786on_val > $o,P_10: produc1746408499on_val,Q_1: produc1746408499on_val] :
( ( P_10 = Q_1 )
=> ( ( produc1624062875_val_o @ C_7 @ P_10 )
<=> ( produc1624062875_val_o @ C_7 @ Q_1 ) ) ) ).
thf(fact_283_split__weak__cong,axiom,
! [C_7: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,P_10: produc2090907612on_val,Q_1: produc2090907612on_val] :
( ( P_10 = Q_1 )
=> ( ( produc252486962_val_o @ C_7 @ P_10 )
<=> ( produc252486962_val_o @ C_7 @ Q_1 ) ) ) ).
thf(fact_284_split__twice,axiom,
! [F_5: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,G_1: list_char > list_char > produc2090907612on_val,P_9: produc1278157519t_char] :
( ( produc252486962_val_o @ F_5 @ ( produc835075084on_val @ G_1 @ P_9 ) )
<=> ( produc282231039char_o
@ ^ [X_1: list_char,Y: list_char] : ( produc252486962_val_o @ F_5 @ ( G_1 @ X_1 @ Y ) )
@ P_9 ) ) ).
thf(fact_285_split__twice,axiom,
! [F_5: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,G_1: list_char > ( produc1278157519t_char > option_val ) > produc2090907612on_val,P_9: produc2088785539on_val] :
( ( produc252486962_val_o @ F_5 @ ( produc1349598016on_val @ G_1 @ P_9 ) )
<=> ( produc765165771_val_o
@ ^ [X_1: list_char,Y: produc1278157519t_char > option_val] : ( produc252486962_val_o @ F_5 @ ( G_1 @ X_1 @ Y ) )
@ P_9 ) ) ).
thf(fact_286_split__twice,axiom,
! [F_5: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,G_1: list_val > exp_list_char > produc2090907612on_val,P_9: produc662261637t_char] :
( ( produc252486962_val_o @ F_5 @ ( produc371942594on_val @ G_1 @ P_9 ) )
<=> ( produc525137097char_o
@ ^ [X_1: list_val,Y: exp_list_char] : ( produc252486962_val_o @ F_5 @ ( G_1 @ X_1 @ Y ) )
@ P_9 ) ) ).
thf(fact_287_split__twice,axiom,
! [F_5: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,G_1: list_ty > produc662261637t_char > produc2090907612on_val,P_9: produc220283002t_char] :
( ( produc252486962_val_o @ F_5 @ ( produc1533215415on_val @ G_1 @ P_9 ) )
<=> ( produc861054100char_o
@ ^ [X_1: list_ty,Y: produc662261637t_char] : ( produc252486962_val_o @ F_5 @ ( G_1 @ X_1 @ Y ) )
@ P_9 ) ) ).
thf(fact_288_split__twice,axiom,
! [F_5: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,G_1: list_list_char > produc220283002t_char > produc2090907612on_val,P_9: produc1285161482t_char] :
( ( produc252486962_val_o @ F_5 @ ( produc762569315on_val @ G_1 @ P_9 ) )
<=> ( produc1530867176char_o
@ ^ [X_1: list_list_char,Y: produc220283002t_char] : ( produc252486962_val_o @ F_5 @ ( G_1 @ X_1 @ Y ) )
@ P_9 ) ) ).
thf(fact_289_split__twice,axiom,
! [F_5: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,G_1: list_exp_list_char > produc2090907612on_val > produc2090907612on_val,P_9: produc1180562163on_val] :
( ( produc252486962_val_o @ F_5 @ ( produc1128742220on_val @ G_1 @ P_9 ) )
<=> ( produc1841295295_val_o
@ ^ [X_1: list_exp_list_char,Y: produc2090907612on_val] : ( produc252486962_val_o @ F_5 @ ( G_1 @ X_1 @ Y ) )
@ P_9 ) ) ).
thf(fact_290_split__twice,axiom,
! [F_5: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,G_1: produc1180562163on_val > produc1180562163on_val > produc2090907612on_val,P_9: produc618524391on_val] :
( ( produc252486962_val_o @ F_5 @ ( produc27101214on_val @ G_1 @ P_9 ) )
<=> ( produc2136448621_val_o
@ ^ [X_1: produc1180562163on_val,Y: produc1180562163on_val] : ( produc252486962_val_o @ F_5 @ ( G_1 @ X_1 @ Y ) )
@ P_9 ) ) ).
thf(fact_291_split__twice,axiom,
! [F_5: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,G_1: exp_list_char > produc2090907612on_val > produc2090907612on_val,P_9: produc1282892786on_val] :
( ( produc252486962_val_o @ F_5 @ ( produc69760047on_val @ G_1 @ P_9 ) )
<=> ( produc1835097372_val_o
@ ^ [X_1: exp_list_char,Y: produc2090907612on_val] : ( produc252486962_val_o @ F_5 @ ( G_1 @ X_1 @ Y ) )
@ P_9 ) ) ).
thf(fact_292_split__twice,axiom,
! [F_5: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,G_1: produc1282892786on_val > produc1282892786on_val > produc2090907612on_val,P_9: produc1746408499on_val] :
( ( produc252486962_val_o @ F_5 @ ( produc511181936on_val @ G_1 @ P_9 ) )
<=> ( produc1624062875_val_o
@ ^ [X_1: produc1282892786on_val,Y: produc1282892786on_val] : ( produc252486962_val_o @ F_5 @ ( G_1 @ X_1 @ Y ) )
@ P_9 ) ) ).
thf(fact_293_split__twice,axiom,
! [F_5: list_char > list_char > $o,G_1: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1278157519t_char,P_9: produc2090907612on_val] :
( ( produc282231039char_o @ F_5 @ ( produc562949388t_char @ G_1 @ P_9 ) )
<=> ( produc252486962_val_o
@ ^ [X_1: nat > option1728594148on_val,Y: list_char > option_val] : ( produc282231039char_o @ F_5 @ ( G_1 @ X_1 @ Y ) )
@ P_9 ) ) ).
thf(fact_294_split__twice,axiom,
! [F_5: list_char > ( produc1278157519t_char > option_val ) > $o,G_1: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc2088785539on_val,P_9: produc2090907612on_val] :
( ( produc765165771_val_o @ F_5 @ ( produc2039683648on_val @ G_1 @ P_9 ) )
<=> ( produc252486962_val_o
@ ^ [X_1: nat > option1728594148on_val,Y: list_char > option_val] : ( produc765165771_val_o @ F_5 @ ( G_1 @ X_1 @ Y ) )
@ P_9 ) ) ).
thf(fact_295_split__twice,axiom,
! [F_5: list_val > exp_list_char > $o,G_1: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc662261637t_char,P_9: produc2090907612on_val] :
( ( produc525137097char_o @ F_5 @ ( produc753444290t_char @ G_1 @ P_9 ) )
<=> ( produc252486962_val_o
@ ^ [X_1: nat > option1728594148on_val,Y: list_char > option_val] : ( produc525137097char_o @ F_5 @ ( G_1 @ X_1 @ Y ) )
@ P_9 ) ) ).
thf(fact_296_split__twice,axiom,
! [F_5: list_ty > produc662261637t_char > $o,G_1: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc220283002t_char,P_9: produc2090907612on_val] :
( ( produc861054100char_o @ F_5 @ ( produc97831223t_char @ G_1 @ P_9 ) )
<=> ( produc252486962_val_o
@ ^ [X_1: nat > option1728594148on_val,Y: list_char > option_val] : ( produc861054100char_o @ F_5 @ ( G_1 @ X_1 @ Y ) )
@ P_9 ) ) ).
thf(fact_297_split__twice,axiom,
! [F_5: list_list_char > produc220283002t_char > $o,G_1: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1285161482t_char,P_9: produc2090907612on_val] :
( ( produc1530867176char_o @ F_5 @ ( produc2056656269t_char @ G_1 @ P_9 ) )
<=> ( produc252486962_val_o
@ ^ [X_1: nat > option1728594148on_val,Y: list_char > option_val] : ( produc1530867176char_o @ F_5 @ ( G_1 @ X_1 @ Y ) )
@ P_9 ) ) ).
thf(fact_298_split__twice,axiom,
! [F_5: list_exp_list_char > produc2090907612on_val > $o,G_1: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1180562163on_val,P_9: produc2090907612on_val] :
( ( produc1841295295_val_o @ F_5 @ ( produc1650655734on_val @ G_1 @ P_9 ) )
<=> ( produc252486962_val_o
@ ^ [X_1: nat > option1728594148on_val,Y: list_char > option_val] : ( produc1841295295_val_o @ F_5 @ ( G_1 @ X_1 @ Y ) )
@ P_9 ) ) ).
thf(fact_299_split__twice,axiom,
! [F_5: produc1180562163on_val > produc1180562163on_val > $o,G_1: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc618524391on_val,P_9: produc2090907612on_val] :
( ( produc2136448621_val_o @ F_5 @ ( produc808731044on_val @ G_1 @ P_9 ) )
<=> ( produc252486962_val_o
@ ^ [X_1: nat > option1728594148on_val,Y: list_char > option_val] : ( produc2136448621_val_o @ F_5 @ ( G_1 @ X_1 @ Y ) )
@ P_9 ) ) ).
thf(fact_300_split__twice,axiom,
! [F_5: exp_list_char > produc2090907612on_val > $o,G_1: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1282892786on_val,P_9: produc2090907612on_val] :
( ( produc1835097372_val_o @ F_5 @ ( produc1016489647on_val @ G_1 @ P_9 ) )
<=> ( produc252486962_val_o
@ ^ [X_1: nat > option1728594148on_val,Y: list_char > option_val] : ( produc1835097372_val_o @ F_5 @ ( G_1 @ X_1 @ Y ) )
@ P_9 ) ) ).
thf(fact_301_split__twice,axiom,
! [F_5: produc1282892786on_val > produc1282892786on_val > $o,G_1: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1746408499on_val,P_9: produc2090907612on_val] :
( ( produc1624062875_val_o @ F_5 @ ( produc1186953840on_val @ G_1 @ P_9 ) )
<=> ( produc252486962_val_o
@ ^ [X_1: nat > option1728594148on_val,Y: list_char > option_val] : ( produc1624062875_val_o @ F_5 @ ( G_1 @ X_1 @ Y ) )
@ P_9 ) ) ).
thf(fact_302_splitD,axiom,
! [F_4: produc1278157519t_char > produc1278157519t_char > $o,A_12: produc1278157519t_char,B_10: produc1278157519t_char] :
( ( produc2056220769char_o @ F_4 @ ( produc2080520419t_char @ A_12 @ B_10 ) )
=> ( F_4 @ A_12 @ B_10 ) ) ).
thf(fact_303_splitD,axiom,
! [F_4: produc2088785539on_val > produc2088785539on_val > $o,A_12: produc2088785539on_val,B_10: produc2088785539on_val] :
( ( produc791773177_val_o @ F_4 @ ( produc1773146955on_val @ A_12 @ B_10 ) )
=> ( F_4 @ A_12 @ B_10 ) ) ).
thf(fact_304_splitD,axiom,
! [F_4: produc662261637t_char > produc662261637t_char > $o,A_12: produc662261637t_char,B_10: produc662261637t_char] :
( ( produc1537651445char_o @ F_4 @ ( produc1299387215t_char @ A_12 @ B_10 ) )
=> ( F_4 @ A_12 @ B_10 ) ) ).
thf(fact_305_splitD,axiom,
! [F_4: produc220283002t_char > produc220283002t_char > $o,A_12: produc220283002t_char,B_10: produc220283002t_char] :
( ( produc510191755char_o @ F_4 @ ( produc57279289t_char @ A_12 @ B_10 ) )
=> ( F_4 @ A_12 @ B_10 ) ) ).
thf(fact_306_splitD,axiom,
! [F_4: produc1285161482t_char > produc1285161482t_char > $o,A_12: produc1285161482t_char,B_10: produc1285161482t_char] :
( ( produc865480877char_o @ F_4 @ ( produc24551831t_char @ A_12 @ B_10 ) )
=> ( F_4 @ A_12 @ B_10 ) ) ).
thf(fact_307_splitD,axiom,
! [F_4: produc618524391on_val > produc618524391on_val > $o,A_12: produc618524391on_val,B_10: produc618524391on_val] :
( ( produc382956337_val_o @ F_4 @ ( produc1347028499on_val @ A_12 @ B_10 ) )
=> ( F_4 @ A_12 @ B_10 ) ) ).
thf(fact_308_splitD,axiom,
! [F_4: produc1746408499on_val > produc1746408499on_val > $o,A_12: produc1746408499on_val,B_10: produc1746408499on_val] :
( ( produc154389913_val_o @ F_4 @ ( produc345758123on_val @ A_12 @ B_10 ) )
=> ( F_4 @ A_12 @ B_10 ) ) ).
thf(fact_309_splitD,axiom,
! [F_4: produc2090907612on_val > produc2090907612on_val > $o,A_12: produc2090907612on_val,B_10: produc2090907612on_val] :
( ( produc1377568711_val_o @ F_4 @ ( produc259392253on_val @ A_12 @ B_10 ) )
=> ( F_4 @ A_12 @ B_10 ) ) ).
thf(fact_310_splitD,axiom,
! [F_4: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,A_12: nat > option1728594148on_val,B_10: list_char > option_val] :
( ( produc252486962_val_o @ F_4 @ ( produc755559506on_val @ A_12 @ B_10 ) )
=> ( F_4 @ A_12 @ B_10 ) ) ).
thf(fact_311_splitD,axiom,
! [F_4: produc1282892786on_val > produc1282892786on_val > $o,A_12: produc1282892786on_val,B_10: produc1282892786on_val] :
( ( produc1624062875_val_o @ F_4 @ ( produc833389609on_val @ A_12 @ B_10 ) )
=> ( F_4 @ A_12 @ B_10 ) ) ).
thf(fact_312_splitD,axiom,
! [F_4: exp_list_char > produc2090907612on_val > $o,A_12: exp_list_char,B_10: produc2090907612on_val] :
( ( produc1835097372_val_o @ F_4 @ ( produc235638504on_val @ A_12 @ B_10 ) )
=> ( F_4 @ A_12 @ B_10 ) ) ).
thf(fact_313_splitD,axiom,
! [F_4: produc1180562163on_val > produc1180562163on_val > $o,A_12: produc1180562163on_val,B_10: produc1180562163on_val] :
( ( produc2136448621_val_o @ F_4 @ ( produc747700183on_val @ A_12 @ B_10 ) )
=> ( F_4 @ A_12 @ B_10 ) ) ).
thf(fact_314_splitD,axiom,
! [F_4: list_exp_list_char > produc2090907612on_val > $o,A_12: list_exp_list_char,B_10: produc2090907612on_val] :
( ( produc1841295295_val_o @ F_4 @ ( produc1302104557on_val @ A_12 @ B_10 ) )
=> ( F_4 @ A_12 @ B_10 ) ) ).
thf(fact_315_splitD,axiom,
! [F_4: list_list_char > produc220283002t_char > $o,A_12: list_list_char,B_10: produc220283002t_char] :
( ( produc1530867176char_o @ F_4 @ ( produc921874948t_char @ A_12 @ B_10 ) )
=> ( F_4 @ A_12 @ B_10 ) ) ).
thf(fact_316_splitD,axiom,
! [F_4: list_ty > produc662261637t_char > $o,A_12: list_ty,B_10: produc662261637t_char] :
( ( produc861054100char_o @ F_4 @ ( produc1909267824t_char @ A_12 @ B_10 ) )
=> ( F_4 @ A_12 @ B_10 ) ) ).
thf(fact_317_splitD,axiom,
! [F_4: list_val > exp_list_char > $o,A_12: list_val,B_10: exp_list_char] :
( ( produc525137097char_o @ F_4 @ ( produc1916172923t_char @ A_12 @ B_10 ) )
=> ( F_4 @ A_12 @ B_10 ) ) ).
thf(fact_318_splitD,axiom,
! [F_4: list_char > ( produc1278157519t_char > option_val ) > $o,A_12: list_char,B_10: produc1278157519t_char > option_val] :
( ( produc765165771_val_o @ F_4 @ ( produc926070009on_val @ A_12 @ B_10 ) )
=> ( F_4 @ A_12 @ B_10 ) ) ).
thf(fact_319_splitD,axiom,
! [F_4: list_char > list_char > $o,A_12: list_char,B_10: list_char] :
( ( produc282231039char_o @ F_4 @ ( produc5062597t_char @ A_12 @ B_10 ) )
=> ( F_4 @ A_12 @ B_10 ) ) ).
thf(fact_320_prod_Osimps_I2_J,axiom,
! [F1: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,A_11: nat > option1728594148on_val,B_9: list_char > option_val] :
( ( produc252486962_val_o @ F1 @ ( produc755559506on_val @ A_11 @ B_9 ) )
<=> ( F1 @ A_11 @ B_9 ) ) ).
thf(fact_321_prod_Osimps_I2_J,axiom,
! [F1: produc1282892786on_val > produc1282892786on_val > $o,A_11: produc1282892786on_val,B_9: produc1282892786on_val] :
( ( produc1624062875_val_o @ F1 @ ( produc833389609on_val @ A_11 @ B_9 ) )
<=> ( F1 @ A_11 @ B_9 ) ) ).
thf(fact_322_prod_Osimps_I2_J,axiom,
! [F1: exp_list_char > produc2090907612on_val > $o,A_11: exp_list_char,B_9: produc2090907612on_val] :
( ( produc1835097372_val_o @ F1 @ ( produc235638504on_val @ A_11 @ B_9 ) )
<=> ( F1 @ A_11 @ B_9 ) ) ).
thf(fact_323_prod_Osimps_I2_J,axiom,
! [F1: produc1180562163on_val > produc1180562163on_val > $o,A_11: produc1180562163on_val,B_9: produc1180562163on_val] :
( ( produc2136448621_val_o @ F1 @ ( produc747700183on_val @ A_11 @ B_9 ) )
<=> ( F1 @ A_11 @ B_9 ) ) ).
thf(fact_324_prod_Osimps_I2_J,axiom,
! [F1: list_exp_list_char > produc2090907612on_val > $o,A_11: list_exp_list_char,B_9: produc2090907612on_val] :
( ( produc1841295295_val_o @ F1 @ ( produc1302104557on_val @ A_11 @ B_9 ) )
<=> ( F1 @ A_11 @ B_9 ) ) ).
thf(fact_325_prod_Osimps_I2_J,axiom,
! [F1: list_list_char > produc220283002t_char > $o,A_11: list_list_char,B_9: produc220283002t_char] :
( ( produc1530867176char_o @ F1 @ ( produc921874948t_char @ A_11 @ B_9 ) )
<=> ( F1 @ A_11 @ B_9 ) ) ).
thf(fact_326_prod_Osimps_I2_J,axiom,
! [F1: list_ty > produc662261637t_char > $o,A_11: list_ty,B_9: produc662261637t_char] :
( ( produc861054100char_o @ F1 @ ( produc1909267824t_char @ A_11 @ B_9 ) )
<=> ( F1 @ A_11 @ B_9 ) ) ).
thf(fact_327_prod_Osimps_I2_J,axiom,
! [F1: list_val > exp_list_char > $o,A_11: list_val,B_9: exp_list_char] :
( ( produc525137097char_o @ F1 @ ( produc1916172923t_char @ A_11 @ B_9 ) )
<=> ( F1 @ A_11 @ B_9 ) ) ).
thf(fact_328_prod_Osimps_I2_J,axiom,
! [F1: list_char > ( produc1278157519t_char > option_val ) > $o,A_11: list_char,B_9: produc1278157519t_char > option_val] :
( ( produc765165771_val_o @ F1 @ ( produc926070009on_val @ A_11 @ B_9 ) )
<=> ( F1 @ A_11 @ B_9 ) ) ).
thf(fact_329_prod_Osimps_I2_J,axiom,
! [F1: list_char > list_char > $o,A_11: list_char,B_9: list_char] :
( ( produc282231039char_o @ F1 @ ( produc5062597t_char @ A_11 @ B_9 ) )
<=> ( F1 @ A_11 @ B_9 ) ) ).
thf(fact_330_split__conv,axiom,
! [F_3: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,A_10: nat > option1728594148on_val,B_8: list_char > option_val] :
( ( produc252486962_val_o @ F_3 @ ( produc755559506on_val @ A_10 @ B_8 ) )
<=> ( F_3 @ A_10 @ B_8 ) ) ).
thf(fact_331_split__conv,axiom,
! [F_3: produc1282892786on_val > produc1282892786on_val > $o,A_10: produc1282892786on_val,B_8: produc1282892786on_val] :
( ( produc1624062875_val_o @ F_3 @ ( produc833389609on_val @ A_10 @ B_8 ) )
<=> ( F_3 @ A_10 @ B_8 ) ) ).
thf(fact_332_split__conv,axiom,
! [F_3: exp_list_char > produc2090907612on_val > $o,A_10: exp_list_char,B_8: produc2090907612on_val] :
( ( produc1835097372_val_o @ F_3 @ ( produc235638504on_val @ A_10 @ B_8 ) )
<=> ( F_3 @ A_10 @ B_8 ) ) ).
thf(fact_333_split__conv,axiom,
! [F_3: produc1180562163on_val > produc1180562163on_val > $o,A_10: produc1180562163on_val,B_8: produc1180562163on_val] :
( ( produc2136448621_val_o @ F_3 @ ( produc747700183on_val @ A_10 @ B_8 ) )
<=> ( F_3 @ A_10 @ B_8 ) ) ).
thf(fact_334_split__conv,axiom,
! [F_3: list_exp_list_char > produc2090907612on_val > $o,A_10: list_exp_list_char,B_8: produc2090907612on_val] :
( ( produc1841295295_val_o @ F_3 @ ( produc1302104557on_val @ A_10 @ B_8 ) )
<=> ( F_3 @ A_10 @ B_8 ) ) ).
thf(fact_335_split__conv,axiom,
! [F_3: list_list_char > produc220283002t_char > $o,A_10: list_list_char,B_8: produc220283002t_char] :
( ( produc1530867176char_o @ F_3 @ ( produc921874948t_char @ A_10 @ B_8 ) )
<=> ( F_3 @ A_10 @ B_8 ) ) ).
