TSTP Solution File: SWW478+3 by Leo-III---1.7.7

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SWW478+3 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:24:28 EDT 2023

% Result   : Theorem 32.87s 10.98s
% Output   : Refutation 34.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      : 2174
% Syntax   : Number of formulae    : 3432 ( 894 unt; 918 typ;   0 def)
%            Number of atoms       : 6311 (2116 equ;   0 cnn)
%            Maximal formula atoms :   16 (   2 avg)
%            Number of connectives : 53900 ( 959   ~;  86   |; 527   &;49144   @)
%                                         ( 239 <=>;2945  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   44 (  12 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  : 1310 (1310   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  920 ( 918 usr; 235 con; 0-6 aty)
%            Number of variables   : 10805 (   0   ^;10634   !; 171   ?;10805   :)

% Comments : 
%------------------------------------------------------------------------------
thf(hBOOL_type,type,
    hBOOL: $i > $o ).

thf(hAPP_f1453283057l_bool_type,type,
    hAPP_f1453283057l_bool: $i > $i > $i ).

thf(hAPP_P1303341961l_bool_type,type,
    hAPP_P1303341961l_bool: $i > $i > $i ).

thf(member773094996on_val_type,type,
    member773094996on_val: $i ).

thf(hAPP_P1886180715on_val_type,type,
    hAPP_P1886180715on_val: $i > $i > $i ).

thf(hAPP_P1870962205on_val_type,type,
    hAPP_P1870962205on_val: $i > $i > $i ).

thf(produc1441475159on_val_type,type,
    produc1441475159on_val: $i ).

thf(hAPP_P604205461on_val_type,type,
    hAPP_P604205461on_val: $i > $i > $i ).

thf(hAPP_e1659493427on_val_type,type,
    hAPP_e1659493427on_val: $i > $i > $i ).

thf(produc1259058957on_val_type,type,
    produc1259058957on_val: $i ).

thf(ea_type,type,
    ea: $i ).

thf(hAPP_f1727192346on_val_type,type,
    hAPP_f1727192346on_val: $i > $i > $i ).

thf(hAPP_f1849790461on_val_type,type,
    hAPP_f1849790461on_val: $i > $i > $i ).

thf(produc899768717on_val_type,type,
    produc899768717on_val: $i ).

thf(ha_type,type,
    ha: $i ).

thf(fun_up1149430426on_val_type,type,
    fun_up1149430426on_val: $i > $i > $i > $i ).

thf(la_type,type,
    la: $i ).

thf(v_1_type,type,
    v_1: $i ).

thf(hAPP_val_option_val_type,type,
    hAPP_val_option_val: $i > $i > $i ).

thf(some_val_type,type,
    some_val: $i ).

thf(v_type,type,
    v: $i ).

thf(e_a_type,type,
    e_a: $i ).

thf(h_a_type,type,
    h_a: $i ).

thf(l_a_type,type,
    l_a: $i ).

thf(red_type,type,
    red: $i > $i ).

thf(p_type,type,
    p: $i ).

thf(hAPP_P1423780764t_char_type,type,
    hAPP_P1423780764t_char: $i > $i > $i ).

thf(hAPP_l309186817t_char_type,type,
    hAPP_l309186817t_char: $i > $i > $i ).

thf(produc1483578759t_char_type,type,
    produc1483578759t_char: $i ).

thf(hAPP_P1680401186r_bool_type,type,
    hAPP_P1680401186r_bool: $i > $i > $i ).

thf(hAPP_P1224499548t_char_type,type,
    hAPP_P1224499548t_char: $i > $i > $i ).

thf(hAPP_l902950593t_char_type,type,
    hAPP_l902950593t_char: $i > $i > $i ).

thf(produc822965838t_char_type,type,
    produc822965838t_char: $i ).

thf(hAPP_l277216047t_char_type,type,
    hAPP_l277216047t_char: $i > $i > $i ).

thf(hAPP_l352172327t_char_type,type,
    hAPP_l352172327t_char: $i > $i > $i ).

thf(produc1152259904t_char_type,type,
    produc1152259904t_char: $i ).

thf(hAPP_P1240100515r_bool_type,type,
    hAPP_P1240100515r_bool: $i > $i > $i ).

thf(hAPP_P1333668416t_char_type,type,
    hAPP_P1333668416t_char: $i > $i > $i ).

thf(hAPP_P1859316965t_char_type,type,
    hAPP_P1859316965t_char: $i > $i > $i ).

thf(produc57279289t_char_type,type,
    produc57279289t_char: $i ).

thf(is_bool_type,type,
    is_bool: $i > $o ).

thf(hAPP_f258424141l_bool_type,type,
    hAPP_f258424141l_bool: $i > $i > $i ).

thf(hAPP_f1715346603l_bool_type,type,
    hAPP_f1715346603l_bool: $i > $i > $i ).

thf(hAPP_P409642305l_bool_type,type,
    hAPP_P409642305l_bool: $i > $i > $i ).

thf(member125098544t_char_type,type,
    member125098544t_char: $i ).

thf(hAPP_P1392904962t_char_type,type,
    hAPP_P1392904962t_char: $i > $i > $i ).

thf(hAPP_l14371579t_char_type,type,
    hAPP_l14371579t_char: $i > $i > $i ).

thf(produc1909267824t_char_type,type,
    produc1909267824t_char: $i ).

thf(transi1257872013t_char_type,type,
    transi1257872013t_char: $i > $i ).

thf(hAPP_P2118621157r_bool_type,type,
    hAPP_P2118621157r_bool: $i > $i > $i ).

thf(hAPP_l1987619678r_bool_type,type,
    hAPP_l1987619678r_bool: $i > $i > $i ).

thf(hAPP_P801803911r_bool_type,type,
    hAPP_P801803911r_bool: $i > $i > $i ).

thf(hAPP_e544220455r_bool_type,type,
    hAPP_e544220455r_bool: $i > $i > $i ).

thf(hAPP_P1183499705r_bool_type,type,
    hAPP_P1183499705r_bool: $i > $i > $i ).

thf(hAPP_l902158906r_bool_type,type,
    hAPP_l902158906r_bool: $i > $i > $i ).

thf(hAPP_P242904598t_char_type,type,
    hAPP_P242904598t_char: $i > $i > $i ).

thf(hAPP_l1388836853t_char_type,type,
    hAPP_l1388836853t_char: $i > $i > $i ).

thf(produc1331140167t_char_type,type,
    produc1331140167t_char: $i ).

thf(hAPP_P1384137393r_bool_type,type,
    hAPP_P1384137393r_bool: $i > $i > $i ).

thf(hAPP_P2123720426al_val_type,type,
    hAPP_P2123720426al_val: $i > $i > $i ).

thf(hAPP_P1538518401al_val_type,type,
    hAPP_P1538518401al_val: $i > $i > $i ).

thf(produc1924279125al_val_type,type,
    produc1924279125al_val: $i ).

thf(wf_pro755087577t_char_type,type,
    wf_pro755087577t_char: $i > $i > $i ).

thf(wf_J_mdecl_type,type,
    wf_J_mdecl: $i ).

thf(hAPP_f515912112l_bool_type,type,
    hAPP_f515912112l_bool: $i > $i > $i ).

thf(hAPP_P205570445l_bool_type,type,
    hAPP_P205570445l_bool: $i > $i > $i ).

thf(member1467889965t_char_type,type,
    member1467889965t_char: $i ).

thf(set_Pr1494163115t_char_type,type,
    set_Pr1494163115t_char: $i > $i ).

thf(hAPP_f483496539l_bool_type,type,
    hAPP_f483496539l_bool: $i > $i > $i ).

thf(hAPP_P7095645l_bool_type,type,
    hAPP_P7095645l_bool: $i > $i > $i ).

thf(member1601084734t_char_type,type,
    member1601084734t_char: $i ).

thf(set_Pr2033386304t_char_type,type,
    set_Pr2033386304t_char: $i > $i ).

thf(hAPP_l2054741776r_bool_type,type,
    hAPP_l2054741776r_bool: $i > $i > $i ).

thf(hAPP_l2138409430r_bool_type,type,
    hAPP_l2138409430r_bool: $i > $i > $i ).

thf(hAPP_f1145574243l_bool_type,type,
    hAPP_f1145574243l_bool: $i > $i > $i ).

thf(hAPP_P2139822957l_bool_type,type,
    hAPP_P2139822957l_bool: $i > $i > $i ).

thf(member1161907014t_char_type,type,
    member1161907014t_char: $i ).

thf(hAPP_P1220989409t_char_type,type,
    hAPP_P1220989409t_char: $i > $i > $i ).

thf(hAPP_P1668407995t_char_type,type,
    hAPP_P1668407995t_char: $i > $i > $i ).

thf(produc1299387215t_char_type,type,
    produc1299387215t_char: $i ).

thf(hAPP_e1752110927t_char_type,type,
    hAPP_e1752110927t_char: $i > $i > $i ).

thf(hAPP_l1859255743t_char_type,type,
    hAPP_l1859255743t_char: $i > $i > $i ).

thf(produc1916172923t_char_type,type,
    produc1916172923t_char: $i ).

thf(transi1789604888t_char_type,type,
    transi1789604888t_char: $i > $i ).

thf(hAPP_l1062423959r_bool_type,type,
    hAPP_l1062423959r_bool: $i > $i > $i ).

thf(wTrt_1_type,type,
    wTrt_1: $i > $i > $i > $i > $i > $i ).

thf(fAcc_list_char_type,type,
    fAcc_list_char: $i > $i > $i > $i ).

thf(hAPP_list_char_ty_type,type,
    hAPP_list_char_ty: $i > $i > $i ).

thf(class_type,type,
    class: $i ).

thf(hAPP_list_char_bool_type,type,
    hAPP_list_char_bool: $i > $i > $i ).

thf(has_fi1183600461t_char_type,type,
    has_fi1183600461t_char: $i > $i > $i > $i > $i ).

thf(nt_type,type,
    nt: $i ).

thf(hAPP_P1539798428t_char_type,type,
    hAPP_P1539798428t_char: $i > $i > $i ).

thf(hAPP_P719127871t_char_type,type,
    hAPP_P719127871t_char: $i > $i > $i ).

thf(produc24551831t_char_type,type,
    produc24551831t_char: $i ).

thf(hAPP_P767818445t_char_type,type,
    hAPP_P767818445t_char: $i > $i > $i ).

thf(hAPP_l1873467853t_char_type,type,
    hAPP_l1873467853t_char: $i > $i > $i ).

thf(produc921874948t_char_type,type,
    produc921874948t_char: $i ).

thf(hAPP_f665343921l_bool_type,type,
    hAPP_f665343921l_bool: $i > $i > $i ).

thf(hAPP_P502294281l_bool_type,type,
    hAPP_P502294281l_bool: $i > $i > $i ).

thf(member1322055188on_val_type,type,
    member1322055188on_val: $i ).

thf(hAPP_P330218428on_val_type,type,
    hAPP_P330218428on_val: $i > $i > $i ).

thf(hAPP_P1875010047on_val_type,type,
    hAPP_P1875010047on_val: $i > $i > $i ).

thf(produc499151895on_val_type,type,
    produc499151895on_val: $i ).

thf(hAPP_f900686428on_val_type,type,
    hAPP_f900686428on_val: $i > $i > $i ).

thf(hAPP_l1786340417on_val_type,type,
    hAPP_l1786340417on_val: $i > $i > $i ).

thf(produc823076510on_val_type,type,
    produc823076510on_val: $i ).

thf(transi61620055on_val_type,type,
    transi61620055on_val: $i > $i ).

thf(hAPP_l465799708l_bool_type,type,
    hAPP_l465799708l_bool: $i > $i > $i ).

thf(is_bop_type,type,
    is_bop: $i > $o ).

thf(hAPP_P929466802al_val_type,type,
    hAPP_P929466802al_val: $i > $i > $i ).

thf(hAPP_b1229254591al_val_type,type,
    hAPP_b1229254591al_val: $i > $i > $i ).

thf(produc621191550al_val_type,type,
    produc621191550al_val: $i ).

thf(new_list_char_type,type,
    new_list_char: $i > $i ).

thf(is_cla570604648t_char_type,type,
    is_cla570604648t_char: $i > $i ).

thf(hAPP_P449474095r_bool_type,type,
    hAPP_P449474095r_bool: $i > $i > $i ).

thf(hAPP_l2100324114t_char_type,type,
    hAPP_l2100324114t_char: $i > $i > $i ).

thf(hAPP_l208357873t_char_type,type,
    hAPP_l208357873t_char: $i > $i > $i ).

thf(produc5062597t_char_type,type,
    produc5062597t_char: $i ).

thf(hAPP_l1361600383r_bool_type,type,
    hAPP_l1361600383r_bool: $i > $i > $i ).

thf(produc95371820r_bool_type,type,
    produc95371820r_bool: $i > $i ).

thf(hAPP_P1333315679l_bool_type,type,
    hAPP_P1333315679l_bool: $i > $i > $i ).

thf(finals_list_char_type,type,
    finals_list_char: $i > $i ).

thf(hAPP_P1247668062t_char_type,type,
    hAPP_P1247668062t_char: $i > $i > $i ).

thf(hAPP_P1756548163t_char_type,type,
    hAPP_P1756548163t_char: $i > $i > $i ).

thf(produc635935767t_char_type,type,
    produc635935767t_char: $i ).

thf(map_ad325961431ar_val_type,type,
    map_ad325961431ar_val: $i > $i > $i ).

thf(hAPP_o538043682on_val_type,type,
    hAPP_o538043682on_val: $i > $i > $i ).

thf(cOMBK_1097134891t_char_type,type,
    cOMBK_1097134891t_char: $i ).

thf(none_val_type,type,
    none_val: $i ).

thf(hAPP_P71593144l_bool_type,type,
    hAPP_P71593144l_bool: $i > $i > $i ).

thf(hAPP_P1183008383l_bool_type,type,
    hAPP_P1183008383l_bool: $i > $i > $i ).

thf(produc2053127004l_bool_type,type,
    produc2053127004l_bool: $i > $i ).

thf(hAPP_P658340954on_val_type,type,
    hAPP_P658340954on_val: $i > $i > $i ).

thf(hAPP_P1526035745on_val_type,type,
    hAPP_P1526035745on_val: $i > $i > $i ).

thf(produc1611380469on_val_type,type,
    produc1611380469on_val: $i ).

thf(wTrt_type,type,
    wTrt: $i > $i > $i > $i > $i > $i ).

thf(hAPP_ty_bool_type,type,
    hAPP_ty_bool: $i > $i > $i ).

thf(hAPP_ty_fun_ty_bool_type,type,
    hAPP_ty_fun_ty_bool: $i > $i > $i ).

thf(widen_2090681816t_char_type,type,
    widen_2090681816t_char: $i > $i ).

thf(fAss_list_char_type,type,
    fAss_list_char: $i > $i > $i > $i > $i ).

thf(void_type,type,
    void: $i ).

thf(hAPP_f851858423l_bool_type,type,
    hAPP_f851858423l_bool: $i > $i > $i ).

thf(hAPP_P786771093l_bool_type,type,
    hAPP_P786771093l_bool: $i > $i > $i ).

thf(member794220506t_char_type,type,
    member794220506t_char: $i ).

thf(hAPP_P1657265855t_char_type,type,
    hAPP_P1657265855t_char: $i > $i > $i ).

thf(hAPP_P1071727823t_char_type,type,
    hAPP_P1071727823t_char: $i > $i > $i ).

thf(produc2080520419t_char_type,type,
    produc2080520419t_char: $i ).

thf(transi1095029602t_char_type,type,
    transi1095029602t_char: $i > $i ).

thf(none_P179726773on_val_type,type,
    none_P179726773on_val: $i ).

thf(hAPP_P1510515380on_val_type,type,
    hAPP_P1510515380on_val: $i > $i > $i ).

thf(some_P948696889on_val_type,type,
    some_P948696889on_val: $i ).

thf(hAPP_P2094403585on_val_type,type,
    hAPP_P2094403585on_val: $i > $i > $i ).

thf(hAPP_o1269033393on_val_type,type,
    hAPP_o1269033393on_val: $i > $i > $i ).

thf(cOMBK_1867744698t_char_type,type,
    cOMBK_1867744698t_char: $i ).

thf(hAPP_P1758592847on_val_type,type,
    hAPP_P1758592847on_val: $i > $i > $i ).

thf(hAPP_P2015431471on_val_type,type,
    hAPP_P2015431471on_val: $i > $i > $i ).

thf(produc1951691075on_val_type,type,
    produc1951691075on_val: $i ).

thf(hAPP_P1963616220on_val_type,type,
    hAPP_P1963616220on_val: $i > $i > $i ).

thf(hAPP_l1275479261on_val_type,type,
    hAPP_l1275479261on_val: $i > $i > $i ).

thf(produc379668296on_val_type,type,
    produc379668296on_val: $i ).

thf(hAPP_P824029447r_bool_type,type,
    hAPP_P824029447r_bool: $i > $i > $i ).

thf(hAPP_P2028072621l_bool_type,type,
    hAPP_P2028072621l_bool: $i > $i > $i ).

thf(list_all2_ty_ty_type,type,
    list_all2_ty_ty: $i > $i > $i > $i ).

thf(hAPP_f1579743228l_bool_type,type,
    hAPP_f1579743228l_bool: $i > $i > $i ).

thf(hAPP_f1166017719l_bool_type,type,
    hAPP_f1166017719l_bool: $i > $i > $i ).

thf(cOMBC_317789649l_bool_type,type,
    cOMBC_317789649l_bool: $i ).

thf(hAPP_f1134950784l_bool_type,type,
    hAPP_f1134950784l_bool: $i > $i > $i ).

thf(hAPP_f749178132l_bool_type,type,
    hAPP_f749178132l_bool: $i > $i > $i ).

thf(hAPP_val_option_ty_type,type,
    hAPP_val_option_ty: $i > $i > $i ).

thf(typeof_h_type,type,
    typeof_h: $i > $i ).

thf(unit_type,type,
    unit: $i ).

thf(hAPP_ty_option_ty_type,type,
    hAPP_ty_option_ty: $i > $i > $i ).

thf(some_ty_type,type,
    some_ty: $i ).

thf(hAPP_f126445617l_bool_type,type,
    hAPP_f126445617l_bool: $i > $i > $i ).

thf(hAPP_P1313790473l_bool_type,type,
    hAPP_P1313790473l_bool: $i > $i > $i ).

thf(member1551446420t_char_type,type,
    member1551446420t_char: $i ).

thf(transi772168185t_char_type,type,
    transi772168185t_char: $i > $i ).

thf(hAPP_l24694616r_bool_type,type,
    hAPP_l24694616r_bool: $i > $i > $i ).

thf(semila919158006r_bool_type,type,
    semila919158006r_bool: $i > $i > $i ).

thf(hAPP_P1907982426r_bool_type,type,
    hAPP_P1907982426r_bool: $i > $i > $i ).

thf(hAPP_f1874697593r_bool_type,type,
    hAPP_f1874697593r_bool: $i > $i > $i ).

thf(hAPP_f1707979241r_bool_type,type,
    hAPP_f1707979241r_bool: $i > $i > $i ).

thf(cOMBC_407285762l_bool_type,type,
    cOMBC_407285762l_bool: $i ).

thf(hAPP_f1780084320l_bool_type,type,
    hAPP_f1780084320l_bool: $i > $i > $i ).

thf(hAPP_P1562529797l_bool_type,type,
    hAPP_P1562529797l_bool: $i > $i > $i ).

thf(hAPP_v834067052t_char_type,type,
    hAPP_v834067052t_char: $i > $i > $i ).

thf(val_list_char_type,type,
    val_list_char: $i ).

thf(hAPP_P1235399154l_bool_type,type,
    hAPP_P1235399154l_bool: $i > $i > $i ).

thf(hAPP_f1724656343r_bool_type,type,
    hAPP_f1724656343r_bool: $i > $i > $i ).

thf(hAPP_f388097003r_bool_type,type,
    hAPP_f388097003r_bool: $i > $i > $i ).

thf(cOMBC_818212448l_bool_type,type,
    cOMBC_818212448l_bool: $i ).

thf(hAPP_f1314764175l_bool_type,type,
    hAPP_f1314764175l_bool: $i > $i > $i ).

thf(hAPP_e53687815l_bool_type,type,
    hAPP_e53687815l_bool: $i > $i > $i ).

thf(is_refT_type,type,
    is_refT: $i > $i ).

thf(cast_list_char_type,type,
    cast_list_char: $i > $i > $i ).

thf(hAPP_P738987199l_bool_type,type,
    hAPP_P738987199l_bool: $i > $i > $i ).

thf(wTrts_type,type,
    wTrts: $i > $i > $i > $i > $i > $i ).

thf(cons_exp_list_char_type,type,
    cons_exp_list_char: $i > $i > $i ).

thf(cons_ty_type,type,
    cons_ty: $i > $i > $i ).

thf(hAPP_e952791821t_char_type,type,
    hAPP_e952791821t_char: $i > $i > $i ).

thf(hAPP_l796364813t_char_type,type,
    hAPP_l796364813t_char: $i > $i > $i ).

thf(produc1147572817t_char_type,type,
    produc1147572817t_char: $i ).

thf(hAPP_P943837928l_bool_type,type,
    hAPP_P943837928l_bool: $i > $i > $i ).

thf(hAPP_P929938951l_bool_type,type,
    hAPP_P929938951l_bool: $i > $i > $i ).

thf(hAPP_b97269396l_bool_type,type,
    hAPP_b97269396l_bool: $i > $i > $i ).

thf(produc1555310053l_bool_type,type,
    produc1555310053l_bool: $i > $i ).

thf(hAPP_f1317381998l_bool_type,type,
    hAPP_f1317381998l_bool: $i > $i > $i ).

thf(hAPP_f1734997943l_bool_type,type,
    hAPP_f1734997943l_bool: $i > $i > $i ).

thf(cOMBC_1491642377l_bool_type,type,
    cOMBC_1491642377l_bool: $i ).

thf(hAPP_f458849545l_bool_type,type,
    hAPP_f458849545l_bool: $i > $i > $i ).

thf(hAPP_P88824722l_bool_type,type,
    hAPP_P88824722l_bool: $i > $i > $i ).

thf(hAPP_f595031537l_bool_type,type,
    hAPP_f595031537l_bool: $i > $i > $i ).

thf(hAPP_P1862681481l_bool_type,type,
    hAPP_P1862681481l_bool: $i > $i > $i ).

thf(member1999287380t_char_type,type,
    member1999287380t_char: $i ).

thf(hAPP_P1342907945t_char_type,type,
    hAPP_P1342907945t_char: $i > $i > $i ).

thf(hAPP_P91410073t_char_type,type,
    hAPP_P91410073t_char: $i > $i > $i ).

thf(produc1897818327t_char_type,type,
    produc1897818327t_char: $i ).

thf(transi198989188t_char_type,type,
    transi198989188t_char: $i > $i ).

thf(throw_list_char_type,type,
    throw_list_char: $i > $i ).

thf(hAPP_l214204733r_bool_type,type,
    hAPP_l214204733r_bool: $i > $i > $i ).

thf(add_type,type,
    add: $i ).

thf(hAPP_l217977712r_bool_type,type,
    hAPP_l217977712r_bool: $i > $i > $i ).

thf(produc1574020101r_bool_type,type,
    produc1574020101r_bool: $i > $i ).

thf(hAPP_P92196306r_bool_type,type,
    hAPP_P92196306r_bool: $i > $i > $i ).

thf(c_Expr_Obop_OEq_type,type,
    c_Expr_Obop_OEq: $i ).

thf(preallocated_type,type,
    preallocated: $i > $i ).

thf(addr_type,type,
    addr: $i > $i ).

thf(addr_of_sys_xcpt_type,type,
    addr_of_sys_xcpt: $i > $i ).

thf(outOfMemory_type,type,
    outOfMemory: $i ).

thf(null_type,type,
    null: $i ).

thf(produc156891095r_bool_type,type,
    produc156891095r_bool: $i > $i ).

thf(hAPP_f1298720864r_bool_type,type,
    hAPP_f1298720864r_bool: $i > $i > $i ).

thf(hAPP_f225832321r_bool_type,type,
    hAPP_f225832321r_bool: $i > $i > $i ).

thf(cOMBC_1365742487l_bool_type,type,
    cOMBC_1365742487l_bool: $i ).

thf(hAPP_f1746574980l_bool_type,type,
    hAPP_f1746574980l_bool: $i > $i > $i ).

thf(hAPP_P2028292026l_bool_type,type,
    hAPP_P2028292026l_bool: $i > $i > $i ).

thf(hAPP_f1161798306l_bool_type,type,
    hAPP_f1161798306l_bool: $i > $i > $i ).

thf(hAPP_P1327510541l_bool_type,type,
    hAPP_P1327510541l_bool: $i > $i > $i ).

thf(member1379348767t_char_type,type,
    member1379348767t_char: $i ).

thf(hAPP_f82569901l_bool_type,type,
    hAPP_f82569901l_bool: $i > $i > $i ).

thf(hAPP_P1293136973l_bool_type,type,
    hAPP_P1293136973l_bool: $i > $i > $i ).

thf(member1840112042t_char_type,type,
    member1840112042t_char: $i ).

thf(method1809630380t_char_type,type,
    method1809630380t_char: $i > $i > $i > $i > $i > $i > $i ).

thf(wTrts_1_type,type,
    wTrts_1: $i > $i > $i > $i > $i > $i ).

thf(call_list_char_type,type,
    call_list_char: $i > $i > $i > $i ).

thf(hAPP_f335969926r_bool_type,type,
    hAPP_f335969926r_bool: $i > $i > $i ).

thf(hAPP_f1367982615r_bool_type,type,
    hAPP_f1367982615r_bool: $i > $i > $i ).

thf(cOMBC_1603044337l_bool_type,type,
    cOMBC_1603044337l_bool: $i ).

thf(hAPP_f2106398425l_bool_type,type,
    hAPP_f2106398425l_bool: $i > $i > $i ).

thf(hAPP_l553007690l_bool_type,type,
    hAPP_l553007690l_bool: $i > $i > $i ).

thf(lex_pr1588300168t_char_type,type,
    lex_pr1588300168t_char: $i > $i > $i ).

thf(hAPP_f433445541l_bool_type,type,
    hAPP_f433445541l_bool: $i > $i > $i ).

thf(hAPP_P1019319281l_bool_type,type,
    hAPP_P1019319281l_bool: $i > $i > $i ).

thf(member104734088ist_ty_type,type,
    member104734088ist_ty: $i ).

thf(hAPP_l1319068228ist_ty_type,type,
    hAPP_l1319068228ist_ty: $i > $i > $i ).

thf(hAPP_l1770520637ist_ty_type,type,
    hAPP_l1770520637ist_ty: $i > $i > $i ).

thf(produc512429457ist_ty_type,type,
    produc512429457ist_ty: $i ).

thf(hAPP_f1335946228l_bool_type,type,
    hAPP_f1335946228l_bool: $i > $i > $i ).

thf(hAPP_f263393637l_bool_type,type,
    hAPP_f263393637l_bool: $i > $i > $i ).

thf(cOMBC_813705475l_bool_type,type,
    cOMBC_813705475l_bool: $i ).

thf(hAPP_f742333458l_bool_type,type,
    hAPP_f742333458l_bool: $i > $i > $i ).

thf(hAPP_P1614880106l_bool_type,type,
    hAPP_P1614880106l_bool: $i > $i > $i ).

thf(hAPP_l207779698on_val_type,type,
    hAPP_l207779698on_val: $i > $i > $i ).

thf(nullPointer_type,type,
    nullPointer: $i ).

thf(seq_list_char_type,type,
    seq_list_char: $i > $i > $i ).

thf(classCast_type,type,
    classCast: $i ).

thf(hAPP_P159683425l_bool_type,type,
    hAPP_P159683425l_bool: $i > $i > $i ).

thf(hAPP_e1833980889l_bool_type,type,
    hAPP_e1833980889l_bool: $i > $i > $i ).

thf(eval_type,type,
    eval: $i > $i > $i > $i ).

thf(hAPP_l146377954l_bool_type,type,
    hAPP_l146377954l_bool: $i > $i > $i ).

thf(evals_type,type,
    evals: $i > $i > $i > $i ).

thf(append_exp_list_char_type,type,
    append_exp_list_char: $i > $i > $i ).

thf(map_va1934808527t_char_type,type,
    map_va1934808527t_char: $i > $i > $i ).

thf(hAPP_f1748390065l_bool_type,type,
    hAPP_f1748390065l_bool: $i > $i > $i ).

thf(lAss_list_char_type,type,
    lAss_list_char: $i > $i > $i ).

thf(redp_type,type,
    redp: $i > $i > $i > $i ).

thf(hAPP_P1708370145l_bool_type,type,
    hAPP_P1708370145l_bool: $i > $i > $i ).

thf(binOp_list_char_type,type,
    binOp_list_char: $i > $i > $i > $i ).

thf(hAPP_f2071159779l_bool_type,type,
    hAPP_f2071159779l_bool: $i > $i > $i ).

thf(while_list_char_type,type,
    while_list_char: $i > $i > $i ).

thf(cond_list_char_type,type,
    cond_list_char: $i > $i > $i > $i ).

thf(fun_up2041264236on_val_type,type,
    fun_up2041264236on_val: $i > $i > $i > $i ).

thf(hAPP_n546249108on_val_type,type,
    hAPP_n546249108on_val: $i > $i > $i ).

thf(hAPP_f986089162l_bool_type,type,
    hAPP_f986089162l_bool: $i > $i > $i ).

thf(hAPP_l1903254203l_bool_type,type,
    hAPP_l1903254203l_bool: $i > $i > $i ).

thf(member_list_char_type,type,
    member_list_char: $i ).

thf(sys_xcpts_type,type,
    sys_xcpts: $i ).

thf(fv_type,type,
    fv: $i > $i ).

thf(hAPP_v852496844al_val_type,type,
    hAPP_v852496844al_val: $i > $i > $i ).

thf(hAPP_v1519391al_val_type,type,
    hAPP_v1519391al_val: $i > $i > $i ).

thf(product_Pair_val_val_type,type,
    product_Pair_val_val: $i ).

thf(hAPP_val_bool_type,type,
    hAPP_val_bool: $i > $i > $i ).

thf(hAPP_v1392248405l_bool_type,type,
    hAPP_v1392248405l_bool: $i > $i > $i ).

thf(hAPP_f1534412387l_bool_type,type,
    hAPP_f1534412387l_bool: $i > $i > $i ).

thf(produc769963999l_bool_type,type,
    produc769963999l_bool: $i ).

thf(hAPP_P126004409l_bool_type,type,
    hAPP_P126004409l_bool: $i > $i > $i ).

thf(member875476972on_val_type,type,
    member875476972on_val: $i ).

thf(transi374442731on_val_type,type,
    transi374442731on_val: $i > $i ).

thf(hAPP_f570766339l_bool_type,type,
    hAPP_f570766339l_bool: $i > $i > $i ).

thf(hAPP_f1099622285l_bool_type,type,
    hAPP_f1099622285l_bool: $i > $i > $i ).

thf(hAPP_f919000597l_bool_type,type,
    hAPP_f919000597l_bool: $i > $i > $i ).

thf(cOMBB_1153773871on_val_type,type,
    cOMBB_1153773871on_val: $i ).

thf(hAPP_P1217996045l_bool_type,type,
    hAPP_P1217996045l_bool: $i > $i > $i ).

thf(hAPP_l1334098948t_char_type,type,
    hAPP_l1334098948t_char: $i > $i > $i ).

thf(hAPP_l1450984463t_char_type,type,
    hAPP_l1450984463t_char: $i > $i > $i ).

thf(produc436875159t_char_type,type,
    produc436875159t_char: $i ).

thf(hAPP_l753659065r_bool_type,type,
    hAPP_l753659065r_bool: $i > $i > $i ).