thf(fact_336_split__conv,axiom,
! [F_3: list_ty > produc662261637t_char > $o,A_10: list_ty,B_8: produc662261637t_char] :
( ( produc861054100char_o @ F_3 @ ( produc1909267824t_char @ A_10 @ B_8 ) )
<=> ( F_3 @ A_10 @ B_8 ) ) ).
thf(fact_337_split__conv,axiom,
! [F_3: list_val > exp_list_char > $o,A_10: list_val,B_8: exp_list_char] :
( ( produc525137097char_o @ F_3 @ ( produc1916172923t_char @ A_10 @ B_8 ) )
<=> ( F_3 @ A_10 @ B_8 ) ) ).
thf(fact_338_split__conv,axiom,
! [F_3: list_char > ( produc1278157519t_char > option_val ) > $o,A_10: list_char,B_8: produc1278157519t_char > option_val] :
( ( produc765165771_val_o @ F_3 @ ( produc926070009on_val @ A_10 @ B_8 ) )
<=> ( F_3 @ A_10 @ B_8 ) ) ).
thf(fact_339_split__conv,axiom,
! [F_3: list_char > list_char > $o,A_10: list_char,B_8: list_char] :
( ( produc282231039char_o @ F_3 @ ( produc5062597t_char @ A_10 @ B_8 ) )
<=> ( F_3 @ A_10 @ B_8 ) ) ).
thf(fact_340_mem__def,axiom,
! [X_3: produc1278157519t_char,A_9: produc1278157519t_char > $o] :
( ( member1251428284t_char @ X_3 @ A_9 )
<=> ( A_9 @ X_3 ) ) ).
thf(fact_341_mem__def,axiom,
! [X_3: produc1350825965t_char,A_9: produc1350825965t_char > $o] :
( ( member794220506t_char @ X_3 @ A_9 )
<=> ( A_9 @ X_3 ) ) ).
thf(fact_342_mem__def,axiom,
! [X_3: produc1368416213on_val,A_9: produc1368416213on_val > $o] :
( ( member1235075778on_val @ X_3 @ A_9 )
<=> ( A_9 @ X_3 ) ) ).
thf(fact_343_mem__def,axiom,
! [X_3: produc1826280281t_char,A_9: produc1826280281t_char > $o] :
( ( member1161907014t_char @ X_3 @ A_9 )
<=> ( A_9 @ X_3 ) ) ).
thf(fact_344_mem__def,axiom,
! [X_3: produc1406897475t_char,A_9: produc1406897475t_char > $o] :
( ( member125098544t_char @ X_3 @ A_9 )
<=> ( A_9 @ X_3 ) ) ).
thf(fact_345_mem__def,axiom,
! [X_3: produc349695911t_char,A_9: produc349695911t_char > $o] :
( ( member1420286996t_char @ X_3 @ A_9 )
<=> ( A_9 @ X_3 ) ) ).
thf(fact_346_mem__def,axiom,
! [X_3: produc1250491293on_val,A_9: produc1250491293on_val > $o] :
( ( member1145216138on_val @ X_3 @ A_9 )
<=> ( A_9 @ X_3 ) ) ).
thf(fact_347_mem__def,axiom,
! [X_3: produc652964533on_val,A_9: produc652964533on_val > $o] :
( ( member1714424482on_val @ X_3 @ A_9 )
<=> ( A_9 @ X_3 ) ) ).
thf(fact_348_mem__def,axiom,
! [X_3: produc1581780743on_val,A_9: produc1581780743on_val > $o] :
( ( member565037556on_val @ X_3 @ A_9 )
<=> ( A_9 @ X_3 ) ) ).
thf(fact_349_mem__def,axiom,
! [X_3: produc2088785539on_val,A_9: produc2088785539on_val > $o] :
( ( member1374264560on_val @ X_3 @ A_9 )
<=> ( A_9 @ X_3 ) ) ).
thf(fact_350_mem__def,axiom,
! [X_3: produc662261637t_char,A_9: produc662261637t_char > $o] :
( ( member699351154t_char @ X_3 @ A_9 )
<=> ( A_9 @ X_3 ) ) ).
thf(fact_351_mem__def,axiom,
! [X_3: produc220283002t_char,A_9: produc220283002t_char > $o] :
( ( member140606439t_char @ X_3 @ A_9 )
<=> ( A_9 @ X_3 ) ) ).
thf(fact_352_mem__def,axiom,
! [X_3: produc1285161482t_char,A_9: produc1285161482t_char > $o] :
( ( member133545693t_char @ X_3 @ A_9 )
<=> ( A_9 @ X_3 ) ) ).
thf(fact_353_mem__def,axiom,
! [X_3: produc1180562163on_val,A_9: produc1180562163on_val > $o] :
( ( member1224782662on_val @ X_3 @ A_9 )
<=> ( A_9 @ X_3 ) ) ).
thf(fact_354_mem__def,axiom,
! [X_3: produc1282892786on_val,A_9: produc1282892786on_val > $o] :
( ( member1072200031on_val @ X_3 @ A_9 )
<=> ( A_9 @ X_3 ) ) ).
thf(fact_355_mem__def,axiom,
! [X_3: produc2090907612on_val,A_9: produc2090907612on_val > $o] :
( ( member1846553161on_val @ X_3 @ A_9 )
<=> ( A_9 @ X_3 ) ) ).
thf(fact_356_mem__def,axiom,
! [X_3: produc1746408499on_val,A_9: produc1746408499on_val > $o] :
( ( member1913460000on_val @ X_3 @ A_9 )
<=> ( A_9 @ X_3 ) ) ).
thf(fact_357_mem__def,axiom,
! [X_3: produc618524391on_val,A_9: produc618524391on_val > $o] :
( ( member2042188884on_val @ X_3 @ A_9 )
<=> ( A_9 @ X_3 ) ) ).
thf(fact_358_exp_Osimps_I176_J,axiom,
! [Exp1_13: exp_list_char,List1_9: list_char,List2_9: list_char,Exp2_13: exp_list_char,Exp1_12: exp_list_char,Exp2_12: exp_list_char,Exp3_3: exp_list_char] :
( ( fAss_list_char @ Exp1_13 @ List1_9 @ List2_9 @ Exp2_13 )
!= ( cond_list_char @ Exp1_12 @ Exp2_12 @ Exp3_3 ) ) ).
thf(fact_359_exp_Osimps_I178_J,axiom,
! [Exp1_11: exp_list_char,List1_8: list_char,List2_8: list_char,Exp2_11: exp_list_char,Exp1_10: exp_list_char,Exp2_10: exp_list_char] :
( ( fAss_list_char @ Exp1_11 @ List1_8 @ List2_8 @ Exp2_11 )
!= ( while_list_char @ Exp1_10 @ Exp2_10 ) ) ).
thf(fact_360_exp_Osimps_I177_J,axiom,
! [Exp1_9: exp_list_char,Exp2_9: exp_list_char,Exp3_2: exp_list_char,Exp1_8: exp_list_char,List1_7: list_char,List2_7: list_char,Exp2_8: exp_list_char] :
( ( cond_list_char @ Exp1_9 @ Exp2_9 @ Exp3_2 )
!= ( fAss_list_char @ Exp1_8 @ List1_7 @ List2_7 @ Exp2_8 ) ) ).
thf(fact_361_exp_Osimps_I179_J,axiom,
! [Exp1_7: exp_list_char,Exp2_7: exp_list_char,Exp1_6: exp_list_char,List1_6: list_char,List2_6: list_char,Exp2_6: exp_list_char] :
( ( while_list_char @ Exp1_7 @ Exp2_7 )
!= ( fAss_list_char @ Exp1_6 @ List1_6 @ List2_6 @ Exp2_6 ) ) ).
thf(fact_362_exp_Osimps_I162_J,axiom,
! [Exp_7: exp_list_char,List1_5: list_char,List2_5: list_char,Exp1_5: exp_list_char,Exp2_5: exp_list_char,Exp3_1: exp_list_char] :
( ( fAcc_list_char @ Exp_7 @ List1_5 @ List2_5 )
!= ( cond_list_char @ Exp1_5 @ Exp2_5 @ Exp3_1 ) ) ).
thf(fact_363_exp_Osimps_I163_J,axiom,
! [Exp1_4: exp_list_char,Exp2_4: exp_list_char,Exp3: exp_list_char,Exp_6: exp_list_char,List1_4: list_char,List2_4: list_char] :
( ( cond_list_char @ Exp1_4 @ Exp2_4 @ Exp3 )
!= ( fAcc_list_char @ Exp_6 @ List1_4 @ List2_4 ) ) ).
thf(fact_364_exp_Osimps_I164_J,axiom,
! [Exp_5: exp_list_char,List1_3: list_char,List2_3: list_char,Exp1_3: exp_list_char,Exp2_3: exp_list_char] :
( ( fAcc_list_char @ Exp_5 @ List1_3 @ List2_3 )
!= ( while_list_char @ Exp1_3 @ Exp2_3 ) ) ).
thf(fact_365_exp_Osimps_I165_J,axiom,
! [Exp1_2: exp_list_char,Exp2_2: exp_list_char,Exp_4: exp_list_char,List1_2: list_char,List2_2: list_char] :
( ( while_list_char @ Exp1_2 @ Exp2_2 )
!= ( fAcc_list_char @ Exp_4 @ List1_2 @ List2_2 ) ) ).
thf(fact_366_split__eta,axiom,
! [F_2: produc2090907612on_val > $o] :
( ( produc252486962_val_o
@ ^ [X_1: nat > option1728594148on_val,Y: list_char > option_val] : ( F_2 @ ( produc755559506on_val @ X_1 @ Y ) ) )
= F_2 ) ).
thf(fact_367_split__eta,axiom,
! [F_2: produc1746408499on_val > $o] :
( ( produc1624062875_val_o
@ ^ [X_1: produc1282892786on_val,Y: produc1282892786on_val] : ( F_2 @ ( produc833389609on_val @ X_1 @ Y ) ) )
= F_2 ) ).
thf(fact_368_split__eta,axiom,
! [F_2: produc1282892786on_val > $o] :
( ( produc1835097372_val_o
@ ^ [X_1: exp_list_char,Y: produc2090907612on_val] : ( F_2 @ ( produc235638504on_val @ X_1 @ Y ) ) )
= F_2 ) ).
thf(fact_369_split__eta,axiom,
! [F_2: produc618524391on_val > $o] :
( ( produc2136448621_val_o
@ ^ [X_1: produc1180562163on_val,Y: produc1180562163on_val] : ( F_2 @ ( produc747700183on_val @ X_1 @ Y ) ) )
= F_2 ) ).
thf(fact_370_split__eta,axiom,
! [F_2: produc1180562163on_val > $o] :
( ( produc1841295295_val_o
@ ^ [X_1: list_exp_list_char,Y: produc2090907612on_val] : ( F_2 @ ( produc1302104557on_val @ X_1 @ Y ) ) )
= F_2 ) ).
thf(fact_371_split__eta,axiom,
! [F_2: produc1285161482t_char > $o] :
( ( produc1530867176char_o
@ ^ [X_1: list_list_char,Y: produc220283002t_char] : ( F_2 @ ( produc921874948t_char @ X_1 @ Y ) ) )
= F_2 ) ).
thf(fact_372_split__eta,axiom,
! [F_2: produc220283002t_char > $o] :
( ( produc861054100char_o
@ ^ [X_1: list_ty,Y: produc662261637t_char] : ( F_2 @ ( produc1909267824t_char @ X_1 @ Y ) ) )
= F_2 ) ).
thf(fact_373_split__eta,axiom,
! [F_2: produc662261637t_char > $o] :
( ( produc525137097char_o
@ ^ [X_1: list_val,Y: exp_list_char] : ( F_2 @ ( produc1916172923t_char @ X_1 @ Y ) ) )
= F_2 ) ).
thf(fact_374_split__eta,axiom,
! [F_2: produc2088785539on_val > $o] :
( ( produc765165771_val_o
@ ^ [X_1: list_char,Y: produc1278157519t_char > option_val] : ( F_2 @ ( produc926070009on_val @ X_1 @ Y ) ) )
= F_2 ) ).
thf(fact_375_split__eta,axiom,
! [F_2: produc1278157519t_char > $o] :
( ( produc282231039char_o
@ ^ [X_1: list_char,Y: list_char] : ( F_2 @ ( produc5062597t_char @ X_1 @ Y ) ) )
= F_2 ) ).
thf(fact_376_red__reds_OCondRed,axiom,
! [E_1_1: exp_list_char,E_2_1: exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cond_list_char @ E @ E_1_1 @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( cond_list_char @ E_2 @ E_1_1 @ E_2_1 ) @ S_1 ) ) @ ( red @ P ) ) ) ).
thf(fact_377_hext__trans,axiom,
! [H_2: nat > option1728594148on_val,H: nat > option1728594148on_val,H_1: nat > option1728594148on_val] :
( ( hext @ H @ H_1 )
=> ( ( hext @ H_1 @ H_2 )
=> ( hext @ H @ H_2 ) ) ) ).
thf(fact_378_WTrt__elim__cases_I3_J,axiom,
! [P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: list_char > option_ty,E: exp_list_char,C_1: exp_list_char,T: ty] :
( ( wTrt @ P @ H @ E_1 @ ( while_list_char @ E @ C_1 ) @ T )
=> ~ ( ( T = void )
=> ( ( wTrt @ P @ H @ E_1 @ E @ boolean )
=> ! [T_1: ty] :
~ ( wTrt @ P @ H @ E_1 @ C_1 @ T_1 ) ) ) ) ).
thf(fact_379_WTrt__elim__cases_I2_J,axiom,
! [P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: list_char > option_ty,E: exp_list_char,E_1_1: exp_list_char,E_2_1: exp_list_char,T: ty] :
( ( wTrt @ P @ H @ E_1 @ ( cond_list_char @ E @ E_1_1 @ E_2_1 ) @ T )
=> ~ ( ( wTrt @ P @ H @ E_1 @ E @ boolean )
=> ! [T_1_2: ty] :
( ( wTrt @ P @ H @ E_1 @ E_1_1 @ T_1_2 )
=> ! [T_2_2: ty] :
( ( wTrt @ P @ H @ E_1 @ E_2_1 @ T_2_2 )
=> ( ( ( widen_2090681816t_char @ P @ T_1_2 @ T_2_2 )
| ( widen_2090681816t_char @ P @ T_2_2 @ T_1_2 ) )
=> ( ( ( widen_2090681816t_char @ P @ T_1_2 @ T_2_2 )
=> ( T = T_2_2 ) )
=> ~ ( ( widen_2090681816t_char @ P @ T_2_2 @ T_1_2 )
=> ( T = T_1_2 ) ) ) ) ) ) ) ) ).
thf(fact_380_splitE,axiom,
! [C_6: produc1278157519t_char > produc1278157519t_char > $o,P_8: produc1350825965t_char] :
( ( produc2056220769char_o @ C_6 @ P_8 )
=> ~ ! [X_1: produc1278157519t_char,Y: produc1278157519t_char] :
( ( P_8
= ( produc2080520419t_char @ X_1 @ Y ) )
=> ~ ( C_6 @ X_1 @ Y ) ) ) ).
thf(fact_381_splitE,axiom,
! [C_6: produc2088785539on_val > produc2088785539on_val > $o,P_8: produc1368416213on_val] :
( ( produc791773177_val_o @ C_6 @ P_8 )
=> ~ ! [X_1: produc2088785539on_val,Y: produc2088785539on_val] :
( ( P_8
= ( produc1773146955on_val @ X_1 @ Y ) )
=> ~ ( C_6 @ X_1 @ Y ) ) ) ).
thf(fact_382_splitE,axiom,
! [C_6: produc662261637t_char > produc662261637t_char > $o,P_8: produc1826280281t_char] :
( ( produc1537651445char_o @ C_6 @ P_8 )
=> ~ ! [X_1: produc662261637t_char,Y: produc662261637t_char] :
( ( P_8
= ( produc1299387215t_char @ X_1 @ Y ) )
=> ~ ( C_6 @ X_1 @ Y ) ) ) ).
thf(fact_383_splitE,axiom,
! [C_6: produc220283002t_char > produc220283002t_char > $o,P_8: produc1406897475t_char] :
( ( produc510191755char_o @ C_6 @ P_8 )
=> ~ ! [X_1: produc220283002t_char,Y: produc220283002t_char] :
( ( P_8
= ( produc57279289t_char @ X_1 @ Y ) )
=> ~ ( C_6 @ X_1 @ Y ) ) ) ).
thf(fact_384_splitE,axiom,
! [C_6: produc1285161482t_char > produc1285161482t_char > $o,P_8: produc349695911t_char] :
( ( produc865480877char_o @ C_6 @ P_8 )
=> ~ ! [X_1: produc1285161482t_char,Y: produc1285161482t_char] :
( ( P_8
= ( produc24551831t_char @ X_1 @ Y ) )
=> ~ ( C_6 @ X_1 @ Y ) ) ) ).
thf(fact_385_splitE,axiom,
! [C_6: produc618524391on_val > produc618524391on_val > $o,P_8: produc1250491293on_val] :
( ( produc382956337_val_o @ C_6 @ P_8 )
=> ~ ! [X_1: produc618524391on_val,Y: produc618524391on_val] :
( ( P_8
= ( produc1347028499on_val @ X_1 @ Y ) )
=> ~ ( C_6 @ X_1 @ Y ) ) ) ).
thf(fact_386_splitE,axiom,
! [C_6: produc1746408499on_val > produc1746408499on_val > $o,P_8: produc652964533on_val] :
( ( produc154389913_val_o @ C_6 @ P_8 )
=> ~ ! [X_1: produc1746408499on_val,Y: produc1746408499on_val] :
( ( P_8
= ( produc345758123on_val @ X_1 @ Y ) )
=> ~ ( C_6 @ X_1 @ Y ) ) ) ).
thf(fact_387_splitE,axiom,
! [C_6: produc2090907612on_val > produc2090907612on_val > $o,P_8: produc1581780743on_val] :
( ( produc1377568711_val_o @ C_6 @ P_8 )
=> ~ ! [X_1: produc2090907612on_val,Y: produc2090907612on_val] :
( ( P_8
= ( produc259392253on_val @ X_1 @ Y ) )
=> ~ ( C_6 @ X_1 @ Y ) ) ) ).
thf(fact_388_splitE,axiom,
! [C_6: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,P_8: produc2090907612on_val] :
( ( produc252486962_val_o @ C_6 @ P_8 )
=> ~ ! [X_1: nat > option1728594148on_val,Y: list_char > option_val] :
( ( P_8
= ( produc755559506on_val @ X_1 @ Y ) )
=> ~ ( C_6 @ X_1 @ Y ) ) ) ).
thf(fact_389_splitE,axiom,
! [C_6: produc1282892786on_val > produc1282892786on_val > $o,P_8: produc1746408499on_val] :
( ( produc1624062875_val_o @ C_6 @ P_8 )
=> ~ ! [X_1: produc1282892786on_val,Y: produc1282892786on_val] :
( ( P_8
= ( produc833389609on_val @ X_1 @ Y ) )
=> ~ ( C_6 @ X_1 @ Y ) ) ) ).
thf(fact_390_splitE,axiom,
! [C_6: exp_list_char > produc2090907612on_val > $o,P_8: produc1282892786on_val] :
( ( produc1835097372_val_o @ C_6 @ P_8 )
=> ~ ! [X_1: exp_list_char,Y: produc2090907612on_val] :
( ( P_8
= ( produc235638504on_val @ X_1 @ Y ) )
=> ~ ( C_6 @ X_1 @ Y ) ) ) ).
thf(fact_391_splitE,axiom,
! [C_6: produc1180562163on_val > produc1180562163on_val > $o,P_8: produc618524391on_val] :
( ( produc2136448621_val_o @ C_6 @ P_8 )
=> ~ ! [X_1: produc1180562163on_val,Y: produc1180562163on_val] :
( ( P_8
= ( produc747700183on_val @ X_1 @ Y ) )
=> ~ ( C_6 @ X_1 @ Y ) ) ) ).
thf(fact_392_splitE,axiom,
! [C_6: list_exp_list_char > produc2090907612on_val > $o,P_8: produc1180562163on_val] :
( ( produc1841295295_val_o @ C_6 @ P_8 )
=> ~ ! [X_1: list_exp_list_char,Y: produc2090907612on_val] :
( ( P_8
= ( produc1302104557on_val @ X_1 @ Y ) )
=> ~ ( C_6 @ X_1 @ Y ) ) ) ).
thf(fact_393_splitE,axiom,
! [C_6: list_list_char > produc220283002t_char > $o,P_8: produc1285161482t_char] :
( ( produc1530867176char_o @ C_6 @ P_8 )
=> ~ ! [X_1: list_list_char,Y: produc220283002t_char] :
( ( P_8
= ( produc921874948t_char @ X_1 @ Y ) )
=> ~ ( C_6 @ X_1 @ Y ) ) ) ).
thf(fact_394_splitE,axiom,
! [C_6: list_ty > produc662261637t_char > $o,P_8: produc220283002t_char] :
( ( produc861054100char_o @ C_6 @ P_8 )
=> ~ ! [X_1: list_ty,Y: produc662261637t_char] :
( ( P_8
= ( produc1909267824t_char @ X_1 @ Y ) )
=> ~ ( C_6 @ X_1 @ Y ) ) ) ).
thf(fact_395_splitE,axiom,
! [C_6: list_val > exp_list_char > $o,P_8: produc662261637t_char] :
( ( produc525137097char_o @ C_6 @ P_8 )
=> ~ ! [X_1: list_val,Y: exp_list_char] :
( ( P_8
= ( produc1916172923t_char @ X_1 @ Y ) )
=> ~ ( C_6 @ X_1 @ Y ) ) ) ).
thf(fact_396_splitE,axiom,
! [C_6: list_char > ( produc1278157519t_char > option_val ) > $o,P_8: produc2088785539on_val] :
( ( produc765165771_val_o @ C_6 @ P_8 )
=> ~ ! [X_1: list_char,Y: produc1278157519t_char > option_val] :
( ( P_8
= ( produc926070009on_val @ X_1 @ Y ) )
=> ~ ( C_6 @ X_1 @ Y ) ) ) ).
thf(fact_397_splitE,axiom,
! [C_6: list_char > list_char > $o,P_8: produc1278157519t_char] :
( ( produc282231039char_o @ C_6 @ P_8 )
=> ~ ! [X_1: list_char,Y: list_char] :
( ( P_8
= ( produc5062597t_char @ X_1 @ Y ) )
=> ~ ( C_6 @ X_1 @ Y ) ) ) ).
thf(fact_398_splitI2,axiom,
! [C_5: produc1278157519t_char > produc1278157519t_char > $o,P_7: produc1350825965t_char] :
( ! [A_1: produc1278157519t_char,B_4: produc1278157519t_char] :
( ( P_7
= ( produc2080520419t_char @ A_1 @ B_4 ) )
=> ( C_5 @ A_1 @ B_4 ) )
=> ( produc2056220769char_o @ C_5 @ P_7 ) ) ).
thf(fact_399_splitI2,axiom,
! [C_5: produc2088785539on_val > produc2088785539on_val > $o,P_7: produc1368416213on_val] :
( ! [A_1: produc2088785539on_val,B_4: produc2088785539on_val] :
( ( P_7
= ( produc1773146955on_val @ A_1 @ B_4 ) )
=> ( C_5 @ A_1 @ B_4 ) )
=> ( produc791773177_val_o @ C_5 @ P_7 ) ) ).
thf(fact_400_splitI2,axiom,
! [C_5: produc662261637t_char > produc662261637t_char > $o,P_7: produc1826280281t_char] :
( ! [A_1: produc662261637t_char,B_4: produc662261637t_char] :
( ( P_7
= ( produc1299387215t_char @ A_1 @ B_4 ) )
=> ( C_5 @ A_1 @ B_4 ) )
=> ( produc1537651445char_o @ C_5 @ P_7 ) ) ).
thf(fact_401_splitI2,axiom,
! [C_5: produc220283002t_char > produc220283002t_char > $o,P_7: produc1406897475t_char] :
( ! [A_1: produc220283002t_char,B_4: produc220283002t_char] :
( ( P_7
= ( produc57279289t_char @ A_1 @ B_4 ) )
=> ( C_5 @ A_1 @ B_4 ) )
=> ( produc510191755char_o @ C_5 @ P_7 ) ) ).
thf(fact_402_splitI2,axiom,
! [C_5: produc1285161482t_char > produc1285161482t_char > $o,P_7: produc349695911t_char] :
( ! [A_1: produc1285161482t_char,B_4: produc1285161482t_char] :
( ( P_7
= ( produc24551831t_char @ A_1 @ B_4 ) )
=> ( C_5 @ A_1 @ B_4 ) )
=> ( produc865480877char_o @ C_5 @ P_7 ) ) ).
thf(fact_403_splitI2,axiom,
! [C_5: produc618524391on_val > produc618524391on_val > $o,P_7: produc1250491293on_val] :
( ! [A_1: produc618524391on_val,B_4: produc618524391on_val] :
( ( P_7
= ( produc1347028499on_val @ A_1 @ B_4 ) )
=> ( C_5 @ A_1 @ B_4 ) )
=> ( produc382956337_val_o @ C_5 @ P_7 ) ) ).
thf(fact_404_splitI2,axiom,
! [C_5: produc1746408499on_val > produc1746408499on_val > $o,P_7: produc652964533on_val] :
( ! [A_1: produc1746408499on_val,B_4: produc1746408499on_val] :
( ( P_7
= ( produc345758123on_val @ A_1 @ B_4 ) )
=> ( C_5 @ A_1 @ B_4 ) )
=> ( produc154389913_val_o @ C_5 @ P_7 ) ) ).
thf(fact_405_splitI2,axiom,
! [C_5: produc2090907612on_val > produc2090907612on_val > $o,P_7: produc1581780743on_val] :
( ! [A_1: produc2090907612on_val,B_4: produc2090907612on_val] :
( ( P_7
= ( produc259392253on_val @ A_1 @ B_4 ) )
=> ( C_5 @ A_1 @ B_4 ) )
=> ( produc1377568711_val_o @ C_5 @ P_7 ) ) ).
thf(fact_406_splitI2,axiom,
! [C_5: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,P_7: produc2090907612on_val] :
( ! [A_1: nat > option1728594148on_val,B_4: list_char > option_val] :
( ( P_7
= ( produc755559506on_val @ A_1 @ B_4 ) )
=> ( C_5 @ A_1 @ B_4 ) )
=> ( produc252486962_val_o @ C_5 @ P_7 ) ) ).
thf(fact_407_splitI2,axiom,
! [C_5: produc1282892786on_val > produc1282892786on_val > $o,P_7: produc1746408499on_val] :
( ! [A_1: produc1282892786on_val,B_4: produc1282892786on_val] :
( ( P_7
= ( produc833389609on_val @ A_1 @ B_4 ) )
=> ( C_5 @ A_1 @ B_4 ) )
=> ( produc1624062875_val_o @ C_5 @ P_7 ) ) ).
thf(fact_408_splitI2,axiom,
! [C_5: exp_list_char > produc2090907612on_val > $o,P_7: produc1282892786on_val] :
( ! [A_1: exp_list_char,B_4: produc2090907612on_val] :
( ( P_7
= ( produc235638504on_val @ A_1 @ B_4 ) )
=> ( C_5 @ A_1 @ B_4 ) )
=> ( produc1835097372_val_o @ C_5 @ P_7 ) ) ).
thf(fact_409_splitI2,axiom,
! [C_5: produc1180562163on_val > produc1180562163on_val > $o,P_7: produc618524391on_val] :
( ! [A_1: produc1180562163on_val,B_4: produc1180562163on_val] :
( ( P_7
= ( produc747700183on_val @ A_1 @ B_4 ) )
=> ( C_5 @ A_1 @ B_4 ) )
=> ( produc2136448621_val_o @ C_5 @ P_7 ) ) ).
thf(fact_410_splitI2,axiom,
! [C_5: list_exp_list_char > produc2090907612on_val > $o,P_7: produc1180562163on_val] :
( ! [A_1: list_exp_list_char,B_4: produc2090907612on_val] :
( ( P_7
= ( produc1302104557on_val @ A_1 @ B_4 ) )
=> ( C_5 @ A_1 @ B_4 ) )
=> ( produc1841295295_val_o @ C_5 @ P_7 ) ) ).
thf(fact_411_splitI2,axiom,
! [C_5: list_list_char > produc220283002t_char > $o,P_7: produc1285161482t_char] :
( ! [A_1: list_list_char,B_4: produc220283002t_char] :
( ( P_7
= ( produc921874948t_char @ A_1 @ B_4 ) )
=> ( C_5 @ A_1 @ B_4 ) )
=> ( produc1530867176char_o @ C_5 @ P_7 ) ) ).
thf(fact_412_splitI2,axiom,
! [C_5: list_ty > produc662261637t_char > $o,P_7: produc220283002t_char] :
( ! [A_1: list_ty,B_4: produc662261637t_char] :
( ( P_7
= ( produc1909267824t_char @ A_1 @ B_4 ) )
=> ( C_5 @ A_1 @ B_4 ) )
=> ( produc861054100char_o @ C_5 @ P_7 ) ) ).
thf(fact_413_splitI2,axiom,
! [C_5: list_val > exp_list_char > $o,P_7: produc662261637t_char] :
( ! [A_1: list_val,B_4: exp_list_char] :
( ( P_7
= ( produc1916172923t_char @ A_1 @ B_4 ) )
=> ( C_5 @ A_1 @ B_4 ) )
=> ( produc525137097char_o @ C_5 @ P_7 ) ) ).
thf(fact_414_splitI2,axiom,
! [C_5: list_char > ( produc1278157519t_char > option_val ) > $o,P_7: produc2088785539on_val] :
( ! [A_1: list_char,B_4: produc1278157519t_char > option_val] :
( ( P_7
= ( produc926070009on_val @ A_1 @ B_4 ) )
=> ( C_5 @ A_1 @ B_4 ) )
=> ( produc765165771_val_o @ C_5 @ P_7 ) ) ).
thf(fact_415_splitI2,axiom,
! [C_5: list_char > list_char > $o,P_7: produc1278157519t_char] :
( ! [A_1: list_char,B_4: list_char] :
( ( P_7
= ( produc5062597t_char @ A_1 @ B_4 ) )
=> ( C_5 @ A_1 @ B_4 ) )
=> ( produc282231039char_o @ C_5 @ P_7 ) ) ).
thf(fact_416_FAccReds,axiom,
! [F: list_char,D: list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAcc_list_char @ E @ F @ D ) @ S ) @ ( produc235638504on_val @ ( fAcc_list_char @ E_2 @ F @ D ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_417_CondReds,axiom,
! [E_1_1: exp_list_char,E_2_1: exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cond_list_char @ E @ E_1_1 @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( cond_list_char @ E_2 @ E_1_1 @ E_2_1 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_418_FAssReds1,axiom,
! [F: list_char,D: list_char,E_2_1: exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ E @ F @ D @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( fAss_list_char @ E_2 @ F @ D @ E_2_1 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_419_rtrancl_Ortrancl__refl,axiom,
! [A_8: produc1278157519t_char,R_12: produc1350825965t_char > $o] : ( member794220506t_char @ ( produc2080520419t_char @ A_8 @ A_8 ) @ ( transi1095029602t_char @ R_12 ) ) ).
thf(fact_420_rtrancl_Ortrancl__refl,axiom,
! [A_8: produc2088785539on_val,R_12: produc1368416213on_val > $o] : ( member1235075778on_val @ ( produc1773146955on_val @ A_8 @ A_8 ) @ ( transi1669211542on_val @ R_12 ) ) ).
thf(fact_421_rtrancl_Ortrancl__refl,axiom,
! [A_8: produc662261637t_char,R_12: produc1826280281t_char > $o] : ( member1161907014t_char @ ( produc1299387215t_char @ A_8 @ A_8 ) @ ( transi1789604888t_char @ R_12 ) ) ).
thf(fact_422_rtrancl_Ortrancl__refl,axiom,
! [A_8: produc220283002t_char,R_12: produc1406897475t_char > $o] : ( member125098544t_char @ ( produc57279289t_char @ A_8 @ A_8 ) @ ( transi1257872013t_char @ R_12 ) ) ).
thf(fact_423_rtrancl_Ortrancl__refl,axiom,
! [A_8: produc1285161482t_char,R_12: produc349695911t_char > $o] : ( member1420286996t_char @ ( produc24551831t_char @ A_8 @ A_8 ) @ ( transi122195895t_char @ R_12 ) ) ).
thf(fact_424_rtrancl_Ortrancl__refl,axiom,
! [A_8: produc618524391on_val,R_12: produc1250491293on_val > $o] : ( member1145216138on_val @ ( produc1347028499on_val @ A_8 @ A_8 ) @ ( transi1457397498on_val @ R_12 ) ) ).
thf(fact_425_rtrancl_Ortrancl__refl,axiom,
! [A_8: produc1746408499on_val,R_12: produc652964533on_val > $o] : ( member1714424482on_val @ ( produc345758123on_val @ A_8 @ A_8 ) @ ( transi130214086on_val @ R_12 ) ) ).
thf(fact_426_rtrancl_Ortrancl__refl,axiom,
! [A_8: produc2090907612on_val,R_12: produc1581780743on_val > $o] : ( member565037556on_val @ ( produc259392253on_val @ A_8 @ A_8 ) @ ( transi466770671on_val @ R_12 ) ) ).
thf(fact_427_rtrancl_Ortrancl__refl,axiom,
! [A_8: list_char,R_12: produc1278157519t_char > $o] : ( member1251428284t_char @ ( produc5062597t_char @ A_8 @ A_8 ) @ ( transi1395422419t_char @ R_12 ) ) ).
thf(fact_428_rtrancl_Ortrancl__refl,axiom,
! [A_8: produc1282892786on_val,R_12: produc1746408499on_val > $o] : ( member1913460000on_val @ ( produc833389609on_val @ A_8 @ A_8 ) @ ( transi2118771717on_val @ R_12 ) ) ).
thf(fact_429_rtrancl_Ortrancl__refl,axiom,
! [A_8: produc1180562163on_val,R_12: produc618524391on_val > $o] : ( member2042188884on_val @ ( produc747700183on_val @ A_8 @ A_8 ) @ ( transi808828192on_val @ R_12 ) ) ).
thf(fact_430_cond__split__eta,axiom,
! [G: produc2090907612on_val > $o,F_1: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o] :
( ! [X_1: nat > option1728594148on_val,Y: list_char > option_val] :
( ( F_1 @ X_1 @ Y )
<=> ( G @ ( produc755559506on_val @ X_1 @ Y ) ) )
=> ( ( produc252486962_val_o @ F_1 )
= G ) ) ).
thf(fact_431_r__into__rtrancl,axiom,
! [P_6: produc618524391on_val,R_11: produc618524391on_val > $o] :
( ( member2042188884on_val @ P_6 @ R_11 )
=> ( member2042188884on_val @ P_6 @ ( transi808828192on_val @ R_11 ) ) ) ).
thf(fact_432_r__into__rtrancl,axiom,
! [P_6: produc1746408499on_val,R_11: produc1746408499on_val > $o] :
( ( member1913460000on_val @ P_6 @ R_11 )
=> ( member1913460000on_val @ P_6 @ ( transi2118771717on_val @ R_11 ) ) ) ).
thf(fact_433_rtrancl__idemp,axiom,
! [R_10: produc618524391on_val > $o] :
( ( transi808828192on_val @ ( transi808828192on_val @ R_10 ) )
= ( transi808828192on_val @ R_10 ) ) ).
thf(fact_434_rtrancl__idemp,axiom,
! [R_10: produc1746408499on_val > $o] :
( ( transi2118771717on_val @ ( transi2118771717on_val @ R_10 ) )
= ( transi2118771717on_val @ R_10 ) ) ).
thf(fact_435_rtrancl__trans,axiom,
! [C_4: produc1180562163on_val,A_7: produc1180562163on_val,B_7: produc1180562163on_val,R_9: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ A_7 @ B_7 ) @ ( transi808828192on_val @ R_9 ) )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ B_7 @ C_4 ) @ ( transi808828192on_val @ R_9 ) )
=> ( member2042188884on_val @ ( produc747700183on_val @ A_7 @ C_4 ) @ ( transi808828192on_val @ R_9 ) ) ) ) ).
thf(fact_436_rtrancl__trans,axiom,
! [C_4: produc1282892786on_val,A_7: produc1282892786on_val,B_7: produc1282892786on_val,R_9: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_7 @ B_7 ) @ ( transi2118771717on_val @ R_9 ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ B_7 @ C_4 ) @ ( transi2118771717on_val @ R_9 ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ A_7 @ C_4 ) @ ( transi2118771717on_val @ R_9 ) ) ) ) ).
thf(fact_437_rtrancl__trans,axiom,
! [C_4: list_char,A_7: list_char,B_7: list_char,R_9: produc1278157519t_char > $o] :
( ( member1251428284t_char @ ( produc5062597t_char @ A_7 @ B_7 ) @ ( transi1395422419t_char @ R_9 ) )
=> ( ( member1251428284t_char @ ( produc5062597t_char @ B_7 @ C_4 ) @ ( transi1395422419t_char @ R_9 ) )
=> ( member1251428284t_char @ ( produc5062597t_char @ A_7 @ C_4 ) @ ( transi1395422419t_char @ R_9 ) ) ) ) ).
thf(fact_438_rtrancl_Ortrancl__into__rtrancl,axiom,
! [C_3: produc1180562163on_val,A_6: produc1180562163on_val,B_6: produc1180562163on_val,R_8: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ A_6 @ B_6 ) @ ( transi808828192on_val @ R_8 ) )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ B_6 @ C_3 ) @ R_8 )
=> ( member2042188884on_val @ ( produc747700183on_val @ A_6 @ C_3 ) @ ( transi808828192on_val @ R_8 ) ) ) ) ).
thf(fact_439_rtrancl_Ortrancl__into__rtrancl,axiom,
! [C_3: produc1282892786on_val,A_6: produc1282892786on_val,B_6: produc1282892786on_val,R_8: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_6 @ B_6 ) @ ( transi2118771717on_val @ R_8 ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ B_6 @ C_3 ) @ R_8 )
=> ( member1913460000on_val @ ( produc833389609on_val @ A_6 @ C_3 ) @ ( transi2118771717on_val @ R_8 ) ) ) ) ).
thf(fact_440_rtrancl_Ortrancl__into__rtrancl,axiom,
! [C_3: list_char,A_6: list_char,B_6: list_char,R_8: produc1278157519t_char > $o] :
( ( member1251428284t_char @ ( produc5062597t_char @ A_6 @ B_6 ) @ ( transi1395422419t_char @ R_8 ) )
=> ( ( member1251428284t_char @ ( produc5062597t_char @ B_6 @ C_3 ) @ R_8 )
=> ( member1251428284t_char @ ( produc5062597t_char @ A_6 @ C_3 ) @ ( transi1395422419t_char @ R_8 ) ) ) ) ).
thf(fact_441_converse__rtrancl__into__rtrancl,axiom,
! [C_2: produc1180562163on_val,A_5: produc1180562163on_val,B_5: produc1180562163on_val,R_7: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ A_5 @ B_5 ) @ R_7 )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ B_5 @ C_2 ) @ ( transi808828192on_val @ R_7 ) )
=> ( member2042188884on_val @ ( produc747700183on_val @ A_5 @ C_2 ) @ ( transi808828192on_val @ R_7 ) ) ) ) ).
thf(fact_442_converse__rtrancl__into__rtrancl,axiom,
! [C_2: produc1282892786on_val,A_5: produc1282892786on_val,B_5: produc1282892786on_val,R_7: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_5 @ B_5 ) @ R_7 )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ B_5 @ C_2 ) @ ( transi2118771717on_val @ R_7 ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ A_5 @ C_2 ) @ ( transi2118771717on_val @ R_7 ) ) ) ) ).
thf(fact_443_converse__rtrancl__into__rtrancl,axiom,
! [C_2: list_char,A_5: list_char,B_5: list_char,R_7: produc1278157519t_char > $o] :
( ( member1251428284t_char @ ( produc5062597t_char @ A_5 @ B_5 ) @ R_7 )
=> ( ( member1251428284t_char @ ( produc5062597t_char @ B_5 @ C_2 ) @ ( transi1395422419t_char @ R_7 ) )
=> ( member1251428284t_char @ ( produc5062597t_char @ A_5 @ C_2 ) @ ( transi1395422419t_char @ R_7 ) ) ) ) ).
thf(fact_444_rtrancl__induct2,axiom,
! [P_5: list_exp_list_char > produc2090907612on_val > $o,Ax_1: list_exp_list_char,Ay_1: produc2090907612on_val,Bx_1: list_exp_list_char,By_1: produc2090907612on_val,R_6: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Ax_1 @ Ay_1 ) @ ( produc1302104557on_val @ Bx_1 @ By_1 ) ) @ ( transi808828192on_val @ R_6 ) )
=> ( ( P_5 @ Ax_1 @ Ay_1 )
=> ( ! [A_1: list_exp_list_char,B_4: produc2090907612on_val,Aa: list_exp_list_char,Ba: produc2090907612on_val] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Ax_1 @ Ay_1 ) @ ( produc1302104557on_val @ A_1 @ B_4 ) ) @ ( transi808828192on_val @ R_6 ) )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ A_1 @ B_4 ) @ ( produc1302104557on_val @ Aa @ Ba ) ) @ R_6 )
=> ( ( P_5 @ A_1 @ B_4 )
=> ( P_5 @ Aa @ Ba ) ) ) )
=> ( P_5 @ Bx_1 @ By_1 ) ) ) ) ).
thf(fact_445_rtrancl__induct2,axiom,
! [P_5: exp_list_char > produc2090907612on_val > $o,Ax_1: exp_list_char,Ay_1: produc2090907612on_val,Bx_1: exp_list_char,By_1: produc2090907612on_val,R_6: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ Ax_1 @ Ay_1 ) @ ( produc235638504on_val @ Bx_1 @ By_1 ) ) @ ( transi2118771717on_val @ R_6 ) )
=> ( ( P_5 @ Ax_1 @ Ay_1 )
=> ( ! [A_1: exp_list_char,B_4: produc2090907612on_val,Aa: exp_list_char,Ba: produc2090907612on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ Ax_1 @ Ay_1 ) @ ( produc235638504on_val @ A_1 @ B_4 ) ) @ ( transi2118771717on_val @ R_6 ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ A_1 @ B_4 ) @ ( produc235638504on_val @ Aa @ Ba ) ) @ R_6 )
=> ( ( P_5 @ A_1 @ B_4 )
=> ( P_5 @ Aa @ Ba ) ) ) )
=> ( P_5 @ Bx_1 @ By_1 ) ) ) ) ).
thf(fact_446_rtrancl__induct2,axiom,
! [P_5: list_char > list_char > $o,Ax_1: list_char,Ay_1: list_char,Bx_1: list_char,By_1: list_char,R_6: produc1350825965t_char > $o] :
( ( member794220506t_char @ ( produc2080520419t_char @ ( produc5062597t_char @ Ax_1 @ Ay_1 ) @ ( produc5062597t_char @ Bx_1 @ By_1 ) ) @ ( transi1095029602t_char @ R_6 ) )
=> ( ( P_5 @ Ax_1 @ Ay_1 )
=> ( ! [A_1: list_char,B_4: list_char,Aa: list_char,Ba: list_char] :
( ( member794220506t_char @ ( produc2080520419t_char @ ( produc5062597t_char @ Ax_1 @ Ay_1 ) @ ( produc5062597t_char @ A_1 @ B_4 ) ) @ ( transi1095029602t_char @ R_6 ) )
=> ( ( member794220506t_char @ ( produc2080520419t_char @ ( produc5062597t_char @ A_1 @ B_4 ) @ ( produc5062597t_char @ Aa @ Ba ) ) @ R_6 )
=> ( ( P_5 @ A_1 @ B_4 )
=> ( P_5 @ Aa @ Ba ) ) ) )
=> ( P_5 @ Bx_1 @ By_1 ) ) ) ) ).