thf(hAPP_f2059406941r_bool_type,type,
    hAPP_f2059406941r_bool: $i > $i > $i ).

thf(hAPP_f108089737r_bool_type,type,
    hAPP_f108089737r_bool: $i > $i > $i ).

thf(cOMBB_2143526097t_char_type,type,
    cOMBB_2143526097t_char: $i ).

thf(hAPP_f1766231913r_bool_type,type,
    hAPP_f1766231913r_bool: $i > $i > $i ).

thf(hAPP_l551544901l_bool_type,type,
    hAPP_l551544901l_bool: $i > $i > $i ).

thf(hAPP_f2028441009l_bool_type,type,
    hAPP_f2028441009l_bool: $i > $i > $i ).

thf(hAPP_P530382601l_bool_type,type,
    hAPP_P530382601l_bool: $i > $i > $i ).

thf(member649088532al_val_type,type,
    member649088532al_val: $i ).

thf(transi935034983cl_val_type,type,
    transi935034983cl_val: $i > $i ).

thf(redsp_type,type,
    redsp: $i > $i > $i > $i ).

thf(reds_type,type,
    reds: $i > $i ).

thf(hAPP_P1180869721l_bool_type,type,
    hAPP_P1180869721l_bool: $i > $i > $i ).

thf(member1251428284t_char_type,type,
    member1251428284t_char: $i ).

thf(transi1395422419t_char_type,type,
    transi1395422419t_char: $i > $i ).

thf(bool_type,type,
    bool: $i > $i ).

thf(hAPP_f2121594859l_bool_type,type,
    hAPP_f2121594859l_bool: $i > $i > $i ).

thf(produc1958875245l_bool_type,type,
    produc1958875245l_bool: $i ).

thf(produc2062775566l_bool_type,type,
    produc2062775566l_bool: $i > $i ).

thf(ord_le640323803r_bool_type,type,
    ord_le640323803r_bool: $i > $i ).

thf(produc2128769400l_bool_type,type,
    produc2128769400l_bool: $i ).

thf(semila449273525l_bool_type,type,
    semila449273525l_bool: $i > $i > $i ).

thf(ord_le1987888477r_bool_type,type,
    ord_le1987888477r_bool: $i > $i ).

thf(binop_type,type,
    binop: $i > $i ).

thf(new_Addr_type,type,
    new_Addr: $i > $i ).

thf(hAPP_nat_option_nat_type,type,
    hAPP_nat_option_nat: $i > $i > $i ).

thf(some_nat_type,type,
    some_nat: $i ).

thf(fields1147507508t_char_type,type,
    fields1147507508t_char: $i > $i > $i > $i ).

thf(init_fields_type,type,
    init_fields: $i > $i ).

thf(hAPP_option_val_bool_type,type,
    hAPP_option_val_bool: $i > $i > $i ).

thf(hAPP_l512744617ion_ty_type,type,
    hAPP_l512744617ion_ty: $i > $i > $i ).

thf(fun_up424764369ion_ty_type,type,
    fun_up424764369ion_ty: $i > $i > $i > $i ).

thf(hAPP_f198821591l_bool_type,type,
    hAPP_f198821591l_bool: $i > $i > $i ).

thf(hAPP_f1880802701l_bool_type,type,
    hAPP_f1880802701l_bool: $i > $i > $i ).

thf(cOMBC_1979963740l_bool_type,type,
    cOMBC_1979963740l_bool: $i ).

thf(hAPP_f1728541444l_bool_type,type,
    hAPP_f1728541444l_bool: $i > $i > $i ).

thf(hAPP_v1988122071l_bool_type,type,
    hAPP_v1988122071l_bool: $i > $i > $i ).

thf(hAPP_f1734260017l_bool_type,type,
    hAPP_f1734260017l_bool: $i > $i > $i ).

thf(produc1838470831l_bool_type,type,
    produc1838470831l_bool: $i > $i ).

thf(hAPP_b1909667208op_bop_type,type,
    hAPP_b1909667208op_bop: $i > $i > $i ).

thf(hAPP_b1058859669op_bop_type,type,
    hAPP_b1058859669op_bop: $i > $i > $i ).

thf(product_Pair_bop_bop_type,type,
    product_Pair_bop_bop: $i ).

thf(ord_le2092826700r_bool_type,type,
    ord_le2092826700r_bool: $i > $i ).

thf(is_fun1083000568p_bool_type,type,
    is_fun1083000568p_bool: $i > $o ).

thf(hAPP_f1854361213l_bool_type,type,
    hAPP_f1854361213l_bool: $i > $i > $i ).

thf(hAPP_f363827556r_bool_type,type,
    hAPP_f363827556r_bool: $i > $i > $i ).

thf(some_f80346385r_bool_type,type,
    some_f80346385r_bool: $i ).

thf(ord_le1438917387l_bool_type,type,
    ord_le1438917387l_bool: $i > $i ).

thf(hAPP_bool_bool_type,type,
    hAPP_bool_bool: $i > $i > $i ).

thf(ord_less_eq_bool_type,type,
    ord_less_eq_bool: $i > $i ).

thf(hAPP_P1574824955y_bool_type,type,
    hAPP_P1574824955y_bool: $i > $i > $i ).

thf(fTrue_type,type,
    fTrue: $i ).

thf(map_ad61982421on_val_type,type,
    map_ad61982421on_val: $i > $i > $i ).

thf(hAPP_f1044627221r_bool_type,type,
    hAPP_f1044627221r_bool: $i > $i > $i ).

thf(hAPP_f308875635r_bool_type,type,
    hAPP_f308875635r_bool: $i > $i > $i ).

thf(cOMBC_1718404842r_bool_type,type,
    cOMBC_1718404842r_bool: $i ).

thf(hAPP_l1783480313r_bool_type,type,
    hAPP_l1783480313r_bool: $i > $i > $i ).

thf(hAPP_l1591404153l_bool_type,type,
    hAPP_l1591404153l_bool: $i > $i > $i ).

thf(hAPP_f333583909l_bool_type,type,
    hAPP_f333583909l_bool: $i > $i > $i ).

thf(hAPP_f1407048615l_bool_type,type,
    hAPP_f1407048615l_bool: $i > $i > $i ).

thf(cOMBB_741416308t_char_type,type,
    cOMBB_741416308t_char: $i ).

thf(hAPP_f1107475085l_bool_type,type,
    hAPP_f1107475085l_bool: $i > $i > $i ).

thf(hAPP_P1402001845l_bool_type,type,
    hAPP_P1402001845l_bool: $i > $i > $i ).

thf(hAPP_f379976829l_bool_type,type,
    hAPP_f379976829l_bool: $i > $i > $i ).

thf(hAPP_f606945057l_bool_type,type,
    hAPP_f606945057l_bool: $i > $i > $i ).

thf(cOMBB_705522285on_val_type,type,
    cOMBB_705522285on_val: $i ).

thf(hAPP_b589554111l_bool_type,type,
    hAPP_b589554111l_bool: $i > $i > $i ).

thf(hAPP_P282169671l_bool_type,type,
    hAPP_P282169671l_bool: $i > $i > $i ).

thf(hAPP_P1198052655l_bool_type,type,
    hAPP_P1198052655l_bool: $i > $i > $i ).

thf(member140606439t_char_type,type,
    member140606439t_char: $i ).

thf(hAPP_f1001225811y_bool_type,type,
    hAPP_f1001225811y_bool: $i > $i > $i ).

thf(hAPP_f2060496320y_bool_type,type,
    hAPP_f2060496320y_bool: $i > $i > $i ).

thf(hAPP_f1213370163y_bool_type,type,
    hAPP_f1213370163y_bool: $i > $i > $i ).

thf(lconf_496643946t_char_type,type,
    lconf_496643946t_char: $i > $i ).

thf(conf_P373316194t_char_type,type,
    conf_P373316194t_char: $i > $i > $i > $i > $i ).

thf(hAPP_f588675559l_bool_type,type,
    hAPP_f588675559l_bool: $i > $i > $i ).

thf(hAPP_P1860450421l_bool_type,type,
    hAPP_P1860450421l_bool: $i > $i > $i ).

thf(member1199939018t_char_type,type,
    member1199939018t_char: $i ).

thf(hAPP_e817857447t_char_type,type,
    hAPP_e817857447t_char: $i > $i > $i ).

thf(hAPP_e1376201919t_char_type,type,
    hAPP_e1376201919t_char: $i > $i > $i ).

thf(produc943465171t_char_type,type,
    produc943465171t_char: $i ).

thf(block_list_char_type,type,
    block_list_char: $i > $i > $i > $i ).

thf(semila1168318597r_bool_type,type,
    semila1168318597r_bool: $i > $i > $i ).

thf(hAPP_f539072365l_bool_type,type,
    hAPP_f539072365l_bool: $i > $i > $i ).

thf(fun_up204312361on_val_type,type,
    fun_up204312361on_val: $i > $i > $i > $i ).

thf(hAPP_t1875766236har_ty_type,type,
    hAPP_t1875766236har_ty: $i > $i > $i ).

thf(hAPP_l1948972481har_ty_type,type,
    hAPP_l1948972481har_ty: $i > $i > $i ).

thf(produc251930284har_ty_type,type,
    produc251930284har_ty: $i ).

thf(hAPP_P594889876l_bool_type,type,
    hAPP_P594889876l_bool: $i > $i > $i ).

thf(hAPP_f375531599l_bool_type,type,
    hAPP_f375531599l_bool: $i > $i > $i ).

thf(hAPP_f1564338425l_bool_type,type,
    hAPP_f1564338425l_bool: $i > $i > $i ).

thf(cOMBB_1078680455on_val_type,type,
    cOMBB_1078680455on_val: $i ).

thf(hAPP_P483670507l_bool_type,type,
    hAPP_P483670507l_bool: $i > $i > $i ).

thf(hAPP_P504978887l_bool_type,type,
    hAPP_P504978887l_bool: $i > $i > $i ).

thf(hAPP_f434955681l_bool_type,type,
    hAPP_f434955681l_bool: $i > $i > $i ).

thf(lex_pr1971266694on_val_type,type,
    lex_pr1971266694on_val: $i > $i > $i ).

thf(hAPP_f983152497l_bool_type,type,
    hAPP_f983152497l_bool: $i > $i > $i ).

thf(hAPP_P1953134729l_bool_type,type,
    hAPP_P1953134729l_bool: $i > $i > $i ).

thf(member781783252on_val_type,type,
    member781783252on_val: $i ).

thf(hAPP_f1146435765on_val_type,type,
    hAPP_f1146435765on_val: $i > $i > $i ).

thf(hAPP_f1744304433on_val_type,type,
    hAPP_f1744304433on_val: $i > $i > $i ).

thf(produc1618304727on_val_type,type,
    produc1618304727on_val: $i ).

thf(hAPP_f1666729379r_bool_type,type,
    hAPP_f1666729379r_bool: $i > $i > $i ).

thf(hAPP_f1020753317r_bool_type,type,
    hAPP_f1020753317r_bool: $i > $i > $i ).

thf(cOMBC_1297648632l_bool_type,type,
    cOMBC_1297648632l_bool: $i ).

thf(hAPP_l1249476511st_val_type,type,
    hAPP_l1249476511st_val: $i > $i > $i ).

thf(hAPP_l103437071st_val_type,type,
    hAPP_l103437071st_val: $i > $i > $i ).

thf(produc2078839843st_val_type,type,
    produc2078839843st_val: $i ).

thf(hAPP_f1741070310on_val_type,type,
    hAPP_f1741070310on_val: $i > $i > $i ).

thf(hAPP_f864891091on_val_type,type,
    hAPP_f864891091on_val: $i > $i > $i ).

thf(produc1960514199on_val_type,type,
    produc1960514199on_val: $i ).

thf(ord_le117566470r_bool_type,type,
    ord_le117566470r_bool: $i > $i ).

thf(hAPP_P124632071l_bool_type,type,
    hAPP_P124632071l_bool: $i > $i > $i ).

thf(hAPP_f1754555101l_bool_type,type,
    hAPP_f1754555101l_bool: $i > $i > $i ).

thf(dom_list_char_val_type,type,
    dom_list_char_val: $i > $i ).

thf(hp_type,type,
    hp: $i > $i ).

thf(transi1065307915t_char_type,type,
    transi1065307915t_char: $i > $i ).

thf(subcls744239332t_char_type,type,
    subcls744239332t_char: $i > $i ).

thf(subcls851966956t_char_type,type,
    subcls851966956t_char: $i > $i ).

thf(tryCatch_list_char_type,type,
    tryCatch_list_char: $i > $i > $i > $i > $i ).

thf(produc886919678l_bool_type,type,
    produc886919678l_bool: $i > $i ).

thf(none_ty_type,type,
    none_ty: $i ).

thf(hAPP_f61040418l_bool_type,type,
    hAPP_f61040418l_bool: $i > $i > $i ).

thf(hconf_97414254t_char_type,type,
    hconf_97414254t_char: $i > $i ).

thf(oconf_1869808039t_char_type,type,
    oconf_1869808039t_char: $i > $i > $i ).

thf(hAPP_f1145256474l_bool_type,type,
    hAPP_f1145256474l_bool: $i > $i > $i ).

thf(hAPP_f1452292669l_bool_type,type,
    hAPP_f1452292669l_bool: $i > $i > $i ).

thf(hAPP_f1977633121l_bool_type,type,
    hAPP_f1977633121l_bool: $i > $i > $i ).

thf(cOMBB_1303934920on_val_type,type,
    cOMBB_1303934920on_val: $i ).

thf(hAPP_l1294856089har_ty_type,type,
    hAPP_l1294856089har_ty: $i > $i > $i ).

thf(hAPP_l1657578379har_ty_type,type,
    hAPP_l1657578379har_ty: $i > $i > $i ).

thf(produc1860789535har_ty_type,type,
    produc1860789535har_ty: $i ).

thf(none_f478147469r_bool_type,type,
    none_f478147469r_bool: $i ).

thf(fFalse_type,type,
    fFalse: $i ).

thf(fdisj_type,type,
    fdisj: $i ).

thf(hAPP_l1739862107l_bool_type,type,
    hAPP_l1739862107l_bool: $i > $i > $i ).

thf(hAPP_f1094343359l_bool_type,type,
    hAPP_f1094343359l_bool: $i > $i > $i ).

thf(hAPP_f876671127l_bool_type,type,
    hAPP_f876671127l_bool: $i > $i > $i ).

thf(cOMBB_1200577438t_char_type,type,
    cOMBB_1200577438t_char: $i ).

thf(hAPP_l2111308793l_bool_type,type,
    hAPP_l2111308793l_bool: $i > $i > $i ).

thf(hext_type,type,
    hext: $i > $i > $i ).

thf(hAPP_P291613419on_val_type,type,
    hAPP_P291613419on_val: $i > $i > $i ).

thf(hAPP_P265246237on_val_type,type,
    hAPP_P265246237on_val: $i > $i > $i ).

thf(produc870913623on_val_type,type,
    produc870913623on_val: $i ).

thf(hAPP_l165010689r_bool_type,type,
    hAPP_l165010689r_bool: $i > $i > $i ).

thf(hAPP_f1209019955r_bool_type,type,
    hAPP_f1209019955r_bool: $i > $i > $i ).

thf(hAPP_f521496323r_bool_type,type,
    hAPP_f521496323r_bool: $i > $i > $i ).

thf(cOMBC_654453230r_bool_type,type,
    cOMBC_654453230r_bool: $i ).

thf(hAPP_f279818502r_bool_type,type,
    hAPP_f279818502r_bool: $i > $i > $i ).

thf(hAPP_l2053770731r_bool_type,type,
    hAPP_l2053770731r_bool: $i > $i > $i ).

thf(hAPP_t708040077har_ty_type,type,
    hAPP_t708040077har_ty: $i > $i > $i ).

thf(hAPP_P827589667har_ty_type,type,
    hAPP_P827589667har_ty: $i > $i > $i ).

thf(produc1265154397har_ty_type,type,
    produc1265154397har_ty: $i ).

thf(size_size_list_val_type,type,
    size_size_list_val: $i > $i ).

thf(size_s2113983095t_char_type,type,
    size_s2113983095t_char: $i > $i ).

thf(size_size_list_ty_type,type,
    size_size_list_ty: $i > $i ).

thf(blocks_type,type,
    blocks: $i > $i ).

thf(cons_list_char_type,type,
    cons_list_char: $i > $i > $i ).

thf(this_type,type,
    this: $i ).

thf(cons_val_type,type,
    cons_val: $i > $i > $i ).

thf(hAPP_f1297673713l_bool_type,type,
    hAPP_f1297673713l_bool: $i > $i > $i ).

thf(hAPP_l1571522437l_bool_type,type,
    hAPP_l1571522437l_bool: $i > $i > $i ).

thf(hAPP_f1136362289l_bool_type,type,
    hAPP_f1136362289l_bool: $i > $i > $i ).

thf(hAPP_f1736484361l_bool_type,type,
    hAPP_f1736484361l_bool: $i > $i > $i ).

thf(cOMBB_2042763133t_char_type,type,
    cOMBB_2042763133t_char: $i ).

thf(hAPP_f1233028029l_bool_type,type,
    hAPP_f1233028029l_bool: $i > $i > $i ).

thf(hAPP_f678833350l_bool_type,type,
    hAPP_f678833350l_bool: $i > $i > $i ).

thf(member1542417277on_val_type,type,
    member1542417277on_val: $i ).

thf(hAPP_l1342015621r_bool_type,type,
    hAPP_l1342015621r_bool: $i > $i > $i ).

thf(hAPP_f719350875r_bool_type,type,
    hAPP_f719350875r_bool: $i > $i > $i ).

thf(hAPP_f2133563379r_bool_type,type,
    hAPP_f2133563379r_bool: $i > $i > $i ).

thf(cOMBC_1025440566r_bool_type,type,
    cOMBC_1025440566r_bool: $i ).

thf(hAPP_f764724814r_bool_type,type,
    hAPP_f764724814r_bool: $i > $i > $i ).

thf(hAPP_l1988620845r_bool_type,type,
    hAPP_l1988620845r_bool: $i > $i > $i ).

thf(hAPP_P2077557811l_bool_type,type,
    hAPP_P2077557811l_bool: $i > $i > $i ).

thf(hAPP_P468446343l_bool_type,type,
    hAPP_P468446343l_bool: $i > $i > $i ).

thf(final_list_char_type,type,
    final_list_char: $i > $i ).

thf(cOMBS_1319864284l_bool_type,type,
    cOMBS_1319864284l_bool: $i > $i > $i ).

thf(hAPP_f1889282162l_bool_type,type,
    hAPP_f1889282162l_bool: $i > $i > $i ).

thf(hAPP_l923073979r_bool_type,type,
    hAPP_l923073979r_bool: $i > $i > $i ).

thf(hAPP_f29105311r_bool_type,type,
    hAPP_f29105311r_bool: $i > $i > $i ).

thf(hAPP_f953097879r_bool_type,type,
    hAPP_f953097879r_bool: $i > $i > $i ).

thf(cOMBB_672864638t_char_type,type,
    cOMBB_672864638t_char: $i ).

thf(hAPP_f454222487r_bool_type,type,
    hAPP_f454222487r_bool: $i > $i > $i ).

thf(hAPP_P2053453961y_bool_type,type,
    hAPP_P2053453961y_bool: $i > $i > $i ).

thf(hAPP_f165071409l_bool_type,type,
    hAPP_f165071409l_bool: $i > $i > $i ).

thf(hAPP_f1174637065l_bool_type,type,
    hAPP_f1174637065l_bool: $i > $i > $i ).

thf(cOMBB_33167485t_char_type,type,
    cOMBB_33167485t_char: $i ).

thf(hAPP_f901718717l_bool_type,type,
    hAPP_f901718717l_bool: $i > $i > $i ).

thf(hAPP_f257113085l_bool_type,type,
    hAPP_f257113085l_bool: $i > $i > $i ).

thf(hAPP_f1100052969l_bool_type,type,
    hAPP_f1100052969l_bool: $i > $i > $i ).

thf(cOMBC_199425070l_bool_type,type,
    cOMBC_199425070l_bool: $i ).

thf(hAPP_b1257035143l_bool_type,type,
    hAPP_b1257035143l_bool: $i > $i > $i ).

thf(hAPP_P1002912327r_bool_type,type,
    hAPP_P1002912327r_bool: $i > $i > $i ).

thf(fequal_val_type,type,
    fequal_val: $i ).

thf(hAPP_f2041029616l_bool_type,type,
    hAPP_f2041029616l_bool: $i > $i > $i ).

thf(hAPP_f361629773l_bool_type,type,
    hAPP_f361629773l_bool: $i > $i > $i ).

thf(hAPP_f1612138403l_bool_type,type,
    hAPP_f1612138403l_bool: $i > $i > $i ).

thf(cOMBB_961360819t_char_type,type,
    cOMBB_961360819t_char: $i ).

thf(hAPP_P845017029l_bool_type,type,
    hAPP_P845017029l_bool: $i > $i > $i ).

thf(hAPP_P2010574925r_bool_type,type,
    hAPP_P2010574925r_bool: $i > $i > $i ).

thf(hAPP_f1634841927l_bool_type,type,
    hAPP_f1634841927l_bool: $i > $i > $i ).

thf(produc1491230096l_bool_type,type,
    produc1491230096l_bool: $i ).

thf(hAPP_P1221872711l_bool_type,type,
    hAPP_P1221872711l_bool: $i > $i > $i ).

thf(hAPP_P76086873l_bool_type,type,
    hAPP_P76086873l_bool: $i > $i > $i ).

thf(hAPP_f1082373989l_bool_type,type,
    hAPP_f1082373989l_bool: $i > $i > $i ).

thf(hAPP_f869803751l_bool_type,type,
    hAPP_f869803751l_bool: $i > $i > $i ).

thf(cOMBB_555068556on_val_type,type,
    cOMBB_555068556on_val: $i ).

thf(hAPP_f1776493709l_bool_type,type,
    hAPP_f1776493709l_bool: $i > $i > $i ).

thf(hAPP_l1117138611l_bool_type,type,
    hAPP_l1117138611l_bool: $i > $i > $i ).

thf(hAPP_f2047757465l_bool_type,type,
    hAPP_f2047757465l_bool: $i > $i > $i ).

thf(hAPP_f466945179l_bool_type,type,
    hAPP_f466945179l_bool: $i > $i > $i ).

thf(cOMBB_68065882ist_ty_type,type,
    cOMBB_68065882ist_ty: $i ).

thf(hAPP_f921434893l_bool_type,type,
    hAPP_f921434893l_bool: $i > $i > $i ).

thf(hAPP_l1883348915t_char_type,type,
    hAPP_l1883348915t_char: $i > $i > $i ).

thf(hAPP_l2019537453t_char_type,type,
    hAPP_l2019537453t_char: $i > $i > $i ).

thf(produc2035944023t_char_type,type,
    produc2035944023t_char: $i ).

thf(hAPP_f1776070952l_bool_type,type,
    hAPP_f1776070952l_bool: $i > $i > $i ).

thf(hAPP_o2007402111l_bool_type,type,
    hAPP_o2007402111l_bool: $i > $i > $i ).

thf(hAPP_f732843907r_bool_type,type,
    hAPP_f732843907r_bool: $i > $i > $i ).

thf(hAPP_f1563448447r_bool_type,type,
    hAPP_f1563448447r_bool: $i > $i > $i ).

thf(cOMBB_1490692730t_char_type,type,
    cOMBB_1490692730t_char: $i ).

thf(hAPP_f1419180947r_bool_type,type,
    hAPP_f1419180947r_bool: $i > $i > $i ).

thf(hAPP_l1845912621l_bool_type,type,
    hAPP_l1845912621l_bool: $i > $i > $i ).

thf(hAPP_f1033709212l_bool_type,type,
    hAPP_f1033709212l_bool: $i > $i > $i ).

thf(hAPP_f603925568l_bool_type,type,
    hAPP_f603925568l_bool: $i > $i > $i ).

thf(hAPP_f181262431l_bool_type,type,
    hAPP_f181262431l_bool: $i > $i > $i ).

thf(cOMBC_832625297y_bool_type,type,
    cOMBC_832625297y_bool: $i ).

thf(hAPP_f1661305905l_bool_type,type,
    hAPP_f1661305905l_bool: $i > $i > $i ).

thf(hAPP_f844901525l_bool_type,type,
    hAPP_f844901525l_bool: $i > $i > $i ).

thf(hAPP_f348508809l_bool_type,type,
    hAPP_f348508809l_bool: $i > $i > $i ).

thf(cOMBC_622308798l_bool_type,type,
    cOMBC_622308798l_bool: $i ).

thf(hAPP_f1526206996l_bool_type,type,
    hAPP_f1526206996l_bool: $i > $i > $i ).

thf(hAPP_l177734933l_bool_type,type,
    hAPP_l177734933l_bool: $i > $i > $i ).

thf(hAPP_f2050077417l_bool_type,type,
    hAPP_f2050077417l_bool: $i > $i > $i ).

thf(hAPP_f2080627739l_bool_type,type,
    hAPP_f2080627739l_bool: $i > $i > $i ).

thf(hAPP_f350189921l_bool_type,type,
    hAPP_f350189921l_bool: $i > $i > $i ).

thf(cOMBC_1535683812l_bool_type,type,
    cOMBC_1535683812l_bool: $i ).

thf(transi2024712006on_val_type,type,
    transi2024712006on_val: $i > $i ).

thf(hAPP_f1853572245r_bool_type,type,
    hAPP_f1853572245r_bool: $i > $i > $i ).

thf(hAPP_f1933376467r_bool_type,type,
    hAPP_f1933376467r_bool: $i > $i > $i ).

thf(cOMBC_36589090l_bool_type,type,
    cOMBC_36589090l_bool: $i ).

thf(fconj_type,type,
    fconj: $i ).

thf(hAPP_P499022727r_bool_type,type,
    hAPP_P499022727r_bool: $i > $i > $i ).

thf(hAPP_P1926698759r_bool_type,type,
    hAPP_P1926698759r_bool: $i > $i > $i ).

thf(map_val_option_ty_type,type,
    map_val_option_ty: $i > $i > $i ).

thf(map_ty_option_ty_type,type,
    map_ty_option_ty: $i > $i > $i ).

thf(d_list_char_type,type,
    d_list_char: $i > $i > $i ).

thf(hAPP_l2140727500r_bool_type,type,
    hAPP_l2140727500r_bool: $i > $i > $i ).

thf(hAPP_f2025561243r_bool_type,type,
    hAPP_f2025561243r_bool: $i > $i > $i ).

thf(hAPP_f1500560577r_bool_type,type,
    hAPP_f1500560577r_bool: $i > $i > $i ).

thf(cOMBC_1784597444r_bool_type,type,
    cOMBC_1784597444r_bool: $i ).

thf(hAPP_f658521820r_bool_type,type,
    hAPP_f658521820r_bool: $i > $i > $i ).

thf(hAPP_f306469557r_bool_type,type,
    hAPP_f306469557r_bool: $i > $i > $i ).

thf(hAPP_f197435839r_bool_type,type,
    hAPP_f197435839r_bool: $i > $i > $i ).

thf(cOMBC_886773442r_bool_type,type,
    cOMBC_886773442r_bool: $i ).

thf(hAPP_f605643693r_bool_type,type,
    hAPP_f605643693r_bool: $i > $i > $i ).

thf(hAPP_l1129005983r_bool_type,type,
    hAPP_l1129005983r_bool: $i > $i > $i ).

thf(hAPP_option_nat_nat_type,type,
    hAPP_option_nat_nat: $i > $i > $i ).

thf(the_nat_type,type,
    the_nat: $i ).

thf(none_nat_type,type,
    none_nat: $i ).

thf(hAPP_f1868463117l_bool_type,type,
    hAPP_f1868463117l_bool: $i > $i > $i ).

thf(hAPP_f1365840271l_bool_type,type,
    hAPP_f1365840271l_bool: $i > $i > $i ).

thf(cOMBB_1705938036t_char_type,type,
    cOMBB_1705938036t_char: $i ).

thf(hAPP_f1239832973l_bool_type,type,
    hAPP_f1239832973l_bool: $i > $i > $i ).

thf(hAPP_l1536299231l_bool_type,type,
    hAPP_l1536299231l_bool: $i > $i > $i ).

thf(hAPP_f935003377l_bool_type,type,
    hAPP_f935003377l_bool: $i > $i > $i ).

thf(hAPP_f162154931l_bool_type,type,
    hAPP_f162154931l_bool: $i > $i > $i ).

thf(cOMBB_859890145har_ty_type,type,
    cOMBB_859890145har_ty: $i ).

thf(hAPP_f156692813l_bool_type,type,
    hAPP_f156692813l_bool: $i > $i > $i ).

thf(hAPP_f1467537159l_bool_type,type,
    hAPP_f1467537159l_bool: $i > $i > $i ).

thf(cOMBC_2141828763l_bool_type,type,
    cOMBC_2141828763l_bool: $i ).

thf(hAPP_f837795298l_bool_type,type,
    hAPP_f837795298l_bool: $i > $i > $i ).

thf(hAPP_f2071340985r_bool_type,type,
    hAPP_f2071340985r_bool: $i > $i > $i ).

thf(hAPP_f133320957r_bool_type,type,
    hAPP_f133320957r_bool: $i > $i > $i ).

thf(cOMBC_1127703214r_bool_type,type,
    cOMBC_1127703214r_bool: $i ).

thf(hAPP_l96108383r_bool_type,type,
    hAPP_l96108383r_bool: $i > $i > $i ).

thf(hAPP_f1149562121l_bool_type,type,
    hAPP_f1149562121l_bool: $i > $i > $i ).

thf(hAPP_f1850037271l_bool_type,type,
    hAPP_f1850037271l_bool: $i > $i > $i ).

thf(cOMBB_773375802t_char_type,type,
    cOMBB_773375802t_char: $i ).

thf(hAPP_l232580245l_bool_type,type,
    hAPP_l232580245l_bool: $i > $i > $i ).

thf(hAPP_l810309945l_bool_type,type,
    hAPP_l810309945l_bool: $i > $i > $i ).

thf(hAPP_f1817350437l_bool_type,type,
    hAPP_f1817350437l_bool: $i > $i > $i ).

thf(hAPP_f614662951l_bool_type,type,
    hAPP_f614662951l_bool: $i > $i > $i ).

thf(cOMBB_1558246132t_char_type,type,
    cOMBB_1558246132t_char: $i ).

thf(hAPP_f2037329933l_bool_type,type,
    hAPP_f2037329933l_bool: $i > $i > $i ).

thf(hAPP_P1486793863on_val_type,type,
    hAPP_P1486793863on_val: $i > $i > $i ).

thf(hAPP_P2077211775on_val_type,type,
    hAPP_P2077211775on_val: $i > $i > $i ).

thf(produc1564932627on_val_type,type,
    produc1564932627on_val: $i ).

thf(hAPP_P768428603l_bool_type,type,
    hAPP_P768428603l_bool: $i > $i > $i ).

thf(hAPP_f1427871743l_bool_type,type,
    hAPP_f1427871743l_bool: $i > $i > $i ).

thf(hAPP_f32926423l_bool_type,type,
    hAPP_f32926423l_bool: $i > $i > $i ).

thf(cOMBB_779086262on_val_type,type,
    cOMBB_779086262on_val: $i ).

thf(lex_pr307591827t_char_type,type,
    lex_pr307591827t_char: $i > $i > $i ).

thf(hAPP_f348753975l_bool_type,type,
    hAPP_f348753975l_bool: $i > $i > $i ).

thf(hAPP_P1033205013l_bool_type,type,
    hAPP_P1033205013l_bool: $i > $i > $i ).

thf(member273646106st_val_type,type,
    member273646106st_val: $i ).

thf(wwf_J_mdecl_type,type,
    wwf_J_mdecl: $i ).