thf(fact_447_rtrancl__induct2,axiom,
! [P_5: list_char > ( produc1278157519t_char > option_val ) > $o,Ax_1: list_char,Ay_1: produc1278157519t_char > option_val,Bx_1: list_char,By_1: produc1278157519t_char > option_val,R_6: produc1368416213on_val > $o] :
( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ Ax_1 @ Ay_1 ) @ ( produc926070009on_val @ Bx_1 @ By_1 ) ) @ ( transi1669211542on_val @ R_6 ) )
=> ( ( P_5 @ Ax_1 @ Ay_1 )
=> ( ! [A_1: list_char,B_4: produc1278157519t_char > option_val,Aa: list_char,Ba: produc1278157519t_char > option_val] :
( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ Ax_1 @ Ay_1 ) @ ( produc926070009on_val @ A_1 @ B_4 ) ) @ ( transi1669211542on_val @ R_6 ) )
=> ( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ A_1 @ B_4 ) @ ( produc926070009on_val @ Aa @ Ba ) ) @ R_6 )
=> ( ( P_5 @ A_1 @ B_4 )
=> ( P_5 @ Aa @ Ba ) ) ) )
=> ( P_5 @ Bx_1 @ By_1 ) ) ) ) ).
thf(fact_448_rtrancl__induct2,axiom,
! [P_5: list_val > exp_list_char > $o,Ax_1: list_val,Ay_1: exp_list_char,Bx_1: list_val,By_1: exp_list_char,R_6: produc1826280281t_char > $o] :
( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ Ax_1 @ Ay_1 ) @ ( produc1916172923t_char @ Bx_1 @ By_1 ) ) @ ( transi1789604888t_char @ R_6 ) )
=> ( ( P_5 @ Ax_1 @ Ay_1 )
=> ( ! [A_1: list_val,B_4: exp_list_char,Aa: list_val,Ba: exp_list_char] :
( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ Ax_1 @ Ay_1 ) @ ( produc1916172923t_char @ A_1 @ B_4 ) ) @ ( transi1789604888t_char @ R_6 ) )
=> ( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ A_1 @ B_4 ) @ ( produc1916172923t_char @ Aa @ Ba ) ) @ R_6 )
=> ( ( P_5 @ A_1 @ B_4 )
=> ( P_5 @ Aa @ Ba ) ) ) )
=> ( P_5 @ Bx_1 @ By_1 ) ) ) ) ).
thf(fact_449_rtrancl__induct2,axiom,
! [P_5: list_ty > produc662261637t_char > $o,Ax_1: list_ty,Ay_1: produc662261637t_char,Bx_1: list_ty,By_1: produc662261637t_char,R_6: produc1406897475t_char > $o] :
( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ Ax_1 @ Ay_1 ) @ ( produc1909267824t_char @ Bx_1 @ By_1 ) ) @ ( transi1257872013t_char @ R_6 ) )
=> ( ( P_5 @ Ax_1 @ Ay_1 )
=> ( ! [A_1: list_ty,B_4: produc662261637t_char,Aa: list_ty,Ba: produc662261637t_char] :
( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ Ax_1 @ Ay_1 ) @ ( produc1909267824t_char @ A_1 @ B_4 ) ) @ ( transi1257872013t_char @ R_6 ) )
=> ( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ A_1 @ B_4 ) @ ( produc1909267824t_char @ Aa @ Ba ) ) @ R_6 )
=> ( ( P_5 @ A_1 @ B_4 )
=> ( P_5 @ Aa @ Ba ) ) ) )
=> ( P_5 @ Bx_1 @ By_1 ) ) ) ) ).
thf(fact_450_rtrancl__induct2,axiom,
! [P_5: list_list_char > produc220283002t_char > $o,Ax_1: list_list_char,Ay_1: produc220283002t_char,Bx_1: list_list_char,By_1: produc220283002t_char,R_6: produc349695911t_char > $o] :
( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ Ax_1 @ Ay_1 ) @ ( produc921874948t_char @ Bx_1 @ By_1 ) ) @ ( transi122195895t_char @ R_6 ) )
=> ( ( P_5 @ Ax_1 @ Ay_1 )
=> ( ! [A_1: list_list_char,B_4: produc220283002t_char,Aa: list_list_char,Ba: produc220283002t_char] :
( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ Ax_1 @ Ay_1 ) @ ( produc921874948t_char @ A_1 @ B_4 ) ) @ ( transi122195895t_char @ R_6 ) )
=> ( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ A_1 @ B_4 ) @ ( produc921874948t_char @ Aa @ Ba ) ) @ R_6 )
=> ( ( P_5 @ A_1 @ B_4 )
=> ( P_5 @ Aa @ Ba ) ) ) )
=> ( P_5 @ Bx_1 @ By_1 ) ) ) ) ).
thf(fact_451_rtrancl__induct2,axiom,
! [P_5: produc1180562163on_val > produc1180562163on_val > $o,Ax_1: produc1180562163on_val,Ay_1: produc1180562163on_val,Bx_1: produc1180562163on_val,By_1: produc1180562163on_val,R_6: produc1250491293on_val > $o] :
( ( member1145216138on_val @ ( produc1347028499on_val @ ( produc747700183on_val @ Ax_1 @ Ay_1 ) @ ( produc747700183on_val @ Bx_1 @ By_1 ) ) @ ( transi1457397498on_val @ R_6 ) )
=> ( ( P_5 @ Ax_1 @ Ay_1 )
=> ( ! [A_1: produc1180562163on_val,B_4: produc1180562163on_val,Aa: produc1180562163on_val,Ba: produc1180562163on_val] :
( ( member1145216138on_val @ ( produc1347028499on_val @ ( produc747700183on_val @ Ax_1 @ Ay_1 ) @ ( produc747700183on_val @ A_1 @ B_4 ) ) @ ( transi1457397498on_val @ R_6 ) )
=> ( ( member1145216138on_val @ ( produc1347028499on_val @ ( produc747700183on_val @ A_1 @ B_4 ) @ ( produc747700183on_val @ Aa @ Ba ) ) @ R_6 )
=> ( ( P_5 @ A_1 @ B_4 )
=> ( P_5 @ Aa @ Ba ) ) ) )
=> ( P_5 @ Bx_1 @ By_1 ) ) ) ) ).
thf(fact_452_rtrancl__induct2,axiom,
! [P_5: produc1282892786on_val > produc1282892786on_val > $o,Ax_1: produc1282892786on_val,Ay_1: produc1282892786on_val,Bx_1: produc1282892786on_val,By_1: produc1282892786on_val,R_6: produc652964533on_val > $o] :
( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ Ax_1 @ Ay_1 ) @ ( produc833389609on_val @ Bx_1 @ By_1 ) ) @ ( transi130214086on_val @ R_6 ) )
=> ( ( P_5 @ Ax_1 @ Ay_1 )
=> ( ! [A_1: produc1282892786on_val,B_4: produc1282892786on_val,Aa: produc1282892786on_val,Ba: produc1282892786on_val] :
( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ Ax_1 @ Ay_1 ) @ ( produc833389609on_val @ A_1 @ B_4 ) ) @ ( transi130214086on_val @ R_6 ) )
=> ( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ A_1 @ B_4 ) @ ( produc833389609on_val @ Aa @ Ba ) ) @ R_6 )
=> ( ( P_5 @ A_1 @ B_4 )
=> ( P_5 @ Aa @ Ba ) ) ) )
=> ( P_5 @ Bx_1 @ By_1 ) ) ) ) ).
thf(fact_453_rtrancl__induct2,axiom,
! [P_5: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,Ax_1: nat > option1728594148on_val,Ay_1: list_char > option_val,Bx_1: nat > option1728594148on_val,By_1: list_char > option_val,R_6: produc1581780743on_val > $o] :
( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ Ax_1 @ Ay_1 ) @ ( produc755559506on_val @ Bx_1 @ By_1 ) ) @ ( transi466770671on_val @ R_6 ) )
=> ( ( P_5 @ Ax_1 @ Ay_1 )
=> ( ! [A_1: nat > option1728594148on_val,B_4: list_char > option_val,Aa: nat > option1728594148on_val,Ba: list_char > option_val] :
( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ Ax_1 @ Ay_1 ) @ ( produc755559506on_val @ A_1 @ B_4 ) ) @ ( transi466770671on_val @ R_6 ) )
=> ( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ A_1 @ B_4 ) @ ( produc755559506on_val @ Aa @ Ba ) ) @ R_6 )
=> ( ( P_5 @ A_1 @ B_4 )
=> ( P_5 @ Aa @ Ba ) ) ) )
=> ( P_5 @ Bx_1 @ By_1 ) ) ) ) ).
thf(fact_454_converse__rtrancl__induct2,axiom,
! [P_4: list_exp_list_char > produc2090907612on_val > $o,Ax: list_exp_list_char,Ay: produc2090907612on_val,Bx: list_exp_list_char,By: produc2090907612on_val,R_5: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Ax @ Ay ) @ ( produc1302104557on_val @ Bx @ By ) ) @ ( transi808828192on_val @ R_5 ) )
=> ( ( P_4 @ Bx @ By )
=> ( ! [A_1: list_exp_list_char,B_4: produc2090907612on_val,Aa: list_exp_list_char,Ba: produc2090907612on_val] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ A_1 @ B_4 ) @ ( produc1302104557on_val @ Aa @ Ba ) ) @ R_5 )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Aa @ Ba ) @ ( produc1302104557on_val @ Bx @ By ) ) @ ( transi808828192on_val @ R_5 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_4 ) ) ) )
=> ( P_4 @ Ax @ Ay ) ) ) ) ).
thf(fact_455_converse__rtrancl__induct2,axiom,
! [P_4: exp_list_char > produc2090907612on_val > $o,Ax: exp_list_char,Ay: produc2090907612on_val,Bx: exp_list_char,By: produc2090907612on_val,R_5: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ Ax @ Ay ) @ ( produc235638504on_val @ Bx @ By ) ) @ ( transi2118771717on_val @ R_5 ) )
=> ( ( P_4 @ Bx @ By )
=> ( ! [A_1: exp_list_char,B_4: produc2090907612on_val,Aa: exp_list_char,Ba: produc2090907612on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ A_1 @ B_4 ) @ ( produc235638504on_val @ Aa @ Ba ) ) @ R_5 )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ Aa @ Ba ) @ ( produc235638504on_val @ Bx @ By ) ) @ ( transi2118771717on_val @ R_5 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_4 ) ) ) )
=> ( P_4 @ Ax @ Ay ) ) ) ) ).
thf(fact_456_converse__rtrancl__induct2,axiom,
! [P_4: list_char > list_char > $o,Ax: list_char,Ay: list_char,Bx: list_char,By: list_char,R_5: produc1350825965t_char > $o] :
( ( member794220506t_char @ ( produc2080520419t_char @ ( produc5062597t_char @ Ax @ Ay ) @ ( produc5062597t_char @ Bx @ By ) ) @ ( transi1095029602t_char @ R_5 ) )
=> ( ( P_4 @ Bx @ By )
=> ( ! [A_1: list_char,B_4: list_char,Aa: list_char,Ba: list_char] :
( ( member794220506t_char @ ( produc2080520419t_char @ ( produc5062597t_char @ A_1 @ B_4 ) @ ( produc5062597t_char @ Aa @ Ba ) ) @ R_5 )
=> ( ( member794220506t_char @ ( produc2080520419t_char @ ( produc5062597t_char @ Aa @ Ba ) @ ( produc5062597t_char @ Bx @ By ) ) @ ( transi1095029602t_char @ R_5 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_4 ) ) ) )
=> ( P_4 @ Ax @ Ay ) ) ) ) ).
thf(fact_457_converse__rtrancl__induct2,axiom,
! [P_4: list_char > ( produc1278157519t_char > option_val ) > $o,Ax: list_char,Ay: produc1278157519t_char > option_val,Bx: list_char,By: produc1278157519t_char > option_val,R_5: produc1368416213on_val > $o] :
( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ Ax @ Ay ) @ ( produc926070009on_val @ Bx @ By ) ) @ ( transi1669211542on_val @ R_5 ) )
=> ( ( P_4 @ Bx @ By )
=> ( ! [A_1: list_char,B_4: produc1278157519t_char > option_val,Aa: list_char,Ba: produc1278157519t_char > option_val] :
( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ A_1 @ B_4 ) @ ( produc926070009on_val @ Aa @ Ba ) ) @ R_5 )
=> ( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ Aa @ Ba ) @ ( produc926070009on_val @ Bx @ By ) ) @ ( transi1669211542on_val @ R_5 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_4 ) ) ) )
=> ( P_4 @ Ax @ Ay ) ) ) ) ).
thf(fact_458_converse__rtrancl__induct2,axiom,
! [P_4: list_val > exp_list_char > $o,Ax: list_val,Ay: exp_list_char,Bx: list_val,By: exp_list_char,R_5: produc1826280281t_char > $o] :
( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ Ax @ Ay ) @ ( produc1916172923t_char @ Bx @ By ) ) @ ( transi1789604888t_char @ R_5 ) )
=> ( ( P_4 @ Bx @ By )
=> ( ! [A_1: list_val,B_4: exp_list_char,Aa: list_val,Ba: exp_list_char] :
( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ A_1 @ B_4 ) @ ( produc1916172923t_char @ Aa @ Ba ) ) @ R_5 )
=> ( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ Aa @ Ba ) @ ( produc1916172923t_char @ Bx @ By ) ) @ ( transi1789604888t_char @ R_5 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_4 ) ) ) )
=> ( P_4 @ Ax @ Ay ) ) ) ) ).
thf(fact_459_converse__rtrancl__induct2,axiom,
! [P_4: list_ty > produc662261637t_char > $o,Ax: list_ty,Ay: produc662261637t_char,Bx: list_ty,By: produc662261637t_char,R_5: produc1406897475t_char > $o] :
( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ Ax @ Ay ) @ ( produc1909267824t_char @ Bx @ By ) ) @ ( transi1257872013t_char @ R_5 ) )
=> ( ( P_4 @ Bx @ By )
=> ( ! [A_1: list_ty,B_4: produc662261637t_char,Aa: list_ty,Ba: produc662261637t_char] :
( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ A_1 @ B_4 ) @ ( produc1909267824t_char @ Aa @ Ba ) ) @ R_5 )
=> ( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ Aa @ Ba ) @ ( produc1909267824t_char @ Bx @ By ) ) @ ( transi1257872013t_char @ R_5 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_4 ) ) ) )
=> ( P_4 @ Ax @ Ay ) ) ) ) ).
thf(fact_460_converse__rtrancl__induct2,axiom,
! [P_4: list_list_char > produc220283002t_char > $o,Ax: list_list_char,Ay: produc220283002t_char,Bx: list_list_char,By: produc220283002t_char,R_5: produc349695911t_char > $o] :
( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ Ax @ Ay ) @ ( produc921874948t_char @ Bx @ By ) ) @ ( transi122195895t_char @ R_5 ) )
=> ( ( P_4 @ Bx @ By )
=> ( ! [A_1: list_list_char,B_4: produc220283002t_char,Aa: list_list_char,Ba: produc220283002t_char] :
( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ A_1 @ B_4 ) @ ( produc921874948t_char @ Aa @ Ba ) ) @ R_5 )
=> ( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ Aa @ Ba ) @ ( produc921874948t_char @ Bx @ By ) ) @ ( transi122195895t_char @ R_5 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_4 ) ) ) )
=> ( P_4 @ Ax @ Ay ) ) ) ) ).
thf(fact_461_converse__rtrancl__induct2,axiom,
! [P_4: produc1180562163on_val > produc1180562163on_val > $o,Ax: produc1180562163on_val,Ay: produc1180562163on_val,Bx: produc1180562163on_val,By: produc1180562163on_val,R_5: produc1250491293on_val > $o] :
( ( member1145216138on_val @ ( produc1347028499on_val @ ( produc747700183on_val @ Ax @ Ay ) @ ( produc747700183on_val @ Bx @ By ) ) @ ( transi1457397498on_val @ R_5 ) )
=> ( ( P_4 @ Bx @ By )
=> ( ! [A_1: produc1180562163on_val,B_4: produc1180562163on_val,Aa: produc1180562163on_val,Ba: produc1180562163on_val] :
( ( member1145216138on_val @ ( produc1347028499on_val @ ( produc747700183on_val @ A_1 @ B_4 ) @ ( produc747700183on_val @ Aa @ Ba ) ) @ R_5 )
=> ( ( member1145216138on_val @ ( produc1347028499on_val @ ( produc747700183on_val @ Aa @ Ba ) @ ( produc747700183on_val @ Bx @ By ) ) @ ( transi1457397498on_val @ R_5 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_4 ) ) ) )
=> ( P_4 @ Ax @ Ay ) ) ) ) ).
thf(fact_462_converse__rtrancl__induct2,axiom,
! [P_4: produc1282892786on_val > produc1282892786on_val > $o,Ax: produc1282892786on_val,Ay: produc1282892786on_val,Bx: produc1282892786on_val,By: produc1282892786on_val,R_5: produc652964533on_val > $o] :
( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ Ax @ Ay ) @ ( produc833389609on_val @ Bx @ By ) ) @ ( transi130214086on_val @ R_5 ) )
=> ( ( P_4 @ Bx @ By )
=> ( ! [A_1: produc1282892786on_val,B_4: produc1282892786on_val,Aa: produc1282892786on_val,Ba: produc1282892786on_val] :
( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ A_1 @ B_4 ) @ ( produc833389609on_val @ Aa @ Ba ) ) @ R_5 )
=> ( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ Aa @ Ba ) @ ( produc833389609on_val @ Bx @ By ) ) @ ( transi130214086on_val @ R_5 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_4 ) ) ) )
=> ( P_4 @ Ax @ Ay ) ) ) ) ).
thf(fact_463_converse__rtrancl__induct2,axiom,
! [P_4: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,Ax: nat > option1728594148on_val,Ay: list_char > option_val,Bx: nat > option1728594148on_val,By: list_char > option_val,R_5: produc1581780743on_val > $o] :
( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ Ax @ Ay ) @ ( produc755559506on_val @ Bx @ By ) ) @ ( transi466770671on_val @ R_5 ) )
=> ( ( P_4 @ Bx @ By )
=> ( ! [A_1: nat > option1728594148on_val,B_4: list_char > option_val,Aa: nat > option1728594148on_val,Ba: list_char > option_val] :
( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ A_1 @ B_4 ) @ ( produc755559506on_val @ Aa @ Ba ) ) @ R_5 )
=> ( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ Aa @ Ba ) @ ( produc755559506on_val @ Bx @ By ) ) @ ( transi466770671on_val @ R_5 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_4 ) ) ) )
=> ( P_4 @ Ax @ Ay ) ) ) ) ).
thf(fact_464_converse__rtranclE2,axiom,
! [Xa_1: list_exp_list_char,Xb_1: produc2090907612on_val,Za: list_exp_list_char,Zb: produc2090907612on_val,R_4: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Xa_1 @ Xb_1 ) @ ( produc1302104557on_val @ Za @ Zb ) ) @ ( transi808828192on_val @ R_4 ) )
=> ( ( ( produc1302104557on_val @ Xa_1 @ Xb_1 )
!= ( produc1302104557on_val @ Za @ Zb ) )
=> ~ ! [A_1: list_exp_list_char,B_4: produc2090907612on_val] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Xa_1 @ Xb_1 ) @ ( produc1302104557on_val @ A_1 @ B_4 ) ) @ R_4 )
=> ~ ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ A_1 @ B_4 ) @ ( produc1302104557on_val @ Za @ Zb ) ) @ ( transi808828192on_val @ R_4 ) ) ) ) ) ).
thf(fact_465_converse__rtranclE2,axiom,
! [Xa_1: exp_list_char,Xb_1: produc2090907612on_val,Za: exp_list_char,Zb: produc2090907612on_val,R_4: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ Xa_1 @ Xb_1 ) @ ( produc235638504on_val @ Za @ Zb ) ) @ ( transi2118771717on_val @ R_4 ) )
=> ( ( ( produc235638504on_val @ Xa_1 @ Xb_1 )
!= ( produc235638504on_val @ Za @ Zb ) )
=> ~ ! [A_1: exp_list_char,B_4: produc2090907612on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ Xa_1 @ Xb_1 ) @ ( produc235638504on_val @ A_1 @ B_4 ) ) @ R_4 )
=> ~ ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ A_1 @ B_4 ) @ ( produc235638504on_val @ Za @ Zb ) ) @ ( transi2118771717on_val @ R_4 ) ) ) ) ) ).
thf(fact_466_converse__rtranclE2,axiom,
! [Xa_1: list_char,Xb_1: list_char,Za: list_char,Zb: list_char,R_4: produc1350825965t_char > $o] :
( ( member794220506t_char @ ( produc2080520419t_char @ ( produc5062597t_char @ Xa_1 @ Xb_1 ) @ ( produc5062597t_char @ Za @ Zb ) ) @ ( transi1095029602t_char @ R_4 ) )
=> ( ( ( produc5062597t_char @ Xa_1 @ Xb_1 )
!= ( produc5062597t_char @ Za @ Zb ) )
=> ~ ! [A_1: list_char,B_4: list_char] :
( ( member794220506t_char @ ( produc2080520419t_char @ ( produc5062597t_char @ Xa_1 @ Xb_1 ) @ ( produc5062597t_char @ A_1 @ B_4 ) ) @ R_4 )
=> ~ ( member794220506t_char @ ( produc2080520419t_char @ ( produc5062597t_char @ A_1 @ B_4 ) @ ( produc5062597t_char @ Za @ Zb ) ) @ ( transi1095029602t_char @ R_4 ) ) ) ) ) ).