thf(fvs_type,type,
    fvs: $i > $i ).

thf(hAPP_l296209613r_bool_type,type,
    hAPP_l296209613r_bool: $i > $i > $i ).

thf(hAPP_f1449341487r_bool_type,type,
    hAPP_f1449341487r_bool: $i > $i > $i ).

thf(hAPP_f1823921107r_bool_type,type,
    hAPP_f1823921107r_bool: $i > $i > $i ).

thf(cOMBB_308691073st_val_type,type,
    cOMBB_308691073st_val: $i ).

thf(hAPP_l1842007287l_bool_type,type,
    hAPP_l1842007287l_bool: $i > $i > $i ).

thf(hAPP_f966411375l_bool_type,type,
    hAPP_f966411375l_bool: $i > $i > $i ).

thf(hAPP_f2091926485r_bool_type,type,
    hAPP_f2091926485r_bool: $i > $i > $i ).

thf(hAPP_f1820115955r_bool_type,type,
    hAPP_f1820115955r_bool: $i > $i > $i ).

thf(cOMBC_790582442r_bool_type,type,
    cOMBC_790582442r_bool: $i ).

thf(hAPP_f1466436665r_bool_type,type,
    hAPP_f1466436665r_bool: $i > $i > $i ).

thf(hAPP_f368284312on_val_type,type,
    hAPP_f368284312on_val: $i > $i > $i ).

thf(hAPP_f1805337205on_val_type,type,
    hAPP_f1805337205on_val: $i > $i > $i ).

thf(produc1712663241on_val_type,type,
    produc1712663241on_val: $i ).

thf(hAPP_f1617787571l_bool_type,type,
    hAPP_f1617787571l_bool: $i > $i > $i ).

thf(hAPP_f857351829l_bool_type,type,
    hAPP_f857351829l_bool: $i > $i > $i ).

thf(hAPP_f348318673l_bool_type,type,
    hAPP_f348318673l_bool: $i > $i > $i ).

thf(cOMBB_1518282696on_val_type,type,
    cOMBB_1518282696on_val: $i ).

thf(hAPP_f1931964053l_bool_type,type,
    hAPP_f1931964053l_bool: $i > $i > $i ).

thf(hAPP_f531187933r_bool_type,type,
    hAPP_f531187933r_bool: $i > $i > $i ).

thf(hAPP_f179418505r_bool_type,type,
    hAPP_f179418505r_bool: $i > $i > $i ).

thf(cOMBB_550632017t_char_type,type,
    cOMBB_550632017t_char: $i ).

thf(distinct_list_char_type,type,
    distinct_list_char: $i > $i ).

thf(hAPP_P1472618637l_bool_type,type,
    hAPP_P1472618637l_bool: $i > $i > $i ).

thf(member133545693t_char_type,type,
    member133545693t_char: $i ).

thf(hAPP_l1425867561l_bool_type,type,
    hAPP_l1425867561l_bool: $i > $i > $i ).

thf(hAPP_f1764180741l_bool_type,type,
    hAPP_f1764180741l_bool: $i > $i > $i ).

thf(hAPP_f247798919l_bool_type,type,
    hAPP_f247798919l_bool: $i > $i > $i ).

thf(cOMBB_526805108t_char_type,type,
    cOMBB_526805108t_char: $i ).

thf(hAPP_f558380429l_bool_type,type,
    hAPP_f558380429l_bool: $i > $i > $i ).

thf(hAPP_f1175362209l_bool_type,type,
    hAPP_f1175362209l_bool: $i > $i > $i ).

thf(hAPP_f101237475l_bool_type,type,
    hAPP_f101237475l_bool: $i > $i > $i ).

thf(cOMBC_1585774710l_bool_type,type,
    cOMBC_1585774710l_bool: $i ).

thf(hAPP_f91506671l_bool_type,type,
    hAPP_f91506671l_bool: $i > $i > $i ).

thf(hAPP_P1609485901l_bool_type,type,
    hAPP_P1609485901l_bool: $i > $i > $i ).

thf(hAPP_f479632753l_bool_type,type,
    hAPP_f479632753l_bool: $i > $i > $i ).

thf(hAPP_f1764548711l_bool_type,type,
    hAPP_f1764548711l_bool: $i > $i > $i ).

thf(cOMBC_331963401l_bool_type,type,
    cOMBC_331963401l_bool: $i ).

thf(hAPP_v3604996l_bool_type,type,
    hAPP_v3604996l_bool: $i > $i > $i ).

thf(hAPP_f1370205989l_bool_type,type,
    hAPP_f1370205989l_bool: $i > $i > $i ).

thf(hAPP_f1406462375l_bool_type,type,
    hAPP_f1406462375l_bool: $i > $i > $i ).

thf(cOMBB_109816436t_char_type,type,
    cOMBB_109816436t_char: $i ).

thf(member1972431429on_val_type,type,
    member1972431429on_val: $i ).

thf(hAPP_f1749915625r_bool_type,type,
    hAPP_f1749915625r_bool: $i > $i > $i ).

thf(hAPP_f842743203r_bool_type,type,
    hAPP_f842743203r_bool: $i > $i > $i ).

thf(cOMBB_657296617har_ty_type,type,
    cOMBB_657296617har_ty: $i ).

thf(hAPP_f841257045r_bool_type,type,
    hAPP_f841257045r_bool: $i > $i > $i ).

thf(hAPP_option_ty_ty_type,type,
    hAPP_option_ty_ty: $i > $i > $i ).

thf(the_ty_type,type,
    the_ty: $i ).

thf(hAPP_l1648260346t_char_type,type,
    hAPP_l1648260346t_char: $i > $i > $i ).

thf(hAPP_l1105836155t_char_type,type,
    hAPP_l1105836155t_char: $i > $i > $i ).

thf(produc1237966615t_char_type,type,
    produc1237966615t_char: $i ).

thf(hAPP_P378063101l_bool_type,type,
    hAPP_P378063101l_bool: $i > $i > $i ).

thf(hAPP_f288221747l_bool_type,type,
    hAPP_f288221747l_bool: $i > $i > $i ).

thf(hAPP_f1646911885l_bool_type,type,
    hAPP_f1646911885l_bool: $i > $i > $i ).

thf(hAPP_f62511709l_bool_type,type,
    hAPP_f62511709l_bool: $i > $i > $i ).

thf(cOMBB_2139740953al_val_type,type,
    cOMBB_2139740953al_val: $i ).

thf(hAPP_P1653675595l_bool_type,type,
    hAPP_P1653675595l_bool: $i > $i > $i ).

thf(hAPP_f2118054305l_bool_type,type,
    hAPP_f2118054305l_bool: $i > $i > $i ).

thf(hAPP_f1687138147l_bool_type,type,
    hAPP_f1687138147l_bool: $i > $i > $i ).

thf(cOMBB_2078271971st_val_type,type,
    cOMBB_2078271971st_val: $i ).

thf(member699351154t_char_type,type,
    member699351154t_char: $i ).

thf(hAPP_P1116729363l_bool_type,type,
    hAPP_P1116729363l_bool: $i > $i > $i ).

thf(hAPP_f1200025813l_bool_type,type,
    hAPP_f1200025813l_bool: $i > $i > $i ).

thf(hAPP_f1089788553l_bool_type,type,
    hAPP_f1089788553l_bool: $i > $i > $i ).

thf(cOMBC_967917532l_bool_type,type,
    cOMBC_967917532l_bool: $i ).

thf(hAPP_f973018659l_bool_type,type,
    hAPP_f973018659l_bool: $i > $i > $i ).

thf(hAPP_P609938901l_bool_type,type,
    hAPP_P609938901l_bool: $i > $i > $i ).

thf(assigned_type,type,
    assigned: $i > $i > $i ).

thf(lex_pr1787105337t_char_type,type,
    lex_pr1787105337t_char: $i > $i > $i ).

thf(hAPP_P153687689l_bool_type,type,
    hAPP_P153687689l_bool: $i > $i > $i ).

thf(member817832404t_char_type,type,
    member817832404t_char: $i ).

thf(map_up1085636310ar_val_type,type,
    map_up1085636310ar_val: $i > $i > $i > $i ).

thf(hAPP_P1085566419p_bool_type,type,
    hAPP_P1085566419p_bool: $i > $i > $i ).

thf(hAPP_f1118567467l_bool_type,type,
    hAPP_f1118567467l_bool: $i > $i > $i ).

thf(hAPP_P476431815r_bool_type,type,
    hAPP_P476431815r_bool: $i > $i > $i ).

thf(hAPP_P2115985549l_bool_type,type,
    hAPP_P2115985549l_bool: $i > $i > $i ).

thf(hAPP_f447422815l_bool_type,type,
    hAPP_f447422815l_bool: $i > $i > $i ).

thf(hAPP_f2052909183l_bool_type,type,
    hAPP_f2052909183l_bool: $i > $i > $i ).

thf(cOMBC_766524526l_bool_type,type,
    cOMBC_766524526l_bool: $i ).

thf(hAPP_f144783951l_bool_type,type,
    hAPP_f144783951l_bool: $i > $i > $i ).

thf(cOMBB_1586673472t_char_type,type,
    cOMBB_1586673472t_char: $i ).

thf(hAPP_f893576377l_bool_type,type,
    hAPP_f893576377l_bool: $i > $i > $i ).

thf(hAPP_f1250221913l_bool_type,type,
    hAPP_f1250221913l_bool: $i > $i > $i ).

thf(hAPP_f1860331535l_bool_type,type,
    hAPP_f1860331535l_bool: $i > $i > $i ).

thf(cOMBB_2084052674on_val_type,type,
    cOMBB_2084052674on_val: $i ).

thf(hAPP_f510152537l_bool_type,type,
    hAPP_f510152537l_bool: $i > $i > $i ).

thf(hAPP_f613075253l_bool_type,type,
    hAPP_f613075253l_bool: $i > $i > $i ).

thf(hAPP_f1261741735l_bool_type,type,
    hAPP_f1261741735l_bool: $i > $i > $i ).

thf(hAPP_v417179479l_bool_type,type,
    hAPP_v417179479l_bool: $i > $i > $i ).

thf(hAPP_f293485653l_bool_type,type,
    hAPP_f293485653l_bool: $i > $i > $i ).

thf(hAPP_f565735867l_bool_type,type,
    hAPP_f565735867l_bool: $i > $i > $i ).

thf(cOMBB_815843940ol_val_type,type,
    cOMBB_815843940ol_val: $i ).

thf(hAPP_f1394668591l_bool_type,type,
    hAPP_f1394668591l_bool: $i > $i > $i ).

thf(hAPP_f1175813647l_bool_type,type,
    hAPP_f1175813647l_bool: $i > $i > $i ).

thf(hAPP_f550652027l_bool_type,type,
    hAPP_f550652027l_bool: $i > $i > $i ).

thf(hAPP_f838396643l_bool_type,type,
    hAPP_f838396643l_bool: $i > $i > $i ).

thf(cOMBC_2027949654l_bool_type,type,
    cOMBC_2027949654l_bool: $i ).

thf(hAPP_o1977518472on_val_type,type,
    hAPP_o1977518472on_val: $i > $i > $i ).

thf(the_Pr431167171on_val_type,type,
    the_Pr431167171on_val: $i ).

thf(cOMBS_570216337l_bool_type,type,
    cOMBS_570216337l_bool: $i > $i > $i ).

thf(hAPP_f1074020887l_bool_type,type,
    hAPP_f1074020887l_bool: $i > $i > $i ).

thf(hAPP_f1492320500l_bool_type,type,
    hAPP_f1492320500l_bool: $i > $i > $i ).

thf(hAPP_f1608277885r_bool_type,type,
    hAPP_f1608277885r_bool: $i > $i > $i ).

thf(hAPP_f1134248971r_bool_type,type,
    hAPP_f1134248971r_bool: $i > $i > $i ).

thf(cOMBB_338473166ist_ty_type,type,
    cOMBB_338473166ist_ty: $i ).

thf(hAPP_f1795246582l_bool_type,type,
    hAPP_f1795246582l_bool: $i > $i > $i ).

thf(hAPP_P748443392y_bool_type,type,
    hAPP_P748443392y_bool: $i > $i > $i ).

thf(hAPP_f1409772418l_bool_type,type,
    hAPP_f1409772418l_bool: $i > $i > $i ).

thf(lex_pr1541028704on_val_type,type,
    lex_pr1541028704on_val: $i > $i > $i ).

thf(hAPP_P53416969l_bool_type,type,
    hAPP_P53416969l_bool: $i > $i > $i ).

thf(member894971540t_char_type,type,
    member894971540t_char: $i ).

thf(hAPP_P240409993l_bool_type,type,
    hAPP_P240409993l_bool: $i > $i > $i ).

thf(member563141460on_val_type,type,
    member563141460on_val: $i ).

thf(hAPP_f1957374161r_bool_type,type,
    hAPP_f1957374161r_bool: $i > $i > $i ).

thf(hAPP_f304993943r_bool_type,type,
    hAPP_f304993943r_bool: $i > $i > $i ).

thf(cOMBB_847828016t_char_type,type,
    cOMBB_847828016t_char: $i ).

thf(hAPP_f1410576713r_bool_type,type,
    hAPP_f1410576713r_bool: $i > $i > $i ).

thf(hAPP_P27757617y_bool_type,type,
    hAPP_P27757617y_bool: $i > $i > $i ).

thf(hAPP_P1632759357r_bool_type,type,
    hAPP_P1632759357r_bool: $i > $i > $i ).

thf(hAPP_f183649339l_bool_type,type,
    hAPP_f183649339l_bool: $i > $i > $i ).

thf(cOMBB_2078984970ol_val_type,type,
    cOMBB_2078984970ol_val: $i ).

thf(hAPP_f998390560l_bool_type,type,
    hAPP_f998390560l_bool: $i > $i > $i ).

thf(hAPP_f1752856401l_bool_type,type,
    hAPP_f1752856401l_bool: $i > $i > $i ).

thf(hAPP_f552300311l_bool_type,type,
    hAPP_f552300311l_bool: $i > $i > $i ).

thf(cOMBB_1270208498t_char_type,type,
    cOMBB_1270208498t_char: $i ).

thf(hAPP_f810261999l_bool_type,type,
    hAPP_f810261999l_bool: $i > $i > $i ).

thf(cOMBB_1034324152on_val_type,type,
    cOMBB_1034324152on_val: $i ).

thf(hAPP_f1715733055l_bool_type,type,
    hAPP_f1715733055l_bool: $i > $i > $i ).

thf(cOMBB_123628846t_char_type,type,
    cOMBB_123628846t_char: $i ).

thf(hAPP_f1523875321l_bool_type,type,
    hAPP_f1523875321l_bool: $i > $i > $i ).

thf(hAPP_f592397849l_bool_type,type,
    hAPP_f592397849l_bool: $i > $i > $i ).

thf(cOMBB_1718333400on_val_type,type,
    cOMBB_1718333400on_val: $i ).

thf(hAPP_f1863694447l_bool_type,type,
    hAPP_f1863694447l_bool: $i > $i > $i ).

thf(dom_list_char_ty_type,type,
    dom_list_char_ty: $i > $i ).

thf(map_add_list_char_ty_type,type,
    map_add_list_char_ty: $i > $i > $i ).

thf(hAPP_f344506159r_bool_type,type,
    hAPP_f344506159r_bool: $i > $i > $i ).

thf(hAPP_f447563647r_bool_type,type,
    hAPP_f447563647r_bool: $i > $i > $i ).

thf(cOMBC_389248878r_bool_type,type,
    cOMBC_389248878r_bool: $i ).

thf(hAPP_l1335043179r_bool_type,type,
    hAPP_l1335043179r_bool: $i > $i > $i ).

thf(hAPP_f1051205629r_bool_type,type,
    hAPP_f1051205629r_bool: $i > $i > $i ).

thf(hAPP_f987862447r_bool_type,type,
    hAPP_f987862447r_bool: $i > $i > $i ).

thf(cOMBC_1387630958r_bool_type,type,
    cOMBC_1387630958r_bool: $i ).

thf(typeSa1700205512_sconf_type,type,
    typeSa1700205512_sconf: $i > $i > $i ).

thf(lex_pr213428520t_char_type,type,
    lex_pr213428520t_char: $i > $i > $i ).

thf(hAPP_P569585933l_bool_type,type,
    hAPP_P569585933l_bool: $i > $i > $i ).

thf(member520253462har_ty_type,type,
    member520253462har_ty: $i ).

thf(hAPP_P1503283977l_bool_type,type,
    hAPP_P1503283977l_bool: $i > $i > $i ).

thf(member1580476948t_char_type,type,
    member1580476948t_char: $i ).

thf(map_up891053837har_ty_type,type,
    map_up891053837har_ty: $i > $i > $i > $i ).

thf(hAPP_f1520735791l_bool_type,type,
    hAPP_f1520735791l_bool: $i > $i > $i ).

thf(hAPP_f989077673l_bool_type,type,
    hAPP_f989077673l_bool: $i > $i > $i ).

thf(hAPP_f40682957l_bool_type,type,
    hAPP_f40682957l_bool: $i > $i > $i ).

thf(cOMBC_562612496l_bool_type,type,
    cOMBC_562612496l_bool: $i ).

thf(hAPP_e1705922617l_bool_type,type,
    hAPP_e1705922617l_bool: $i > $i > $i ).

thf(lex_pr280535005t_char_type,type,
    lex_pr280535005t_char: $i > $i > $i ).

thf(hAPP_f2095325577l_bool_type,type,
    hAPP_f2095325577l_bool: $i > $i > $i ).

thf(hAPP_f1135930489l_bool_type,type,
    hAPP_f1135930489l_bool: $i > $i > $i ).

thf(cOMBB_1223415373on_val_type,type,
    cOMBB_1223415373on_val: $i ).

thf(hAPP_f961387813l_bool_type,type,
    hAPP_f961387813l_bool: $i > $i > $i ).

thf(hAPP_P527298901l_bool_type,type,
    hAPP_P527298901l_bool: $i > $i > $i ).

thf(hAPP_f861853459l_bool_type,type,
    hAPP_f861853459l_bool: $i > $i > $i ).

thf(hAPP_f1475571983l_bool_type,type,
    hAPP_f1475571983l_bool: $i > $i > $i ).

thf(hAPP_f1946480059l_bool_type,type,
    hAPP_f1946480059l_bool: $i > $i > $i ).

thf(cOMBB_673739729t_char_type,type,
    cOMBB_673739729t_char: $i ).

thf(hAPP_e286792811l_bool_type,type,
    hAPP_e286792811l_bool: $i > $i > $i ).

thf(cOMBB_383678192on_val_type,type,
    cOMBB_383678192on_val: $i ).

thf(hAPP_f388705405r_bool_type,type,
    hAPP_f388705405r_bool: $i > $i > $i ).

thf(hAPP_f33142364l_bool_type,type,
    hAPP_f33142364l_bool: $i > $i > $i ).

thf(cOMBC_1518234801l_bool_type,type,
    cOMBC_1518234801l_bool: $i ).

thf(hAPP_f720086610l_bool_type,type,
    hAPP_f720086610l_bool: $i > $i > $i ).

thf(hAPP_f47713631l_bool_type,type,
    hAPP_f47713631l_bool: $i > $i > $i ).

thf(hAPP_f77033475l_bool_type,type,
    hAPP_f77033475l_bool: $i > $i > $i ).

thf(cOMBC_1317565126l_bool_type,type,
    cOMBC_1317565126l_bool: $i ).

thf(member1417904245al_val_type,type,
    member1417904245al_val: $i ).

thf(hAPP_f1859053709l_bool_type,type,
    hAPP_f1859053709l_bool: $i > $i > $i ).

thf(hAPP_f400269243l_bool_type,type,
    hAPP_f400269243l_bool: $i > $i > $i ).

thf(cOMBB_1701031980ol_val_type,type,
    cOMBB_1701031980ol_val: $i ).

thf(hAPP_f2100207721l_bool_type,type,
    hAPP_f2100207721l_bool: $i > $i > $i ).

thf(hAPP_f1374595987l_bool_type,type,
    hAPP_f1374595987l_bool: $i > $i > $i ).

thf(cOMBB_761748254ol_bop_type,type,
    cOMBB_761748254ol_bop: $i ).

thf(hAPP_b406740087l_bool_type,type,
    hAPP_b406740087l_bool: $i > $i > $i ).

thf(hAPP_f1032444159r_bool_type,type,
    hAPP_f1032444159r_bool: $i > $i > $i ).

thf(hAPP_f254182519r_bool_type,type,
    hAPP_f254182519r_bool: $i > $i > $i ).

thf(cOMBB_1551681790t_char_type,type,
    cOMBB_1551681790t_char: $i ).

thf(hAPP_f1450446905l_bool_type,type,
    hAPP_f1450446905l_bool: $i > $i > $i ).

thf(hAPP_f693085049l_bool_type,type,
    hAPP_f693085049l_bool: $i > $i > $i ).

thf(cOMBB_147773915t_char_type,type,
    cOMBB_147773915t_char: $i ).

thf(hAPP_o285151112r_bool_type,type,
    hAPP_o285151112r_bool: $i > $i > $i ).

thf(the_fu297177755r_bool_type,type,
    the_fu297177755r_bool: $i ).

thf(hAPP_f866074145l_bool_type,type,
    hAPP_f866074145l_bool: $i > $i > $i ).

thf(hAPP_f877616419l_bool_type,type,
    hAPP_f877616419l_bool: $i > $i > $i ).

thf(cOMBB_1458388806ol_bop_type,type,
    cOMBB_1458388806ol_bop: $i ).

thf(hAPP_f1776419603l_bool_type,type,
    hAPP_f1776419603l_bool: $i > $i > $i ).

thf(hAPP_f826324045l_bool_type,type,
    hAPP_f826324045l_bool: $i > $i > $i ).

thf(hAPP_f1639555093l_bool_type,type,
    hAPP_f1639555093l_bool: $i > $i > $i ).

thf(cOMBB_985659173on_val_type,type,
    cOMBB_985659173on_val: $i ).

thf(hAPP_P2015860941l_bool_type,type,
    hAPP_P2015860941l_bool: $i > $i > $i ).

thf(produc1911975310l_bool_type,type,
    produc1911975310l_bool: $i > $i ).

thf(hAPP_f292637069l_bool_type,type,
    hAPP_f292637069l_bool: $i > $i > $i ).

thf(hAPP_f1168269397l_bool_type,type,
    hAPP_f1168269397l_bool: $i > $i > $i ).

thf(cOMBB_1293776864on_val_type,type,
    cOMBB_1293776864on_val: $i ).

thf(hAPP_P998768845l_bool_type,type,
    hAPP_P998768845l_bool: $i > $i > $i ).

thf(ord_le989574145r_bool_type,type,
    ord_le989574145r_bool: $i > $i ).

thf(ord_le1852058257r_bool_type,type,
    ord_le1852058257r_bool: $i > $i ).

thf(hAPP_o1968908095l_bool_type,type,
    hAPP_o1968908095l_bool: $i > $i > $i ).

thf(fequal1937332960on_val_type,type,
    fequal1937332960on_val: $i ).

thf(hAPP_f1930574389l_bool_type,type,
    hAPP_f1930574389l_bool: $i > $i > $i ).

thf(produc1815960045l_bool_type,type,
    produc1815960045l_bool: $i ).

thf(ord_le2008677227r_bool_type,type,
    ord_le2008677227r_bool: $i > $i ).

thf(cOMBC_390659185l_bool_type,type,
    cOMBC_390659185l_bool: $i ).

thf(hAPP_f1937828171l_bool_type,type,
    hAPP_f1937828171l_bool: $i > $i > $i ).

thf(cOMBB_1681501894t_char_type,type,
    cOMBB_1681501894t_char: $i ).

thf(hAPP_P1362631157l_bool_type,type,
    hAPP_P1362631157l_bool: $i > $i > $i ).

thf(member808015754on_val_type,type,
    member808015754on_val: $i ).

thf(transi910771962on_val_type,type,
    transi910771962on_val: $i > $i ).

thf(produc1159035454l_bool_type,type,
    produc1159035454l_bool: $i > $i ).

thf(hAPP_option_val_val_type,type,
    hAPP_option_val_val: $i > $i > $i ).

thf(the_val_type,type,
    the_val: $i ).

thf(hAPP_f635218277l_bool_type,type,
    hAPP_f635218277l_bool: $i > $i > $i ).

thf(produc1911463199l_bool_type,type,
    produc1911463199l_bool: $i ).

thf(hAPP_o586881855l_bool_type,type,
    hAPP_o586881855l_bool: $i > $i > $i ).

thf(fequal_option_val_type,type,
    fequal_option_val: $i ).

thf(map_list_char_val_type,type,
    map_list_char_val: $i > $i > $i ).

thf(comp_o1129292306t_char_type,type,
    comp_o1129292306t_char: $i > $i > $i ).

thf(overri2012515291on_val_type,type,
    overri2012515291on_val: $i > $i > $i > $i ).

thf(set_list_char_type,type,
    set_list_char: $i > $i ).

thf(ord_le1871967977r_bool_type,type,
    ord_le1871967977r_bool: $i > $i ).

thf(ord_le285175110l_bool_type,type,
    ord_le285175110l_bool: $i > $i ).

thf(ord_le1461833060l_bool_type,type,
    ord_le1461833060l_bool: $i > $i ).

thf(semila751111325l_bool_type,type,
    semila751111325l_bool: $i > $i > $i ).

thf(ord_le1776148979l_bool_type,type,
    ord_le1776148979l_bool: $i > $i ).

thf(size_s1143674878t_char_type,type,
    size_s1143674878t_char: $i > $i ).

thf(restri761823004ar_val_type,type,
    restri761823004ar_val: $i > $i > $i ).

thf(ord_le817953186r_bool_type,type,
    ord_le817953186r_bool: $i > $i ).

thf(ord_le1579844278r_bool_type,type,
    ord_le1579844278r_bool: $i > $i ).

thf(hAPP_f1008932791l_bool_type,type,
    hAPP_f1008932791l_bool: $i > $i > $i ).

thf(hAPP_f2057883639l_bool_type,type,
    hAPP_f2057883639l_bool: $i > $i > $i ).

thf(cOMBB_1750801836on_val_type,type,
    cOMBB_1750801836on_val: $i ).

thf(transi921647814on_val_type,type,
    transi921647814on_val: $i > $i ).

thf(fNot_type,type,
    fNot: $i ).

thf(lex_pr69619957on_val_type,type,
    lex_pr69619957on_val: $i > $i > $i ).

thf(ord_le1270183657l_bool_type,type,
    ord_le1270183657l_bool: $i > $i ).

thf(ord_le408082617l_bool_type,type,
    ord_le408082617l_bool: $i > $i ).

thf(ord_le310098611l_bool_type,type,
    ord_le310098611l_bool: $i > $i ).

thf(ord_le458107652r_bool_type,type,
    ord_le458107652r_bool: $i > $i ).

thf(cOMBC_1407716098l_bool_type,type,
    cOMBC_1407716098l_bool: $i ).

thf(hAPP_f1847120981l_bool_type,type,
    hAPP_f1847120981l_bool: $i > $i > $i ).

thf(cOMBB_1035649854t_char_type,type,
    cOMBB_1035649854t_char: $i ).

thf(ord_le1734858744r_bool_type,type,
    ord_le1734858744r_bool: $i > $i ).

thf(dom_Pr695701035ar_val_type,type,
    dom_Pr695701035ar_val: $i > $i ).

thf(map_ad1185064968ar_val_type,type,
    map_ad1185064968ar_val: $i > $i > $i ).

thf(hAPP_f1670595613l_bool_type,type,
    hAPP_f1670595613l_bool: $i > $i > $i ).

thf(hAPP_f1472899487l_bool_type,type,
    hAPP_f1472899487l_bool: $i > $i > $i ).

thf(cOMBB_588525814on_val_type,type,
    cOMBB_588525814on_val: $i ).

thf(hAPP_P638161699l_bool_type,type,
    hAPP_P638161699l_bool: $i > $i > $i ).

thf(hAPP_f762728813l_bool_type,type,
    hAPP_f762728813l_bool: $i > $i > $i ).

thf(hAPP_f1510763001l_bool_type,type,
    hAPP_f1510763001l_bool: $i > $i > $i ).

thf(cOMBB_565412073on_val_type,type,
    cOMBB_565412073on_val: $i ).

thf(hAPP_f1363667773l_bool_type,type,
    hAPP_f1363667773l_bool: $i > $i > $i ).

thf(hAPP_f1050935001l_bool_type,type,
    hAPP_f1050935001l_bool: $i > $i > $i ).

thf(cOMBB_1153617344on_val_type,type,
    cOMBB_1153617344on_val: $i ).

thf(lex_pr731210613on_val_type,type,
    lex_pr731210613on_val: $i > $i > $i ).

thf(hAPP_P1679186017l_bool_type,type,
    hAPP_P1679186017l_bool: $i > $i > $i ).

thf(member1337019328on_val_type,type,
    member1337019328on_val: $i ).

thf(hAPP_P1878549513l_bool_type,type,
    hAPP_P1878549513l_bool: $i > $i > $i ).

thf(member490182804on_val_type,type,
    member490182804on_val: $i ).

thf(cOMBC_1608987946l_bool_type,type,
    cOMBC_1608987946l_bool: $i ).

thf(ord_le125655867l_bool_type,type,
    ord_le125655867l_bool: $i > $i ).

thf(member763590124on_val_type,type,
    member763590124on_val: $i ).

thf(ord_le1908998213l_bool_type,type,
    ord_le1908998213l_bool: $i > $i ).

thf(hAPP_f1614195593l_bool_type,type,
    hAPP_f1614195593l_bool: $i > $i > $i ).

thf(hAPP_f705562443l_bool_type,type,
    hAPP_f705562443l_bool: $i > $i > $i ).

thf(cOMBB_507006011t_char_type,type,
    cOMBB_507006011t_char: $i ).

thf(ord_le176694639r_bool_type,type,
    ord_le176694639r_bool: $i > $i ).

thf(cOMBC_220519196l_bool_type,type,
    cOMBC_220519196l_bool: $i ).

thf(hAPP_f380623487l_bool_type,type,
    hAPP_f380623487l_bool: $i > $i > $i ).

thf(cOMBB_1033145403t_char_type,type,
    cOMBB_1033145403t_char: $i ).

thf(ord_le715555971r_bool_type,type,
    ord_le715555971r_bool: $i > $i ).

thf(collec718040978on_val_type,type,
    collec718040978on_val: $i > $i ).

thf(hAPP_f2036784149l_bool_type,type,
    hAPP_f2036784149l_bool: $i > $i > $i ).

thf(hAPP_f1720452391l_bool_type,type,
    hAPP_f1720452391l_bool: $i > $i > $i ).

thf(cOMBC_1021753250l_bool_type,type,
    cOMBC_1021753250l_bool: $i ).

thf(ord_le735260024r_bool_type,type,
    ord_le735260024r_bool: $i > $i ).

thf(cOMBC_1338332465l_bool_type,type,
    cOMBC_1338332465l_bool: $i ).

thf(hAPP_f937861397l_bool_type,type,
    hAPP_f937861397l_bool: $i > $i > $i ).

thf(cOMBB_1520154591t_char_type,type,
    cOMBB_1520154591t_char: $i ).

thf(member840932460on_val_type,type,
    member840932460on_val: $i ).

thf(ord_le1449176264r_bool_type,type,
    ord_le1449176264r_bool: $i > $i ).

thf(ord_le1218729222r_bool_type,type,
    ord_le1218729222r_bool: $i > $i ).

thf(lex_pr1038007919on_val_type,type,
    lex_pr1038007919on_val: $i > $i > $i ).

thf(ord_le1080391173l_bool_type,type,
    ord_le1080391173l_bool: $i > $i ).

thf(ord_le1668954565l_bool_type,type,
    ord_le1668954565l_bool: $i > $i ).

thf(e_type,type,
    e: $i ).