thf(fact_467_converse__rtranclE2,axiom,
! [Xa_1: list_char,Xb_1: produc1278157519t_char > option_val,Za: list_char,Zb: produc1278157519t_char > option_val,R_4: produc1368416213on_val > $o] :
( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ Xa_1 @ Xb_1 ) @ ( produc926070009on_val @ Za @ Zb ) ) @ ( transi1669211542on_val @ R_4 ) )
=> ( ( ( produc926070009on_val @ Xa_1 @ Xb_1 )
!= ( produc926070009on_val @ Za @ Zb ) )
=> ~ ! [A_1: list_char,B_4: produc1278157519t_char > option_val] :
( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ Xa_1 @ Xb_1 ) @ ( produc926070009on_val @ A_1 @ B_4 ) ) @ R_4 )
=> ~ ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ A_1 @ B_4 ) @ ( produc926070009on_val @ Za @ Zb ) ) @ ( transi1669211542on_val @ R_4 ) ) ) ) ) ).
thf(fact_468_converse__rtranclE2,axiom,
! [Xa_1: list_val,Xb_1: exp_list_char,Za: list_val,Zb: exp_list_char,R_4: produc1826280281t_char > $o] :
( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ Xa_1 @ Xb_1 ) @ ( produc1916172923t_char @ Za @ Zb ) ) @ ( transi1789604888t_char @ R_4 ) )
=> ( ( ( produc1916172923t_char @ Xa_1 @ Xb_1 )
!= ( produc1916172923t_char @ Za @ Zb ) )
=> ~ ! [A_1: list_val,B_4: exp_list_char] :
( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ Xa_1 @ Xb_1 ) @ ( produc1916172923t_char @ A_1 @ B_4 ) ) @ R_4 )
=> ~ ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ A_1 @ B_4 ) @ ( produc1916172923t_char @ Za @ Zb ) ) @ ( transi1789604888t_char @ R_4 ) ) ) ) ) ).
thf(fact_469_converse__rtranclE2,axiom,
! [Xa_1: list_ty,Xb_1: produc662261637t_char,Za: list_ty,Zb: produc662261637t_char,R_4: produc1406897475t_char > $o] :
( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ Xa_1 @ Xb_1 ) @ ( produc1909267824t_char @ Za @ Zb ) ) @ ( transi1257872013t_char @ R_4 ) )
=> ( ( ( produc1909267824t_char @ Xa_1 @ Xb_1 )
!= ( produc1909267824t_char @ Za @ Zb ) )
=> ~ ! [A_1: list_ty,B_4: produc662261637t_char] :
( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ Xa_1 @ Xb_1 ) @ ( produc1909267824t_char @ A_1 @ B_4 ) ) @ R_4 )
=> ~ ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ A_1 @ B_4 ) @ ( produc1909267824t_char @ Za @ Zb ) ) @ ( transi1257872013t_char @ R_4 ) ) ) ) ) ).
thf(fact_470_converse__rtranclE2,axiom,
! [Xa_1: list_list_char,Xb_1: produc220283002t_char,Za: list_list_char,Zb: produc220283002t_char,R_4: produc349695911t_char > $o] :
( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ Xa_1 @ Xb_1 ) @ ( produc921874948t_char @ Za @ Zb ) ) @ ( transi122195895t_char @ R_4 ) )
=> ( ( ( produc921874948t_char @ Xa_1 @ Xb_1 )
!= ( produc921874948t_char @ Za @ Zb ) )
=> ~ ! [A_1: list_list_char,B_4: produc220283002t_char] :
( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ Xa_1 @ Xb_1 ) @ ( produc921874948t_char @ A_1 @ B_4 ) ) @ R_4 )
=> ~ ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ A_1 @ B_4 ) @ ( produc921874948t_char @ Za @ Zb ) ) @ ( transi122195895t_char @ R_4 ) ) ) ) ) ).
thf(fact_471_converse__rtranclE2,axiom,
! [Xa_1: produc1180562163on_val,Xb_1: produc1180562163on_val,Za: produc1180562163on_val,Zb: produc1180562163on_val,R_4: produc1250491293on_val > $o] :
( ( member1145216138on_val @ ( produc1347028499on_val @ ( produc747700183on_val @ Xa_1 @ Xb_1 ) @ ( produc747700183on_val @ Za @ Zb ) ) @ ( transi1457397498on_val @ R_4 ) )
=> ( ( ( produc747700183on_val @ Xa_1 @ Xb_1 )
!= ( produc747700183on_val @ Za @ Zb ) )
=> ~ ! [A_1: produc1180562163on_val,B_4: produc1180562163on_val] :
( ( member1145216138on_val @ ( produc1347028499on_val @ ( produc747700183on_val @ Xa_1 @ Xb_1 ) @ ( produc747700183on_val @ A_1 @ B_4 ) ) @ R_4 )
=> ~ ( member1145216138on_val @ ( produc1347028499on_val @ ( produc747700183on_val @ A_1 @ B_4 ) @ ( produc747700183on_val @ Za @ Zb ) ) @ ( transi1457397498on_val @ R_4 ) ) ) ) ) ).
thf(fact_472_converse__rtranclE2,axiom,
! [Xa_1: produc1282892786on_val,Xb_1: produc1282892786on_val,Za: produc1282892786on_val,Zb: produc1282892786on_val,R_4: produc652964533on_val > $o] :
( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ Xa_1 @ Xb_1 ) @ ( produc833389609on_val @ Za @ Zb ) ) @ ( transi130214086on_val @ R_4 ) )
=> ( ( ( produc833389609on_val @ Xa_1 @ Xb_1 )
!= ( produc833389609on_val @ Za @ Zb ) )
=> ~ ! [A_1: produc1282892786on_val,B_4: produc1282892786on_val] :
( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ Xa_1 @ Xb_1 ) @ ( produc833389609on_val @ A_1 @ B_4 ) ) @ R_4 )
=> ~ ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ A_1 @ B_4 ) @ ( produc833389609on_val @ Za @ Zb ) ) @ ( transi130214086on_val @ R_4 ) ) ) ) ) ).
thf(fact_473_converse__rtranclE2,axiom,
! [Xa_1: nat > option1728594148on_val,Xb_1: list_char > option_val,Za: nat > option1728594148on_val,Zb: list_char > option_val,R_4: produc1581780743on_val > $o] :
( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ Xa_1 @ Xb_1 ) @ ( produc755559506on_val @ Za @ Zb ) ) @ ( transi466770671on_val @ R_4 ) )
=> ( ( ( produc755559506on_val @ Xa_1 @ Xb_1 )
!= ( produc755559506on_val @ Za @ Zb ) )
=> ~ ! [A_1: nat > option1728594148on_val,B_4: list_char > option_val] :
( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ Xa_1 @ Xb_1 ) @ ( produc755559506on_val @ A_1 @ B_4 ) ) @ R_4 )
=> ~ ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ A_1 @ B_4 ) @ ( produc755559506on_val @ Za @ Zb ) ) @ ( transi466770671on_val @ R_4 ) ) ) ) ) ).
thf(fact_474_splitE2,axiom,
! [Q: $o > $o,P_3: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,Z_2: produc2090907612on_val] :
( ( Q @ ( produc252486962_val_o @ P_3 @ Z_2 ) )
=> ~ ! [X_1: nat > option1728594148on_val,Y: list_char > option_val] :
( ( Z_2
= ( produc755559506on_val @ X_1 @ Y ) )
=> ~ ( Q @ ( P_3 @ X_1 @ Y ) ) ) ) ).
thf(fact_475_rtranclE,axiom,
! [A_4: produc1180562163on_val,B_3: produc1180562163on_val,R_3: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ A_4 @ B_3 ) @ ( transi808828192on_val @ R_3 ) )
=> ( ( A_4 != B_3 )
=> ~ ! [Y: produc1180562163on_val] :
( ( member2042188884on_val @ ( produc747700183on_val @ A_4 @ Y ) @ ( transi808828192on_val @ R_3 ) )
=> ~ ( member2042188884on_val @ ( produc747700183on_val @ Y @ B_3 ) @ R_3 ) ) ) ) ).
thf(fact_476_rtranclE,axiom,
! [A_4: produc1282892786on_val,B_3: produc1282892786on_val,R_3: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_4 @ B_3 ) @ ( transi2118771717on_val @ R_3 ) )
=> ( ( A_4 != B_3 )
=> ~ ! [Y: produc1282892786on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_4 @ Y ) @ ( transi2118771717on_val @ R_3 ) )
=> ~ ( member1913460000on_val @ ( produc833389609on_val @ Y @ B_3 ) @ R_3 ) ) ) ) ).
thf(fact_477_rtranclE,axiom,
! [A_4: list_char,B_3: list_char,R_3: produc1278157519t_char > $o] :
( ( member1251428284t_char @ ( produc5062597t_char @ A_4 @ B_3 ) @ ( transi1395422419t_char @ R_3 ) )
=> ( ( A_4 != B_3 )
=> ~ ! [Y: list_char] :
( ( member1251428284t_char @ ( produc5062597t_char @ A_4 @ Y ) @ ( transi1395422419t_char @ R_3 ) )
=> ~ ( member1251428284t_char @ ( produc5062597t_char @ Y @ B_3 ) @ R_3 ) ) ) ) ).
thf(fact_478_converse__rtranclE,axiom,
! [X_2: produc1180562163on_val,Z_1: produc1180562163on_val,R_2: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ X_2 @ Z_1 ) @ ( transi808828192on_val @ R_2 ) )
=> ( ( X_2 != Z_1 )
=> ~ ! [Y: produc1180562163on_val] :
( ( member2042188884on_val @ ( produc747700183on_val @ X_2 @ Y ) @ R_2 )
=> ~ ( member2042188884on_val @ ( produc747700183on_val @ Y @ Z_1 ) @ ( transi808828192on_val @ R_2 ) ) ) ) ) ).
thf(fact_479_converse__rtranclE,axiom,
! [X_2: produc1282892786on_val,Z_1: produc1282892786on_val,R_2: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ X_2 @ Z_1 ) @ ( transi2118771717on_val @ R_2 ) )
=> ( ( X_2 != Z_1 )
=> ~ ! [Y: produc1282892786on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ X_2 @ Y ) @ R_2 )
=> ~ ( member1913460000on_val @ ( produc833389609on_val @ Y @ Z_1 ) @ ( transi2118771717on_val @ R_2 ) ) ) ) ) ).
thf(fact_480_converse__rtranclE,axiom,
! [X_2: list_char,Z_1: list_char,R_2: produc1278157519t_char > $o] :
( ( member1251428284t_char @ ( produc5062597t_char @ X_2 @ Z_1 ) @ ( transi1395422419t_char @ R_2 ) )
=> ( ( X_2 != Z_1 )
=> ~ ! [Y: list_char] :
( ( member1251428284t_char @ ( produc5062597t_char @ X_2 @ Y ) @ R_2 )
=> ~ ( member1251428284t_char @ ( produc5062597t_char @ Y @ Z_1 ) @ ( transi1395422419t_char @ R_2 ) ) ) ) ) ).
thf(fact_481_converse__rtrancl__induct,axiom,
! [P_2: produc1180562163on_val > $o,A_3: produc1180562163on_val,B_2: produc1180562163on_val,R_1: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ A_3 @ B_2 ) @ ( transi808828192on_val @ R_1 ) )
=> ( ( P_2 @ B_2 )
=> ( ! [Y: produc1180562163on_val,Z: produc1180562163on_val] :
( ( member2042188884on_val @ ( produc747700183on_val @ Y @ Z ) @ R_1 )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ Z @ B_2 ) @ ( transi808828192on_val @ R_1 ) )
=> ( ( P_2 @ Z )
=> ( P_2 @ Y ) ) ) )
=> ( P_2 @ A_3 ) ) ) ) ).
thf(fact_482_converse__rtrancl__induct,axiom,
! [P_2: produc1282892786on_val > $o,A_3: produc1282892786on_val,B_2: produc1282892786on_val,R_1: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_3 @ B_2 ) @ ( transi2118771717on_val @ R_1 ) )
=> ( ( P_2 @ B_2 )
=> ( ! [Y: produc1282892786on_val,Z: produc1282892786on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ Y @ Z ) @ R_1 )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ Z @ B_2 ) @ ( transi2118771717on_val @ R_1 ) )
=> ( ( P_2 @ Z )
=> ( P_2 @ Y ) ) ) )
=> ( P_2 @ A_3 ) ) ) ) ).
thf(fact_483_converse__rtrancl__induct,axiom,
! [P_2: list_char > $o,A_3: list_char,B_2: list_char,R_1: produc1278157519t_char > $o] :
( ( member1251428284t_char @ ( produc5062597t_char @ A_3 @ B_2 ) @ ( transi1395422419t_char @ R_1 ) )
=> ( ( P_2 @ B_2 )
=> ( ! [Y: list_char,Z: list_char] :
( ( member1251428284t_char @ ( produc5062597t_char @ Y @ Z ) @ R_1 )
=> ( ( member1251428284t_char @ ( produc5062597t_char @ Z @ B_2 ) @ ( transi1395422419t_char @ R_1 ) )
=> ( ( P_2 @ Z )
=> ( P_2 @ Y ) ) ) )
=> ( P_2 @ A_3 ) ) ) ) ).
thf(fact_484_rtrancl__induct,axiom,
! [P_1: produc1180562163on_val > $o,A_2: produc1180562163on_val,B_1: produc1180562163on_val,R: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ A_2 @ B_1 ) @ ( transi808828192on_val @ R ) )
=> ( ( P_1 @ A_2 )
=> ( ! [Y: produc1180562163on_val,Z: produc1180562163on_val] :
( ( member2042188884on_val @ ( produc747700183on_val @ A_2 @ Y ) @ ( transi808828192on_val @ R ) )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ Y @ Z ) @ R )
=> ( ( P_1 @ Y )
=> ( P_1 @ Z ) ) ) )
=> ( P_1 @ B_1 ) ) ) ) ).
thf(fact_485_rtrancl__induct,axiom,
! [P_1: produc1282892786on_val > $o,A_2: produc1282892786on_val,B_1: produc1282892786on_val,R: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_2 @ B_1 ) @ ( transi2118771717on_val @ R ) )
=> ( ( P_1 @ A_2 )
=> ( ! [Y: produc1282892786on_val,Z: produc1282892786on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_2 @ Y ) @ ( transi2118771717on_val @ R ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ Y @ Z ) @ R )
=> ( ( P_1 @ Y )
=> ( P_1 @ Z ) ) ) )
=> ( P_1 @ B_1 ) ) ) ) ).
thf(fact_486_rtrancl__induct,axiom,
! [P_1: list_char > $o,A_2: list_char,B_1: list_char,R: produc1278157519t_char > $o] :
( ( member1251428284t_char @ ( produc5062597t_char @ A_2 @ B_1 ) @ ( transi1395422419t_char @ R ) )
=> ( ( P_1 @ A_2 )
=> ( ! [Y: list_char,Z: list_char] :
( ( member1251428284t_char @ ( produc5062597t_char @ A_2 @ Y ) @ ( transi1395422419t_char @ R ) )
=> ( ( member1251428284t_char @ ( produc5062597t_char @ Y @ Z ) @ R )
=> ( ( P_1 @ Y )
=> ( P_1 @ Z ) ) ) )
=> ( P_1 @ B_1 ) ) ) ) ).
thf(fact_487_FAssReds2,axiom,
! [V: val,F: list_char,D: list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ ( val_list_char @ V ) @ F @ D @ E ) @ S ) @ ( produc235638504on_val @ ( fAss_list_char @ ( val_list_char @ V ) @ F @ D @ E_2 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_488_WhileRedsThrow,axiom,
! [C_1: exp_list_char,B: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ B @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( while_list_char @ B @ C_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_489_FAccRedsThrow,axiom,
! [F: list_char,D: list_char,E: exp_list_char,S: produc2090907612on_val,A: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAcc_list_char @ E @ F @ D ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_490_exp_Osimps_I14_J,axiom,
! [Exp_3: exp_list_char,Exp_2: exp_list_char] :
( ( ( throw_list_char @ Exp_3 )
= ( throw_list_char @ Exp_2 ) )
<=> ( Exp_3 = Exp_2 ) ) ).
thf(fact_491_exp_Osimps_I3_J,axiom,
! [Val_5: val,Val_4: val] :
( ( ( val_list_char @ Val_5 )
= ( val_list_char @ Val_4 ) )
<=> ( Val_5 = Val_4 ) ) ).
thf(fact_492_exp_Osimps_I91_J,axiom,
! [Exp_1: exp_list_char,Val_3: val] :
( ( throw_list_char @ Exp_1 )
!= ( val_list_char @ Val_3 ) ) ).
thf(fact_493_exp_Osimps_I90_J,axiom,
! [Val_2: val,Exp: exp_list_char] :
( ( val_list_char @ Val_2 )
!= ( throw_list_char @ Exp ) ) ).
thf(fact_494_exp_Osimps_I78_J,axiom,
! [Val_1: val,Exp1_1: exp_list_char,List1_1: list_char,List2_1: list_char,Exp2_1: exp_list_char] :
( ( val_list_char @ Val_1 )
!= ( fAss_list_char @ Exp1_1 @ List1_1 @ List2_1 @ Exp2_1 ) ) ).
thf(fact_495_exp_Osimps_I79_J,axiom,
! [Exp1: exp_list_char,List1: list_char,List2: list_char,Exp2: exp_list_char,Val: val] :
( ( fAss_list_char @ Exp1 @ List1 @ List2 @ Exp2 )
!= ( val_list_char @ Val ) ) ).
thf(fact_496_red__reds_OFAssThrow2,axiom,
! [V: val,F: list_char,D: list_char,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ ( val_list_char @ V ) @ F @ D @ ( throw_list_char @ E ) ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_497_FAssRedsThrow2,axiom,
! [F: list_char,D: list_char,E_2_1: exp_list_char,E: exp_list_char,S_2_1: produc2090907612on_val,E_1_1: exp_list_char,S_0: produc2090907612on_val,V: val,S_1_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1_1 @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ S_1_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_2_1 @ S_1_1 ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ E_1_1 @ F @ D @ E_2_1 ) @ S_0 ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_498_red__reds_OThrowThrow,axiom,
! [E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( throw_list_char @ ( throw_list_char @ E ) ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_499_red__reds_OThrowRed,axiom,
! [E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E_2 ) @ S_1 ) ) @ ( red @ P ) ) ) ).
thf(fact_500_ThrowReds,axiom,
! [E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E_2 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_501_ThrowRedsThrow,axiom,
! [E: exp_list_char,S: produc2090907612on_val,A: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_502_red__reds_OFAssThrow1,axiom,
! [E: exp_list_char,F: list_char,D: list_char,E_2_1: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ ( throw_list_char @ E ) @ F @ D @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_503_red__reds_OCondThrow,axiom,
! [E: exp_list_char,E_1_1: exp_list_char,E_2_1: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cond_list_char @ ( throw_list_char @ E ) @ E_1_1 @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_504_red__reds_OFAccThrow,axiom,
! [E: exp_list_char,F: list_char,D: list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAcc_list_char @ ( throw_list_char @ E ) @ F @ D ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_505_red__reds_OFAssRed2,axiom,
! [V: val,F: list_char,D: list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ ( val_list_char @ V ) @ F @ D @ E ) @ S ) @ ( produc235638504on_val @ ( fAss_list_char @ ( val_list_char @ V ) @ F @ D @ E_2 ) @ S_1 ) ) @ ( red @ P ) ) ) ).
thf(fact_506_FAssRedsThrow1,axiom,
! [F: list_char,D: list_char,E_2_1: exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E_2 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ E @ F @ D @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E_2 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_507_CondRedsThrow,axiom,
! [E_1_1: exp_list_char,E_2_1: exp_list_char,E: exp_list_char,S: produc2090907612on_val,A: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cond_list_char @ E @ E_1_1 @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_508_WhileTRedsThrow,axiom,
! [C_1: exp_list_char,E: exp_list_char,S_2_1: produc2090907612on_val,B: exp_list_char,S_0: produc2090907612on_val,S_1_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ B @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ ( bool @ $true ) ) @ S_1_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ C_1 @ S_1_1 ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( while_list_char @ B @ C_1 ) @ S_0 ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_509_WhileTReds,axiom,
! [E: exp_list_char,S_3_1: produc2090907612on_val,C_1: exp_list_char,V_1_2: val,S_2_1: produc2090907612on_val,B: exp_list_char,S_0: produc2090907612on_val,S_1_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ B @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ ( bool @ $true ) ) @ S_1_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ C_1 @ S_1_1 ) @ ( produc235638504on_val @ ( val_list_char @ V_1_2 ) @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( while_list_char @ B @ C_1 ) @ S_2_1 ) @ ( produc235638504on_val @ E @ S_3_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( while_list_char @ B @ C_1 ) @ S_0 ) @ ( produc235638504on_val @ E @ S_3_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ).
thf(fact_510_CondReds2F,axiom,
! [E_1_1: exp_list_char,E_2_1: exp_list_char,E_2: exp_list_char,S_2_1: produc2090907612on_val,E: exp_list_char,S_0: produc2090907612on_val,S_1_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ ( bool @ $false ) ) @ S_1_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_2_1 @ S_1_1 ) @ ( produc235638504on_val @ E_2 @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cond_list_char @ E @ E_1_1 @ E_2_1 ) @ S_0 ) @ ( produc235638504on_val @ E_2 @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_511_CondReds2T,axiom,
! [E_2_1: exp_list_char,E_1_1: exp_list_char,E_2: exp_list_char,S_2_1: produc2090907612on_val,E: exp_list_char,S_0: produc2090907612on_val,S_1_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ ( bool @ $true ) ) @ S_1_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1_1 @ S_1_1 ) @ ( produc235638504on_val @ E_2 @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cond_list_char @ E @ E_1_1 @ E_2_1 ) @ S_0 ) @ ( produc235638504on_val @ E_2 @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_512_WTrtThrow,axiom,
! [T: ty,P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: list_char > option_ty,E: exp_list_char,T_r_1: ty] :
( ( wTrt @ P @ H @ E_1 @ E @ T_r_1 )
=> ( ( is_refT @ T_r_1 )
=> ( wTrt @ P @ H @ E_1 @ ( throw_list_char @ E ) @ T ) ) ) ).
thf(fact_513_BinOpRedsThrow2,axiom,
! [Bop: bop,E_2_1: exp_list_char,E: exp_list_char,S_2_1: produc2090907612on_val,E_1_1: exp_list_char,S_0: produc2090907612on_val,V_1_2: val,S_1_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1_1 @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ V_1_2 ) @ S_1_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_2_1 @ S_1_1 ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ E_1_1 @ Bop @ E_2_1 ) @ S_0 ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_514_red__reds_ORedCondT,axiom,
! [E_1_1: exp_list_char,E_2_1: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cond_list_char @ ( val_list_char @ ( bool @ $true ) ) @ E_1_1 @ E_2_1 ) @ S ) @ ( produc235638504on_val @ E_1_1 @ S ) ) @ ( red @ P ) ) ).
thf(fact_515_red__reds_OBinOpRed1,axiom,
! [Bop: bop,E_2_1: exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ E @ Bop @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( binOp_list_char @ E_2 @ Bop @ E_2_1 ) @ S_1 ) ) @ ( red @ P ) ) ) ).
thf(fact_516_red__reds_OBinOpRed2,axiom,
! [V_1_2: val,Bop: bop,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ ( val_list_char @ V_1_2 ) @ Bop @ E ) @ S ) @ ( produc235638504on_val @ ( binOp_list_char @ ( val_list_char @ V_1_2 ) @ Bop @ E_2 ) @ S_1 ) ) @ ( red @ P ) ) ) ).
thf(fact_517_red__reds_OBinOpThrow1,axiom,
! [E: exp_list_char,Bop: bop,E_2_1: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ ( throw_list_char @ E ) @ Bop @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_518_BinOp1Reds,axiom,
! [Bop: bop,E_2_1: exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ E @ Bop @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( binOp_list_char @ E_2 @ Bop @ E_2_1 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_519_red__reds_OBinOpThrow2,axiom,
! [V_1_2: val,Bop: bop,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ ( val_list_char @ V_1_2 ) @ Bop @ ( throw_list_char @ E ) ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_520_BinOp2Reds,axiom,
! [V: val,Bop: bop,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ ( val_list_char @ V ) @ Bop @ E ) @ S ) @ ( produc235638504on_val @ ( binOp_list_char @ ( val_list_char @ V ) @ Bop @ E_2 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_521_BinOpRedsThrow1,axiom,
! [Bop: bop,E_2_1: exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E_2 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ E @ Bop @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E_2 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_522_red__reds_ORedCondF,axiom,
! [E_1_1: exp_list_char,E_2_1: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cond_list_char @ ( val_list_char @ ( bool @ $false ) ) @ E_1_1 @ E_2_1 ) @ S ) @ ( produc235638504on_val @ E_2_1 @ S ) ) @ ( red @ P ) ) ).
thf(fact_523_WTrt__elim__cases_I4_J,axiom,
! [P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: list_char > option_ty,E: exp_list_char,T: ty] :
( ( wTrt @ P @ H @ E_1 @ ( throw_list_char @ E ) @ T )
=> ~ ! [T_r: ty] :
( ( wTrt @ P @ H @ E_1 @ E @ T_r )
=> ~ ( is_refT @ T_r ) ) ) ).
thf(fact_524_WhileFReds,axiom,
! [C_1: exp_list_char,B: exp_list_char,S: produc2090907612on_val,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ B @ S ) @ ( produc235638504on_val @ ( val_list_char @ ( bool @ $false ) ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( while_list_char @ B @ C_1 ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ unit ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_525_WTrtBinOpEq,axiom,
! [E_2_1: exp_list_char,T_2_1: ty,P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: list_char > option_ty,E_1_1: exp_list_char,T_1_1: ty] :
( ( wTrt @ P @ H @ E_1 @ E_1_1 @ T_1_1 )
=> ( ( wTrt @ P @ H @ E_1 @ E_2_1 @ T_2_1 )
=> ( wTrt @ P @ H @ E_1 @ ( binOp_list_char @ E_1_1 @ c_Expr_Obop_OEq @ E_2_1 ) @ boolean ) ) ) ).
thf(fact_526_TryRedsVal,axiom,
! [C: list_char,V_1: list_char,E_2_1: exp_list_char,E: exp_list_char,S: produc2090907612on_val,V: val,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( tryCatch_list_char @ E @ C @ V_1 @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_527_CastRedsThrow,axiom,
! [C: list_char,E: exp_list_char,S: produc2090907612on_val,A: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C @ E ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_528_CallRedsThrowObj,axiom,
! [M: list_char,Es: list_exp_list_char,E: exp_list_char,S0: produc2090907612on_val,A: exp_list_char,S_1_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S0 ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_1_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ E @ M @ Es ) @ S0 ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_1_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_529_red__reds_OCallObj,axiom,
! [M: list_char,Es: list_exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ E @ M @ Es ) @ S ) @ ( produc235638504on_val @ ( call_list_char @ E_2 @ M @ Es ) @ S_1 ) ) @ ( red @ P ) ) ) ).
thf(fact_530_red__reds_OCastRed,axiom,
! [C: list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C @ E ) @ S ) @ ( produc235638504on_val @ ( cast_list_char @ C @ E_2 ) @ S_1 ) ) @ ( red @ P ) ) ) ).
thf(fact_531_red__reds_OTryRed,axiom,
! [C: list_char,V_1: list_char,E_2_1: exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( tryCatch_list_char @ E @ C @ V_1 @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( tryCatch_list_char @ E_2 @ C @ V_1 @ E_2_1 ) @ S_1 ) ) @ ( red @ P ) ) ) ).
thf(fact_532_red__reds_OCallThrowObj,axiom,
! [E: exp_list_char,M: list_char,Es: list_exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ ( throw_list_char @ E ) @ M @ Es ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_533_CallRedsObj,axiom,
! [M: list_char,Es: list_exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ E @ M @ Es ) @ S ) @ ( produc235638504on_val @ ( call_list_char @ E_2 @ M @ Es ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_534_red__reds_OCastThrow,axiom,
! [C: list_char,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C @ ( throw_list_char @ E ) ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_535_CastReds,axiom,
! [C: list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C @ E ) @ S ) @ ( produc235638504on_val @ ( cast_list_char @ C @ E_2 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_536_red__reds_ORedTry,axiom,
! [V: val,C: list_char,V_1: list_char,E_2_1: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( tryCatch_list_char @ ( val_list_char @ V ) @ C @ V_1 @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_537_TryReds,axiom,
! [C: list_char,V_1: list_char,E_2_1: exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( tryCatch_list_char @ E @ C @ V_1 @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( tryCatch_list_char @ E_2 @ C @ V_1 @ E_2_1 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_538_CallRedsParams,axiom,
! [V: val,M: list_char,Es: list_exp_list_char,S: produc2090907612on_val,Es_3: list_exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ S ) @ ( produc1302104557on_val @ Es_3 @ S_1 ) ) @ ( transi808828192on_val @ ( reds @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ ( val_list_char @ V ) @ M @ Es ) @ S ) @ ( produc235638504on_val @ ( call_list_char @ ( val_list_char @ V ) @ M @ Es_3 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_539_val_Osimps_I7_J,axiom,
! [Bool_1: $o] :
( ( bool @ Bool_1 )
!= unit ) ).
thf(fact_540_val_Osimps_I6_J,axiom,
! [Bool_1: $o] :
( unit
!= ( bool @ Bool_1 ) ) ).
thf(fact_541_red__reds_ORedWhile,axiom,
! [B: exp_list_char,C_1: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( while_list_char @ B @ C_1 ) @ S ) @ ( produc235638504on_val @ ( cond_list_char @ B @ ( seq_list_char @ C_1 @ ( while_list_char @ B @ C_1 ) ) @ ( val_list_char @ unit ) ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_542_CastRedsNull,axiom,
! [C: list_char,E: exp_list_char,S: produc2090907612on_val,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ ( val_list_char @ null ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C @ E ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ null ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_543_WTrtSeq,axiom,
! [E_2_1: exp_list_char,T_2_1: ty,P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: list_char > option_ty,E_1_1: exp_list_char,T_1_1: ty] :
( ( wTrt @ P @ H @ E_1 @ E_1_1 @ T_1_1 )
=> ( ( wTrt @ P @ H @ E_1 @ E_2_1 @ T_2_1 )
=> ( wTrt @ P @ H @ E_1 @ ( seq_list_char @ E_1_1 @ E_2_1 ) @ T_2_1 ) ) ) ).
thf(fact_544_val_Osimps_I5_J,axiom,
null != unit ).
thf(fact_545_val_Osimps_I4_J,axiom,
unit != null ).
thf(fact_546_val_Osimps_I12_J,axiom,
! [Bool_1: $o] :
( null
!= ( bool @ Bool_1 ) ) ).
thf(fact_547_val_Osimps_I13_J,axiom,
! [Bool_1: $o] :
( ( bool @ Bool_1 )
!= null ) ).
thf(fact_548_red__reds_OSeqRed,axiom,
! [E_2_1: exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( seq_list_char @ E @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( seq_list_char @ E_2 @ E_2_1 ) @ S_1 ) ) @ ( red @ P ) ) ) ).
thf(fact_549_reds__hext__incr,axiom,
! [Es: list_exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,Es_3: list_exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,P: list_P1999446415t_char] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ ( produc755559506on_val @ H @ L ) ) @ ( produc1302104557on_val @ Es_3 @ ( produc755559506on_val @ H_1 @ L_1 ) ) ) @ ( reds @ P ) )
=> ( hext @ H @ H_1 ) ) ).
thf(fact_550_val_Osimps_I1_J,axiom,
! [Bool: $o,Bool_1: $o] :
( ( ( bool @ Bool )
= ( bool @ Bool_1 ) )
<=> ( Bool
<=> Bool_1 ) ) ).
thf(fact_551_red__reds_ORedSeq,axiom,
! [V: val,E_2_1: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( seq_list_char @ ( val_list_char @ V ) @ E_2_1 ) @ S ) @ ( produc235638504on_val @ E_2_1 @ S ) ) @ ( red @ P ) ) ).
thf(fact_552_red__reds_OSeqThrow,axiom,
! [E: exp_list_char,E_2_1: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( seq_list_char @ ( throw_list_char @ E ) @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_553_SeqReds,axiom,
! [E_2_1: exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( seq_list_char @ E @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( seq_list_char @ E_2 @ E_2_1 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_554_SeqReds2,axiom,
! [E_2_1: exp_list_char,E_2_2: exp_list_char,S_2_1: produc2090907612on_val,E_1_1: exp_list_char,S_0: produc2090907612on_val,V_1_2: val,S_1_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1_1 @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ V_1_2 ) @ S_1_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_2_1 @ S_1_1 ) @ ( produc235638504on_val @ E_2_2 @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( seq_list_char @ E_1_1 @ E_2_1 ) @ S_0 ) @ ( produc235638504on_val @ E_2_2 @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_555_SeqRedsThrow,axiom,
! [E_2_1: exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E_2 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( seq_list_char @ E @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E_2 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_556_red__reds_ORedCastNull,axiom,
! [C: list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C @ ( val_list_char @ null ) ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ null ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_557_red__reds_OCallParams,axiom,
! [V: val,M: list_char,Es: list_exp_list_char,S: produc2090907612on_val,Es_3: list_exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ S ) @ ( produc1302104557on_val @ Es_3 @ S_1 ) ) @ ( reds @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ ( val_list_char @ V ) @ M @ Es ) @ S ) @ ( produc235638504on_val @ ( call_list_char @ ( val_list_char @ V ) @ M @ Es_3 ) @ S_1 ) ) @ ( red @ P ) ) ) ).
thf(fact_558_ListRedsVal,axiom,
! [Es: list_exp_list_char,Es_3: list_exp_list_char,S_2_1: produc2090907612on_val,E: exp_list_char,S_0: produc2090907612on_val,V: val,S_1_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ S_1_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ S_1_1 ) @ ( produc1302104557on_val @ Es_3 @ S_2_1 ) ) @ ( transi808828192on_val @ ( reds @ P ) ) )
=> ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ ( cons_exp_list_char @ E @ Es ) @ S_0 ) @ ( produc1302104557on_val @ ( cons_exp_list_char @ ( val_list_char @ V ) @ Es_3 ) @ S_2_1 ) ) @ ( transi808828192on_val @ ( reds @ P ) ) ) ) ) ).
thf(fact_559_ListReds1,axiom,
! [Es: list_exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ ( cons_exp_list_char @ E @ Es ) @ S ) @ ( produc1302104557on_val @ ( cons_exp_list_char @ E_2 @ Es ) @ S_1 ) ) @ ( transi808828192on_val @ ( reds @ P ) ) ) ) ).
thf(fact_560_reds__preserves__sconf,axiom,
! [E_1: list_char > option_ty,Ts: list_ty,Es: list_exp_list_char,S: produc2090907612on_val,Es_3: list_exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ S ) @ ( produc1302104557on_val @ Es_3 @ S_1 ) ) @ ( reds @ P ) )
=> ( ( wTrts @ P @ ( hp @ S ) @ E_1 @ Es @ Ts )
=> ( ( typeSa1102574168_sconf @ P @ E_1 @ S )
=> ( typeSa1102574168_sconf @ P @ E_1 @ S_1 ) ) ) ) ).
thf(fact_561_redsp__reds__eq,axiom,
! [P: list_P1999446415t_char,X_1: list_exp_list_char,Xa: produc2090907612on_val,Xb: list_exp_list_char,Xc: produc2090907612on_val] :
( ( redsp @ P @ X_1 @ Xa @ Xb @ Xc )
<=> ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ X_1 @ Xa ) @ ( produc1302104557on_val @ Xb @ Xc ) ) @ ( reds @ P ) ) ) ).
thf(fact_562_redp__redsp_OListRed2,axiom,
! [V: val,P: list_P1999446415t_char,Es: list_exp_list_char,S: produc2090907612on_val,Es_3: list_exp_list_char,S_1: produc2090907612on_val] :
( ( redsp @ P @ Es @ S @ Es_3 @ S_1 )
=> ( redsp @ P @ ( cons_exp_list_char @ ( val_list_char @ V ) @ Es ) @ S @ ( cons_exp_list_char @ ( val_list_char @ V ) @ Es_3 ) @ S_1 ) ) ).
thf(fact_563_WTrts__hext__mono,axiom,
! [H_1: nat > option1728594148on_val,P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: list_char > option_ty,Es: list_exp_list_char,Ts: list_ty] :
( ( wTrts @ P @ H @ E_1 @ Es @ Ts )
=> ( ( hext @ H @ H_1 )
=> ( wTrts @ P @ H_1 @ E_1 @ Es @ Ts ) ) ) ).
thf(fact_564_red__reds_OListRed2,axiom,
! [V: val,Es: list_exp_list_char,S: produc2090907612on_val,Es_3: list_exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ S ) @ ( produc1302104557on_val @ Es_3 @ S_1 ) ) @ ( reds @ P ) )
=> ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ ( cons_exp_list_char @ ( val_list_char @ V ) @ Es ) @ S ) @ ( produc1302104557on_val @ ( cons_exp_list_char @ ( val_list_char @ V ) @ Es_3 ) @ S_1 ) ) @ ( reds @ P ) ) ) ).
thf(fact_565_WTrtCallNT,axiom,
! [M: list_char,T: ty,Es: list_exp_list_char,Ts: list_ty,P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: list_char > option_ty,E: exp_list_char] :
( ( wTrt @ P @ H @ E_1 @ E @ nt )
=> ( ( wTrts @ P @ H @ E_1 @ Es @ Ts )
=> ( wTrt @ P @ H @ E_1 @ ( call_list_char @ E @ M @ Es ) @ T ) ) ) ).
thf(fact_566_ListReds2,axiom,
! [V: val,Es: list_exp_list_char,S: produc2090907612on_val,Es_3: list_exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ S ) @ ( produc1302104557on_val @ Es_3 @ S_1 ) ) @ ( transi808828192on_val @ ( reds @ P ) ) )
=> ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ ( cons_exp_list_char @ ( val_list_char @ V ) @ Es ) @ S ) @ ( produc1302104557on_val @ ( cons_exp_list_char @ ( val_list_char @ V ) @ Es_3 ) @ S_1 ) ) @ ( transi808828192on_val @ ( reds @ P ) ) ) ) ).
thf(fact_567_red__reds_OListRed1,axiom,
! [Es: list_exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( red @ P ) )
=> ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ ( cons_exp_list_char @ E @ Es ) @ S ) @ ( produc1302104557on_val @ ( cons_exp_list_char @ E_2 @ Es ) @ S_1 ) ) @ ( reds @ P ) ) ) ).
thf(fact_568_reds__preserves__hconf,axiom,
! [E_1: list_char > option_ty,Ts: list_ty,Es: list_exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,Es_3: list_exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,P: list_P1999446415t_char] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ ( produc755559506on_val @ H @ L ) ) @ ( produc1302104557on_val @ Es_3 @ ( produc755559506on_val @ H_1 @ L_1 ) ) ) @ ( reds @ P ) )
=> ( ( wTrts @ P @ H @ E_1 @ Es @ Ts )
=> ( ( hconf_97414254t_char @ P @ H )
=> ( hconf_97414254t_char @ P @ H_1 ) ) ) ) ).
thf(fact_569_reds__preserves__lconf,axiom,
! [E_1: list_char > option_ty,Ts: list_ty,Es: list_exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,Es_3: list_exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,P: list_P1999446415t_char] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ ( produc755559506on_val @ H @ L ) ) @ ( produc1302104557on_val @ Es_3 @ ( produc755559506on_val @ H_1 @ L_1 ) ) ) @ ( reds @ P ) )
=> ( ( wTrts @ P @ H @ E_1 @ Es @ Ts )
=> ( ( lconf_496643946t_char @ P @ H @ L @ E_1 )
=> ( lconf_496643946t_char @ P @ H_1 @ L_1 @ E_1 ) ) ) ) ).
thf(fact_570_CallRedsThrowParams,axiom,
! [M: list_char,Es: list_exp_list_char,Vs_1_1: list_val,A: exp_list_char,Es_2_1: list_exp_list_char,S_2_1: produc2090907612on_val,E: exp_list_char,S0: produc2090907612on_val,V: val,S_1_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S0 ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ S_1_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ S_1_1 ) @ ( produc1302104557on_val @ ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ Vs_1_1 ) @ ( cons_exp_list_char @ ( throw_list_char @ A ) @ Es_2_1 ) ) @ S_2_1 ) ) @ ( transi808828192on_val @ ( reds @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ E @ M @ Es ) @ S0 ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_571_red__reds_OCallThrowParams,axiom,
! [V: val,M: list_char,S: produc2090907612on_val,P: list_P1999446415t_char,Es: list_exp_list_char,Vs: list_val,E: exp_list_char,Es_3: list_exp_list_char] :
( ( Es
= ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ Vs ) @ ( cons_exp_list_char @ ( throw_list_char @ E ) @ Es_3 ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ ( val_list_char @ V ) @ M @ Es ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( red @ P ) ) ) ).
thf(fact_572_WTrtCons,axiom,
! [Es: list_exp_list_char,Ts: list_ty,P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: list_char > option_ty,E: exp_list_char,T: ty] :
( ( wTrt @ P @ H @ E_1 @ E @ T )
=> ( ( wTrts @ P @ H @ E_1 @ Es @ Ts )
=> ( wTrts @ P @ H @ E_1 @ ( cons_exp_list_char @ E @ Es ) @ ( cons_ty @ T @ Ts ) ) ) ) ).
thf(fact_573_redp__redsp_OCallThrowParams,axiom,
! [P: list_P1999446415t_char,V: val,M: list_char,S: produc2090907612on_val,Es: list_exp_list_char,Vs: list_val,E: exp_list_char,Es_3: list_exp_list_char] :
( ( Es
= ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ Vs ) @ ( cons_exp_list_char @ ( throw_list_char @ E ) @ Es_3 ) ) )
=> ( redp @ P @ ( call_list_char @ ( val_list_char @ V ) @ M @ Es ) @ S @ ( throw_list_char @ E ) @ S ) ) ).
thf(fact_574_redp__redsp_OSeqRed,axiom,
! [E_2_1: exp_list_char,P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( redp @ P @ E @ S @ E_2 @ S_1 )
=> ( redp @ P @ ( seq_list_char @ E @ E_2_1 ) @ S @ ( seq_list_char @ E_2 @ E_2_1 ) @ S_1 ) ) ).
thf(fact_575_redp__redsp_OThrowRed,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( redp @ P @ E @ S @ E_2 @ S_1 )
=> ( redp @ P @ ( throw_list_char @ E ) @ S @ ( throw_list_char @ E_2 ) @ S_1 ) ) ).
thf(fact_576_redp__redsp_OThrowThrow,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( throw_list_char @ ( throw_list_char @ E ) ) @ S @ ( throw_list_char @ E ) @ S ) ).
thf(fact_577_redp__redsp_OTryRed,axiom,
! [C: list_char,V_1: list_char,E_2_1: exp_list_char,P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( redp @ P @ E @ S @ E_2 @ S_1 )
=> ( redp @ P @ ( tryCatch_list_char @ E @ C @ V_1 @ E_2_1 ) @ S @ ( tryCatch_list_char @ E_2 @ C @ V_1 @ E_2_1 ) @ S_1 ) ) ).
thf(fact_578_redp__redsp_OFAccRed,axiom,
! [F: list_char,D: list_char,P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( redp @ P @ E @ S @ E_2 @ S_1 )
=> ( redp @ P @ ( fAcc_list_char @ E @ F @ D ) @ S @ ( fAcc_list_char @ E_2 @ F @ D ) @ S_1 ) ) ).
thf(fact_579_redp__redsp_OCastRed,axiom,
! [C: list_char,P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( redp @ P @ E @ S @ E_2 @ S_1 )
=> ( redp @ P @ ( cast_list_char @ C @ E ) @ S @ ( cast_list_char @ C @ E_2 ) @ S_1 ) ) ).