thf(ord_le1151384881r_bool_type,type,
    ord_le1151384881r_bool: $i > $i ).

thf(cOMBC_516637475l_bool_type,type,
    cOMBC_516637475l_bool: $i ).

thf(hAPP_f251669717l_bool_type,type,
    hAPP_f251669717l_bool: $i > $i > $i ).

thf(cOMBB_773661144t_char_type,type,
    cOMBB_773661144t_char: $i ).

thf(member1771544038t_char_type,type,
    member1771544038t_char: $i ).

thf(ord_le725666495r_bool_type,type,
    ord_le725666495r_bool: $i > $i ).

thf(hAPP_f1204100177l_bool_type,type,
    hAPP_f1204100177l_bool: $i > $i > $i ).

thf(hAPP_f2026692601l_bool_type,type,
    hAPP_f2026692601l_bool: $i > $i > $i ).

thf(cOMBB_1977588741on_val_type,type,
    cOMBB_1977588741on_val: $i ).

thf(t_1_type,type,
    t_1: $i ).

thf(t_type,type,
    t: $i ).

thf(ord_le188521288l_bool_type,type,
    ord_le188521288l_bool: $i > $i ).

thf(ord_le1744419030l_bool_type,type,
    ord_le1744419030l_bool: $i > $i ).

thf(ord_le1050317687l_bool_type,type,
    ord_le1050317687l_bool: $i > $i ).

thf(ord_le1725884030l_bool_type,type,
    ord_le1725884030l_bool: $i > $i ).

thf(ord_le1467847572l_bool_type,type,
    ord_le1467847572l_bool: $i > $i ).

thf(v_2_type,type,
    v_2: $i ).

thf(hAPP_P1034346913l_bool_type,type,
    hAPP_P1034346913l_bool: $i > $i > $i ).

thf(member978285664op_bop_type,type,
    member978285664op_bop: $i ).

thf(1079,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ ( throw_list_char @ B ) ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ B ) ) @ C ) ) ) @ ( red @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_989_red__reds_OCastThrow) ).

thf(5385,plain,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ ( throw_list_char @ B ) ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ B ) ) @ C ) ) ) @ ( red @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).

thf(1073,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( C = D )
       => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ D @ B ) @ C )
          = B ) )
      & ( ( C != D )
       => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ D @ B ) @ C )
          = ( hAPP_l207779698on_val @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_fun__upd__apply) ).

thf(5365,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( C = D )
       => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ D @ B ) @ C )
          = B ) )
      & ( ( C != D )
       => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ D @ B ) @ C )
          = ( hAPP_l207779698on_val @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).

thf(733,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f998390560l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_M_001) ).

thf(4094,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f998390560l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).

thf(406,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P2010574925r_bool @ B @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ C ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P2010574925r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_prod__induct3) ).

thf(2889,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P2010574925r_bool @ B @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ C ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P2010574925r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(652,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B )
        = ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_Pair__eq) ).

thf(3798,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B )
          = ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B )
          = ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).

thf(715,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( seq_list_char @ A @ B )
     != ( lAss_list_char @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_583_exp_Osimps_I145_J) ).

thf(4022,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( seq_list_char @ A @ B )
     != ( lAss_list_char @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).

thf(302,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1754555101l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc_016) ).

thf(2463,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1754555101l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(882,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ G @ H ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ I ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ C @ I ) @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ ( fAss_list_char @ G @ A @ B @ C ) @ H ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1044_FAssNull) ).

thf(4682,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ G @ H ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ I ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ C @ I ) @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ ( fAss_list_char @ G @ A @ B @ C ) @ H ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).

thf(492,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) @ ( transi374442731on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ A ) ) @ ( transi374442731on_val @ D ) ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ A ) ) @ ( transi374442731on_val @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_730_rtrancl__trans) ).

thf(3172,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) @ ( transi374442731on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ A ) ) @ ( transi374442731on_val @ D ) ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ A ) ) @ ( transi374442731on_val @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(1112,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ B ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ B ) @ ( semila751111325l_bool @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_872_UnCI) ).

thf(5509,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ B ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ B ) @ ( semila751111325l_bool @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).

thf(673,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( cond_list_char @ B @ C @ D ) @ E ) @ F ) @ G ) )
     => ( ! [H: $i] :
            ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fTrue ) ) ) @ H ) )
           => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ C @ H ) @ F ) @ G ) ) )
       => ( ! [H: $i] :
              ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fFalse ) ) ) @ H ) )
             => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ D @ H ) @ F ) @ G ) ) )
         => ~ ! [H: $i] :
                ( ( F
                  = ( throw_list_char @ H ) )
               => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ E ) @ ( throw_list_char @ H ) ) @ G ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1123_eval__cases_I10_J) ).

thf(3873,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( cond_list_char @ B @ C @ D ) @ E ) @ F ) @ G ) )
     => ( ! [H: $i] :
            ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fTrue ) ) ) @ H ) )
           => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ C @ H ) @ F ) @ G ) ) )
       => ( ! [H: $i] :
              ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fFalse ) ) ) @ H ) )
             => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ D @ H ) @ F ) @ G ) ) )
         => ~ ! [H: $i] :
                ( ( F
                  = ( throw_list_char @ H ) )
               => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ E ) @ ( throw_list_char @ H ) ) @ G ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).

thf(854,axiom,
    ! [A: $i,B: $i] :
      ( ( ( hAPP_P1510515380on_val @ some_P948696889on_val @ A )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_option_Oinject) ).

thf(4560,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( hAPP_P1510515380on_val @ some_P948696889on_val @ A )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( hAPP_P1510515380on_val @ some_P948696889on_val @ A )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).

thf(698,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ G ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( map_va1934808527t_char @ val_list_char @ C ) ) @ D ) ) ) @ ( transi374442731on_val @ ( reds @ H ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ E @ A @ B ) ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1143_CallRedsNull) ).

thf(3962,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ G ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( map_va1934808527t_char @ val_list_char @ C ) ) @ D ) ) ) @ ( transi374442731on_val @ ( reds @ H ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ E @ A @ B ) ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).

thf(1086,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P1708370145l_bool @ ( hAPP_f973018659l_bool @ ( hAPP_f961387813l_bool @ cOMBC_1608987946l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1453283057l_bool @ ( hAPP_P638161699l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O) ).

thf(5422,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P1708370145l_bool @ ( hAPP_f973018659l_bool @ ( hAPP_f961387813l_bool @ cOMBC_1608987946l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1453283057l_bool @ ( hAPP_P638161699l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).

thf(120,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( wTrt_1 @ E @ F @ G @ H @ nt ) )
     => ( ( hBOOL @ ( wTrt_1 @ E @ F @ G @ C @ D ) )
       => ( hBOOL @ ( wTrt_1 @ E @ F @ G @ ( fAss_list_char @ H @ A @ B @ C ) @ void ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1117_WTrtFAssNT) ).

thf(1718,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( wTrt_1 @ E @ F @ G @ H @ nt ) )
     => ( ( hBOOL @ ( wTrt_1 @ E @ F @ G @ C @ D ) )
       => ( hBOOL @ ( wTrt_1 @ E @ F @ G @ ( fAss_list_char @ H @ A @ B @ C ) @ void ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(539,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P768428603l_bool @ ( hAPP_f1427871743l_bool @ ( hAPP_f32926423l_bool @ cOMBB_779086262on_val @ A ) @ B ) @ C )
      = ( hAPP_f1734997943l_bool @ A @ ( hAPP_P76086873l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc___085) ).

thf(3345,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P768428603l_bool @ ( hAPP_f1427871743l_bool @ ( hAPP_f32926423l_bool @ cOMBB_779086262on_val @ A ) @ B ) @ C )
      = ( hAPP_f1734997943l_bool @ A @ ( hAPP_P76086873l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(453,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_ty_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Type__Oty_000tc__HOL__Obool) ).

thf(3053,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_ty_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(736,axiom,
    ! [A: $i] :
      ( none_f478147469r_bool
     != ( hAPP_f363827556r_bool @ some_f80346385r_bool @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_608_option_Osimps_I2_J) ).

thf(4101,plain,
    ! [A: $i] :
      ( none_f478147469r_bool
     != ( hAPP_f363827556r_bool @ some_f80346385r_bool @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).

thf(49,axiom,
    ! [A: $i] :
      ( none_P179726773on_val
     != ( hAPP_P1510515380on_val @ some_P948696889on_val @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_606_option_Osimps_I2_J) ).

thf(1454,plain,
    ! [A: $i] :
      ( none_P179726773on_val
     != ( hAPP_P1510515380on_val @ some_P948696889on_val @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(193,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ G @ H @ I ) @ ( hAPP_v834067052t_char @ val_list_char @ J ) ) @ K ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ G @ B @ K ) @ ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ C ) @ ( cons_exp_list_char @ ( throw_list_char @ D ) @ E ) ) ) @ F ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ G @ ( call_list_char @ H @ A @ B ) @ I ) @ ( throw_list_char @ D ) ) @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1163_CallParamsThrow) ).

thf(2031,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ G @ H @ I ) @ ( hAPP_v834067052t_char @ val_list_char @ J ) ) @ K ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ G @ B @ K ) @ ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ C ) @ ( cons_exp_list_char @ ( throw_list_char @ D ) @ E ) ) ) @ F ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ G @ ( call_list_char @ H @ A @ B ) @ I ) @ ( throw_list_char @ D ) ) @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(1011,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_prod_Oexhaust) ).

thf(5136,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).

thf(100,axiom,
    is_bop @ add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Expr_Obop_OAdd) ).

thf(1633,plain,
    is_bop @ add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(763,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ ( dom_list_char_val @ C ) ) )
     => ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ A @ C ) @ B )
        = ( hAPP_l207779698on_val @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_429_map__add__dom__app__simps_I3_J) ).

thf(4183,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ ( dom_list_char_val @ C ) ) )
     => ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ A @ C ) @ B )
        = ( hAPP_l207779698on_val @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).

thf(628,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_673_subsetD) ).

thf(3698,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(1150,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ D ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ A ) ) @ E ) ) ) @ ( red @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_968_red__reds_ORedTry) ).

thf(5676,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ D ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ A ) ) @ E ) ) ) @ ( red @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).

thf(337,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l165010689r_bool @ ( hAPP_f1209019955r_bool @ ( hAPP_f521496323r_bool @ cOMBC_654453230r_bool @ A ) @ B ) @ C )
      = ( hAPP_f279818502r_bool @ ( hAPP_l2053770731r_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_049) ).

thf(2595,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l165010689r_bool @ ( hAPP_f1209019955r_bool @ ( hAPP_f521496323r_bool @ cOMBC_654453230r_bool @ A ) @ B ) @ C )
      = ( hAPP_f279818502r_bool @ ( hAPP_l2053770731r_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(145,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( hBOOL @ ( wTrt_1 @ F @ G @ H @ I @ ( hAPP_list_char_ty @ class @ J ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( has_fi1183600461t_char @ F @ J @ C @ D ) @ E ) )
       => ( ( hBOOL @ ( wTrt_1 @ F @ G @ H @ A @ B ) )
         => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ F ) @ B ) @ D ) )
           => ( hBOOL @ ( wTrt_1 @ F @ G @ H @ ( fAss_list_char @ I @ C @ E @ A ) @ void ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_991_WTrtFAss) ).

thf(1850,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( hBOOL @ ( wTrt_1 @ F @ G @ H @ I @ ( hAPP_list_char_ty @ class @ J ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( has_fi1183600461t_char @ F @ J @ C @ D ) @ E ) )
       => ( ( hBOOL @ ( wTrt_1 @ F @ G @ H @ A @ B ) )
         => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ F ) @ B ) @ D ) )
           => ( hBOOL @ ( wTrt_1 @ F @ G @ H @ ( fAss_list_char @ I @ C @ E @ A ) @ void ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(19,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_PairE) ).

thf(1315,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(668,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P476431815r_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J__023) ).

thf(3863,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P476431815r_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).

thf(295,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_818_xt1_I5_J) ).

thf(2427,plain,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(700,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f91506671l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_005) ).

thf(3969,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f91506671l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).

thf(1033,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( hBOOL @ ( hAPP_option_val_bool @ ( hAPP_o586881855l_bool @ fequal_option_val @ A ) @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Option__Ooption_Itc__Value__Oval_J_T) ).

thf(5205,plain,
    ! [A: $i,B: $i] :
      ( ~ ( hBOOL @ ( hAPP_option_val_bool @ ( hAPP_o586881855l_bool @ fequal_option_val @ A ) @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).

thf(1244,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P71593144l_bool @ B @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P71593144l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_prod__induct3) ).

thf(6074,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P71593144l_bool @ B @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P71593144l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244]) ).

thf(986,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f998390560l_bool @ ( ord_le817953186r_bool @ ( hAPP_f1044627221r_bool @ ( hAPP_f308875635r_bool @ cOMBC_1718404842r_bool @ ( hAPP_f531187933r_bool @ ( hAPP_f179418505r_bool @ cOMBB_550632017t_char @ cOMBC_407285762l_bool ) @ ( hAPP_f1136362289l_bool @ ( hAPP_f1736484361l_bool @ cOMBB_2042763133t_char @ ( hAPP_f1715733055l_bool @ cOMBB_123628846t_char @ member133545693t_char ) ) @ produc921874948t_char ) ) ) @ A ) ) @ ( hAPP_f1044627221r_bool @ ( hAPP_f308875635r_bool @ cOMBC_1718404842r_bool @ ( hAPP_f531187933r_bool @ ( hAPP_f179418505r_bool @ cOMBB_550632017t_char @ cOMBC_407285762l_bool ) @ ( hAPP_f1136362289l_bool @ ( hAPP_f1736484361l_bool @ cOMBB_2042763133t_char @ ( hAPP_f1715733055l_bool @ cOMBB_123628846t_char @ member133545693t_char ) ) @ produc921874948t_char ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1780084320l_bool @ ( ord_le1579844278r_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_810_pred__subset__eq2) ).

thf(5028,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( hAPP_f998390560l_bool @ ( ord_le817953186r_bool @ ( hAPP_f1044627221r_bool @ ( hAPP_f308875635r_bool @ cOMBC_1718404842r_bool @ ( hAPP_f531187933r_bool @ ( hAPP_f179418505r_bool @ cOMBB_550632017t_char @ cOMBC_407285762l_bool ) @ ( hAPP_f1136362289l_bool @ ( hAPP_f1736484361l_bool @ cOMBB_2042763133t_char @ ( hAPP_f1715733055l_bool @ cOMBB_123628846t_char @ member133545693t_char ) ) @ produc921874948t_char ) ) ) @ A ) ) @ ( hAPP_f1044627221r_bool @ ( hAPP_f308875635r_bool @ cOMBC_1718404842r_bool @ ( hAPP_f531187933r_bool @ ( hAPP_f179418505r_bool @ cOMBB_550632017t_char @ cOMBC_407285762l_bool ) @ ( hAPP_f1136362289l_bool @ ( hAPP_f1736484361l_bool @ cOMBB_2042763133t_char @ ( hAPP_f1715733055l_bool @ cOMBB_123628846t_char @ member133545693t_char ) ) @ produc921874948t_char ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f1780084320l_bool @ ( ord_le1579844278r_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1780084320l_bool @ ( ord_le1579844278r_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f998390560l_bool @ ( ord_le817953186r_bool @ ( hAPP_f1044627221r_bool @ ( hAPP_f308875635r_bool @ cOMBC_1718404842r_bool @ ( hAPP_f531187933r_bool @ ( hAPP_f179418505r_bool @ cOMBB_550632017t_char @ cOMBC_407285762l_bool ) @ ( hAPP_f1136362289l_bool @ ( hAPP_f1736484361l_bool @ cOMBB_2042763133t_char @ ( hAPP_f1715733055l_bool @ cOMBB_123628846t_char @ member133545693t_char ) ) @ produc921874948t_char ) ) ) @ A ) ) @ ( hAPP_f1044627221r_bool @ ( hAPP_f308875635r_bool @ cOMBC_1718404842r_bool @ ( hAPP_f531187933r_bool @ ( hAPP_f179418505r_bool @ cOMBB_550632017t_char @ cOMBC_407285762l_bool ) @ ( hAPP_f1136362289l_bool @ ( hAPP_f1736484361l_bool @ cOMBB_2042763133t_char @ ( hAPP_f1715733055l_bool @ cOMBB_123628846t_char @ member133545693t_char ) ) @ produc921874948t_char ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).

thf(893,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ D ) @ ( throw_list_char @ E ) ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ ( seq_list_char @ C @ A ) @ D ) @ ( throw_list_char @ E ) ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_918_eval__evals_OSeqThrow) ).

thf(4728,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ D ) @ ( throw_list_char @ E ) ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ ( seq_list_char @ C @ A ) @ D ) @ ( throw_list_char @ E ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).

thf(1127,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_453_splitD) ).

thf(5582,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).

thf(972,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ D ) @ E ) @ F ) @ G ) )
     => ( ( hBOOL @ ( conf_P373316194t_char @ D @ E @ B @ C ) )
       => ( ( ( hAPP_l512744617ion_ty @ G @ A )
            = ( hAPP_ty_option_ty @ some_ty @ C ) )
         => ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ D ) @ E ) @ ( fun_up1149430426on_val @ F @ A @ ( hAPP_val_option_val @ some_val @ B ) ) ) @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_374_lconf__upd) ).

thf(4992,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ D ) @ E ) @ F ) @ G ) )
     => ( ( hBOOL @ ( conf_P373316194t_char @ D @ E @ B @ C ) )
       => ( ( ( hAPP_l512744617ion_ty @ G @ A )
            = ( hAPP_ty_option_ty @ some_ty @ C ) )
         => ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ D ) @ E ) @ ( fun_up1149430426on_val @ F @ A @ ( hAPP_val_option_val @ some_val @ B ) ) ) @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).

thf(1197,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_P282169671l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_477_mem__def) ).

thf(5898,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_P282169671l_bool @ B @ A ) ) )
      & ( ( hBOOL @ ( hAPP_P282169671l_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).

thf(163,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P824029447r_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P824029447r_bool @ A @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_split__paired__All) ).

thf(1924,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P824029447r_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P824029447r_bool @ A @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P824029447r_bool @ A @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P824029447r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(219,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ ( transi1395422419t_char @ A ) ) @ ( transi1395422419t_char @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_677_rtrancl__mono) ).

thf(2117,plain,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ ( transi1395422419t_char @ A ) ) @ ( transi1395422419t_char @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(774,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( is_bop @ A )
        & ( is_bop @ B )
        & ( is_bop @ C )
        & ( is_bop @ D ) )
     => ( ( ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ A ) @ B )
          = ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) )
      <=> ( ( A = C )
          & ( B = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_Pair__eq) ).

thf(4226,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( is_bop @ A )
        & ( is_bop @ B )
        & ( is_bop @ C )
        & ( is_bop @ D ) )
     => ( ( ( ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ A ) @ B )
            = ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) )
         => ( ( A = C )
            & ( B = D ) ) )
        & ( ( ( A = C )
            & ( B = D ) )
         => ( ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ A ) @ B )
            = ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).

thf(312,axiom,
    ! [A: $i] :
      ( ( A != none_ty )
    <=> ? [B: $i] :
          ( A
          = ( hAPP_ty_option_ty @ some_ty @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_620_not__None__eq) ).

thf(2495,plain,
    ! [A: $i] :
      ( ( ( A != none_ty )
       => ? [B: $i] :
            ( A
            = ( hAPP_ty_option_ty @ some_ty @ B ) ) )
      & ( ? [B: $i] :
            ( A
            = ( hAPP_ty_option_ty @ some_ty @ B ) )
       => ( A != none_ty ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(449,axiom,
    ! [A: $i] :
      ( ? [B: $i] : ( hBOOL @ ( hAPP_P1235399154l_bool @ A @ B ) )
    <=> ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1235399154l_bool @ A @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_split__paired__Ex) ).

thf(3040,plain,
    ! [A: $i] :
      ( ( ? [B: $i] : ( hBOOL @ ( hAPP_P1235399154l_bool @ A @ B ) )
       => ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1235399154l_bool @ A @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) ) )
      & ( ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1235399154l_bool @ A @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) )
       => ? [B: $i] : ( hBOOL @ ( hAPP_P1235399154l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(441,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B )
        = ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_Pair__inject) ).

thf(3012,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B )
        = ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(1148,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P499022727r_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P499022727r_bool @ A @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_split__paired__All) ).

thf(5669,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P499022727r_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P499022727r_bool @ A @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P499022727r_bool @ A @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P499022727r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).

thf(218,axiom,
    ! [A: $i] :
      ( ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ ( produc2062775566l_bool @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_434_split__curry) ).

thf(2114,plain,
    ! [A: $i] :
      ( ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ ( produc2062775566l_bool @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(554,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ E ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ E @ A @ B ) @ C ) @ D ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) ) @ ( transi374442731on_val @ ( reds @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1147_bigs__by__smalls) ).

thf(3402,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ E ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ E @ A @ B ) @ C ) @ D ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) ) @ ( transi374442731on_val @ ( reds @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(110,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( is_bool @ ( wTrt @ A @ B @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Progress_OWTrt_H) ).

thf(1692,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( is_bool @ ( wTrt @ A @ B @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(1231,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ D @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) )
     => ( ( A
          = ( fun_up1149430426on_val @ H @ B @ ( hAPP_val_option_val @ some_val @ F ) ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( lAss_list_char @ B @ D ) @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_853_LAss) ).

thf(6017,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ D @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) )
     => ( ( A
          = ( fun_up1149430426on_val @ H @ B @ ( hAPP_val_option_val @ some_val @ F ) ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( lAss_list_char @ B @ D ) @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231]) ).

thf(547,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i,F: $i,G: $i] : ( hBOOL @ ( hAPP_P824029447r_bool @ B @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ C ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ D ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ E ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ F ) @ G ) ) ) ) ) )
     => ( hBOOL @ ( hAPP_P824029447r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_prod__induct5) ).

thf(3382,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i,F: $i,G: $i] : ( hBOOL @ ( hAPP_P824029447r_bool @ B @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ C ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ D ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ E ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ F ) @ G ) ) ) ) ) )
     => ( hBOOL @ ( hAPP_P824029447r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(254,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_669_subsetD) ).

thf(2231,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(666,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_820_order__antisym) ).

thf(3858,plain,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).

thf(1144,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fFalse ) ) @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) @ ( red @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1105_red__reds_ORedCondF) ).

thf(5644,plain,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fFalse ) ) @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) @ ( red @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).

thf(1189,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_917_FAccRedsThrow) ).

thf(5842,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).

thf(45,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( wTrt_1 @ D @ E @ F @ G @ ( hAPP_list_char_ty @ class @ H ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( has_fi1183600461t_char @ D @ H @ A @ B ) @ C ) )
       => ( hBOOL @ ( wTrt_1 @ D @ E @ F @ ( fAcc_list_char @ G @ A @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_987_WTrtFAcc) ).

thf(1443,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( wTrt_1 @ D @ E @ F @ G @ ( hAPP_list_char_ty @ class @ H ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( has_fi1183600461t_char @ D @ H @ A @ B ) @ C ) )
       => ( hBOOL @ ( wTrt_1 @ D @ E @ F @ ( fAcc_list_char @ G @ A @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(560,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ ( semila919158006r_bool @ B @ C ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_864_UnE) ).

thf(3417,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ ( semila919158006r_bool @ B @ C ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(358,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( binOp_list_char @ B @ C @ D ) @ E ) @ F ) @ G ) )
     => ( ! [H: $i,I: $i,J: $i,K: $i] :
            ( ( F
              = ( hAPP_v834067052t_char @ val_list_char @ K ) )
           => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ I ) )
             => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ D @ I ) @ ( hAPP_v834067052t_char @ val_list_char @ J ) ) @ G ) )
               => ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ H ) @ J ) ) )
                 != ( hAPP_val_option_val @ some_val @ K ) ) ) ) )
       => ( ! [H: $i] :
              ( ( F
                = ( throw_list_char @ H ) )
             => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ E ) @ ( throw_list_char @ H ) ) @ G ) ) )
         => ~ ! [H: $i,I: $i,J: $i] :
                ( ( F
                  = ( throw_list_char @ J ) )
               => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ I ) )
                 => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ D @ I ) @ ( throw_list_char @ J ) ) @ G ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1005_eval__cases_I3_J) ).

thf(2676,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( binOp_list_char @ B @ C @ D ) @ E ) @ F ) @ G ) )
     => ( ! [H: $i,I: $i,J: $i,K: $i] :
            ( ( F
              = ( hAPP_v834067052t_char @ val_list_char @ K ) )
           => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ I ) )
             => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ D @ I ) @ ( hAPP_v834067052t_char @ val_list_char @ J ) ) @ G ) )
               => ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ H ) @ J ) ) )
                 != ( hAPP_val_option_val @ some_val @ K ) ) ) ) )
       => ( ! [H: $i] :
              ( ( F
                = ( throw_list_char @ H ) )
             => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ E ) @ ( throw_list_char @ H ) ) @ G ) ) )
         => ~ ! [H: $i,I: $i,J: $i] :
                ( ( F
                  = ( throw_list_char @ J ) )
               => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ I ) )
                 => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ D @ I ) @ ( throw_list_char @ J ) ) @ G ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(187,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_b97269396l_bool @ ( produc1555310053l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P943837928l_bool @ A @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_492_curryE) ).

thf(2014,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_b97269396l_bool @ ( produc1555310053l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P943837928l_bool @ A @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(583,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1783480313r_bool @ ( hAPP_f531187933r_bool @ ( hAPP_f179418505r_bool @ cOMBB_550632017t_char @ A ) @ B ) @ C )
      = ( hAPP_f1707979241r_bool @ A @ ( hAPP_l1571522437l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__067) ).

thf(3498,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1783480313r_bool @ ( hAPP_f531187933r_bool @ ( hAPP_f179418505r_bool @ cOMBB_550632017t_char @ A ) @ B ) @ C )
      = ( hAPP_f1707979241r_bool @ A @ ( hAPP_l1571522437l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(284,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P594889876l_bool @ ( hAPP_f375531599l_bool @ ( hAPP_f1564338425l_bool @ cOMBB_1078680455on_val @ A ) @ B ) @ C )
      = ( hAPP_P483670507l_bool @ A @ ( hAPP_P1963616220on_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Oli) ).

thf(2380,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P594889876l_bool @ ( hAPP_f375531599l_bool @ ( hAPP_f1564338425l_bool @ cOMBB_1078680455on_val @ A ) @ B ) @ C )
      = ( hAPP_P483670507l_bool @ A @ ( hAPP_P1963616220on_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(59,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1145574243l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mt) ).

thf(1486,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1145574243l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(737,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l232580245l_bool @ ( hAPP_f1752856401l_bool @ ( hAPP_f552300311l_bool @ cOMBB_1270208498t_char @ A ) @ B ) @ C )
      = ( hAPP_f375531599l_bool @ A @ ( hAPP_l1275479261on_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_078) ).

thf(4105,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l232580245l_bool @ ( hAPP_f1752856401l_bool @ ( hAPP_f552300311l_bool @ cOMBB_1270208498t_char @ A ) @ B ) @ C )
      = ( hAPP_f375531599l_bool @ A @ ( hAPP_l1275479261on_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).

thf(39,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( new_list_char @ D ) @ E ) )
     => ~ ( ( E
            = ( hAPP_list_char_ty @ class @ D ) )
         => ~ ( hBOOL @ ( hAPP_list_char_bool @ ( is_cla570604648t_char @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1126_WTrt__elim__cases_I10_J) ).

thf(1426,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( new_list_char @ D ) @ E ) )
     => ~ ( ( E
            = ( hAPP_list_char_ty @ class @ D ) )
         => ~ ( hBOOL @ ( hAPP_list_char_bool @ ( is_cla570604648t_char @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(565,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f983152497l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String_) ).

thf(3429,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f983152497l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(897,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f837795298l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olis_007) ).

thf(4739,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f837795298l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).

thf(339,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_710_set__mp) ).

thf(2607,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(195,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ D ) @ ( throw_list_char @ E ) ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ ( lAss_list_char @ A @ C ) @ D ) @ ( throw_list_char @ E ) ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_919_eval__evals_OLAssThrow) ).

thf(2035,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ D ) @ ( throw_list_char @ E ) ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ ( lAss_list_char @ A @ C ) @ D ) @ ( throw_list_char @ E ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(716,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P27757617y_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List) ).

thf(4026,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P27757617y_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).

thf(227,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ B )
        = ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_Pair__eq) ).

thf(2141,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ B )
          = ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ B )
          = ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(365,axiom,
    ! [A: $i] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ null ) @ A ) ) )
      = none_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1041_binop_Osimps_I4_J) ).

thf(2712,plain,
    ! [A: $i] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ null ) @ A ) ) )
      = none_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(598,axiom,
    ! [A: $i] :
      ( ( transi374442731on_val @ ( transi374442731on_val @ A ) )
      = ( transi374442731on_val @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_718_rtrancl__idemp) ).

thf(3562,plain,
    ! [A: $i] :
      ( ( transi374442731on_val @ ( transi374442731on_val @ A ) )
      = ( transi374442731on_val @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(50,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ A ) @ B )
        = ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_Pair__inject) ).

thf(1458,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ A ) @ B )
        = ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(525,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P159683425l_bool @ ( hAPP_f1526206996l_bool @ ( hAPP_f1467537159l_bool @ cOMBC_2141828763l_bool @ A ) @ B ) @ C )
      = ( hAPP_f837795298l_bool @ ( hAPP_P594889876l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_059) ).

thf(3276,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P159683425l_bool @ ( hAPP_f1526206996l_bool @ ( hAPP_f1467537159l_bool @ cOMBC_2141828763l_bool @ A ) @ B ) @ C )
      = ( hAPP_f837795298l_bool @ ( hAPP_P594889876l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(662,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ D @ E @ F ) @ G ) @ H ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ D @ ( tryCatch_list_char @ E @ A @ B @ C ) @ F ) @ ( tryCatch_list_char @ G @ A @ B @ C ) ) @ H ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_954_redp__redsp_OTryRed) ).

thf(3848,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ D @ E @ F ) @ G ) @ H ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ D @ ( tryCatch_list_char @ E @ A @ B @ C ) @ F ) @ ( tryCatch_list_char @ G @ A @ B @ C ) ) @ H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(116,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P1183499705r_bool @ B @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ C ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1183499705r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_prod__induct3) ).

thf(1705,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P1183499705r_bool @ B @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ C ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1183499705r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(442,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ C @ D ) @ E ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( redsp @ B @ ( cons_exp_list_char @ C @ A ) @ D ) @ ( cons_exp_list_char @ E @ A ) ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1180_redp__redsp_OListRed1) ).

thf(3017,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ C @ D ) @ E ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( redsp @ B @ ( cons_exp_list_char @ C @ A ) @ D ) @ ( cons_exp_list_char @ E @ A ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(1219,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ B @ C ) @ B )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_fun__upd__same) ).

thf(5967,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ B @ C ) @ B )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219]) ).

thf(1087,axiom,
    ! [A: $i,B: $i] :
      ( ( fun_up1149430426on_val @ A @ B @ ( hAPP_l207779698on_val @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_fun__upd__triv) ).

thf(5425,plain,
    ! [A: $i,B: $i] :
      ( ( fun_up1149430426on_val @ A @ B @ ( hAPP_l207779698on_val @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).

thf(1184,axiom,
    hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ea ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( hAPP_val_option_val @ some_val @ v ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ e_a ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ h_a ) @ l_a ) ) ) ) @ ( red @ p ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_InitBlockRed_I1_J) ).

thf(5814,plain,
    hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ea ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( hAPP_val_option_val @ some_val @ v ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ e_a ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ h_a ) @ l_a ) ) ) ) @ ( red @ p ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).

thf(775,axiom,
    ! [A: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wf_J_mdecl @ A ) )
     => ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_831_wf__prog__wwf__prog) ).

thf(4234,plain,
    ! [A: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wf_J_mdecl @ A ) )
     => ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).

thf(106,axiom,
    ! [A: $i] :
      ( ( hBOOL @ ( preallocated @ A ) )
     => ( ( hAPP_val_option_ty @ ( typeof_h @ A ) @ ( addr @ ( addr_of_sys_xcpt @ outOfMemory ) ) )
        = ( hAPP_ty_option_ty @ some_ty @ ( hAPP_list_char_ty @ class @ outOfMemory ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1015_typeof__OutOfMemory) ).

thf(1671,plain,
    ! [A: $i] :
      ( ( hBOOL @ ( preallocated @ A ) )
     => ( ( hAPP_val_option_ty @ ( typeof_h @ A ) @ ( addr @ ( addr_of_sys_xcpt @ outOfMemory ) ) )
        = ( hAPP_ty_option_ty @ some_ty @ ( hAPP_list_char_ty @ class @ outOfMemory ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(651,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i,O: $i,P: $i,Q: $i,R: $i,S: $i,T: $i,U: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ U ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Q ) @ R ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ S ) ) ) @ T ) ) ) @ ( transi2024712006on_val @ ( red @ U ) ) ) )
       => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ M ) @ T ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( map_va1934808527t_char @ val_list_char @ N ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ O ) @ P ) ) ) ) @ ( transi374442731on_val @ ( reds @ U ) ) ) )
         => ( ( ( hAPP_n546249108on_val @ O @ S )
              = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ K ) @ L ) ) )
           => ( ( hBOOL @ ( hAPP_list_char_bool @ ( method1809630380t_char @ U @ K @ E @ F @ G @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ H ) @ I ) ) @ J ) )
             => ( ( ( size_size_list_val @ N )
                  = ( size_s2113983095t_char @ H ) )
               => ( ( D
                    = ( map_up1085636310ar_val @ ( fun_up1149430426on_val @ ( hAPP_o538043682on_val @ cOMBK_1097134891t_char @ none_val ) @ this @ ( hAPP_val_option_val @ some_val @ ( addr @ S ) ) ) @ H @ N ) )
                 => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ I ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ O ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ) @ ( transi2024712006on_val @ ( red @ U ) ) ) )
                   => ( ( hBOOL @ ( final_list_char @ A ) )
                     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ Q @ E @ M ) ) @ R ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ P ) ) ) ) @ ( transi2024712006on_val @ ( red @ U ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1183_CallRedsFinal) ).

thf(3794,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i,O: $i,P: $i,Q: $i,R: $i,S: $i,T: $i,U: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ U ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Q ) @ R ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ S ) ) ) @ T ) ) ) @ ( transi2024712006on_val @ ( red @ U ) ) ) )
       => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ M ) @ T ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( map_va1934808527t_char @ val_list_char @ N ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ O ) @ P ) ) ) ) @ ( transi374442731on_val @ ( reds @ U ) ) ) )
         => ( ( ( hAPP_n546249108on_val @ O @ S )
              = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ K ) @ L ) ) )
           => ( ( hBOOL @ ( hAPP_list_char_bool @ ( method1809630380t_char @ U @ K @ E @ F @ G @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ H ) @ I ) ) @ J ) )
             => ( ( ( size_size_list_val @ N )
                  = ( size_s2113983095t_char @ H ) )
               => ( ( D
                    = ( map_up1085636310ar_val @ ( fun_up1149430426on_val @ ( hAPP_o538043682on_val @ cOMBK_1097134891t_char @ none_val ) @ this @ ( hAPP_val_option_val @ some_val @ ( addr @ S ) ) ) @ H @ N ) )
                 => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ I ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ O ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ) @ ( transi2024712006on_val @ ( red @ U ) ) ) )
                   => ( ( hBOOL @ ( final_list_char @ A ) )
                     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ Q @ E @ M ) ) @ R ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ P ) ) ) ) @ ( transi2024712006on_val @ ( red @ U ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

thf(94,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ A ) @ B )
        = ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_Pair__eq) ).

thf(1608,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ A ) @ B )
          = ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ A ) @ B )
          = ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(870,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( wTrt_1 @ B @ C @ D @ E @ F ) )
     => ( ( hBOOL @ ( is_refT @ F ) )
       => ( hBOOL @ ( wTrt_1 @ B @ C @ D @ ( throw_list_char @ E ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_950_WTrtThrow) ).

thf(4633,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( wTrt_1 @ B @ C @ D @ E @ F ) )
     => ( ( hBOOL @ ( is_refT @ F ) )
       => ( hBOOL @ ( wTrt_1 @ B @ C @ D @ ( throw_list_char @ E ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).

thf(820,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ C ) ) @ D )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ E ) )
    <=> ( ( ( D = B )
          & ( C = E ) )
        | ( ( D != B )
          & ( ( hAPP_n546249108on_val @ A @ D )
            = ( hAPP_P1510515380on_val @ some_P948696889on_val @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_map__upd__Some__unfold) ).

thf(4403,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ C ) ) @ D )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ E ) )
       => ( ( ( D = B )
            & ( C = E ) )
          | ( ( D != B )
            & ( ( hAPP_n546249108on_val @ A @ D )
              = ( hAPP_P1510515380on_val @ some_P948696889on_val @ E ) ) ) ) )
      & ( ( ( ( D = B )
            & ( C = E ) )
          | ( ( D != B )
            & ( ( hAPP_n546249108on_val @ A @ D )
              = ( hAPP_P1510515380on_val @ some_P948696889on_val @ E ) ) ) )
       => ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ C ) ) @ D )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).

thf(126,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P929938951l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__HOL__Obool) ).

thf(1756,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P929938951l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(18,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_split__paired__All) ).

thf(1310,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(298,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ A ) @ B )
        = ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_Pair__eq) ).

thf(2448,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ A ) @ B )
          = ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ A ) @ B )
          = ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(418,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( block_list_char @ B @ C @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_643_redp__redsp_ORedBlock) ).

thf(2933,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( block_list_char @ B @ C @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(1149,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_939_SeqRedsThrow) ).

thf(5674,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).

thf(515,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ ( transi1395422419t_char @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ A ) ) @ D ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ A ) ) @ ( transi1395422419t_char @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_727_rtrancl_Ortrancl__into__rtrancl) ).

thf(3253,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ ( transi1395422419t_char @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ A ) ) @ D ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ A ) ) @ ( transi1395422419t_char @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(300,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_695_in__mono) ).

thf(2459,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(534,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( fun_up424764369ion_ty @ A @ B @ ( hAPP_ty_option_ty @ some_ty @ C ) )
        = ( fun_up424764369ion_ty @ D @ B @ ( hAPP_ty_option_ty @ some_ty @ E ) ) )
     => ( C = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_map__upd__eqD1) ).

thf(3313,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( fun_up424764369ion_ty @ A @ B @ ( hAPP_ty_option_ty @ some_ty @ C ) )
        = ( fun_up424764369ion_ty @ D @ B @ ( hAPP_ty_option_ty @ some_ty @ E ) ) )
     => ( C = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(1177,axiom,
    ! [A: $i] :
      ( ( A != none_val )
     => ~ ! [B: $i] :
            ( A
           != ( hAPP_val_option_val @ some_val @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_793_option_Oexhaust) ).

thf(5782,plain,
    ! [A: $i] :
      ( ( A != none_val )
     => ~ ! [B: $i] :
            ( A
           != ( hAPP_val_option_val @ some_val @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).

thf(1022,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ E ) @ F ) ) ) @ ( transi374442731on_val @ ( reds @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1152_CallRedsParams) ).

thf(5178,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ E ) @ F ) ) ) @ ( transi374442731on_val @ ( reds @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).

thf(396,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B )
        = ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_Pair__eq) ).

thf(2844,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B )
          = ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B )
          = ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(1029,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ ( hAPP_f1853572245r_bool @ ( hAPP_f1933376467r_bool @ cOMBC_36589090l_bool @ member1601084734t_char ) @ A ) ) @ ( hAPP_f1853572245r_bool @ ( hAPP_f1933376467r_bool @ cOMBC_36589090l_bool @ member1601084734t_char ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_597_pred__subset__eq) ).

thf(5192,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ ( hAPP_f1853572245r_bool @ ( hAPP_f1933376467r_bool @ cOMBC_36589090l_bool @ member1601084734t_char ) @ A ) ) @ ( hAPP_f1853572245r_bool @ ( hAPP_f1933376467r_bool @ cOMBC_36589090l_bool @ member1601084734t_char ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ ( hAPP_f1853572245r_bool @ ( hAPP_f1933376467r_bool @ cOMBC_36589090l_bool @ member1601084734t_char ) @ A ) ) @ ( hAPP_f1853572245r_bool @ ( hAPP_f1933376467r_bool @ cOMBC_36589090l_bool @ member1601084734t_char ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).

thf(279,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f539072365l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_M) ).

thf(2360,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f539072365l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(1256,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( wTrts @ A @ B @ C @ D @ E ) )
    <=> ( hBOOL @ ( wTrts_1 @ A @ B @ C @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1193_wts_H__iff__wts) ).

thf(6138,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( hBOOL @ ( wTrts @ A @ B @ C @ D @ E ) )
       => ( hBOOL @ ( wTrts_1 @ A @ B @ C @ D @ E ) ) )
      & ( ( hBOOL @ ( wTrts_1 @ A @ B @ C @ D @ E ) )
       => ( hBOOL @ ( wTrts @ A @ B @ C @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1256]) ).

thf(592,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1425867561l_bool @ ( hAPP_f1764180741l_bool @ ( hAPP_f247798919l_bool @ cOMBB_526805108t_char @ A ) @ B ) @ C )
      = ( hAPP_f558380429l_bool @ A @ ( hAPP_l208357873t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_) ).

thf(3545,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1425867561l_bool @ ( hAPP_f1764180741l_bool @ ( hAPP_f247798919l_bool @ cOMBB_526805108t_char @ A ) @ B ) @ C )
      = ( hAPP_f558380429l_bool @ A @ ( hAPP_l208357873t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(1115,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( wTrts_1 @ B @ C @ D @ E @ F ) )
     => ( ( hBOOL @ ( hext @ C @ A ) )
       => ( hBOOL @ ( wTrts_1 @ B @ A @ D @ E @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1172_WTrts__hext__mono) ).

thf(5518,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( wTrts_1 @ B @ C @ D @ E @ F ) )
     => ( ( hBOOL @ ( hext @ C @ A ) )
       => ( hBOOL @ ( wTrts_1 @ B @ A @ D @ E @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).

thf(1165,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P124632071l_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P124632071l_bool @ A @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_split__paired__All) ).

thf(5745,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P124632071l_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P124632071l_bool @ A @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P124632071l_bool @ A @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P124632071l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).

thf(185,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_list_char_bool @ ( is_cla570604648t_char @ C ) @ D ) )
     => ( hBOOL @ ( wTrt @ C @ A @ B @ ( new_list_char @ D ) @ ( hAPP_list_char_ty @ class @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1128_WTrt_H__WTrts_H_Ointros_I1_J) ).

thf(2010,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_list_char_bool @ ( is_cla570604648t_char @ C ) @ D ) )
     => ( hBOOL @ ( wTrt @ C @ A @ B @ ( new_list_char @ D ) @ ( hAPP_list_char_ty @ class @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(638,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( hBOOL @ ( hAPP_f1314764175l_bool @ ( hAPP_P845017029l_bool @ member699351154t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f1314764175l_bool @ ( hAPP_P845017029l_bool @ member699351154t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_pred__equals__eq2) ).

thf(3730,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f1314764175l_bool @ ( hAPP_P845017029l_bool @ member699351154t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1314764175l_bool @ ( hAPP_P845017029l_bool @ member699351154t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1314764175l_bool @ ( hAPP_P845017029l_bool @ member699351154t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1314764175l_bool @ ( hAPP_P845017029l_bool @ member699351154t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f1314764175l_bool @ ( hAPP_P845017029l_bool @ member699351154t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1314764175l_bool @ ( hAPP_P845017029l_bool @ member699351154t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1314764175l_bool @ ( hAPP_P845017029l_bool @ member699351154t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1314764175l_bool @ ( hAPP_P845017029l_bool @ member699351154t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(1249,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( transi921647814on_val @ E ) ) )
     => ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B )
         != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) )
       => ~ ! [F: $i,G: $i] :
              ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( transi921647814on_val @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_755_converse__rtranclE2) ).

thf(6102,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( transi921647814on_val @ E ) ) )
     => ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B )
         != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) )
       => ~ ! [F: $i,G: $i] :
              ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( transi921647814on_val @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249]) ).

thf(1047,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( transi2024712006on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ D ) @ E ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ H ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ I ) @ J ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( transi2024712006on_val @ F ) ) )
               => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_758_converse__rtrancl__induct2) ).

thf(5269,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( transi2024712006on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ D ) @ E ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ H ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ I ) @ J ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( transi2024712006on_val @ F ) ) )
               => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).

thf(815,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i,E: $i] :
          ( A
         != ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_prod__cases4) ).

thf(4386,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i,E: $i] :
          ( A
         != ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).

thf(427,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1776070952l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Expr__Obop_Mtc__fun_Itc__prod_Itc__Value__Oval_Mtc__V) ).

thf(2972,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1776070952l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(747,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( hBOOL @ B )
      | ~ ( hBOOL @ A )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).

thf(4142,plain,
    ! [A: $i,B: $i] :
      ( ~ ( hBOOL @ B )
      | ~ ( hBOOL @ A )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).

thf(311,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_PairE) ).

thf(2491,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(1104,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ I ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ I ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ F @ A @ B @ C ) ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_941_FAssRedsThrow2) ).

thf(5486,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ I ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ I ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ F @ A @ B @ C ) ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).

thf(431,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_o2007402111l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__String__Ochar_) ).

thf(2985,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_o2007402111l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(1209,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ B @ C ) @ D ) @ E ) )
    <=> ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( red @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_650_redp__red__eq) ).

thf(5935,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ B @ C ) @ D ) @ E ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( red @ A ) ) ) )
      & ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( red @ A ) ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ B @ C ) @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209]) ).

thf(252,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P1574824955y_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__List__Olist_Itc__T) ).

thf(2227,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P1574824955y_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(865,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_prod__cases3) ).

thf(4618,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).

thf(465,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( ( ( hAPP_n546249108on_val @ ( hp @ G ) @ F )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) )
       => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ A ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ H ) ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ D ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_981_CastRedsAddr) ).

thf(3088,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( ( ( hAPP_n546249108on_val @ ( hp @ G ) @ F )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) )
       => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ A ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ H ) ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ D ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(405,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C != D )
     => ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ D @ B ) @ C )
        = ( hAPP_P2094403585on_val @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_fun__upd__other) ).

thf(2886,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C != D )
     => ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ D @ B ) @ C )
        = ( hAPP_P2094403585on_val @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(949,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ B ) )
     => ~ ! [C: $i,D: $i] :
            ( ( B
              = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) )
           => ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_536_splitE) ).

thf(4916,plain,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ B ) )
     => ~ ! [C: $i,D: $i] :
            ( ( B
              = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) )
           => ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).

thf(1198,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i,F: $i,G: $i] : ( hBOOL @ ( hAPP_P378063101l_bool @ B @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ C ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) ) ) ) )
     => ( hBOOL @ ( hAPP_P378063101l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_prod__induct5) ).

thf(5903,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i,F: $i,G: $i] : ( hBOOL @ ( hAPP_P378063101l_bool @ B @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ C ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) ) ) ) )
     => ( hBOOL @ ( hAPP_P378063101l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).

thf(92,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ A ) @ B ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) ) @ ( transi198989188t_char @ E ) ) )
     => ( ( ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ A ) @ B )
         != ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) )
       => ~ ! [F: $i,G: $i] :
              ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ A ) @ B ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ F ) @ G ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) ) @ ( transi198989188t_char @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_743_converse__rtranclE2) ).

thf(1601,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ A ) @ B ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) ) @ ( transi198989188t_char @ E ) ) )
     => ( ( ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ A ) @ B )
         != ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) )
       => ~ ! [F: $i,G: $i] :
              ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ A ) @ B ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ F ) @ G ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) ) @ ( transi198989188t_char @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(33,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ D ) @ E ) ) ) @ ( transi1789604888t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ B ) @ C ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ G ) @ H ) ) ) @ ( transi1789604888t_char @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ G ) @ H ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_779_rtrancl__induct2) ).

thf(1386,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ D ) @ E ) ) ) @ ( transi1789604888t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ B ) @ C ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ G ) @ H ) ) ) @ ( transi1789604888t_char @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ G ) @ H ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(575,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_f1534412387l_bool @ produc769963999l_bool @ A ) @ B ) )
     => ~ ! [C: $i,D: $i] :
            ( ( B
              = ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) )
           => ~ ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_530_splitE) ).

thf(3466,plain,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_f1534412387l_bool @ produc769963999l_bool @ A ) @ B ) )
     => ~ ! [C: $i,D: $i] :
            ( ( B
              = ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) )
           => ~ ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(289,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ B ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) ) @ ( lex_pr1971266694on_val @ E @ F ) ) )
    <=> ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ C ) ) @ E ) )
        | ( ( A = C )
          & ( hBOOL @ ( hAPP_f983152497l_bool @ ( hAPP_P1953134729l_bool @ member781783252on_val @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ B ) @ D ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_389_in__lex__prod) ).

thf(2400,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ B ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) ) @ ( lex_pr1971266694on_val @ E @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f983152497l_bool @ ( hAPP_P1953134729l_bool @ member781783252on_val @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ B ) @ D ) ) @ F ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f983152497l_bool @ ( hAPP_P1953134729l_bool @ member781783252on_val @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ B ) @ D ) ) @ F ) ) ) )
       => ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ B ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) ) @ ( lex_pr1971266694on_val @ E @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(964,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ B ) @ ( transi2024712006on_val @ A ) ) )
       => ( ( transi2024712006on_val @ B )
          = ( transi2024712006on_val @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_681_rtrancl__subset) ).

thf(4963,plain,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ B ) @ ( transi2024712006on_val @ A ) ) )
       => ( ( transi2024712006on_val @ B )
          = ( transi2024712006on_val @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).

thf(1166,axiom,
    hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1700205512_sconf @ p @ e ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ la ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_InitBlockRed_I4_J) ).

thf(5750,plain,
    hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1700205512_sconf @ p @ e ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ la ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).

thf(157,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P2028072621l_bool @ B @ ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ C ) @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ D ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P2028072621l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_prod__induct4) ).

thf(1904,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P2028072621l_bool @ B @ ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ C ) @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ D ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P2028072621l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(70,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( hAPP_val_option_ty @ ( typeof_h @ C ) @ D )
        = ( hAPP_ty_option_ty @ some_ty @ E ) )
     => ( hBOOL @ ( wTrt @ A @ C @ B @ ( hAPP_v834067052t_char @ val_list_char @ D ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1019_WTrt_H__WTrts_H_Ointros_I3_J) ).

thf(1518,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( hAPP_val_option_ty @ ( typeof_h @ C ) @ D )
        = ( hAPP_ty_option_ty @ some_ty @ E ) )
     => ( hBOOL @ ( wTrt @ A @ C @ B @ ( hAPP_v834067052t_char @ val_list_char @ D ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P1240100515r_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1240100515r_bool @ A @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_split__paired__All) ).

thf(1265,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P1240100515r_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1240100515r_bool @ A @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1240100515r_bool @ A @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P1240100515r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(115,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ ( produc156891095r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_487_curryE) ).

thf(1703,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ ( produc156891095r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(984,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fTrue ) ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ E @ B @ A ) ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1108_CondReds2T) ).

thf(5024,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fTrue ) ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ E @ B @ A ) ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).

thf(1066,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_PairE) ).

thf(5342,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).

thf(657,axiom,
    ! [A: $i] :
      ( ( hBOOL @ ( preallocated @ A ) )
    <=> ! [B: $i] :
          ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ sys_xcpts ) )
         => ? [C: $i] :
              ( ( hAPP_n546249108on_val @ A @ ( addr_of_sys_xcpt @ B ) )
              = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1076_preallocated__def) ).

thf(3820,plain,
    ! [A: $i] :
      ( ( ( hBOOL @ ( preallocated @ A ) )
       => ! [B: $i] :
            ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ sys_xcpts ) )
           => ? [C: $i] :
                ( ( hAPP_n546249108on_val @ A @ ( addr_of_sys_xcpt @ B ) )
                = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) ) ) )
      & ( ! [B: $i] :
            ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ sys_xcpts ) )
           => ? [C: $i] :
                ( ( hAPP_n546249108on_val @ A @ ( addr_of_sys_xcpt @ B ) )
                = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) ) )
       => ( hBOOL @ ( preallocated @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

thf(851,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( lAss_list_char @ A @ B )
        = ( lAss_list_char @ C @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_574_exp_Osimps_I6_J) ).

thf(4539,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( lAss_list_char @ A @ B )
          = ( lAss_list_char @ C @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( lAss_list_char @ A @ B )
          = ( lAss_list_char @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).

thf(179,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ B ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_prod__cases3) ).

thf(1985,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ B ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(354,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( fun_up204312361on_val @ ( fun_up204312361on_val @ A @ B @ C ) @ B @ D )
      = ( fun_up204312361on_val @ A @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_fun__upd__upd) ).

thf(2667,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( fun_up204312361on_val @ ( fun_up204312361on_val @ A @ B @ C ) @ B @ D )
      = ( fun_up204312361on_val @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(1200,axiom,
    ! [A: $i] :
      ( ( hAPP_val_option_val @ some_val @ A )
     != none_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_612_option_Osimps_I3_J) ).

thf(5910,plain,
    ! [A: $i] :
      ( ( hAPP_val_option_val @ some_val @ A )
     != none_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).

thf(148,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P943837928l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__Value__Ov) ).

thf(1871,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P943837928l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(1027,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ F @ none_val ) ) ) @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ ( block_list_char @ F @ A @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ F @ ( hAPP_l207779698on_val @ E @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_854_Block) ).

thf(5188,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ F @ none_val ) ) ) @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ ( block_list_char @ F @ A @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ F @ ( hAPP_l207779698on_val @ E @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).

thf(612,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P282169671l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O) ).

thf(3617,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P282169671l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(618,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( block_list_char @ A @ B @ C )
     != ( lAss_list_char @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_569_exp_Osimps_I143_J) ).

thf(3653,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( block_list_char @ A @ B @ C )
     != ( lAss_list_char @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(579,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P449474095r_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P449474095r_bool @ A @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_split__paired__All) ).

thf(3485,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P449474095r_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P449474095r_bool @ A @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P449474095r_bool @ A @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P449474095r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(806,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) ) @ ( lex_pr280535005t_char @ E @ F ) ) )
    <=> ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ C ) ) @ E ) )
        | ( ( A = C )
          & ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ D ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_388_in__lex__prod) ).

thf(4349,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) ) @ ( lex_pr280535005t_char @ E @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ D ) ) @ F ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ D ) ) @ F ) ) ) )
       => ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) ) @ ( lex_pr280535005t_char @ E @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).

thf(1228,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_936_FAccReds) ).

thf(6006,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228]) ).

thf(970,axiom,
    ! [A: $i,B: $i] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ fequal_val @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Value__Oval_T) ).

thf(4984,plain,
    ! [A: $i,B: $i] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ fequal_val @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).

thf(373,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( hAPP_v834067052t_char @ val_list_char @ B ) @ C ) @ D ) @ E ) )
     => ~ ( ( D
            = ( hAPP_v834067052t_char @ val_list_char @ B ) )
         => ( E != C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_885_eval__cases_I2_J) ).

thf(2745,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( hAPP_v834067052t_char @ val_list_char @ B ) @ C ) @ D ) @ E ) )
     => ~ ( ( D
            = ( hAPP_v834067052t_char @ val_list_char @ B ) )
         => ( E != C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(1096,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f1175813647l_bool @ ( hAPP_f1363667773l_bool @ ( hAPP_f1050935001l_bool @ cOMBB_1153617344on_val @ A ) @ B ) @ C )
      = ( hAPP_f1008932791l_bool @ A @ ( hAPP_f1849790461on_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_058) ).

thf(5461,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f1175813647l_bool @ ( hAPP_f1363667773l_bool @ ( hAPP_f1050935001l_bool @ cOMBB_1153617344on_val @ A ) @ B ) @ C )
      = ( hAPP_f1008932791l_bool @ A @ ( hAPP_f1849790461on_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).

thf(1171,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hAPP_l207779698on_val @ A @ B )
        = ( hAPP_val_option_val @ some_val @ C ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ ( dom_list_char_val @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_464_domI) ).

thf(5765,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hAPP_l207779698on_val @ A @ B )
        = ( hAPP_val_option_val @ some_val @ C ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ ( dom_list_char_val @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).

thf(826,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( assigned @ A @ B ) )
    <=> ? [C: $i,D: $i] :
          ( B
          = ( seq_list_char @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_658_assigned__def) ).

thf(4439,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( assigned @ A @ B ) )
       => ? [C: $i,D: $i] :
            ( B
            = ( seq_list_char @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ D ) ) )
      & ( ? [C: $i,D: $i] :
            ( B
            = ( seq_list_char @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ D ) )
       => ( hBOOL @ ( assigned @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).

thf(11,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ A ) @ B )
        = ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_Pair__inject) ).

thf(1287,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ A ) @ B )
        = ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(506,axiom,
    ! [A: $i] :
      ( ( hAPP_f363827556r_bool @ some_f80346385r_bool @ A )
     != none_f478147469r_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_613_option_Osimps_I3_J) ).

thf(3221,plain,
    ! [A: $i] :
      ( ( hAPP_f363827556r_bool @ some_f80346385r_bool @ A )
     != none_f478147469r_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(691,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l96108383r_bool @ ( hAPP_f1608277885r_bool @ ( hAPP_f1134248971r_bool @ cOMBB_338473166ist_ty @ A ) @ B ) @ C )
      = ( hAPP_f225832321r_bool @ A @ ( hAPP_l1117138611l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mt_054) ).

thf(3938,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l96108383r_bool @ ( hAPP_f1608277885r_bool @ ( hAPP_f1134248971r_bool @ cOMBB_338473166ist_ty @ A ) @ B ) @ C )
      = ( hAPP_f225832321r_bool @ A @ ( hAPP_l1117138611l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).

thf(446,axiom,
    ! [A: $i] :
      ( ( addr @ A )
     != null ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1035_val_Osimps_I17_J) ).

thf(3029,plain,
    ! [A: $i] :
      ( ( addr @ A )
     != null ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(899,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_split__paired__All) ).

thf(4743,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).

thf(133,axiom,
    ! [A: $i] :
      ( ( is_bop @ A )
     => ( ( A != c_Expr_Obop_OEq )
       => ( A = add ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1080_bop_Oexhaust) ).

thf(1792,plain,
    ! [A: $i] :
      ( ( is_bop @ A )
     => ( ( A != c_Expr_Obop_OEq )
       => ( A = add ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(40,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P449474095r_bool @ A @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ ( produc95371820r_bool @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_368_curryI) ).

thf(1430,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P449474095r_bool @ A @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ ( produc95371820r_bool @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(197,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P1708370145l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_M_021) ).

thf(2039,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P1708370145l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(1238,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ! [D: $i] :
          ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) ) @ D )
          = none_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_639_map__upd__nonempty) ).

thf(6039,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ! [D: $i] :
          ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) ) @ D )
          = none_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1238]) ).

thf(961,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ H ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) ) ) @ ( transi2024712006on_val @ ( red @ K ) ) ) )
     => ( ( ( hAPP_n546249108on_val @ I @ H )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
       => ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ C ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ K ) ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ F @ C @ A @ B ) ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ H ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) ) ) @ ( transi2024712006on_val @ ( red @ K ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_952_TryRedsFail) ).

thf(4956,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ H ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) ) ) @ ( transi2024712006on_val @ ( red @ K ) ) ) )
     => ( ( ( hAPP_n546249108on_val @ I @ H )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
       => ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ C ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ K ) ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ F @ C @ A @ B ) ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ H ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) ) ) @ ( transi2024712006on_val @ ( red @ K ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).

thf(14,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P1680401186r_bool @ B @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1680401186r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_prod__induct3) ).

thf(1298,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P1680401186r_bool @ B @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1680401186r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(1194,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ A @ B @ C ) @ B @ D )
      = ( fun_up1149430426on_val @ A @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_fun__upd__upd) ).

thf(5883,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ A @ B @ C ) @ B @ D )
      = ( fun_up1149430426on_val @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).

thf(276,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( block_list_char @ A @ B @ C )
        = ( block_list_char @ D @ E @ F ) )
    <=> ( ( A = D )
        & ( B = E )
        & ( C = F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_575_exp_Osimps_I10_J) ).

thf(2339,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( ( block_list_char @ A @ B @ C )
          = ( block_list_char @ D @ E @ F ) )
       => ( ( A = D )
          & ( B = E )
          & ( C = F ) ) )
      & ( ( ( A = D )
          & ( B = E )
          & ( C = F ) )
       => ( ( block_list_char @ A @ B @ C )
          = ( block_list_char @ D @ E @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(885,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( throw_list_char @ D ) @ E ) )
     => ~ ! [F: $i] :
            ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ F ) )
           => ~ ( hBOOL @ ( is_refT @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_977_WTrt__elim__cases_I4_J) ).

thf(4692,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( throw_list_char @ D ) @ E ) )
     => ~ ! [F: $i] :
            ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ F ) )
           => ~ ( hBOOL @ ( is_refT @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).

thf(992,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ E ) @ F ) ) ) @ ( reds @ G ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ E ) ) @ F ) ) ) @ ( red @ G ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1151_red__reds_OCallParams) ).

thf(5064,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ E ) @ F ) ) ) @ ( reds @ G ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ E ) ) @ F ) ) ) @ ( red @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).

thf(1048,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ A @ B @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ ( dom_list_char_val @ D ) ) @ ( dom_list_char_val @ G ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1150_evals__lcl__incr) ).

thf(5274,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ A @ B @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ ( dom_list_char_val @ D ) ) @ ( dom_list_char_val @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).

thf(1008,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ A @ B @ ( seq_list_char @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) ) ) @ ( red @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_438_red__reds_ORedInitBlock) ).

thf(5130,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ A @ B @ ( seq_list_char @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) ) ) @ ( red @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).

thf(239,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ E @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ H ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ A @ H ) @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ ( seq_list_char @ E @ A ) @ F ) @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_857_Seq) ).

thf(2185,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ E @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ H ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ A @ H ) @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ ( seq_list_char @ E @ A ) @ F ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(1252,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B )
        = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_Pair__eq) ).

thf(6113,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252]) ).

thf(1024,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A ) @ ( transi2024712006on_val @ B ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ ( transi2024712006on_val @ A ) ) @ ( transi2024712006on_val @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_684_rtrancl__subset__rtrancl) ).

thf(5182,plain,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A ) @ ( transi2024712006on_val @ B ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ ( transi2024712006on_val @ A ) ) @ ( transi2024712006on_val @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).

thf(823,axiom,
    ! [A: $i] :
      ( ? [B: $i] : ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ B ) )
    <=> ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_split__paired__Ex) ).

thf(4428,plain,
    ! [A: $i] :
      ( ( ? [B: $i] : ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ B ) )
       => ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) ) )
      & ( ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) )
       => ? [B: $i] : ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).

thf(665,axiom,
    ! [A: $i,B: $i] :
      ( ( is_fun1083000568p_bool @ A )
     => ( is_bool @ ( hAPP_P1085566419p_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Expr__Obop_Mtc__Expr__Obop_J_000tc__HOL__Obool) ).

thf(3855,plain,
    ! [A: $i,B: $i] :
      ( ( is_fun1083000568p_bool @ A )
     => ( is_bool @ ( hAPP_P1085566419p_bool @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).