thf(fact_580_redp__redsp_OCondRed,axiom,
! [E_1_1: exp_list_char,E_2_1: exp_list_char,P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( redp @ P @ E @ S @ E_2 @ S_1 )
=> ( redp @ P @ ( cond_list_char @ E @ E_1_1 @ E_2_1 ) @ S @ ( cond_list_char @ E_2 @ E_1_1 @ E_2_1 ) @ S_1 ) ) ).
thf(fact_581_redp__redsp_OBinOpRed1,axiom,
! [Bop: bop,E_2_1: exp_list_char,P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( redp @ P @ E @ S @ E_2 @ S_1 )
=> ( redp @ P @ ( binOp_list_char @ E @ Bop @ E_2_1 ) @ S @ ( binOp_list_char @ E_2 @ Bop @ E_2_1 ) @ S_1 ) ) ).
thf(fact_582_redp__redsp_OCallObj,axiom,
! [M: list_char,Es: list_exp_list_char,P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( redp @ P @ E @ S @ E_2 @ S_1 )
=> ( redp @ P @ ( call_list_char @ E @ M @ Es ) @ S @ ( call_list_char @ E_2 @ M @ Es ) @ S_1 ) ) ).
thf(fact_583_redp__redsp_OFAssRed1,axiom,
! [F: list_char,D: list_char,E_2_1: exp_list_char,P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( redp @ P @ E @ S @ E_2 @ S_1 )
=> ( redp @ P @ ( fAss_list_char @ E @ F @ D @ E_2_1 ) @ S @ ( fAss_list_char @ E_2 @ F @ D @ E_2_1 ) @ S_1 ) ) ).
thf(fact_584_redp__redsp_ORedSeq,axiom,
! [P: list_P1999446415t_char,V: val,E_2_1: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( seq_list_char @ ( val_list_char @ V ) @ E_2_1 ) @ S @ E_2_1 @ S ) ).
thf(fact_585_redp__redsp_OFAssRed2,axiom,
! [V: val,F: list_char,D: list_char,P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( redp @ P @ E @ S @ E_2 @ S_1 )
=> ( redp @ P @ ( fAss_list_char @ ( val_list_char @ V ) @ F @ D @ E ) @ S @ ( fAss_list_char @ ( val_list_char @ V ) @ F @ D @ E_2 ) @ S_1 ) ) ).
thf(fact_586_redp__redsp_OBinOpRed2,axiom,
! [V_1_2: val,Bop: bop,P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( redp @ P @ E @ S @ E_2 @ S_1 )
=> ( redp @ P @ ( binOp_list_char @ ( val_list_char @ V_1_2 ) @ Bop @ E ) @ S @ ( binOp_list_char @ ( val_list_char @ V_1_2 ) @ Bop @ E_2 ) @ S_1 ) ) ).
thf(fact_587_redp__redsp_OSeqThrow,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,E_2_1: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( seq_list_char @ ( throw_list_char @ E ) @ E_2_1 ) @ S @ ( throw_list_char @ E ) @ S ) ).
thf(fact_588_redp__redsp_OFAssThrow1,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,F: list_char,D: list_char,E_2_1: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( fAss_list_char @ ( throw_list_char @ E ) @ F @ D @ E_2_1 ) @ S @ ( throw_list_char @ E ) @ S ) ).
thf(fact_589_redp__redsp_OCallThrowObj,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,M: list_char,Es: list_exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( call_list_char @ ( throw_list_char @ E ) @ M @ Es ) @ S @ ( throw_list_char @ E ) @ S ) ).
thf(fact_590_redp__redsp_OBinOpThrow1,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,Bop: bop,E_2_1: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( binOp_list_char @ ( throw_list_char @ E ) @ Bop @ E_2_1 ) @ S @ ( throw_list_char @ E ) @ S ) ).
thf(fact_591_redp__redsp_OCondThrow,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,E_1_1: exp_list_char,E_2_1: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( cond_list_char @ ( throw_list_char @ E ) @ E_1_1 @ E_2_1 ) @ S @ ( throw_list_char @ E ) @ S ) ).
thf(fact_592_redp__redsp_OCastThrow,axiom,
! [P: list_P1999446415t_char,C: list_char,E: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( cast_list_char @ C @ ( throw_list_char @ E ) ) @ S @ ( throw_list_char @ E ) @ S ) ).
thf(fact_593_redp__redsp_ORedTry,axiom,
! [P: list_P1999446415t_char,V: val,C: list_char,V_1: list_char,E_2_1: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( tryCatch_list_char @ ( val_list_char @ V ) @ C @ V_1 @ E_2_1 ) @ S @ ( val_list_char @ V ) @ S ) ).
thf(fact_594_redp__redsp_OFAccThrow,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,F: list_char,D: list_char,S: produc2090907612on_val] : ( redp @ P @ ( fAcc_list_char @ ( throw_list_char @ E ) @ F @ D ) @ S @ ( throw_list_char @ E ) @ S ) ).
thf(fact_595_redp__redsp_OListRed1,axiom,
! [Es: list_exp_list_char,P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( redp @ P @ E @ S @ E_2 @ S_1 )
=> ( redsp @ P @ ( cons_exp_list_char @ E @ Es ) @ S @ ( cons_exp_list_char @ E_2 @ Es ) @ S_1 ) ) ).
thf(fact_596_redp__redsp_OFAssThrow2,axiom,
! [P: list_P1999446415t_char,V: val,F: list_char,D: list_char,E: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( fAss_list_char @ ( val_list_char @ V ) @ F @ D @ ( throw_list_char @ E ) ) @ S @ ( throw_list_char @ E ) @ S ) ).
thf(fact_597_redp__redsp_OBinOpThrow2,axiom,
! [P: list_P1999446415t_char,V_1_2: val,Bop: bop,E: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( binOp_list_char @ ( val_list_char @ V_1_2 ) @ Bop @ ( throw_list_char @ E ) ) @ S @ ( throw_list_char @ E ) @ S ) ).
thf(fact_598_redp__redsp_ORedCastNull,axiom,
! [P: list_P1999446415t_char,C: list_char,S: produc2090907612on_val] : ( redp @ P @ ( cast_list_char @ C @ ( val_list_char @ null ) ) @ S @ ( val_list_char @ null ) @ S ) ).
thf(fact_599_redp__redsp_ORedCondT,axiom,
! [P: list_P1999446415t_char,E_1_1: exp_list_char,E_2_1: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( cond_list_char @ ( val_list_char @ ( bool @ $true ) ) @ E_1_1 @ E_2_1 ) @ S @ E_1_1 @ S ) ).
thf(fact_600_redp__redsp_ORedCondF,axiom,
! [P: list_P1999446415t_char,E_1_1: exp_list_char,E_2_1: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( cond_list_char @ ( val_list_char @ ( bool @ $false ) ) @ E_1_1 @ E_2_1 ) @ S @ E_2_1 @ S ) ).
thf(fact_601_redp__redsp_OCallParams,axiom,
! [V: val,M: list_char,P: list_P1999446415t_char,Es: list_exp_list_char,S: produc2090907612on_val,Es_3: list_exp_list_char,S_1: produc2090907612on_val] :
( ( redsp @ P @ Es @ S @ Es_3 @ S_1 )
=> ( redp @ P @ ( call_list_char @ ( val_list_char @ V ) @ M @ Es ) @ S @ ( call_list_char @ ( val_list_char @ V ) @ M @ Es_3 ) @ S_1 ) ) ).
thf(fact_602_redp__red__eq,axiom,
! [P: list_P1999446415t_char,X_1: exp_list_char,Xa: produc2090907612on_val,Xb: exp_list_char,Xc: produc2090907612on_val] :
( ( redp @ P @ X_1 @ Xa @ Xb @ Xc )
<=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ X_1 @ Xa ) @ ( produc235638504on_val @ Xb @ Xc ) ) @ ( red @ P ) ) ) ).
thf(fact_603_redp__redsp_ORedWhile,axiom,
! [P: list_P1999446415t_char,B: exp_list_char,C_1: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( while_list_char @ B @ C_1 ) @ S @ ( cond_list_char @ B @ ( seq_list_char @ C_1 @ ( while_list_char @ B @ C_1 ) ) @ ( val_list_char @ unit ) ) @ S ) ).
thf(fact_604_CallRedsNull,axiom,
! [M: list_char,Es: list_exp_list_char,Vs: list_val,S_2_1: produc2090907612on_val,E: exp_list_char,S_0: produc2090907612on_val,S_1_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ null ) @ S_1_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ S_1_1 ) @ ( produc1302104557on_val @ ( map_va1934808527t_char @ val_list_char @ Vs ) @ S_2_1 ) ) @ ( transi808828192on_val @ ( reds @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ E @ M @ Es ) @ S_0 ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_605_default__val_Osimps_I2_J,axiom,
( ( default_val @ boolean )
= ( bool @ $false ) ) ).
thf(fact_606_redp__redsp_ORedThrowNull,axiom,
! [P: list_P1999446415t_char,S: produc2090907612on_val] : ( redp @ P @ ( throw_list_char @ ( val_list_char @ null ) ) @ S @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S ) ).
thf(fact_607_val_Osimps_I10_J,axiom,
! [Nat: nat] :
( unit
!= ( addr @ Nat ) ) ).
thf(fact_608_val_Osimps_I11_J,axiom,
! [Nat: nat] :
( ( addr @ Nat )
!= unit ) ).
thf(fact_609_val_Osimps_I3_J,axiom,
! [Nat_1: nat,Nat: nat] :
( ( ( addr @ Nat_1 )
= ( addr @ Nat ) )
<=> ( Nat_1 = Nat ) ) ).
thf(fact_610_val_Osimps_I17_J,axiom,
! [Nat: nat] :
( ( addr @ Nat )
!= null ) ).
thf(fact_611_val_Osimps_I16_J,axiom,
! [Nat: nat] :
( null
!= ( addr @ Nat ) ) ).
thf(fact_612_val_Osimps_I21_J,axiom,
! [Nat: nat,Bool: $o] :
( ( addr @ Nat )
!= ( bool @ Bool ) ) ).
thf(fact_613_val_Osimps_I20_J,axiom,
! [Bool: $o,Nat: nat] :
( ( bool @ Bool )
!= ( addr @ Nat ) ) ).
thf(fact_614_redp__redsp_ORedFAssNull,axiom,
! [P: list_P1999446415t_char,F: list_char,D: list_char,V: val,S: produc2090907612on_val] : ( redp @ P @ ( fAss_list_char @ ( val_list_char @ null ) @ F @ D @ ( val_list_char @ V ) ) @ S @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S ) ).
thf(fact_615_redp__redsp_ORedFAccNull,axiom,
! [P: list_P1999446415t_char,F: list_char,D: list_char,S: produc2090907612on_val] : ( redp @ P @ ( fAcc_list_char @ ( val_list_char @ null ) @ F @ D ) @ S @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S ) ).
thf(fact_616_red__reds_ORedThrowNull,axiom,
! [S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ null ) ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_617_redp__redsp_ORedCallNull,axiom,
! [P: list_P1999446415t_char,M: list_char,Vs: list_val,S: produc2090907612on_val] : ( redp @ P @ ( call_list_char @ ( val_list_char @ null ) @ M @ ( map_va1934808527t_char @ val_list_char @ Vs ) ) @ S @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S ) ).
thf(fact_618_ThrowRedsNull,axiom,
! [E: exp_list_char,S: produc2090907612on_val,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ ( val_list_char @ null ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_619_red__reds_ORedFAssNull,axiom,
! [F: list_char,D: list_char,V: val,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ ( val_list_char @ null ) @ F @ D @ ( val_list_char @ V ) ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_620_red__reds_ORedFAccNull,axiom,
! [F: list_char,D: list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAcc_list_char @ ( val_list_char @ null ) @ F @ D ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_621_FAssRedsNull,axiom,
! [F: list_char,D: list_char,E_2_1: exp_list_char,V: val,S_2_1: produc2090907612on_val,E_1_1: exp_list_char,S_0: produc2090907612on_val,S_1_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1_1 @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ null ) @ S_1_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_2_1 @ S_1_1 ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ E_1_1 @ F @ D @ E_2_1 ) @ S_0 ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_622_FAccRedsNull,axiom,
! [F: list_char,D: list_char,E: exp_list_char,S: produc2090907612on_val,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ ( val_list_char @ null ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAcc_list_char @ E @ F @ D ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_623_red__reds_ORedCallNull,axiom,
! [M: list_char,Vs: list_val,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ ( val_list_char @ null ) @ M @ ( map_va1934808527t_char @ val_list_char @ Vs ) ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_624_default__val_Osimps_I4_J,axiom,
( ( default_val @ nt )
= null ) ).
thf(fact_625_default__val_Osimps_I1_J,axiom,
( ( default_val @ void )
= unit ) ).
thf(fact_626_FAccNull,axiom,
! [F: list_char,D: list_char,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( val_list_char @ null ) @ S_1_1 )
=> ( eval @ P @ ( fAcc_list_char @ E @ F @ D ) @ S_0 @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S_1_1 ) ) ).
thf(fact_627_eval__finalId,axiom,
! [P: list_P1999446415t_char,S: produc2090907612on_val,E: exp_list_char] :
( ( final_list_char @ E )
=> ( eval @ P @ E @ S @ E @ S ) ) ).
thf(fact_628_eval__final,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( eval @ P @ E @ S @ E_2 @ S_1 )
=> ( final_list_char @ E_2 ) ) ).
thf(fact_629_Seq,axiom,
! [E_1_1: exp_list_char,E_2_1: exp_list_char,S_2_1: produc2090907612on_val,P: list_P1999446415t_char,E_0: exp_list_char,S_0: produc2090907612on_val,V: val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E_0 @ S_0 @ ( val_list_char @ V ) @ S_1_1 )
=> ( ( eval @ P @ E_1_1 @ S_1_1 @ E_2_1 @ S_2_1 )
=> ( eval @ P @ ( seq_list_char @ E_0 @ E_1_1 ) @ S_0 @ E_2_1 @ S_2_1 ) ) ) ).
thf(fact_630_eval__evals_OSeqThrow,axiom,
! [E_1_1: exp_list_char,P: list_P1999446415t_char,E_0: exp_list_char,S_0: produc2090907612on_val,E: exp_list_char,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E_0 @ S_0 @ ( throw_list_char @ E ) @ S_1_1 )
=> ( eval @ P @ ( seq_list_char @ E_0 @ E_1_1 ) @ S_0 @ ( throw_list_char @ E ) @ S_1_1 ) ) ).
thf(fact_631_eval__cases_I2_J,axiom,
! [P: list_P1999446415t_char,V: val,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( eval @ P @ ( val_list_char @ V ) @ S @ E_2 @ S_1 )
=> ~ ( ( E_2
= ( val_list_char @ V ) )
=> ( S_1 != S ) ) ) ).
thf(fact_632_eval__evals_OThrowThrow,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,E_2: exp_list_char,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 )
=> ( eval @ P @ ( throw_list_char @ E ) @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 ) ) ).
thf(fact_633_Val,axiom,
! [P: list_P1999446415t_char,V: val,S: produc2090907612on_val] : ( eval @ P @ ( val_list_char @ V ) @ S @ ( val_list_char @ V ) @ S ) ).
thf(fact_634_eval__hext,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,E_2: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val] :
( ( eval @ P @ E @ ( produc755559506on_val @ H @ L ) @ E_2 @ ( produc755559506on_val @ H_1 @ L_1 ) )
=> ( hext @ H @ H_1 ) ) ).
thf(fact_635_WhileCondThrow,axiom,
! [C_1: exp_list_char,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,E_2: exp_list_char,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 )
=> ( eval @ P @ ( while_list_char @ E @ C_1 ) @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 ) ) ).
thf(fact_636_eval__evals_OFAccThrow,axiom,
! [F: list_char,D: list_char,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,E_2: exp_list_char,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 )
=> ( eval @ P @ ( fAcc_list_char @ E @ F @ D ) @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 ) ) ).
thf(fact_637_Try,axiom,
! [C: list_char,V_1: list_char,E_2_1: exp_list_char,P: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc2090907612on_val,V_1_2: val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( val_list_char @ V_1_2 ) @ S_1_1 )
=> ( eval @ P @ ( tryCatch_list_char @ E_1_1 @ C @ V_1 @ E_2_1 ) @ S_0 @ ( val_list_char @ V_1_2 ) @ S_1_1 ) ) ).
thf(fact_638_eval__evals_OCastThrow,axiom,
! [C: list_char,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,E_2: exp_list_char,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 )
=> ( eval @ P @ ( cast_list_char @ C @ E ) @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 ) ) ).
thf(fact_639_eval__evals_OCondThrow,axiom,
! [E_1_1: exp_list_char,E_2_1: exp_list_char,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,E_2: exp_list_char,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 )
=> ( eval @ P @ ( cond_list_char @ E @ E_1_1 @ E_2_1 ) @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 ) ) ).
thf(fact_640_eval__evals_OBinOpThrow1,axiom,
! [Bop: bop,E_2_1: exp_list_char,P: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc2090907612on_val,E: exp_list_char,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( throw_list_char @ E ) @ S_1_1 )
=> ( eval @ P @ ( binOp_list_char @ E_1_1 @ Bop @ E_2_1 ) @ S_0 @ ( throw_list_char @ E ) @ S_1_1 ) ) ).
thf(fact_641_CallObjThrow,axiom,
! [M: list_char,Ps: list_exp_list_char,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,E_2: exp_list_char,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 )
=> ( eval @ P @ ( call_list_char @ E @ M @ Ps ) @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 ) ) ).
thf(fact_642_eval__evals_OFAssThrow1,axiom,
! [F: list_char,D: list_char,E_2_1: exp_list_char,P: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc2090907612on_val,E_2: exp_list_char,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 )
=> ( eval @ P @ ( fAss_list_char @ E_1_1 @ F @ D @ E_2_1 ) @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 ) ) ).
thf(fact_643_Throw,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,A: nat,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( val_list_char @ ( addr @ A ) ) @ S_1_1 )
=> ( eval @ P @ ( throw_list_char @ E ) @ S_0 @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) @ S_1_1 ) ) ).
thf(fact_644_eval__evals_OFAssThrow2,axiom,
! [F: list_char,D: list_char,E_2_1: exp_list_char,E_2: exp_list_char,S_2_1: produc2090907612on_val,P: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc2090907612on_val,V: val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( val_list_char @ V ) @ S_1_1 )
=> ( ( eval @ P @ E_2_1 @ S_1_1 @ ( throw_list_char @ E_2 ) @ S_2_1 )
=> ( eval @ P @ ( fAss_list_char @ E_1_1 @ F @ D @ E_2_1 ) @ S_0 @ ( throw_list_char @ E_2 ) @ S_2_1 ) ) ) ).
thf(fact_645_eval__evals_OBinOpThrow2,axiom,
! [Bop: bop,E_2_1: exp_list_char,E: exp_list_char,S_2_1: produc2090907612on_val,P: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc2090907612on_val,V_1_2: val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( val_list_char @ V_1_2 ) @ S_1_1 )
=> ( ( eval @ P @ E_2_1 @ S_1_1 @ ( throw_list_char @ E ) @ S_2_1 )
=> ( eval @ P @ ( binOp_list_char @ E_1_1 @ Bop @ E_2_1 ) @ S_0 @ ( throw_list_char @ E ) @ S_2_1 ) ) ) ).
thf(fact_646_CastNull,axiom,
! [C: list_char,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( val_list_char @ null ) @ S_1_1 )
=> ( eval @ P @ ( cast_list_char @ C @ E ) @ S_0 @ ( val_list_char @ null ) @ S_1_1 ) ) ).
thf(fact_647_CondF,axiom,
! [E_1_1: exp_list_char,E_2_1: exp_list_char,E_2: exp_list_char,S_2_1: produc2090907612on_val,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( val_list_char @ ( bool @ $false ) ) @ S_1_1 )
=> ( ( eval @ P @ E_2_1 @ S_1_1 @ E_2 @ S_2_1 )
=> ( eval @ P @ ( cond_list_char @ E @ E_1_1 @ E_2_1 ) @ S_0 @ E_2 @ S_2_1 ) ) ) ).
thf(fact_648_CondT,axiom,
! [E_2_1: exp_list_char,E_1_1: exp_list_char,E_2: exp_list_char,S_2_1: produc2090907612on_val,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( val_list_char @ ( bool @ $true ) ) @ S_1_1 )
=> ( ( eval @ P @ E_1_1 @ S_1_1 @ E_2 @ S_2_1 )
=> ( eval @ P @ ( cond_list_char @ E @ E_1_1 @ E_2_1 ) @ S_0 @ E_2 @ S_2_1 ) ) ) ).
thf(fact_649_WhileT,axiom,
! [E_3_1: exp_list_char,S_3_1: produc2090907612on_val,C_1: exp_list_char,V_1_2: val,S_2_1: produc2090907612on_val,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( val_list_char @ ( bool @ $true ) ) @ S_1_1 )
=> ( ( eval @ P @ C_1 @ S_1_1 @ ( val_list_char @ V_1_2 ) @ S_2_1 )
=> ( ( eval @ P @ ( while_list_char @ E @ C_1 ) @ S_2_1 @ E_3_1 @ S_3_1 )
=> ( eval @ P @ ( while_list_char @ E @ C_1 ) @ S_0 @ E_3_1 @ S_3_1 ) ) ) ) ).
thf(fact_650_WhileBodyThrow,axiom,
! [C_1: exp_list_char,E_2: exp_list_char,S_2_1: produc2090907612on_val,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( val_list_char @ ( bool @ $true ) ) @ S_1_1 )
=> ( ( eval @ P @ C_1 @ S_1_1 @ ( throw_list_char @ E_2 ) @ S_2_1 )
=> ( eval @ P @ ( while_list_char @ E @ C_1 ) @ S_0 @ ( throw_list_char @ E_2 ) @ S_2_1 ) ) ) ).
thf(fact_651_WhileF,axiom,
! [C_1: exp_list_char,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( val_list_char @ ( bool @ $false ) ) @ S_1_1 )
=> ( eval @ P @ ( while_list_char @ E @ C_1 ) @ S_0 @ ( val_list_char @ unit ) @ S_1_1 ) ) ).