thf(293,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) @ ( transi374442731on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ D ) @ E ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ G ) @ H ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ I ) @ J ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) @ ( transi374442731on_val @ F ) ) )
               => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_757_converse__rtrancl__induct2) ).

thf(2420,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) @ ( transi374442731on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ D ) @ E ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ G ) @ H ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ I ) @ J ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) @ ( transi374442731on_val @ F ) ) )
               => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(31,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ A ) @ B )
        = ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_Pair__inject) ).

thf(1379,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ A ) @ B )
        = ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(234,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ B ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ B ) @ ( semila449273525l_bool @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_868_UnCI) ).

thf(2169,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ B ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ B ) @ ( semila449273525l_bool @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(1031,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1103_CondRedsThrow) ).

thf(5199,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).

thf(20,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ E ) ) ) @ ( transi1257872013t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ D ) @ E ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ G ) @ H ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ I ) @ J ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ E ) ) ) @ ( transi1257872013t_char @ F ) ) )
               => ( ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_764_converse__rtrancl__induct2) ).

thf(1319,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ E ) ) ) @ ( transi1257872013t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ D ) @ E ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ G ) @ H ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ I ) @ J ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ E ) ) ) @ ( transi1257872013t_char @ F ) ) )
               => ( ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(56,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P2028072621l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc_) ).

thf(1479,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P2028072621l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(924,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ E ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ A @ B ) @ C ) @ D ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_850_big__by__small) ).

thf(4830,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ E ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ A @ B ) @ C ) @ D ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).

thf(576,axiom,
    ! [A: $i] :
      ( ? [B: $i] : ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ B ) )
    <=> ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_split__paired__Ex) ).

thf(3470,plain,
    ! [A: $i] :
      ( ( ? [B: $i] : ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ B ) )
       => ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) ) )
      & ( ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) )
       => ? [B: $i] : ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(433,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) ) @ ( transi1395422419t_char @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: $i] :
              ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ D ) ) @ C ) )
             => ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ B ) ) @ ( transi1395422419t_char @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_839_converse__rtranclE) ).

thf(2989,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) ) @ ( transi1395422419t_char @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: $i] :
              ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ D ) ) @ C ) )
             => ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ B ) ) @ ( transi1395422419t_char @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(816,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f861853459l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olis_008) ).

thf(4390,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f861853459l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).

thf(1137,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P1002912327r_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1002912327r_bool @ A @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_split__paired__All) ).

thf(5617,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P1002912327r_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1002912327r_bool @ A @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1002912327r_bool @ A @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P1002912327r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).

thf(522,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_PairE) ).

thf(3268,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(162,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ ( produc156891095r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_503_curryD) ).

thf(1922,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ ( produc156891095r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(1230,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( fun_up1149430426on_val @ A @ B @ C )
        = A )
    <=> ( ( hAPP_l207779698on_val @ A @ B )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_fun__upd__idem__iff) ).

thf(6010,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( fun_up1149430426on_val @ A @ B @ C )
          = A )
       => ( ( hAPP_l207779698on_val @ A @ B )
          = C ) )
      & ( ( ( hAPP_l207779698on_val @ A @ B )
          = C )
       => ( ( fun_up1149430426on_val @ A @ B @ C )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230]) ).

thf(469,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( fun_up2041264236on_val @ A @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ C ) )
        = ( fun_up2041264236on_val @ D @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ E ) ) )
     => ( C = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_map__upd__eqD1) ).

thf(3099,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( fun_up2041264236on_val @ A @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ C ) )
        = ( fun_up2041264236on_val @ D @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ E ) ) )
     => ( C = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(1064,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( wTrts_1 @ A @ B @ C @ D @ E ) )
     => ( hBOOL @ ( wTrts @ A @ B @ C @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1195_wts__wts_H) ).

thf(5338,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( wTrts_1 @ A @ B @ C @ D @ E ) )
     => ( hBOOL @ ( wTrts @ A @ B @ C @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).

thf(761,axiom,
    ! [A: $i,B: $i] : ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ A ) ) @ ( transi935034983cl_val @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_662_rtrancl_Ortrancl__refl) ).

thf(4179,plain,
    ! [A: $i,B: $i] : ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ A ) ) @ ( transi935034983cl_val @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).

thf(378,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_825_order__antisym__conv) ).

thf(2767,plain,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
     => ( ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) )
         => ( B = A ) )
        & ( ( B = A )
         => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(1138,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) ) ) @ ( red @ H ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( map_ad325961431ar_val @ A @ D ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ ( map_ad325961431ar_val @ A @ G ) ) ) ) ) @ ( red @ H ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_373_red__lcl__add) ).

thf(5622,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) ) ) @ ( red @ H ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( map_ad325961431ar_val @ A @ D ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ ( map_ad325961431ar_val @ A @ G ) ) ) ) ) @ ( red @ H ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).

thf(866,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( lAss_list_char @ B @ ( throw_list_char @ C ) ) @ D ) @ ( throw_list_char @ C ) ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_922_redp__redsp_OLAssThrow) ).

thf(4622,plain,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( lAss_list_char @ B @ ( throw_list_char @ C ) ) @ D ) @ ( throw_list_char @ C ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).

thf(83,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( wTrt @ B @ C @ D @ E @ F ) )
     => ( ( hBOOL @ ( is_refT @ F ) )
       => ( ( hBOOL @ ( hAPP_list_char_bool @ ( is_cla570604648t_char @ B ) @ A ) )
         => ( hBOOL @ ( wTrt @ B @ C @ D @ ( cast_list_char @ A @ E ) @ ( hAPP_list_char_ty @ class @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1061_WTrt_H__WTrts_H_Ointros_I2_J) ).

thf(1572,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( wTrt @ B @ C @ D @ E @ F ) )
     => ( ( hBOOL @ ( is_refT @ F ) )
       => ( ( hBOOL @ ( hAPP_list_char_bool @ ( is_cla570604648t_char @ B ) @ A ) )
         => ( hBOOL @ ( wTrt @ B @ C @ D @ ( cast_list_char @ A @ E ) @ ( hAPP_list_char_ty @ class @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(679,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P124632071l_bool @ B @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ C ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P124632071l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_prod__induct3) ).

thf(3902,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P124632071l_bool @ B @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ C ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P124632071l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).

thf(619,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P378063101l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_) ).

thf(3657,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P378063101l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(165,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_b97269396l_bool @ ( produc1555310053l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P943837928l_bool @ A @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_508_curryD) ).

thf(1931,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_b97269396l_bool @ ( produc1555310053l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P943837928l_bool @ A @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(982,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ H ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ H @ B @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) )
       => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ ( fv @ B ) ) @ A ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ H @ B @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( restri761823004ar_val @ D @ A ) ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ ( restri761823004ar_val @ G @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_891_eval__restrict__lcl) ).

thf(5020,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ H ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ H @ B @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) )
       => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ ( fv @ B ) ) @ A ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ H @ B @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( restri761823004ar_val @ D @ A ) ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ ( restri761823004ar_val @ G @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).

thf(1106,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) ) @ ( red @ H ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ D @ A @ B @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ F @ A @ B @ C ) ) @ G ) ) ) @ ( red @ H ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_964_red__reds_OTryRed) ).

thf(5493,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) ) @ ( red @ H ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ D @ A @ B @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ F @ A @ B @ C ) ) @ G ) ) ) @ ( red @ H ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).

thf(1233,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ C ) ) ) @ ( transi2024712006on_val @ ( red @ D ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ C ) ) ) @ ( transi2024712006on_val @ ( red @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1049_ThrowRedsNull) ).

thf(6025,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ C ) ) ) @ ( transi2024712006on_val @ ( red @ D ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ C ) ) ) @ ( transi2024712006on_val @ ( red @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1233]) ).

thf(129,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P824029447r_bool @ B @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ C ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P824029447r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_prod__induct3) ).

thf(1778,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P824029447r_bool @ B @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ C ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P824029447r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(250,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ ( fv @ C ) ) )
       => ( ( hAPP_l207779698on_val @ H @ A )
          = ( hAPP_l207779698on_val @ E @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_848_eval__notfree__unchanged) ).

thf(2222,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ ( fv @ C ) ) )
       => ( ( hAPP_l207779698on_val @ H @ A )
          = ( hAPP_l207779698on_val @ E @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(1226,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ H ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ I ) ) @ J ) ) ) @ ( transi2024712006on_val @ ( red @ K ) ) ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ J ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ C ) @ ( cons_exp_list_char @ ( throw_list_char @ D ) @ E ) ) ) @ F ) ) ) @ ( transi374442731on_val @ ( reds @ K ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ G @ A @ B ) ) @ H ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ K ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1153_CallRedsThrowParams) ).

thf(6002,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ H ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ I ) ) @ J ) ) ) @ ( transi2024712006on_val @ ( red @ K ) ) ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ J ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ C ) @ ( cons_exp_list_char @ ( throw_list_char @ D ) @ E ) ) ) @ F ) ) ) @ ( transi374442731on_val @ ( reds @ K ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ G @ A @ B ) ) @ H ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ K ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226]) ).

thf(566,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f966411375l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc) ).

thf(3431,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f966411375l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(460,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_736_subsetI) ).

thf(3075,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(710,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_P1333315679l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_473_mem__def) ).

thf(4001,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_P1333315679l_bool @ B @ A ) ) )
      & ( ( hBOOL @ ( hAPP_P1333315679l_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).

thf(921,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wf_J_mdecl @ G ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( red @ G ) ) )
       => ( ( hBOOL @ ( d_list_char @ A @ ( hAPP_f363827556r_bool @ some_f80346385r_bool @ ( dom_list_char_val @ C ) ) ) )
         => ( hBOOL @ ( d_list_char @ D @ ( hAPP_f363827556r_bool @ some_f80346385r_bool @ ( dom_list_char_val @ F ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_red__preserves__defass) ).

thf(4820,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wf_J_mdecl @ G ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( red @ G ) ) )
       => ( ( hBOOL @ ( d_list_char @ A @ ( hAPP_f363827556r_bool @ some_f80346385r_bool @ ( dom_list_char_val @ C ) ) ) )
         => ( hBOOL @ ( d_list_char @ D @ ( hAPP_f363827556r_bool @ some_f80346385r_bool @ ( dom_list_char_val @ F ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).

thf(573,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( B = A )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_821_xt1_I4_J) ).

thf(3453,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( B = A )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(706,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1409772418l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__O) ).

thf(3983,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1409772418l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).

thf(1152,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) ) @ ( lex_pr1038007919on_val @ E @ F ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ C ) ) @ E ) )
        | ( ( A = C )
          & ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ D ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_391_in__lex__prod) ).

thf(5680,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) ) @ ( lex_pr1038007919on_val @ E @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ D ) ) @ F ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ D ) ) @ F ) ) ) )
       => ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) ) @ ( lex_pr1038007919on_val @ E @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).

thf(919,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( red @ G ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_928_red__reds_OFAccRed) ).

thf(4815,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( red @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).

thf(1201,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( block_list_char @ B @ C @ D ) @ E ) @ F ) @ G ) )
     => ~ ! [H: $i,I: $i] :
            ( ( E
              = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) )
           => ! [J: $i,K: $i] :
                ( ( G
                  = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ ( fun_up1149430426on_val @ K @ B @ ( hAPP_l207779698on_val @ I @ B ) ) ) )
               => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ D @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ B @ none_val ) ) ) @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ K ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_890_eval__cases_I8_J) ).

thf(5914,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( block_list_char @ B @ C @ D ) @ E ) @ F ) @ G ) )
     => ~ ! [H: $i,I: $i] :
            ( ( E
              = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) )
           => ! [J: $i,K: $i] :
                ( ( G
                  = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ ( fun_up1149430426on_val @ K @ B @ ( hAPP_l207779698on_val @ I @ B ) ) ) )
               => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ D @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ B @ none_val ) ) ) @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ K ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1201]) ).

thf(1017,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ G ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( red @ G ) ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ ( fv @ D ) ) @ ( fv @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_833_Red__fv) ).

thf(5156,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ G ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( red @ G ) ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ ( fv @ D ) ) @ ( fv @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).

thf(935,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f1931964053l_bool @ ( ord_le2008677227r_bool @ ( hAPP_f1209019955r_bool @ ( hAPP_f521496323r_bool @ cOMBC_654453230r_bool @ ( hAPP_f732843907r_bool @ ( hAPP_f1563448447r_bool @ cOMBB_1490692730t_char @ cOMBC_390659185l_bool ) @ ( hAPP_f1868463117l_bool @ ( hAPP_f1365840271l_bool @ cOMBB_1705938036t_char @ ( hAPP_f1937828171l_bool @ cOMBB_1681501894t_char @ member1601084734t_char ) ) @ produc1331140167t_char ) ) ) @ A ) ) @ ( hAPP_f1209019955r_bool @ ( hAPP_f521496323r_bool @ cOMBC_654453230r_bool @ ( hAPP_f732843907r_bool @ ( hAPP_f1563448447r_bool @ cOMBB_1490692730t_char @ cOMBC_390659185l_bool ) @ ( hAPP_f1868463117l_bool @ ( hAPP_f1365840271l_bool @ cOMBB_1705938036t_char @ ( hAPP_f1937828171l_bool @ cOMBB_1681501894t_char @ member1601084734t_char ) ) @ produc1331140167t_char ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_800_pred__subset__eq2) ).

thf(4871,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( hAPP_f1931964053l_bool @ ( ord_le2008677227r_bool @ ( hAPP_f1209019955r_bool @ ( hAPP_f521496323r_bool @ cOMBC_654453230r_bool @ ( hAPP_f732843907r_bool @ ( hAPP_f1563448447r_bool @ cOMBB_1490692730t_char @ cOMBC_390659185l_bool ) @ ( hAPP_f1868463117l_bool @ ( hAPP_f1365840271l_bool @ cOMBB_1705938036t_char @ ( hAPP_f1937828171l_bool @ cOMBB_1681501894t_char @ member1601084734t_char ) ) @ produc1331140167t_char ) ) ) @ A ) ) @ ( hAPP_f1209019955r_bool @ ( hAPP_f521496323r_bool @ cOMBC_654453230r_bool @ ( hAPP_f732843907r_bool @ ( hAPP_f1563448447r_bool @ cOMBB_1490692730t_char @ cOMBC_390659185l_bool ) @ ( hAPP_f1868463117l_bool @ ( hAPP_f1365840271l_bool @ cOMBB_1705938036t_char @ ( hAPP_f1937828171l_bool @ cOMBB_1681501894t_char @ member1601084734t_char ) ) @ produc1331140167t_char ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1931964053l_bool @ ( ord_le2008677227r_bool @ ( hAPP_f1209019955r_bool @ ( hAPP_f521496323r_bool @ cOMBC_654453230r_bool @ ( hAPP_f732843907r_bool @ ( hAPP_f1563448447r_bool @ cOMBB_1490692730t_char @ cOMBC_390659185l_bool ) @ ( hAPP_f1868463117l_bool @ ( hAPP_f1365840271l_bool @ cOMBB_1705938036t_char @ ( hAPP_f1937828171l_bool @ cOMBB_1681501894t_char @ member1601084734t_char ) ) @ produc1331140167t_char ) ) ) @ A ) ) @ ( hAPP_f1209019955r_bool @ ( hAPP_f521496323r_bool @ cOMBC_654453230r_bool @ ( hAPP_f732843907r_bool @ ( hAPP_f1563448447r_bool @ cOMBB_1490692730t_char @ cOMBC_390659185l_bool ) @ ( hAPP_f1868463117l_bool @ ( hAPP_f1365840271l_bool @ cOMBB_1705938036t_char @ ( hAPP_f1937828171l_bool @ cOMBB_1681501894t_char @ member1601084734t_char ) ) @ produc1331140167t_char ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).

thf(207,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) ) @ ( transi374442731on_val @ E ) ) )
     => ( ( ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B )
         != ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) )
       => ~ ! [F: $i,G: $i] :
              ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ F ) @ G ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) ) @ ( transi374442731on_val @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_741_converse__rtranclE2) ).

thf(2073,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) ) @ ( transi374442731on_val @ E ) ) )
     => ( ( ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B )
         != ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) )
       => ~ ! [F: $i,G: $i] :
              ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ F ) @ G ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) ) @ ( transi374442731on_val @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(422,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ B ) ) @ ( transi374442731on_val @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: $i] :
              ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ D ) ) @ C ) )
             => ~ ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ D ) @ B ) ) @ ( transi374442731on_val @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_838_converse__rtranclE) ).

thf(2950,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ B ) ) @ ( transi374442731on_val @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: $i] :
              ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ D ) ) @ C ) )
             => ~ ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ D ) @ B ) ) @ ( transi374442731on_val @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(886,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ E @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ H ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ D @ A @ H ) @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ D @ ( cons_exp_list_char @ E @ A ) @ F ) @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ G ) @ B ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1156_eval__evals_OCons) ).

thf(4696,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ E @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ H ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ D @ A @ H ) @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ D @ ( cons_exp_list_char @ E @ A ) @ F ) @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ G ) @ B ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).

thf(769,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( tryCatch_list_char @ ( hAPP_v834067052t_char @ val_list_char @ B ) @ C @ D @ E ) @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_959_redp__redsp_ORedTry) ).

thf(4205,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( tryCatch_list_char @ ( hAPP_v834067052t_char @ val_list_char @ B ) @ C @ D @ E ) @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).

thf(971,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ B ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_prod__cases3) ).

thf(4988,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ B ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).

thf(342,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ I ) @ J )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ K ) @ L ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( method1809630380t_char @ B @ K @ C @ D @ E @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ F ) @ G ) ) @ H ) )
       => ( ( ( size_size_list_val @ A )
            = ( size_s2113983095t_char @ F ) )
         => ( ( ( size_size_list_ty @ D )
              = ( size_s2113983095t_char @ F ) )
           => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ J ) ) @ C @ ( map_va1934808527t_char @ val_list_char @ A ) ) ) @ I ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ ( cons_list_char @ this @ F ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ ( cons_ty @ ( hAPP_list_char_ty @ class @ H ) @ D ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ ( cons_val @ ( addr @ J ) @ A ) ) @ G ) ) ) ) ) @ I ) ) ) @ ( red @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1185_red__reds_ORedCall) ).

thf(2616,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ I ) @ J )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ K ) @ L ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( method1809630380t_char @ B @ K @ C @ D @ E @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ F ) @ G ) ) @ H ) )
       => ( ( ( size_size_list_val @ A )
            = ( size_s2113983095t_char @ F ) )
         => ( ( ( size_size_list_ty @ D )
              = ( size_s2113983095t_char @ F ) )
           => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ J ) ) @ C @ ( map_va1934808527t_char @ val_list_char @ A ) ) ) @ I ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ ( cons_list_char @ this @ F ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ ( cons_ty @ ( hAPP_list_char_ty @ class @ H ) @ D ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ ( cons_val @ ( addr @ J ) @ A ) ) @ G ) ) ) ) ) @ I ) ) ) @ ( red @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(52,axiom,
    ! [A: $i,B: $i] :
      ( ( hAPP_P2094403585on_val @ ( hAPP_o1269033393on_val @ cOMBK_1867744698t_char @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__prod_Itc__) ).

thf(1465,plain,
    ! [A: $i,B: $i] :
      ( ( hAPP_P2094403585on_val @ ( hAPP_o1269033393on_val @ cOMBK_1867744698t_char @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(799,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( lAss_list_char @ A @ B )
     != ( seq_list_char @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_584_exp_Osimps_I144_J) ).

thf(4329,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( lAss_list_char @ A @ B )
     != ( seq_list_char @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).

thf(676,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l553007690l_bool @ ( hAPP_f558380429l_bool @ ( hAPP_f144783951l_bool @ cOMBB_1586673472t_char @ A ) @ B ) @ C )
      = ( hAPP_P1180869721l_bool @ A @ ( hAPP_l2100324114t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List) ).

thf(3887,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l553007690l_bool @ ( hAPP_f558380429l_bool @ ( hAPP_f144783951l_bool @ cOMBB_1586673472t_char @ A ) @ B ) @ C )
      = ( hAPP_P1180869721l_bool @ A @ ( hAPP_l2100324114t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).

thf(500,axiom,
    ! [A: $i] :
      ( ( hAPP_option_nat_nat @ the_nat @ ( hAPP_nat_option_nat @ some_nat @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_686_the_Osimps) ).

thf(3199,plain,
    ! [A: $i] :
      ( ( hAPP_option_nat_nat @ the_nat @ ( hAPP_nat_option_nat @ some_nat @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(690,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_prod_Oexhaust) ).

thf(3934,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).

thf(550,axiom,
    ! [A: $i] :
      ( ( transi2024712006on_val @ ( transi2024712006on_val @ A ) )
      = ( transi2024712006on_val @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_720_rtrancl__idemp) ).

thf(3393,plain,
    ! [A: $i] :
      ( ( transi2024712006on_val @ ( transi2024712006on_val @ A ) )
      = ( transi2024712006on_val @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(980,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1453283057l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__) ).

thf(5013,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1453283057l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).

thf(830,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( block_list_char @ B @ C @ ( seq_list_char @ ( lAss_list_char @ B @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ ( hAPP_v834067052t_char @ val_list_char @ E ) ) ) @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ E ) ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_652_redp__redsp_ORedInitBlock) ).

thf(4454,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( block_list_char @ B @ C @ ( seq_list_char @ ( lAss_list_char @ B @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ ( hAPP_v834067052t_char @ val_list_char @ E ) ) ) @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ E ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).

thf(380,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ E ) )
     => ( ( hBOOL @ ( is_refT @ E ) )
       => ( ( hBOOL @ ( final_list_char @ D ) )
         => ( ( D
             != ( hAPP_v834067052t_char @ val_list_char @ null ) )
           => ( ( ? [F: $i] :
                    ( D
                    = ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) )
               => ! [F: $i] :
                    ( E
                   != ( hAPP_list_char_ty @ class @ F ) ) )
             => ~ ! [F: $i] :
                    ( D
                   != ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1051_finalRefE) ).

thf(2782,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ E ) )
     => ( ( hBOOL @ ( is_refT @ E ) )
       => ( ( hBOOL @ ( final_list_char @ D ) )
         => ( ( D
             != ( hAPP_v834067052t_char @ val_list_char @ null ) )
           => ( ( ? [F: $i] :
                    ( D
                    = ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) )
               => ! [F: $i] :
                    ( E
                   != ( hAPP_list_char_ty @ class @ F ) ) )
             => ~ ! [F: $i] :
                    ( D
                   != ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(702,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) ) @ ( transi1395422419t_char @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: $i] :
              ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ D ) ) @ ( transi1395422419t_char @ C ) ) )
             => ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ B ) ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_835_rtranclE) ).

thf(3973,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) ) @ ( transi1395422419t_char @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: $i] :
              ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ D ) ) @ ( transi1395422419t_char @ C ) ) )
             => ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ B ) ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).

thf(1181,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i,E: $i,F: $i] :
          ( A
         != ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ B ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_prod__cases5) ).

thf(5804,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i,E: $i,F: $i] :
          ( A
         != ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ B ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).

thf(271,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( hBOOL @ ( hAPP_f1746574980l_bool @ ( hAPP_P1198052655l_bool @ member140606439t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f1746574980l_bool @ ( hAPP_P1198052655l_bool @ member140606439t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_pred__equals__eq2) ).

thf(2291,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f1746574980l_bool @ ( hAPP_P1198052655l_bool @ member140606439t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1746574980l_bool @ ( hAPP_P1198052655l_bool @ member140606439t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1746574980l_bool @ ( hAPP_P1198052655l_bool @ member140606439t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1746574980l_bool @ ( hAPP_P1198052655l_bool @ member140606439t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f1746574980l_bool @ ( hAPP_P1198052655l_bool @ member140606439t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1746574980l_bool @ ( hAPP_P1198052655l_bool @ member140606439t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1746574980l_bool @ ( hAPP_P1198052655l_bool @ member140606439t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1746574980l_bool @ ( hAPP_P1198052655l_bool @ member140606439t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(543,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ B )
        = ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_Pair__eq) ).

thf(3357,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ B )
          = ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ B )
          = ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(261,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1161798306l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__014) ).

thf(2254,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1161798306l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(529,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ A ) @ B )
        = ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_Pair__eq) ).

thf(3290,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ A ) @ B )
          = ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ A ) @ B )
          = ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(467,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ ( semila919158006r_bool @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_871_UnCI) ).

thf(3093,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ ( semila919158006r_bool @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(740,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( seq_list_char @ ( throw_list_char @ B ) @ C ) @ D ) @ ( throw_list_char @ B ) ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_921_redp__redsp_OSeqThrow) ).

thf(4115,plain,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( seq_list_char @ ( throw_list_char @ B ) @ C ) @ D ) @ ( throw_list_char @ B ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).

thf(274,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) @ ( reds @ F ) ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B ) ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ D ) ) @ E ) ) ) @ ( reds @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1158_red__reds_OListRed2) ).

thf(2335,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) @ ( reds @ F ) ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B ) ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ D ) ) @ E ) ) ) @ ( reds @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(1071,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( map_ad325961431ar_val @ A @ ( fun_up1149430426on_val @ B @ C @ ( hAPP_val_option_val @ some_val @ D ) ) )
      = ( fun_up1149430426on_val @ ( map_ad325961431ar_val @ A @ B ) @ C @ ( hAPP_val_option_val @ some_val @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_517_map__add__upd) ).

thf(5360,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( map_ad325961431ar_val @ A @ ( fun_up1149430426on_val @ B @ C @ ( hAPP_val_option_val @ some_val @ D ) ) )
      = ( fun_up1149430426on_val @ ( map_ad325961431ar_val @ A @ B ) @ C @ ( hAPP_val_option_val @ some_val @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).

thf(907,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1776419603l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__List__) ).

thf(4783,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1776419603l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).

thf(486,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ D @ E ) @ ( throw_list_char @ F ) ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( fAcc_list_char @ D @ A @ B ) @ E ) @ ( throw_list_char @ F ) ) @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_909_eval__evals_OFAccThrow) ).

thf(3152,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ D @ E ) @ ( throw_list_char @ F ) ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( fAcc_list_char @ D @ A @ B ) @ E ) @ ( throw_list_char @ F ) ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(645,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ D @ E ) @ ( throw_list_char @ F ) ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( call_list_char @ D @ A @ B ) @ E ) @ ( throw_list_char @ F ) ) @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1136_CallObjThrow) ).

thf(3771,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ D @ E ) @ ( throw_list_char @ F ) ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( call_list_char @ D @ A @ B ) @ E ) @ ( throw_list_char @ F ) ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(755,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f458849545l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__) ).

thf(4162,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f458849545l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).

thf(991,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1700205512_sconf @ A @ B ) @ C ) )
    <=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ ( cOMBS_570216337l_bool @ ( hAPP_f1523875321l_bool @ ( hAPP_f592397849l_bool @ cOMBB_1718333400on_val @ cOMBB_383678192on_val ) @ ( hAPP_f1452292669l_bool @ ( hAPP_f1977633121l_bool @ cOMBB_1303934920on_val @ fconj ) @ ( hconf_97414254t_char @ A ) ) ) @ ( hAPP_f550652027l_bool @ ( hAPP_f838396643l_bool @ cOMBC_2027949654l_bool @ ( hAPP_f857351829l_bool @ ( hAPP_f348318673l_bool @ cOMBB_1518282696on_val @ cOMBC_832625297y_bool ) @ ( lconf_496643946t_char @ A ) ) ) @ B ) ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_sconf__def) ).

thf(5059,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1700205512_sconf @ A @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ ( cOMBS_570216337l_bool @ ( hAPP_f1523875321l_bool @ ( hAPP_f592397849l_bool @ cOMBB_1718333400on_val @ cOMBB_383678192on_val ) @ ( hAPP_f1452292669l_bool @ ( hAPP_f1977633121l_bool @ cOMBB_1303934920on_val @ fconj ) @ ( hconf_97414254t_char @ A ) ) ) @ ( hAPP_f550652027l_bool @ ( hAPP_f838396643l_bool @ cOMBC_2027949654l_bool @ ( hAPP_f857351829l_bool @ ( hAPP_f348318673l_bool @ cOMBB_1518282696on_val @ cOMBC_832625297y_bool ) @ ( lconf_496643946t_char @ A ) ) ) @ B ) ) ) @ C ) ) )
      & ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ ( cOMBS_570216337l_bool @ ( hAPP_f1523875321l_bool @ ( hAPP_f592397849l_bool @ cOMBB_1718333400on_val @ cOMBB_383678192on_val ) @ ( hAPP_f1452292669l_bool @ ( hAPP_f1977633121l_bool @ cOMBB_1303934920on_val @ fconj ) @ ( hconf_97414254t_char @ A ) ) ) @ ( hAPP_f550652027l_bool @ ( hAPP_f838396643l_bool @ cOMBC_2027949654l_bool @ ( hAPP_f857351829l_bool @ ( hAPP_f348318673l_bool @ cOMBB_1518282696on_val @ cOMBC_832625297y_bool ) @ ( lconf_496643946t_char @ A ) ) ) @ B ) ) ) @ C ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1700205512_sconf @ A @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).

thf(901,axiom,
    ! [A: $i,B: $i] :
      ( ( ( hAPP_nat_option_nat @ some_nat @ A )
        = ( hAPP_nat_option_nat @ some_nat @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_option_Oinject) ).

thf(4751,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( hAPP_nat_option_nat @ some_nat @ A )
          = ( hAPP_nat_option_nat @ some_nat @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( hAPP_nat_option_nat @ some_nat @ A )
          = ( hAPP_nat_option_nat @ some_nat @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).

thf(458,axiom,
    ! [A: $i] :
      ( ( is_bool @ A )
     => ( ( A = fTrue )
        | ( A = fFalse ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).

thf(3068,plain,
    ! [A: $i] :
      ( ( is_bool @ A )
     => ( ( A = fTrue )
        | ( A = fFalse ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(562,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_list_char_bool @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_596_predicate1D) ).

thf(3421,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_list_char_bool @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(633,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P1614880106l_bool @ ( hAPP_f1646911885l_bool @ ( hAPP_f62511709l_bool @ cOMBB_2139740953al_val @ A ) @ B ) @ C )
      = ( hAPP_P1653675595l_bool @ A @ ( hAPP_P929466802al_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc_) ).

thf(3712,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P1614880106l_bool @ ( hAPP_f1646911885l_bool @ ( hAPP_f62511709l_bool @ cOMBB_2139740953al_val @ A ) @ B ) @ C )
      = ( hAPP_P1653675595l_bool @ A @ ( hAPP_P929466802al_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(47,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( hBOOL @ ( wTrt @ F @ G @ H @ I @ ( hAPP_list_char_ty @ class @ J ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( has_fi1183600461t_char @ F @ J @ C @ D ) @ E ) )
       => ( ( hBOOL @ ( wTrt @ F @ G @ H @ A @ B ) )
         => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ F ) @ B ) @ D ) )
           => ( hBOOL @ ( wTrt @ F @ G @ H @ ( fAss_list_char @ I @ C @ E @ A ) @ void ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1028_WTrt_H__WTrts_H_Ointros_I10_J) ).

thf(1447,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( hBOOL @ ( wTrt @ F @ G @ H @ I @ ( hAPP_list_char_ty @ class @ J ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( has_fi1183600461t_char @ F @ J @ C @ D ) @ E ) )
       => ( ( hBOOL @ ( wTrt @ F @ G @ H @ A @ B ) )
         => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ F ) @ B ) @ D ) )
           => ( hBOOL @ ( wTrt @ F @ G @ H @ ( fAss_list_char @ I @ C @ E @ A ) @ void ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(153,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ A ) @ B )
        = ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_Pair__inject) ).

thf(1886,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ A ) @ B )
        = ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(890,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ A ) @ B )
        = ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_Pair__eq) ).

thf(4707,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ A ) @ B )
          = ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ A ) @ B )
          = ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).

thf(597,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P159683425l_bool @ ( hAPP_f1175362209l_bool @ ( hAPP_f101237475l_bool @ cOMBC_1585774710l_bool @ A ) @ B ) @ C )
      = ( hAPP_f91506671l_bool @ ( hAPP_P1609485901l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It) ).

thf(3559,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P159683425l_bool @ ( hAPP_f1175362209l_bool @ ( hAPP_f101237475l_bool @ cOMBC_1585774710l_bool @ A ) @ B ) @ C )
      = ( hAPP_f91506671l_bool @ ( hAPP_P1609485901l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(1061,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f613075253l_bool @ ( hAPP_f1670595613l_bool @ ( hAPP_f1472899487l_bool @ cOMBB_588525814on_val @ A ) @ B ) @ C )
      = ( hAPP_f292637069l_bool @ A @ ( hAPP_f1849790461on_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_072) ).

thf(5328,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f613075253l_bool @ ( hAPP_f1670595613l_bool @ ( hAPP_f1472899487l_bool @ cOMBB_588525814on_val @ A ) @ B ) @ C )
      = ( hAPP_f292637069l_bool @ A @ ( hAPP_f1849790461on_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).

thf(112,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P1907982426r_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__Ol) ).

thf(1696,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P1907982426r_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(718,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( map_ad325961431ar_val @ A @ ( map_ad325961431ar_val @ B @ C ) )
      = ( map_ad325961431ar_val @ ( map_ad325961431ar_val @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_432_map__add__assoc) ).

thf(4033,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( map_ad325961431ar_val @ A @ ( map_ad325961431ar_val @ B @ C ) )
      = ( map_ad325961431ar_val @ ( map_ad325961431ar_val @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).

thf(498,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ A ) @ B )
        = ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_Pair__inject) ).

thf(3189,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ A ) @ B )
        = ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(268,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P1402001845l_bool @ ( hAPP_f379976829l_bool @ ( hAPP_f606945057l_bool @ cOMBB_705522285on_val @ A ) @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_P282169671l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_064) ).

thf(2281,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P1402001845l_bool @ ( hAPP_f379976829l_bool @ ( hAPP_f606945057l_bool @ cOMBB_705522285on_val @ A ) @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_P282169671l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(1044,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( red @ F ) ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ D @ A ) ) @ E ) ) ) @ ( reds @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1162_red__reds_OListRed1) ).

thf(5246,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( red @ F ) ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ D @ A ) ) @ E ) ) ) @ ( reds @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).

thf(624,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( throw_list_char @ B ) @ C ) @ D ) @ E ) )
     => ( ! [F: $i] :
            ( ( D
              = ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) )
           => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ C ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ E ) ) )
       => ( ( ( D
              = ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) )
           => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ C ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ E ) ) )
         => ~ ! [F: $i] :
                ( ( D
                  = ( throw_list_char @ F ) )
               => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ C ) @ ( throw_list_char @ F ) ) @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1052_eval__cases_I12_J) ).

thf(3676,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( throw_list_char @ B ) @ C ) @ D ) @ E ) )
     => ( ! [F: $i] :
            ( ( D
              = ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) )
           => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ C ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ E ) ) )
       => ( ( ( D
              = ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) )
           => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ C ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ E ) ) )
         => ~ ! [F: $i] :
                ( ( D
                  = ( throw_list_char @ F ) )
               => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ C ) @ ( throw_list_char @ F ) ) @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(1191,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( hBOOL @ ( hAPP_f1734260017l_bool @ ( hAPP_P53416969l_bool @ member894971540t_char @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f1734260017l_bool @ ( hAPP_P53416969l_bool @ member894971540t_char @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_pred__equals__eq2) ).

thf(5846,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f1734260017l_bool @ ( hAPP_P53416969l_bool @ member894971540t_char @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1734260017l_bool @ ( hAPP_P53416969l_bool @ member894971540t_char @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1734260017l_bool @ ( hAPP_P53416969l_bool @ member894971540t_char @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1734260017l_bool @ ( hAPP_P53416969l_bool @ member894971540t_char @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f1734260017l_bool @ ( hAPP_P53416969l_bool @ member894971540t_char @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1734260017l_bool @ ( hAPP_P53416969l_bool @ member894971540t_char @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1734260017l_bool @ ( hAPP_P53416969l_bool @ member894971540t_char @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1734260017l_bool @ ( hAPP_P53416969l_bool @ member894971540t_char @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).

thf(1059,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
     => ( ( hBOOL @ ( final_list_char @ G ) )
       => ( ( F
            = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ ( fun_up1149430426on_val @ C @ D @ none_val ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ D @ A @ E ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ D @ ( hAPP_l207779698on_val @ C @ D ) ) ) ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_663_BlockRedsFinal) ).

thf(5321,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
     => ( ( hBOOL @ ( final_list_char @ G ) )
       => ( ( F
            = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ ( fun_up1149430426on_val @ C @ D @ none_val ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ D @ A @ E ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ D @ ( hAPP_l207779698on_val @ C @ D ) ) ) ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).

thf(793,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( hAPP_l512744617ion_ty @ E @ F )
        = ( hAPP_ty_option_ty @ some_ty @ G ) )
     => ( ( hBOOL @ ( wTrt_1 @ A @ B @ E @ C @ D ) )
       => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ A ) @ D ) @ G ) )
         => ( hBOOL @ ( wTrt_1 @ A @ B @ E @ ( lAss_list_char @ F @ C ) @ void ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_589_WTrtLAss) ).

thf(4307,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( hAPP_l512744617ion_ty @ E @ F )
        = ( hAPP_ty_option_ty @ some_ty @ G ) )
     => ( ( hBOOL @ ( wTrt_1 @ A @ B @ E @ C @ D ) )
       => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ A ) @ D ) @ G ) )
         => ( hBOOL @ ( wTrt_1 @ A @ B @ E @ ( lAss_list_char @ F @ C ) @ void ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).

thf(183,axiom,
    ! [A: $i] :
      ( ( hBOOL @ ( preallocated @ A ) )
     => ( ( hAPP_val_option_ty @ ( typeof_h @ A ) @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) )
        = ( hAPP_ty_option_ty @ some_ty @ ( hAPP_list_char_ty @ class @ nullPointer ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1016_typeof__NullPointer) ).

thf(2002,plain,
    ! [A: $i] :
      ( ( hBOOL @ ( preallocated @ A ) )
     => ( ( hAPP_val_option_ty @ ( typeof_h @ A ) @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) )
        = ( hAPP_ty_option_ty @ some_ty @ ( hAPP_list_char_ty @ class @ nullPointer ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(642,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( fv @ ( fAss_list_char @ A @ B @ C @ D ) )
      = ( semila919158006r_bool @ ( fv @ A ) @ ( fv @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_895_fv__fvs_Osimps_I8_J) ).

thf(3756,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( fv @ ( fAss_list_char @ A @ B @ C @ D ) )
      = ( semila919158006r_bool @ ( fv @ A ) @ ( fv @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).

thf(1232,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( new_Addr @ F )
        = ( hAPP_nat_option_nat @ some_nat @ G ) )
     => ( ( hBOOL @ ( fields1147507508t_char @ C @ D @ E ) )
       => ( ( B
            = ( fun_up2041264236on_val @ F @ G @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ ( init_fields @ E ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( new_list_char @ D ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ A ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ A ) ) ) ) @ ( red @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1131_red__reds_ORedNew) ).

thf(6021,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( new_Addr @ F )
        = ( hAPP_nat_option_nat @ some_nat @ G ) )
     => ( ( hBOOL @ ( fields1147507508t_char @ C @ D @ E ) )
       => ( ( B
            = ( fun_up2041264236on_val @ F @ G @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ ( init_fields @ E ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( new_list_char @ D ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ A ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ A ) ) ) ) @ ( red @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232]) ).

thf(257,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ B )
        = ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_Pair__inject) ).

thf(2242,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ B )
        = ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(385,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l923073979r_bool @ ( hAPP_f29105311r_bool @ ( hAPP_f953097879r_bool @ cOMBB_672864638t_char @ A ) @ B ) @ C )
      = ( hAPP_f454222487r_bool @ A @ ( hAPP_l1591404153l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J__083) ).

thf(2799,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l923073979r_bool @ ( hAPP_f29105311r_bool @ ( hAPP_f953097879r_bool @ cOMBB_672864638t_char @ A ) @ B ) @ C )
      = ( hAPP_f454222487r_bool @ A @ ( hAPP_l1591404153l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(537,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ A ) @ B )
        = ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_Pair__eq) ).

thf(3327,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ A ) @ B )
          = ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ A ) @ B )
          = ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(888,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ G ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ E ) @ F ) ) ) @ ( reds @ G ) ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ G @ E @ F ) @ A ) @ B ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ G @ C @ D ) @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1145_extend__1__evals) ).

thf(4701,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ G ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ E ) @ F ) ) ) @ ( reds @ G ) ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ G @ E @ F ) @ A ) @ B ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ G @ C @ D ) @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).

thf(374,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ E @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ H ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ ( tryCatch_list_char @ E @ A @ B @ C ) @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ H ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_958_Try) ).

thf(2750,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ E @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ H ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ ( tryCatch_list_char @ E @ A @ B @ C ) @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(37,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( ( is_bop @ C )
         => ( A
           != ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ B ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_prod__cases3) ).

thf(1405,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( ( is_bop @ C )
         => ( A
           != ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ B ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(387,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P1907982426r_bool @ B @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1907982426r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_prod__induct3) ).

thf(2804,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P1907982426r_bool @ B @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1907982426r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(426,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( fun_up204312361on_val @ A @ B @ C )
        = A )
    <=> ( ( hAPP_P2094403585on_val @ A @ B )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_fun__upd__idem__iff) ).

thf(2965,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( fun_up204312361on_val @ A @ B @ C )
          = A )
       => ( ( hAPP_P2094403585on_val @ A @ B )
          = C ) )
      & ( ( ( hAPP_P2094403585on_val @ A @ B )
          = C )
       => ( ( fun_up204312361on_val @ A @ B @ C )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(844,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f1175813647l_bool @ ( hAPP_f47713631l_bool @ ( hAPP_f77033475l_bool @ cOMBC_1317565126l_bool @ A ) @ B ) @ C )
      = ( hAPP_f33142364l_bool @ ( hAPP_f893576377l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It_055) ).

thf(4519,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f1175813647l_bool @ ( hAPP_f47713631l_bool @ ( hAPP_f77033475l_bool @ cOMBC_1317565126l_bool @ A ) @ B ) @ C )
      = ( hAPP_f33142364l_bool @ ( hAPP_f893576377l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).

thf(504,axiom,
    ! [A: $i] :
      ( ! [B: $i] :
          ( A
         != ( hAPP_nat_option_nat @ some_nat @ B ) )
    <=> ( A = none_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_614_not__Some__eq) ).

thf(3211,plain,
    ! [A: $i] :
      ( ( ! [B: $i] :
            ( A
           != ( hAPP_nat_option_nat @ some_nat @ B ) )
       => ( A = none_nat ) )
      & ( ( A = none_nat )
       => ! [B: $i] :
            ( A
           != ( hAPP_nat_option_nat @ some_nat @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(71,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P1235399154l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_) ).

thf(1521,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P1235399154l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(581,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ F @ G ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fTrue ) ) ) @ H ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ B @ H ) @ C ) @ D ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ ( cond_list_char @ F @ B @ A ) @ G ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1098_CondT) ).

thf(3492,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ F @ G ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fTrue ) ) ) @ H ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ B @ H ) @ C ) @ D ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ ( cond_list_char @ F @ B @ A ) @ G ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(367,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( seq_list_char @ A @ B )
     != ( block_list_char @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_585_exp_Osimps_I197_J) ).

thf(2718,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( seq_list_char @ A @ B )
     != ( block_list_char @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(1220,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( hBOOL @ ( hAPP_f1754555101l_bool @ ( hAPP_P1679186017l_bool @ member1337019328on_val @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f1754555101l_bool @ ( hAPP_P1679186017l_bool @ member1337019328on_val @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_pred__equals__eq2) ).

thf(5970,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f1754555101l_bool @ ( hAPP_P1679186017l_bool @ member1337019328on_val @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1754555101l_bool @ ( hAPP_P1679186017l_bool @ member1337019328on_val @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1754555101l_bool @ ( hAPP_P1679186017l_bool @ member1337019328on_val @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1754555101l_bool @ ( hAPP_P1679186017l_bool @ member1337019328on_val @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f1754555101l_bool @ ( hAPP_P1679186017l_bool @ member1337019328on_val @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1754555101l_bool @ ( hAPP_P1679186017l_bool @ member1337019328on_val @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1754555101l_bool @ ( hAPP_P1679186017l_bool @ member1337019328on_val @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1754555101l_bool @ ( hAPP_P1679186017l_bool @ member1337019328on_val @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1220]) ).

thf(175,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P1680401186r_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List) ).

thf(1975,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P1680401186r_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(729,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( new_Addr @ D )
        = none_nat )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( new_list_char @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ C ) ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ outOfMemory ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1130_redp__redsp_ORedNewFail) ).

thf(4082,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( new_Addr @ D )
        = none_nat )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( new_list_char @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ C ) ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ outOfMemory ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).

thf(835,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ C ) @ D ) )
     => ( ( ( hAPP_n546249108on_val @ D @ B )
          = none_P179726773on_val )
       => ( ( hBOOL @ ( hAPP_P1235399154l_bool @ ( oconf_1869808039t_char @ C @ D ) @ A ) )
         => ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ C ) @ ( fun_up2041264236on_val @ D @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_721_hconf__new) ).

thf(4483,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ C ) @ D ) )
     => ( ( ( hAPP_n546249108on_val @ D @ B )
          = none_P179726773on_val )
       => ( ( hBOOL @ ( hAPP_P1235399154l_bool @ ( oconf_1869808039t_char @ C @ D ) @ A ) )
         => ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ C ) @ ( fun_up2041264236on_val @ D @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).

thf(1155,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_938_LAssRedsThrow) ).

thf(5695,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).

thf(416,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ A ) @ B )
        = ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_Pair__eq) ).

thf(2922,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ A ) @ B )
          = ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ A ) @ B )
          = ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(1216,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ ( transi2024712006on_val @ A ) ) @ ( transi2024712006on_val @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_678_rtrancl__mono) ).

thf(5961,plain,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ ( transi2024712006on_val @ A ) ) @ ( transi2024712006on_val @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).

thf(1084,axiom,
    ! [A: $i] :
      ( none_val
     != ( hAPP_val_option_val @ some_val @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_607_option_Osimps_I2_J) ).

thf(5406,plain,
    ! [A: $i] :
      ( none_val
     != ( hAPP_val_option_val @ some_val @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).

thf(600,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hAPP_n546249108on_val @ B @ C )
        = none_P179726773on_val )
     => ( hBOOL @ ( hext @ B @ ( fun_up2041264236on_val @ B @ C @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_717_hext__new) ).

thf(3567,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hAPP_n546249108on_val @ B @ C )
        = none_P179726773on_val )
     => ( hBOOL @ ( hext @ B @ ( fun_up2041264236on_val @ B @ C @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(1020,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B )
        = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_Pair__eq) ).

thf(5167,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B )
          = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B )
          = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).

thf(708,axiom,
    ! [A: $i,B: $i] :
      ( ( addr @ A )
     != ( bool @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1065_val_Osimps_I21_J) ).

thf(3995,plain,
    ! [A: $i,B: $i] :
      ( ( addr @ A )
     != ( bool @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).

thf(212,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l753659065r_bool @ ( hAPP_f2059406941r_bool @ ( hAPP_f108089737r_bool @ cOMBB_2143526097t_char @ A ) @ B ) @ C )
      = ( hAPP_f1766231913r_bool @ A @ ( hAPP_l551544901l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_050) ).

thf(2093,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l753659065r_bool @ ( hAPP_f2059406941r_bool @ ( hAPP_f108089737r_bool @ cOMBB_2143526097t_char @ A ) @ B ) @ C )
      = ( hAPP_f1766231913r_bool @ A @ ( hAPP_l551544901l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(810,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( map_add_list_char_ty @ A @ ( fun_up424764369ion_ty @ B @ C @ ( hAPP_ty_option_ty @ some_ty @ D ) ) )
      = ( fun_up424764369ion_ty @ ( map_add_list_char_ty @ A @ B ) @ C @ ( hAPP_ty_option_ty @ some_ty @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_516_map__add__upd) ).

thf(4370,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( map_add_list_char_ty @ A @ ( fun_up424764369ion_ty @ B @ C @ ( hAPP_ty_option_ty @ some_ty @ D ) ) )
      = ( fun_up424764369ion_ty @ ( map_add_list_char_ty @ A @ B ) @ C @ ( hAPP_ty_option_ty @ some_ty @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).

thf(947,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_455_splitD) ).

thf(4910,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).

thf(952,axiom,
    ! [A: $i,B: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ A ) ) @ ( transi2024712006on_val @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_661_rtrancl_Ortrancl__refl) ).

thf(4925,plain,
    ! [A: $i,B: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ A ) ) @ ( transi2024712006on_val @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).

thf(585,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_prod_Oexhaust) ).

thf(3503,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(767,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1361600383r_bool @ ( hAPP_f344506159r_bool @ ( hAPP_f447563647r_bool @ cOMBC_389248878r_bool @ A ) @ B ) @ C )
      = ( hAPP_f335969926r_bool @ ( hAPP_l1335043179r_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_036) ).

thf(4199,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1361600383r_bool @ ( hAPP_f344506159r_bool @ ( hAPP_f447563647r_bool @ cOMBC_389248878r_bool @ A ) @ B ) @ C )
      = ( hAPP_f335969926r_bool @ ( hAPP_l1335043179r_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).

thf(869,axiom,
    ! [A: $i] :
      ( null
     != ( bool @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1070_val_Osimps_I12_J) ).

thf(4629,plain,
    ! [A: $i] :
      ( null
     != ( bool @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).

thf(1167,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_454_splitD) ).

thf(5751,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).

thf(664,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( D != E )
     => ( ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ A @ D @ B ) @ E @ C )
        = ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ A @ E @ C ) @ D @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_fun__upd__twist) ).

thf(3852,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( D != E )
     => ( ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ A @ D @ B ) @ E @ C )
        = ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ A @ E @ C ) @ D @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(17,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_prod__cases3) ).

thf(1306,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(848,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ C @ D ) @ E ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ ( lAss_list_char @ A @ C ) @ D ) @ ( lAss_list_char @ A @ E ) ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_624_redp__redsp_OLAssRed) ).

thf(4531,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ C @ D ) @ E ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ ( lAss_list_char @ A @ C ) @ D ) @ ( lAss_list_char @ A @ E ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).

thf(281,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( C = D )
       => ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ D @ B ) @ C )
          = B ) )
      & ( ( C != D )
       => ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ D @ B ) @ C )
          = ( hAPP_P2094403585on_val @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_fun__upd__apply) ).

thf(2364,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( C = D )
       => ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ D @ B ) @ C )
          = B ) )
      & ( ( C != D )
       => ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ D @ B ) @ C )
          = ( hAPP_P2094403585on_val @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(232,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ E ) @ F ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( call_list_char @ D @ A @ B ) @ E ) @ ( call_list_char @ F @ A @ B ) ) @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1137_redp__redsp_OCallObj) ).

thf(2164,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ E ) @ F ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( call_list_char @ D @ A @ B ) @ E ) @ ( call_list_char @ F @ A @ B ) ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(1156,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ ( hAPP_f2036784149l_bool @ ( hAPP_f1720452391l_bool @ cOMBC_1021753250l_bool @ member773094996on_val ) @ A ) ) @ ( hAPP_f2036784149l_bool @ ( hAPP_f1720452391l_bool @ cOMBC_1021753250l_bool @ member773094996on_val ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_603_pred__subset__eq) ).

thf(5697,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ ( hAPP_f2036784149l_bool @ ( hAPP_f1720452391l_bool @ cOMBC_1021753250l_bool @ member773094996on_val ) @ A ) ) @ ( hAPP_f2036784149l_bool @ ( hAPP_f1720452391l_bool @ cOMBC_1021753250l_bool @ member773094996on_val ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ ( hAPP_f2036784149l_bool @ ( hAPP_f1720452391l_bool @ cOMBC_1021753250l_bool @ member773094996on_val ) @ A ) ) @ ( hAPP_f2036784149l_bool @ ( hAPP_f1720452391l_bool @ cOMBC_1021753250l_bool @ member773094996on_val ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).

thf(497,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l24694616r_bool @ ( hAPP_f306469557r_bool @ ( hAPP_f197435839r_bool @ cOMBC_886773442r_bool @ A ) @ B ) @ C )
      = ( hAPP_f605643693r_bool @ ( hAPP_l1129005983r_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String___056) ).

thf(3186,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l24694616r_bool @ ( hAPP_f306469557r_bool @ ( hAPP_f197435839r_bool @ cOMBC_886773442r_bool @ A ) @ B ) @ C )
      = ( hAPP_f605643693r_bool @ ( hAPP_l1129005983r_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(1192,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( d_list_char @ ( lAss_list_char @ A @ B ) @ C ) )
    <=> ( hBOOL @ ( d_list_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_568__092_060D_062___092_060D_062s_Osimps_I6_J) ).

thf(5862,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hBOOL @ ( d_list_char @ ( lAss_list_char @ A @ B ) @ C ) )
       => ( hBOOL @ ( d_list_char @ B @ C ) ) )
      & ( ( hBOOL @ ( d_list_char @ B @ C ) )
       => ( hBOOL @ ( d_list_char @ ( lAss_list_char @ A @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).

thf(272,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ A ) @ B ) @ C ) @ D ) )
    <=> ! [E: $i,F: $i] :
          ( ( ( hAPP_l207779698on_val @ C @ E )
            = ( hAPP_val_option_val @ some_val @ F ) )
         => ? [G: $i] :
              ( ( ( hAPP_l512744617ion_ty @ D @ E )
                = ( hAPP_ty_option_ty @ some_ty @ G ) )
              & ( hBOOL @ ( conf_P373316194t_char @ A @ B @ F @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_554_lconf__def) ).

thf(2307,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ A ) @ B ) @ C ) @ D ) )
       => ! [E: $i,F: $i] :
            ( ( ( hAPP_l207779698on_val @ C @ E )
              = ( hAPP_val_option_val @ some_val @ F ) )
           => ? [G: $i] :
                ( ( ( hAPP_l512744617ion_ty @ D @ E )
                  = ( hAPP_ty_option_ty @ some_ty @ G ) )
                & ( hBOOL @ ( conf_P373316194t_char @ A @ B @ F @ G ) ) ) ) )
      & ( ! [E: $i,F: $i] :
            ( ( ( hAPP_l207779698on_val @ C @ E )
              = ( hAPP_val_option_val @ some_val @ F ) )
           => ? [G: $i] :
                ( ( ( hAPP_l512744617ion_ty @ D @ E )
                  = ( hAPP_ty_option_ty @ some_ty @ G ) )
                & ( hBOOL @ ( conf_P373316194t_char @ A @ B @ F @ G ) ) ) )
       => ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ A ) @ B ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(209,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f570766339l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt) ).

thf(2083,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f570766339l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(795,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( is_bool @ ( wTrt_1 @ A @ B @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_WellTypeRT_OWTrt) ).

thf(4312,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( is_bool @ ( wTrt_1 @ A @ B @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).

thf(724,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) @ ( transi374442731on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ A ) ) @ D ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ A ) ) @ ( transi374442731on_val @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_726_rtrancl_Ortrancl__into__rtrancl) ).

thf(4059,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) @ ( transi374442731on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ A ) ) @ D ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ A ) ) @ ( transi374442731on_val @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).

thf(411,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_f1634841927l_bool @ produc1491230096l_bool @ A ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_415_splitI) ).

thf(2905,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_f1634841927l_bool @ produc1491230096l_bool @ A ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(147,axiom,
    c_Expr_Obop_OEq != add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1082_bop_Osimps_I1_J) ).

thf(1868,plain,
    c_Expr_Obop_OEq != add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(203,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( preallocated @ B ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ sys_xcpts ) )
       => ? [C: $i] :
            ( ( hAPP_n546249108on_val @ B @ ( addr_of_sys_xcpt @ A ) )
            = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1075_preallocatedD) ).

thf(2061,plain,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( preallocated @ B ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ sys_xcpts ) )
       => ? [C: $i] :
            ( ( hAPP_n546249108on_val @ B @ ( addr_of_sys_xcpt @ A ) )
            = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(759,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ E ) ) )
        = ( hAPP_val_option_val @ some_val @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ D ) @ C @ ( hAPP_v834067052t_char @ val_list_char @ E ) ) @ B ) @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1001_redp__redsp_ORedBinOp) ).

thf(4172,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ E ) ) )
        = ( hAPP_val_option_val @ some_val @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ D ) @ C @ ( hAPP_v834067052t_char @ val_list_char @ E ) ) @ B ) @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).

thf(379,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_t1875766236har_ty @ ( hAPP_l1948972481har_ty @ produc251930284har_ty @ A ) @ B )
        = ( hAPP_t1875766236har_ty @ ( hAPP_l1948972481har_ty @ produc251930284har_ty @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_Pair__eq) ).

thf(2773,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_t1875766236har_ty @ ( hAPP_l1948972481har_ty @ produc251930284har_ty @ A ) @ B )
          = ( hAPP_t1875766236har_ty @ ( hAPP_l1948972481har_ty @ produc251930284har_ty @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_t1875766236har_ty @ ( hAPP_l1948972481har_ty @ produc251930284har_ty @ A ) @ B )
          = ( hAPP_t1875766236har_ty @ ( hAPP_l1948972481har_ty @ produc251930284har_ty @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(975,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B )
        = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_Pair__inject) ).

thf(4999,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B )
        = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).

thf(182,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P1240100515r_bool @ B @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ C ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P1240100515r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_prod__induct4) ).

thf(2000,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P1240100515r_bool @ B @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ C ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P1240100515r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(102,axiom,
    is_bop @ c_Expr_Obop_OEq,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Expr_Obop_OEq) ).

thf(1636,plain,
    is_bop @ c_Expr_Obop_OEq,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(8,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ E ) ) ) @ ( transi1257872013t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ B ) @ C ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ G ) @ H ) ) ) @ ( transi1257872013t_char @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ G ) @ H ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_780_rtrancl__induct2) ).

thf(1274,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ E ) ) ) @ ( transi1257872013t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ B ) @ C ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ G ) @ H ) ) ) @ ( transi1257872013t_char @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ G ) @ H ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(988,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ F ) )
     => ( ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ F ) @ E ) )
       => ( ( hBOOL @ ( wTrt_1 @ F @ E @ B @ C @ D ) )
         => ( ( hBOOL @ ( d_list_char @ C @ ( hAPP_f363827556r_bool @ some_f80346385r_bool @ ( dom_list_char_val @ A ) ) ) )
           => ( ~ ( hBOOL @ ( final_list_char @ C ) )
             => ? [G: $i,H: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ A ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ H ) ) ) @ ( red @ F ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_789_progress) ).

thf(5049,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ F ) )
     => ( ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ F ) @ E ) )
       => ( ( hBOOL @ ( wTrt_1 @ F @ E @ B @ C @ D ) )
         => ( ( hBOOL @ ( d_list_char @ C @ ( hAPP_f363827556r_bool @ some_f80346385r_bool @ ( dom_list_char_val @ A ) ) ) )
           => ( ~ ( hBOOL @ ( final_list_char @ C ) )
             => ? [G: $i,H: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ A ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ H ) ) ) @ ( red @ F ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).

thf(363,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P159683425l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It) ).

thf(2705,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P159683425l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(156,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ B ) @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_prod__cases3) ).

thf(1900,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ B ) @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(1254,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_split__paired__All) ).

thf(6124,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1254]) ).

thf(1113,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( red @ E ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ C ) ) @ D ) ) ) @ ( red @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_925_red__reds_OThrowRed) ).

thf(5512,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( red @ E ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ C ) ) @ D ) ) ) @ ( red @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).

thf(1046,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_740_subsetI) ).

thf(5266,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).

thf(908,axiom,
    ~ ( hBOOL @ fFalse ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).

thf(4785,plain,
    ~ ( hBOOL @ fFalse ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).

thf(754,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ F @ G ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fFalse ) ) ) @ H ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ B @ H ) @ C ) @ D ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ ( cond_list_char @ F @ A @ B ) @ G ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1097_CondF) ).

thf(4160,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ F @ G ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fFalse ) ) ) @ H ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ B @ H ) @ C ) @ D ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ ( cond_list_char @ F @ A @ B ) @ G ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).

thf(1246,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_split__paired__All) ).

thf(6079,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1246]) ).

thf(1253,axiom,
    ! [A: $i] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) )
      | ~ ( hBOOL @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).

thf(6122,plain,
    ! [A: $i] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) )
      | ~ ( hBOOL @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253]) ).

thf(1141,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f1795246582l_bool @ ( ord_le735260024r_bool @ ( hAPP_f2025561243r_bool @ ( hAPP_f1500560577r_bool @ cOMBC_1784597444r_bool @ ( hAPP_f29105311r_bool @ ( hAPP_f953097879r_bool @ cOMBB_672864638t_char @ cOMBC_1338332465l_bool ) @ ( hAPP_f333583909l_bool @ ( hAPP_f1407048615l_bool @ cOMBB_741416308t_char @ ( hAPP_f937861397l_bool @ cOMBB_1520154591t_char @ member1467889965t_char ) ) @ produc822965838t_char ) ) ) @ A ) ) @ ( hAPP_f2025561243r_bool @ ( hAPP_f1500560577r_bool @ cOMBC_1784597444r_bool @ ( hAPP_f29105311r_bool @ ( hAPP_f953097879r_bool @ cOMBB_672864638t_char @ cOMBC_1338332465l_bool ) @ ( hAPP_f333583909l_bool @ ( hAPP_f1407048615l_bool @ cOMBB_741416308t_char @ ( hAPP_f937861397l_bool @ cOMBB_1520154591t_char @ member1467889965t_char ) ) @ produc822965838t_char ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_801_pred__subset__eq2) ).

thf(5630,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( hAPP_f1795246582l_bool @ ( ord_le735260024r_bool @ ( hAPP_f2025561243r_bool @ ( hAPP_f1500560577r_bool @ cOMBC_1784597444r_bool @ ( hAPP_f29105311r_bool @ ( hAPP_f953097879r_bool @ cOMBB_672864638t_char @ cOMBC_1338332465l_bool ) @ ( hAPP_f333583909l_bool @ ( hAPP_f1407048615l_bool @ cOMBB_741416308t_char @ ( hAPP_f937861397l_bool @ cOMBB_1520154591t_char @ member1467889965t_char ) ) @ produc822965838t_char ) ) ) @ A ) ) @ ( hAPP_f2025561243r_bool @ ( hAPP_f1500560577r_bool @ cOMBC_1784597444r_bool @ ( hAPP_f29105311r_bool @ ( hAPP_f953097879r_bool @ cOMBB_672864638t_char @ cOMBC_1338332465l_bool ) @ ( hAPP_f333583909l_bool @ ( hAPP_f1407048615l_bool @ cOMBB_741416308t_char @ ( hAPP_f937861397l_bool @ cOMBB_1520154591t_char @ member1467889965t_char ) ) @ produc822965838t_char ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1795246582l_bool @ ( ord_le735260024r_bool @ ( hAPP_f2025561243r_bool @ ( hAPP_f1500560577r_bool @ cOMBC_1784597444r_bool @ ( hAPP_f29105311r_bool @ ( hAPP_f953097879r_bool @ cOMBB_672864638t_char @ cOMBC_1338332465l_bool ) @ ( hAPP_f333583909l_bool @ ( hAPP_f1407048615l_bool @ cOMBB_741416308t_char @ ( hAPP_f937861397l_bool @ cOMBB_1520154591t_char @ member1467889965t_char ) ) @ produc822965838t_char ) ) ) @ A ) ) @ ( hAPP_f2025561243r_bool @ ( hAPP_f1500560577r_bool @ cOMBC_1784597444r_bool @ ( hAPP_f29105311r_bool @ ( hAPP_f953097879r_bool @ cOMBB_672864638t_char @ cOMBC_1338332465l_bool ) @ ( hAPP_f333583909l_bool @ ( hAPP_f1407048615l_bool @ cOMBB_741416308t_char @ ( hAPP_f937861397l_bool @ cOMBB_1520154591t_char @ member1467889965t_char ) ) @ produc822965838t_char ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).