thf(fact_652_unfold__while,axiom,
! [P: list_P1999446415t_char,B: exp_list_char,C_1: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( eval @ P @ ( while_list_char @ B @ C_1 ) @ S @ E_2 @ S_1 )
<=> ( eval @ P @ ( cond_list_char @ B @ ( seq_list_char @ C_1 @ ( while_list_char @ B @ C_1 ) ) @ ( val_list_char @ unit ) ) @ S @ E_2 @ S_1 ) ) ).
thf(fact_653_ThrowNull,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( val_list_char @ null ) @ S_1_1 )
=> ( eval @ P @ ( throw_list_char @ E ) @ S_0 @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S_1_1 ) ) ).
thf(fact_654_FAssNull,axiom,
! [F: list_char,D: list_char,E_2_1: exp_list_char,V: val,S_2_1: produc2090907612on_val,P: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc2090907612on_val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( val_list_char @ null ) @ S_1_1 )
=> ( ( eval @ P @ E_2_1 @ S_1_1 @ ( val_list_char @ V ) @ S_2_1 )
=> ( eval @ P @ ( fAss_list_char @ E_1_1 @ F @ D @ E_2_1 ) @ S_0 @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S_2_1 ) ) ) ).
thf(fact_655_eval__cases_I12_J,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( eval @ P @ ( throw_list_char @ E ) @ S @ E_2 @ S_1 )
=> ( ! [A_1: nat] :
( ( E_2
= ( throw_list_char @ ( val_list_char @ ( addr @ A_1 ) ) ) )
=> ~ ( eval @ P @ E @ S @ ( val_list_char @ ( addr @ A_1 ) ) @ S_1 ) )
=> ( ( ( E_2
= ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) )
=> ~ ( eval @ P @ E @ S @ ( val_list_char @ null ) @ S_1 ) )
=> ~ ! [E_3: exp_list_char] :
( ( E_2
= ( throw_list_char @ E_3 ) )
=> ~ ( eval @ P @ E @ S @ ( throw_list_char @ E_3 ) @ S_1 ) ) ) ) ) ).
thf(fact_656_CallNull,axiom,
! [M: list_char,Ps: list_exp_list_char,Vs: list_val,S_2_1: produc2090907612on_val,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( val_list_char @ null ) @ S_1_1 )
=> ( ( evals @ P @ Ps @ S_1_1 @ ( map_va1934808527t_char @ val_list_char @ Vs ) @ S_2_1 )
=> ( eval @ P @ ( call_list_char @ E @ M @ Ps ) @ S_0 @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S_2_1 ) ) ) ).
thf(fact_657_eval__finalsId,axiom,
! [P: list_P1999446415t_char,S: produc2090907612on_val,Es: list_exp_list_char] :
( ( finals_list_char @ Es )
=> ( evals @ P @ Es @ S @ Es @ S ) ) ).
thf(fact_658_evals__final,axiom,
! [P: list_P1999446415t_char,Es: list_exp_list_char,S: produc2090907612on_val,Es_3: list_exp_list_char,S_1: produc2090907612on_val] :
( ( evals @ P @ Es @ S @ Es_3 @ S_1 )
=> ( finals_list_char @ Es_3 ) ) ).
thf(fact_659_evals__hext,axiom,
! [P: list_P1999446415t_char,Es: list_exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,Es_3: list_exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val] :
( ( evals @ P @ Es @ ( produc755559506on_val @ H @ L ) @ Es_3 @ ( produc755559506on_val @ H_1 @ L_1 ) )
=> ( hext @ H @ H_1 ) ) ).
thf(fact_660_eval__evals_OCons,axiom,
! [Es: list_exp_list_char,Es_3: list_exp_list_char,S_2_1: produc2090907612on_val,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,V: val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( val_list_char @ V ) @ S_1_1 )
=> ( ( evals @ P @ Es @ S_1_1 @ Es_3 @ S_2_1 )
=> ( evals @ P @ ( cons_exp_list_char @ E @ Es ) @ S_0 @ ( cons_exp_list_char @ ( val_list_char @ V ) @ Es_3 ) @ S_2_1 ) ) ) ).
thf(fact_661_ConsThrow,axiom,
! [Es: list_exp_list_char,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,E_2: exp_list_char,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 )
=> ( evals @ P @ ( cons_exp_list_char @ E @ Es ) @ S_0 @ ( cons_exp_list_char @ ( throw_list_char @ E_2 ) @ Es ) @ S_1_1 ) ) ).
thf(fact_662_list__eval__Throw,axiom,
! [Vs: list_val,Es_3: list_exp_list_char,P: list_P1999446415t_char,X: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( eval @ P @ ( throw_list_char @ X ) @ S @ E_2 @ S_1 )
=> ( evals @ P @ ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ Vs ) @ ( cons_exp_list_char @ ( throw_list_char @ X ) @ Es_3 ) ) @ S @ ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ Vs ) @ ( cons_exp_list_char @ E_2 @ Es_3 ) ) @ S_1 ) ) ).
thf(fact_663_CallParamsThrow,axiom,
! [M: list_char,Es: list_exp_list_char,Vs: list_val,Ex: exp_list_char,Es_3: list_exp_list_char,S_2_1: produc2090907612on_val,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,V: val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( val_list_char @ V ) @ S_1_1 )
=> ( ( evals @ P @ Es @ S_1_1 @ ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ Vs ) @ ( cons_exp_list_char @ ( throw_list_char @ Ex ) @ Es_3 ) ) @ S_2_1 )
=> ( eval @ P @ ( call_list_char @ E @ M @ Es ) @ S_0 @ ( throw_list_char @ Ex ) @ S_2_1 ) ) ) ).
thf(fact_664_big__iff__small,axiom,
! [E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( wf_pro755087577t_char @ wwf_J_mdecl @ P )
=> ( ( eval @ P @ E @ S @ E_2 @ S_1 )
<=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
& ( final_list_char @ E_2 ) ) ) ) ).
thf(fact_665_small__by__big,axiom,
! [E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( wf_pro755087577t_char @ wwf_J_mdecl @ P )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( final_list_char @ E_2 )
=> ( eval @ P @ E @ S @ E_2 @ S_1 ) ) ) ) ).
thf(fact_666_extend__1__eval,axiom,
! [E_2: exp_list_char,S_1: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,E_5: exp_list_char,S_3: produc2090907612on_val,P: list_P1999446415t_char] :
( ( wf_pro755087577t_char @ wwf_J_mdecl @ P )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_5 @ S_3 ) ) @ ( red @ P ) )
=> ( ( eval @ P @ E_5 @ S_3 @ E_2 @ S_1 )
=> ( eval @ P @ E @ S @ E_2 @ S_1 ) ) ) ) ).
thf(fact_667_extend__1__evals,axiom,
! [Es_3: list_exp_list_char,T_6: produc2090907612on_val,Es: list_exp_list_char,T_5: produc2090907612on_val,Es_2: list_exp_list_char,T_4: produc2090907612on_val,P: list_P1999446415t_char] :
( ( wf_pro755087577t_char @ wwf_J_mdecl @ P )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ T_5 ) @ ( produc1302104557on_val @ Es_2 @ T_4 ) ) @ ( reds @ P ) )
=> ( ( evals @ P @ Es_2 @ T_4 @ Es_3 @ T_6 )
=> ( evals @ P @ Es @ T_5 @ Es_3 @ T_6 ) ) ) ) ).
thf(fact_668_extend__eval,axiom,
! [E_2: exp_list_char,S_1: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,E_5: exp_list_char,S_3: produc2090907612on_val,P: list_P1999446415t_char] :
( ( wf_pro755087577t_char @ wwf_J_mdecl @ P )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_5 @ S_3 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( eval @ P @ E_5 @ S_3 @ E_2 @ S_1 )
=> ( eval @ P @ E @ S @ E_2 @ S_1 ) ) ) ) ).
thf(fact_669_big__by__small,axiom,
! [E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( wf_pro755087577t_char @ wwf_J_mdecl @ P )
=> ( ( eval @ P @ E @ S @ E_2 @ S_1 )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_670_bigs__by__smalls,axiom,
! [Es: list_exp_list_char,S: produc2090907612on_val,Es_3: list_exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( wf_pro755087577t_char @ wwf_J_mdecl @ P )
=> ( ( evals @ P @ Es @ S @ Es_3 @ S_1 )
=> ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ S ) @ ( produc1302104557on_val @ Es_3 @ S_1 ) ) @ ( transi808828192on_val @ ( reds @ P ) ) ) ) ) ).
thf(fact_671_extend__evals,axiom,
! [Es_3: list_exp_list_char,S_1: produc2090907612on_val,Es: list_exp_list_char,S: produc2090907612on_val,Es_2: list_exp_list_char,S_3: produc2090907612on_val,P: list_P1999446415t_char] :
( ( wf_pro755087577t_char @ wwf_J_mdecl @ P )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ S ) @ ( produc1302104557on_val @ Es_2 @ S_3 ) ) @ ( transi808828192on_val @ ( reds @ P ) ) )
=> ( ( evals @ P @ Es_2 @ S_3 @ Es_3 @ S_1 )
=> ( evals @ P @ Es @ S @ Es_3 @ S_1 ) ) ) ) ).
thf(fact_672_wf__prog__wwf__prog,axiom,
! [P: list_P1999446415t_char] :
( ( wf_pro755087577t_char @ wf_J_mdecl @ P )
=> ( wf_pro755087577t_char @ wwf_J_mdecl @ P ) ) ).
thf(fact_673_evals__cases_I2_J,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,Es: list_exp_list_char,S: produc2090907612on_val,E_2: list_exp_list_char,S_1: produc2090907612on_val] :
( ( evals @ P @ ( cons_exp_list_char @ E @ Es ) @ S @ E_2 @ S_1 )
=> ( ! [V_2: val,S_1_2: produc2090907612on_val,Es_1: list_exp_list_char] :
( ( E_2
= ( cons_exp_list_char @ ( val_list_char @ V_2 ) @ Es_1 ) )
=> ( ( eval @ P @ E @ S @ ( val_list_char @ V_2 ) @ S_1_2 )
=> ~ ( evals @ P @ Es @ S_1_2 @ Es_1 @ S_1 ) ) )
=> ~ ! [E_3: exp_list_char] :
( ( E_2
= ( cons_exp_list_char @ ( throw_list_char @ E_3 ) @ Es ) )
=> ~ ( eval @ P @ E @ S @ ( throw_list_char @ E_3 ) @ S_1 ) ) ) ) ).
thf(fact_674_wf__mdecl__wwf__mdecl,axiom,
! [P: list_P1999446415t_char,C: list_char,Md: produc1013743697t_char] :
( ( wf_J_mdecl @ P @ C @ Md )
=> ( wwf_J_mdecl @ P @ C @ Md ) ) ).
thf(fact_675_eval__cases_I11_J,axiom,
! [P: list_P1999446415t_char,B: exp_list_char,C_1: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( eval @ P @ ( while_list_char @ B @ C_1 ) @ S @ E_2 @ S_1 )
=> ( ( ( E_2
= ( val_list_char @ unit ) )
=> ~ ( eval @ P @ B @ S @ ( val_list_char @ ( bool @ $false ) ) @ S_1 ) )
=> ( ! [S_1_2: produc2090907612on_val] :
( ( eval @ P @ B @ S @ ( val_list_char @ ( bool @ $true ) ) @ S_1_2 )
=> ! [V_1_1: val,S_2: produc2090907612on_val] :
( ( eval @ P @ C_1 @ S_1_2 @ ( val_list_char @ V_1_1 ) @ S_2 )
=> ~ ( eval @ P @ ( while_list_char @ B @ C_1 ) @ S_2 @ E_2 @ S_1 ) ) )
=> ( ! [E_3: exp_list_char] :
( ( E_2
= ( throw_list_char @ E_3 ) )
=> ~ ( eval @ P @ B @ S @ ( throw_list_char @ E_3 ) @ S_1 ) )
=> ~ ! [S_1_2: produc2090907612on_val,E_3: exp_list_char] :
( ( E_2
= ( throw_list_char @ E_3 ) )
=> ( ( eval @ P @ B @ S @ ( val_list_char @ ( bool @ $true ) ) @ S_1_2 )
=> ~ ( eval @ P @ C_1 @ S_1_2 @ ( throw_list_char @ E_3 ) @ S_1 ) ) ) ) ) ) ) ).
thf(fact_676_eval__cases_I9_J,axiom,
! [P: list_P1999446415t_char,E_1_1: exp_list_char,E_2_1: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( eval @ P @ ( seq_list_char @ E_1_1 @ E_2_1 ) @ S @ E_2 @ S_1 )
=> ( ! [V_2: val,S_1_2: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S @ ( val_list_char @ V_2 ) @ S_1_2 )
=> ~ ( eval @ P @ E_2_1 @ S_1_2 @ E_2 @ S_1 ) )
=> ~ ! [E_4: exp_list_char] :
( ( E_2
= ( throw_list_char @ E_4 ) )
=> ~ ( eval @ P @ E_1_1 @ S @ ( throw_list_char @ E_4 ) @ S_1 ) ) ) ) ).
thf(fact_677_eval__cases_I10_J,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,E_1_1: exp_list_char,E_2_1: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( eval @ P @ ( cond_list_char @ E @ E_1_1 @ E_2_1 ) @ S @ E_2 @ S_1 )
=> ( ! [S_1_2: produc2090907612on_val] :
( ( eval @ P @ E @ S @ ( val_list_char @ ( bool @ $true ) ) @ S_1_2 )
=> ~ ( eval @ P @ E_1_1 @ S_1_2 @ E_2 @ S_1 ) )
=> ( ! [S_1_2: produc2090907612on_val] :
( ( eval @ P @ E @ S @ ( val_list_char @ ( bool @ $false ) ) @ S_1_2 )
=> ~ ( eval @ P @ E_2_1 @ S_1_2 @ E_2 @ S_1 ) )
=> ~ ! [E_3: exp_list_char] :
( ( E_2
= ( throw_list_char @ E_3 ) )
=> ~ ( eval @ P @ E @ S @ ( throw_list_char @ E_3 ) @ S_1 ) ) ) ) ) ).
thf(fact_678_red__reds_OBlockThrow,axiom,
! [V_1: list_char,T: ty,A: nat,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ V_1 @ T @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_679_redp__redsp_ORedBlock,axiom,
! [P: list_P1999446415t_char,V_1: list_char,T: ty,U: val,S: produc2090907612on_val] : ( redp @ P @ ( block_list_char @ V_1 @ T @ ( val_list_char @ U ) ) @ S @ ( val_list_char @ U ) @ S ) ).
thf(fact_680_red__reds_ORedBlock,axiom,
! [V_1: list_char,T: ty,U: val,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ V_1 @ T @ ( val_list_char @ U ) ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ U ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_681_redp__redsp_OBlockThrow,axiom,
! [P: list_P1999446415t_char,V_1: list_char,T: ty,A: nat,S: produc2090907612on_val] : ( redp @ P @ ( block_list_char @ V_1 @ T @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) ) @ S @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) @ S ) ).
thf(fact_682_red__reds_OInitBlockThrow,axiom,
! [V_1: list_char,T: ty,V: val,A: nat,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ V_1 @ T @ ( seq_list_char @ ( lAss_list_char @ V_1 @ ( val_list_char @ V ) ) @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) ) ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_683_redp__redsp_OInitBlockThrow,axiom,
! [P: list_P1999446415t_char,V_1: list_char,T: ty,V: val,A: nat,S: produc2090907612on_val] : ( redp @ P @ ( block_list_char @ V_1 @ T @ ( seq_list_char @ ( lAss_list_char @ V_1 @ ( val_list_char @ V ) ) @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) ) ) @ S @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) @ S ) ).
thf(fact_684_redp__redsp_OLAssThrow,axiom,
! [P: list_P1999446415t_char,V_1: list_char,E: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( lAss_list_char @ V_1 @ ( throw_list_char @ E ) ) @ S @ ( throw_list_char @ E ) @ S ) ).
thf(fact_685_redp__redsp_OLAssRed,axiom,
! [V_1: list_char,P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( redp @ P @ E @ S @ E_2 @ S_1 )
=> ( redp @ P @ ( lAss_list_char @ V_1 @ E ) @ S @ ( lAss_list_char @ V_1 @ E_2 ) @ S_1 ) ) ).
thf(fact_686_eval__evals_OLAssThrow,axiom,
! [V_1: list_char,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,E_2: exp_list_char,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 )
=> ( eval @ P @ ( lAss_list_char @ V_1 @ E ) @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 ) ) ).
thf(fact_687_red__reds_OLAssRed,axiom,
! [V_1: list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( lAss_list_char @ V_1 @ E ) @ S ) @ ( produc235638504on_val @ ( lAss_list_char @ V_1 @ E_2 ) @ S_1 ) ) @ ( red @ P ) ) ) ).
thf(fact_688_red__reds_OLAssThrow,axiom,
! [V_1: list_char,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( lAss_list_char @ V_1 @ ( throw_list_char @ E ) ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_689_LAssReds,axiom,
! [V_1: list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( lAss_list_char @ V_1 @ E ) @ S ) @ ( produc235638504on_val @ ( lAss_list_char @ V_1 @ E_2 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_690_redp__redsp_ORedInitBlock,axiom,
! [P: list_P1999446415t_char,V_1: list_char,T: ty,V: val,U: val,S: produc2090907612on_val] : ( redp @ P @ ( block_list_char @ V_1 @ T @ ( seq_list_char @ ( lAss_list_char @ V_1 @ ( val_list_char @ V ) ) @ ( val_list_char @ U ) ) ) @ S @ ( val_list_char @ U ) @ S ) ).
thf(fact_691_LAssRedsThrow,axiom,
! [V_1: list_char,E: exp_list_char,S: produc2090907612on_val,A: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( lAss_list_char @ V_1 @ E ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_692_red__reds_ORedInitBlock,axiom,
! [V_1: list_char,T: ty,V: val,U: val,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ V_1 @ T @ ( seq_list_char @ ( lAss_list_char @ V_1 @ ( val_list_char @ V ) ) @ ( val_list_char @ U ) ) ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ U ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_693_blocks_Osimps_I1_J,axiom,
! [V_1: list_char,Vs_1: list_list_char,T: ty,Ts: list_ty,V: val,Vs: list_val,E: exp_list_char] :
( ( blocks @ ( produc921874948t_char @ ( cons_list_char @ V_1 @ Vs_1 ) @ ( produc1909267824t_char @ ( cons_ty @ T @ Ts ) @ ( produc1916172923t_char @ ( cons_val @ V @ Vs ) @ E ) ) ) )
= ( block_list_char @ V_1 @ T @ ( seq_list_char @ ( lAss_list_char @ V_1 @ ( val_list_char @ V ) ) @ ( blocks @ ( produc921874948t_char @ Vs_1 @ ( produc1909267824t_char @ Ts @ ( produc1916172923t_char @ Vs @ E ) ) ) ) ) ) ) ).
thf(fact_694_the__Addr_Osimps,axiom,
! [A: nat] :
( ( the_Addr @ ( addr @ A ) )
= A ) ).
thf(fact_695_WTrtLAss,axiom,
! [P: list_P1999446415t_char,H: nat > option1728594148on_val,E: exp_list_char,T_3: ty,E_1: list_char > option_ty,V_1: list_char,T: ty] :
( ( ( E_1 @ V_1 )
= ( some_ty @ T ) )
=> ( ( wTrt @ P @ H @ E_1 @ E @ T_3 )
=> ( ( widen_2090681816t_char @ P @ T_3 @ T )
=> ( wTrt @ P @ H @ E_1 @ ( lAss_list_char @ V_1 @ E ) @ void ) ) ) ) ).
thf(fact_696_WTrt__elim__cases_I1_J,axiom,
! [P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: list_char > option_ty,V: list_char,E: exp_list_char,T: ty] :
( ( wTrt @ P @ H @ E_1 @ ( lAss_list_char @ V @ E ) @ T )
=> ~ ( ( T = void )
=> ! [T_1: ty] :
( ( ( E_1 @ V )
= ( some_ty @ T_1 ) )
=> ! [T_2: ty] :
( ( wTrt @ P @ H @ E_1 @ E @ T_2 )
=> ~ ( widen_2090681816t_char @ P @ T_2 @ T_1 ) ) ) ) ) ).
thf(fact_697_redp__redsp_ORedFAcc,axiom,
! [P: list_P1999446415t_char,F: list_char,D: list_char,V: val,S: produc2090907612on_val,A: nat,C: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( hp @ S @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs ) ) )
=> ( ( ( Fs @ ( produc5062597t_char @ F @ D ) )
= ( some_val @ V ) )
=> ( redp @ P @ ( fAcc_list_char @ ( val_list_char @ ( addr @ A ) ) @ F @ D ) @ S @ ( val_list_char @ V ) @ S ) ) ) ).
thf(fact_698_FAcc,axiom,
! [F: list_char,D: list_char,V: val,C: list_char,Fs: produc1278157519t_char > option_val,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,A: nat,H: nat > option1728594148on_val,L: list_char > option_val] :
( ( eval @ P @ E @ S_0 @ ( val_list_char @ ( addr @ A ) ) @ ( produc755559506on_val @ H @ L ) )
=> ( ( ( H @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs ) ) )
=> ( ( ( Fs @ ( produc5062597t_char @ F @ D ) )
= ( some_val @ V ) )
=> ( eval @ P @ ( fAcc_list_char @ E @ F @ D ) @ S_0 @ ( val_list_char @ V ) @ ( produc755559506on_val @ H @ L ) ) ) ) ) ).
thf(fact_699_red__reds_ORedFAcc,axiom,
! [P: list_P1999446415t_char,F: list_char,D: list_char,V: val,S: produc2090907612on_val,A: nat,C: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( hp @ S @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs ) ) )
=> ( ( ( Fs @ ( produc5062597t_char @ F @ D ) )
= ( some_val @ V ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAcc_list_char @ ( val_list_char @ ( addr @ A ) ) @ F @ D ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ S ) ) @ ( red @ P ) ) ) ) ).
%----Conjectures (1)
thf(conj_0,conjecture,
wTrt @ p @ h_a @ e @ e_a @ nt ).
%------------------------------------------------------------------------------