thf(371,axiom,
    ! [A: $i] :
      ( ( is_bool @ A )
     => ( ( A = fTrue )
        | ( A = fFalse ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).

thf(2733,plain,
    ! [A: $i] :
      ( ( is_bool @ A )
     => ( ( A = fTrue )
        | ( A = fFalse ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(259,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( map_ad61982421on_val @ A @ ( fun_up2041264236on_val @ B @ C @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ D ) ) )
      = ( fun_up2041264236on_val @ ( map_ad61982421on_val @ A @ B ) @ C @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_515_map__add__upd) ).

thf(2249,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( map_ad61982421on_val @ A @ ( fun_up2041264236on_val @ B @ C @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ D ) ) )
      = ( fun_up2041264236on_val @ ( map_ad61982421on_val @ A @ B ) @ C @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(1225,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ D @ A @ B @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ F @ A @ B @ C ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_969_TryReds) ).

thf(6000,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ D @ A @ B @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ F @ A @ B @ C ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225]) ).

thf(670,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P1333315679l_bool @ B @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1333315679l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_prod__induct3) ).

thf(3867,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P1333315679l_bool @ B @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1333315679l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).

thf(818,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ D @ E ) @ ( throw_list_char @ F ) ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( cond_list_char @ D @ A @ B ) @ E ) @ ( throw_list_char @ F ) ) @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1093_eval__evals_OCondThrow) ).

thf(4397,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ D @ E ) @ ( throw_list_char @ F ) ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( cond_list_char @ D @ A @ B ) @ E ) @ ( throw_list_char @ F ) ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).

thf(950,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( ( size_s2113983095t_char @ I )
        = ( size_size_list_ty @ J ) )
     => ( ( ( size_size_list_val @ H )
          = ( size_size_list_ty @ J ) )
       => ( ( hBOOL @ ( distinct_list_char @ I ) )
         => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ ( map_up1085636310ar_val @ C @ I @ H ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
           => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ I ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ J ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ H ) @ A ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ I ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ J ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ ( map_list_char_val @ ( comp_o1129292306t_char @ the_val @ F ) @ I ) ) @ D ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ ( overri2012515291on_val @ F @ C @ ( set_list_char @ I ) ) ) ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1199_blocksReds) ).

thf(4920,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( ( size_s2113983095t_char @ I )
        = ( size_size_list_ty @ J ) )
     => ( ( ( size_size_list_val @ H )
          = ( size_size_list_ty @ J ) )
       => ( ( hBOOL @ ( distinct_list_char @ I ) )
         => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ ( map_up1085636310ar_val @ C @ I @ H ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
           => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ I ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ J ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ H ) @ A ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ I ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ J ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ ( map_list_char_val @ ( comp_o1129292306t_char @ the_val @ F ) @ I ) ) @ D ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ ( overri2012515291on_val @ F @ C @ ( set_list_char @ I ) ) ) ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).

thf(1235,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ F @ ( hAPP_val_option_val @ some_val @ G ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ H ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) ) ) @ ( red @ K ) ) )
     => ( ( ( hAPP_l207779698on_val @ J @ F )
          = ( hAPP_val_option_val @ some_val @ B ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ F @ A @ ( seq_list_char @ ( lAss_list_char @ F @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ C ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ F @ A @ ( seq_list_char @ ( lAss_list_char @ F @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ H ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ ( fun_up1149430426on_val @ J @ F @ ( hAPP_l207779698on_val @ E @ F ) ) ) ) ) ) @ ( red @ K ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_465_red__reds_OInitBlockRed) ).

thf(6032,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ F @ ( hAPP_val_option_val @ some_val @ G ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ H ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) ) ) @ ( red @ K ) ) )
     => ( ( ( hAPP_l207779698on_val @ J @ F )
          = ( hAPP_val_option_val @ some_val @ B ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ F @ A @ ( seq_list_char @ ( lAss_list_char @ F @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ C ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ F @ A @ ( seq_list_char @ ( lAss_list_char @ F @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ H ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ ( fun_up1149430426on_val @ J @ F @ ( hAPP_l207779698on_val @ E @ F ) ) ) ) ) ) @ ( red @ K ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235]) ).

thf(812,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P609938901l_bool @ ( hAPP_f2095325577l_bool @ ( hAPP_f1135930489l_bool @ cOMBB_1223415373on_val @ A ) @ B ) @ C )
      = ( hAPP_f961387813l_bool @ A @ ( hAPP_P527298901l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc___084) ).

thf(4375,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P609938901l_bool @ ( hAPP_f2095325577l_bool @ ( hAPP_f1135930489l_bool @ cOMBB_1223415373on_val @ A ) @ B ) @ C )
      = ( hAPP_f961387813l_bool @ A @ ( hAPP_P527298901l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).

thf(1180,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ B @ C ) @ D ) )
        <=> ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) )
     => ( ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ B )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_558_cond__split__eta) ).

thf(5794,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ B @ C ) @ D ) )
           => ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) )
          & ( ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) )
           => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ B @ C ) @ D ) ) ) )
     => ( ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).

thf(862,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( B
            = ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ C ) @ D ) ) )
     => ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_f1634841927l_bool @ produc1491230096l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_544_splitI2) ).

thf(4609,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( B
            = ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ C ) @ D ) ) )
     => ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_f1634841927l_bool @ produc1491230096l_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).

thf(1068,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P504978887l_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P504978887l_bool @ A @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_split__paired__All) ).

thf(5349,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P504978887l_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P504978887l_bool @ A @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P504978887l_bool @ A @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P504978887l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).

thf(781,axiom,
    ! [A: $i,B: $i] :
      ( ( fun_up2041264236on_val @ A @ B @ ( hAPP_n546249108on_val @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_fun__upd__triv) ).

thf(4252,plain,
    ! [A: $i,B: $i] :
      ( ( fun_up2041264236on_val @ A @ B @ ( hAPP_n546249108on_val @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).

thf(1185,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ fequal_val @ A ) @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Value__Oval_T) ).

thf(5815,plain,
    ! [A: $i,B: $i] :
      ( ~ ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ fequal_val @ A ) @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).

thf(675,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P1183008383l_bool @ ( hAPP_f447422815l_bool @ ( hAPP_f2052909183l_bool @ cOMBC_766524526l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1317381998l_bool @ ( hAPP_P768428603l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Oli_082) ).

thf(3884,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P1183008383l_bool @ ( hAPP_f447422815l_bool @ ( hAPP_f2052909183l_bool @ cOMBC_766524526l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1317381998l_bool @ ( hAPP_P768428603l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).

thf(420,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( new_Addr @ F )
        = ( hAPP_nat_option_nat @ some_nat @ G ) )
     => ( ( hBOOL @ ( fields1147507508t_char @ C @ D @ E ) )
       => ( ( B
            = ( fun_up2041264236on_val @ F @ G @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ ( init_fields @ E ) ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( new_list_char @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ A ) ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1132_redp__redsp_ORedNew) ).

thf(2937,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( new_Addr @ F )
        = ( hAPP_nat_option_nat @ some_nat @ G ) )
     => ( ( hBOOL @ ( fields1147507508t_char @ C @ D @ E ) )
       => ( ( B
            = ( fun_up2041264236on_val @ F @ G @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ ( init_fields @ E ) ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( new_list_char @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ A ) ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(487,axiom,
    ! [A: $i,B: $i] : ( hBOOL @ ( d_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_582__092_060D_062___092_060D_062s_Osimps_I3_J) ).

thf(3154,plain,
    ! [A: $i,B: $i] : ( hBOOL @ ( d_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(828,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1033709212l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption_002) ).

thf(4449,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1033709212l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).

thf(483,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( wTrts_1 @ A @ B @ C @ ( map_va1934808527t_char @ val_list_char @ D ) @ E ) )
    <=> ( ( map_val_option_ty @ ( typeof_h @ B ) @ D )
        = ( map_ty_option_ty @ some_ty @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1174_WTrts__Val) ).

thf(3134,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( hBOOL @ ( wTrts_1 @ A @ B @ C @ ( map_va1934808527t_char @ val_list_char @ D ) @ E ) )
       => ( ( map_val_option_ty @ ( typeof_h @ B ) @ D )
          = ( map_ty_option_ty @ some_ty @ E ) ) )
      & ( ( ( map_val_option_ty @ ( typeof_h @ B ) @ D )
          = ( map_ty_option_ty @ some_ty @ E ) )
       => ( hBOOL @ ( wTrts_1 @ A @ B @ C @ ( map_va1934808527t_char @ val_list_char @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(999,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_prod_Oexhaust) ).

thf(5085,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).

thf(789,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_702_set__rev__mp) ).

thf(4284,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).

thf(96,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ D ) @ E ) ) ) @ ( transi1789604888t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ D ) @ E ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ G ) @ H ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ I ) @ J ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ D ) @ E ) ) ) @ ( transi1789604888t_char @ F ) ) )
               => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_763_converse__rtrancl__induct2) ).

thf(1619,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ D ) @ E ) ) ) @ ( transi1789604888t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ D ) @ E ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ G ) @ H ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ I ) @ J ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ D ) @ E ) ) ) @ ( transi1789604888t_char @ F ) ) )
               => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(228,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ G @ H ) @ ( hAPP_v834067052t_char @ val_list_char @ I ) ) @ J ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ C @ J ) @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) )
       => ( ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ A ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ I ) @ D ) ) )
            = ( hAPP_val_option_val @ some_val @ B ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ ( binOp_list_char @ G @ A @ C ) @ H ) @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1000_BinOp) ).

thf(2150,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ G @ H ) @ ( hAPP_v834067052t_char @ val_list_char @ I ) ) @ J ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ C @ J ) @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) )
       => ( ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ A ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ I ) @ D ) ) )
            = ( hAPP_val_option_val @ some_val @ B ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ ( binOp_list_char @ G @ A @ C ) @ H ) @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(1250,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i,E: $i] :
          ( A
         != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_prod__cases4) ).

thf(6107,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i,E: $i] :
          ( A
         != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1250]) ).

thf(1005,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( transi2024712006on_val @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: $i] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ D ) ) @ C ) )
             => ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ B ) ) @ ( transi2024712006on_val @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_840_converse__rtranclE) ).

thf(5102,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( transi2024712006on_val @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: $i] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ D ) ) @ C ) )
             => ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ B ) ) @ ( transi2024712006on_val @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).

thf(655,axiom,
    ! [A: $i,B: $i] :
      ( ( fun_up424764369ion_ty @ A @ B @ ( hAPP_l512744617ion_ty @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_fun__upd__triv) ).

thf(3814,plain,
    ! [A: $i,B: $i] :
      ( ( fun_up424764369ion_ty @ A @ B @ ( hAPP_l512744617ion_ty @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).

thf(226,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ A ) @ B )
        = ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_Pair__eq) ).

thf(2132,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ A ) @ B )
          = ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ A ) @ B )
          = ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(927,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1102_CondReds) ).

thf(4836,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).

thf(1204,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_972_BinOp2Reds) ).

thf(5924,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).

thf(152,axiom,
    ! [A: $i,B: $i] :
      ( ( hAPP_l207779698on_val @ ( hAPP_o538043682on_val @ cOMBK_1097134891t_char @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__List__Olis) ).

thf(1883,plain,
    ! [A: $i,B: $i] :
      ( ( hAPP_l207779698on_val @ ( hAPP_o538043682on_val @ cOMBK_1097134891t_char @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(1172,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ ( produc2062775566l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_511_curryD) ).

thf(5769,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ ( produc2062775566l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).

thf(704,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P748443392y_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Type__Oty_J_00) ).

thf(3980,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P748443392y_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).

thf(746,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ ( transi374442731on_val @ A ) ) @ ( transi374442731on_val @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_676_rtrancl__mono) ).

thf(4140,plain,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ ( transi374442731on_val @ A ) ) @ ( transi374442731on_val @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).

thf(355,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( seq_list_char @ ( hAPP_v834067052t_char @ val_list_char @ B ) @ C ) @ D ) @ C ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_638_redp__redsp_ORedSeq) ).

thf(2670,plain,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( seq_list_char @ ( hAPP_v834067052t_char @ val_list_char @ B ) @ C ) @ D ) @ C ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(161,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P824029447r_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String___030) ).

thf(1920,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P824029447r_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(1153,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( lAss_list_char @ B @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ B @ ( hAPP_val_option_val @ some_val @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_592_redp__redsp_ORedLAss) ).

thf(5690,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( lAss_list_char @ B @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ B @ ( hAPP_val_option_val @ some_val @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).

thf(402,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_709_set__mp) ).

thf(2872,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(13,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_e544220455r_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__HOL_) ).

thf(1296,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_e544220455r_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(905,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ A ) @ B )
        = ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Pair__inject) ).

thf(4776,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ A ) @ B )
        = ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).

thf(132,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ A ) @ B )
        = ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_Pair__inject) ).

thf(1787,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ A ) @ B )
        = ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(1032,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_prod__cases3) ).

thf(5201,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).

thf(247,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) @ ( transi374442731on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_P71593144l_bool @ A @ C ) )
       => ( ! [E: $i,F: $i] :
              ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ E ) @ F ) ) @ D ) )
             => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ F ) @ C ) ) @ ( transi374442731on_val @ D ) ) )
               => ( ( hBOOL @ ( hAPP_P71593144l_bool @ A @ F ) )
                 => ( hBOOL @ ( hAPP_P71593144l_bool @ A @ E ) ) ) ) )
         => ( hBOOL @ ( hAPP_P71593144l_bool @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_842_converse__rtrancl__induct) ).

thf(2213,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) @ ( transi374442731on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_P71593144l_bool @ A @ C ) )
       => ( ! [E: $i,F: $i] :
              ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ E ) @ F ) ) @ D ) )
             => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ F ) @ C ) ) @ ( transi374442731on_val @ D ) ) )
               => ( ( hBOOL @ ( hAPP_P71593144l_bool @ A @ F ) )
                 => ( hBOOL @ ( hAPP_P71593144l_bool @ A @ E ) ) ) ) )
         => ( hBOOL @ ( hAPP_P71593144l_bool @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(687,axiom,
    ! [A: $i] :
      ( ( hAPP_o1977518472on_val @ the_Pr431167171on_val @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_687_the_Osimps) ).

thf(3926,plain,
    ! [A: $i] :
      ( ( hAPP_o1977518472on_val @ the_Pr431167171on_val @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).

thf(325,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i,E: $i] :
          ( A
         != ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ B ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_prod__cases4) ).

thf(2547,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i,E: $i] :
          ( A
         != ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ B ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(217,axiom,
    ! [A: $i,B: $i] : ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ A ) ) @ ( transi374442731on_val @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_659_rtrancl_Ortrancl__refl) ).

thf(2112,plain,
    ! [A: $i,B: $i] : ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ A ) ) @ ( transi374442731on_val @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(424,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] : ( hBOOL @ ( hAPP_bool_bool @ ( ord_less_eq_bool @ ( hAPP_list_char_bool @ A @ C ) ) @ ( hAPP_list_char_bool @ B @ C ) ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_846_le__funI) ).

thf(2958,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] : ( hBOOL @ ( hAPP_bool_bool @ ( ord_less_eq_bool @ ( hAPP_list_char_bool @ A @ C ) ) @ ( hAPP_list_char_bool @ B @ C ) ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(532,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l177734933l_bool @ ( hAPP_f1149562121l_bool @ ( hAPP_f1850037271l_bool @ cOMBB_773375802t_char @ A ) @ B ) @ C )
      = ( hAPP_f1467537159l_bool @ A @ ( hAPP_l232580245l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_081) ).

thf(3307,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l177734933l_bool @ ( hAPP_f1149562121l_bool @ ( hAPP_f1850037271l_bool @ cOMBB_773375802t_char @ A ) @ B ) @ C )
      = ( hAPP_f1467537159l_bool @ A @ ( hAPP_l232580245l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(787,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( fAcc_list_char @ ( throw_list_char @ B ) @ C @ D ) @ E ) @ ( throw_list_char @ B ) ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_908_redp__redsp_OFAccThrow) ).

thf(4280,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( fAcc_list_char @ ( throw_list_char @ B ) @ C @ D ) @ E ) @ ( throw_list_char @ B ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).

thf(1081,axiom,
    ! [A: $i] :
      ( ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ ( hAPP_f1363667773l_bool @ ( hAPP_f1050935001l_bool @ cOMBB_1153617344on_val @ ( hAPP_f2057883639l_bool @ cOMBB_1750801836on_val @ A ) ) @ produc899768717on_val ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_479_split__eta) ).

thf(5391,plain,
    ! [A: $i] :
      ( ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ ( hAPP_f1363667773l_bool @ ( hAPP_f1050935001l_bool @ cOMBB_1153617344on_val @ ( hAPP_f2057883639l_bool @ cOMBB_1750801836on_val @ A ) ) @ produc899768717on_val ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).

thf(1157,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_split__paired__All) ).

thf(5702,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).

thf(892,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P2028292026l_bool @ ( hAPP_f921434893l_bool @ ( hAPP_f693085049l_bool @ cOMBB_147773915t_char @ A ) @ B ) @ C )
      = ( hAPP_P1198052655l_bool @ A @ ( hAPP_P1392904962t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc) ).

thf(4725,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P2028292026l_bool @ ( hAPP_f921434893l_bool @ ( hAPP_f693085049l_bool @ cOMBB_147773915t_char @ A ) @ B ) @ C )
      = ( hAPP_P1198052655l_bool @ A @ ( hAPP_P1392904962t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).

thf(330,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i,E: $i] :
          ( ( is_bop @ C )
         => ( A
           != ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ B ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_prod__cases4) ).

thf(2565,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i,E: $i] :
          ( ( is_bop @ C )
         => ( A
           != ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ B ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(1239,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( hBOOL @ ( hAPP_f983152497l_bool @ ( hAPP_P1953134729l_bool @ member781783252on_val @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f983152497l_bool @ ( hAPP_P1953134729l_bool @ member781783252on_val @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_pred__equals__eq2) ).

thf(6043,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f983152497l_bool @ ( hAPP_P1953134729l_bool @ member781783252on_val @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f983152497l_bool @ ( hAPP_P1953134729l_bool @ member781783252on_val @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f983152497l_bool @ ( hAPP_P1953134729l_bool @ member781783252on_val @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f983152497l_bool @ ( hAPP_P1953134729l_bool @ member781783252on_val @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f983152497l_bool @ ( hAPP_P1953134729l_bool @ member781783252on_val @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f983152497l_bool @ ( hAPP_P1953134729l_bool @ member781783252on_val @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f983152497l_bool @ ( hAPP_P1953134729l_bool @ member781783252on_val @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f983152497l_bool @ ( hAPP_P1953134729l_bool @ member781783252on_val @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1239]) ).

thf(752,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f1492320500l_bool @ ( hAPP_f1523875321l_bool @ ( hAPP_f592397849l_bool @ cOMBB_1718333400on_val @ A ) @ B ) @ C )
      = ( hAPP_f1863694447l_bool @ A @ ( hAPP_f1145256474l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc) ).

thf(4155,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f1492320500l_bool @ ( hAPP_f1523875321l_bool @ ( hAPP_f592397849l_bool @ cOMBB_1718333400on_val @ A ) @ B ) @ C )
      = ( hAPP_f1863694447l_bool @ A @ ( hAPP_f1145256474l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).

thf(392,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_b97269396l_bool @ ( hAPP_f257113085l_bool @ ( hAPP_f1100052969l_bool @ cOMBC_199425070l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1335946228l_bool @ ( hAPP_b1257035143l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Expr__Obop_000tc__fun_Itc__prod_Itc__Expr__Obop_Mtc_) ).

thf(2820,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_b97269396l_bool @ ( hAPP_f257113085l_bool @ ( hAPP_f1100052969l_bool @ cOMBC_199425070l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1335946228l_bool @ ( hAPP_b1257035143l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(457,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l146377954l_bool @ ( hAPP_f844901525l_bool @ ( hAPP_f348508809l_bool @ cOMBC_622308798l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1526206996l_bool @ ( hAPP_l177734933l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__St) ).

thf(3065,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l146377954l_bool @ ( hAPP_f844901525l_bool @ ( hAPP_f348508809l_bool @ cOMBC_622308798l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1526206996l_bool @ ( hAPP_l177734933l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(640,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( ( ( hAPP_n546249108on_val @ ( hp @ G ) @ F )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) )
       => ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ A ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ H ) ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ D ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) ) ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_999_CastRedsFail) ).

thf(3750,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( ( ( hAPP_n546249108on_val @ ( hp @ G ) @ F )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) )
       => ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ A ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ H ) ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ D ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) ) ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(596,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( D != E )
     => ( ( fun_up204312361on_val @ ( fun_up204312361on_val @ A @ D @ B ) @ E @ C )
        = ( fun_up204312361on_val @ ( fun_up204312361on_val @ A @ E @ C ) @ D @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_fun__upd__twist) ).

thf(3556,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( D != E )
     => ( ( fun_up204312361on_val @ ( fun_up204312361on_val @ A @ D @ B ) @ E @ C )
        = ( fun_up204312361on_val @ ( fun_up204312361on_val @ A @ E @ C ) @ D @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(1222,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_700_in__mono) ).

thf(5988,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222]) ).

thf(1175,axiom,
    hBOOL @ ( wTrt_1 @ p @ ha @ e @ ( block_list_char @ v_1 @ t_1 @ ( seq_list_char @ ( lAss_list_char @ v_1 @ ( hAPP_v834067052t_char @ val_list_char @ v ) ) @ ea ) ) @ t ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_InitBlockRed_I5_J) ).

thf(5779,plain,
    hBOOL @ ( wTrt_1 @ p @ ha @ e @ ( block_list_char @ v_1 @ t_1 @ ( seq_list_char @ ( lAss_list_char @ v_1 @ ( hAPP_v834067052t_char @ val_list_char @ v ) ) @ ea ) ) @ t ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).

thf(97,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ B ) @ C ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ D ) @ E ) ) ) @ ( transi198989188t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ D ) @ E ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ G ) @ H ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ I ) @ J ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ D ) @ E ) ) ) @ ( transi198989188t_char @ F ) ) )
               => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_759_converse__rtrancl__induct2) ).

thf(1624,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ B ) @ C ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ D ) @ E ) ) ) @ ( transi198989188t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ D ) @ E ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ G ) @ H ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ I ) @ J ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ D ) @ E ) ) ) @ ( transi198989188t_char @ F ) ) )
               => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(1257,axiom,
    ! [A: $i,B: $i] :
      ( ( ( is_fun1083000568p_bool @ A )
        & ( is_fun1083000568p_bool @ B ) )
     => ( ! [C: $i,D: $i] :
            ( ( ( is_bop @ C )
              & ( is_bop @ D ) )
           => ( ( hBOOL @ ( hAPP_f1854361213l_bool @ ( hAPP_P1034346913l_bool @ member978285664op_bop @ ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) ) @ B ) )
            <=> ( hBOOL @ ( hAPP_f1854361213l_bool @ ( hAPP_P1034346913l_bool @ member978285664op_bop @ ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) ) @ A ) ) ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_pred__equals__eq2) ).

thf(6143,plain,
    ! [A: $i,B: $i] :
      ( ( ( is_fun1083000568p_bool @ A )
        & ( is_fun1083000568p_bool @ B ) )
     => ( ( ! [C: $i,D: $i] :
              ( ( ( is_bop @ C )
                & ( is_bop @ D ) )
             => ( ( ( hBOOL @ ( hAPP_f1854361213l_bool @ ( hAPP_P1034346913l_bool @ member978285664op_bop @ ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) ) @ B ) )
                 => ( hBOOL @ ( hAPP_f1854361213l_bool @ ( hAPP_P1034346913l_bool @ member978285664op_bop @ ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) ) @ A ) ) )
                & ( ( hBOOL @ ( hAPP_f1854361213l_bool @ ( hAPP_P1034346913l_bool @ member978285664op_bop @ ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) ) @ A ) )
                 => ( hBOOL @ ( hAPP_f1854361213l_bool @ ( hAPP_P1034346913l_bool @ member978285664op_bop @ ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) ) @ B ) ) ) ) )
         => ( B = A ) )
        & ( ( B = A )
         => ! [C: $i,D: $i] :
              ( ( ( is_bop @ C )
                & ( is_bop @ D ) )
             => ( ( ( hBOOL @ ( hAPP_f1854361213l_bool @ ( hAPP_P1034346913l_bool @ member978285664op_bop @ ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) ) @ B ) )
                 => ( hBOOL @ ( hAPP_f1854361213l_bool @ ( hAPP_P1034346913l_bool @ member978285664op_bop @ ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) ) @ A ) ) )
                & ( ( hBOOL @ ( hAPP_f1854361213l_bool @ ( hAPP_P1034346913l_bool @ member978285664op_bop @ ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) ) @ A ) )
                 => ( hBOOL @ ( hAPP_f1854361213l_bool @ ( hAPP_P1034346913l_bool @ member978285664op_bop @ ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) ) @ B ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1257]) ).

thf(244,axiom,
    ! [A: $i,B: $i] :
      ( ( is_fun1083000568p_bool @ B )
     => ( is_bool @ ( hAPP_f1854361213l_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Obop_Mtc__Expr__Obop_J_Mtc__HOL__Oboo) ).

thf(2200,plain,
    ! [A: $i,B: $i] :
      ( ( is_fun1083000568p_bool @ B )
     => ( is_bool @ ( hAPP_f1854361213l_bool @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(340,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( fAcc_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) @ B @ C ) @ D ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1047_redp__redsp_ORedFAccNull) ).

thf(2609,plain,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( fAcc_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) @ B @ C ) @ D ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(101,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P1907982426r_bool @ ( hAPP_l217977712r_bool @ ( produc1574020101r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P92196306r_bool @ A @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_504_curryD) ).

thf(1634,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P1907982426r_bool @ ( hAPP_l217977712r_bool @ ( produc1574020101r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P92196306r_bool @ A @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(34,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( fAcc_list_char @ D @ E @ F ) @ G ) )
     => ( ! [H: $i] :
            ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ ( hAPP_list_char_ty @ class @ H ) ) )
           => ~ ( hBOOL @ ( hAPP_list_char_bool @ ( has_fi1183600461t_char @ A @ H @ E @ G ) @ F ) ) )
       => ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ nt ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1120_WTrt__elim__cases_I7_J) ).

thf(1392,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( fAcc_list_char @ D @ E @ F ) @ G ) )
     => ( ! [H: $i] :
            ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ ( hAPP_list_char_ty @ class @ H ) ) )
           => ~ ( hBOOL @ ( hAPP_list_char_bool @ ( has_fi1183600461t_char @ A @ H @ E @ G ) @ F ) ) )
       => ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ nt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(623,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ A @ B ) @ C )
        = none_val )
    <=> ( ( ( hAPP_l207779698on_val @ B @ C )
          = none_val )
        & ( ( hAPP_l207779698on_val @ A @ C )
          = none_val ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_631_map__add__None) ).

thf(3667,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ A @ B ) @ C )
          = none_val )
       => ( ( ( hAPP_l207779698on_val @ B @ C )
            = none_val )
          & ( ( hAPP_l207779698on_val @ A @ C )
            = none_val ) ) )
      & ( ( ( ( hAPP_l207779698on_val @ B @ C )
            = none_val )
          & ( ( hAPP_l207779698on_val @ A @ C )
            = none_val ) )
       => ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ A @ B ) @ C )
          = none_val ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(895,axiom,
    ! [A: $i] :
      ( ( hAPP_o285151112r_bool @ the_fu297177755r_bool @ ( hAPP_f363827556r_bool @ some_f80346385r_bool @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_689_the_Osimps) ).

thf(4732,plain,
    ! [A: $i] :
      ( ( hAPP_o285151112r_bool @ the_fu297177755r_bool @ ( hAPP_f363827556r_bool @ some_f80346385r_bool @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).

thf(447,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P1221872711l_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1221872711l_bool @ A @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_split__paired__All) ).

thf(3033,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P1221872711l_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1221872711l_bool @ A @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1221872711l_bool @ A @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P1221872711l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(125,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( hBOOL @ ( hAPP_f1161798306l_bool @ ( hAPP_P1327510541l_bool @ member1379348767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f1161798306l_bool @ ( hAPP_P1327510541l_bool @ member1379348767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_pred__equals__eq2) ).

thf(1740,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f1161798306l_bool @ ( hAPP_P1327510541l_bool @ member1379348767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1161798306l_bool @ ( hAPP_P1327510541l_bool @ member1379348767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1161798306l_bool @ ( hAPP_P1327510541l_bool @ member1379348767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1161798306l_bool @ ( hAPP_P1327510541l_bool @ member1379348767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f1161798306l_bool @ ( hAPP_P1327510541l_bool @ member1379348767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1161798306l_bool @ ( hAPP_P1327510541l_bool @ member1379348767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1161798306l_bool @ ( hAPP_P1327510541l_bool @ member1379348767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1161798306l_bool @ ( hAPP_P1327510541l_bool @ member1379348767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(570,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( block_list_char @ B @ C @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) ) @ E ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_935_redp__redsp_OBlockThrow) ).

thf(3445,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( block_list_char @ B @ C @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) ) @ E ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(1052,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ D @ A @ B @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ F @ A @ B @ C ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_898_FAssReds1) ).

thf(5285,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ D @ A @ B @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ F @ A @ B @ C ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).

thf(993,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ ( produc1159035454l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_497_curryE) ).

thf(5066,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ ( produc1159035454l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).

thf(917,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f1118567467l_bool @ ( ord_le989574145r_bool @ ( hAPP_f1051205629r_bool @ ( hAPP_f987862447r_bool @ cOMBC_1387630958r_bool @ ( hAPP_f1449341487r_bool @ ( hAPP_f1823921107r_bool @ cOMBB_308691073st_val @ cOMBC_818212448l_bool ) @ ( hAPP_f2118054305l_bool @ ( hAPP_f1687138147l_bool @ cOMBB_2078271971st_val @ ( hAPP_f1612138403l_bool @ cOMBB_961360819t_char @ member699351154t_char ) ) @ produc1916172923t_char ) ) ) @ A ) ) @ ( hAPP_f1051205629r_bool @ ( hAPP_f987862447r_bool @ cOMBC_1387630958r_bool @ ( hAPP_f1449341487r_bool @ ( hAPP_f1823921107r_bool @ cOMBB_308691073st_val @ cOMBC_818212448l_bool ) @ ( hAPP_f2118054305l_bool @ ( hAPP_f1687138147l_bool @ cOMBB_2078271971st_val @ ( hAPP_f1612138403l_bool @ cOMBB_961360819t_char @ member699351154t_char ) ) @ produc1916172923t_char ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1314764175l_bool @ ( ord_le1852058257r_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_808_pred__subset__eq2) ).

thf(4808,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( hAPP_f1118567467l_bool @ ( ord_le989574145r_bool @ ( hAPP_f1051205629r_bool @ ( hAPP_f987862447r_bool @ cOMBC_1387630958r_bool @ ( hAPP_f1449341487r_bool @ ( hAPP_f1823921107r_bool @ cOMBB_308691073st_val @ cOMBC_818212448l_bool ) @ ( hAPP_f2118054305l_bool @ ( hAPP_f1687138147l_bool @ cOMBB_2078271971st_val @ ( hAPP_f1612138403l_bool @ cOMBB_961360819t_char @ member699351154t_char ) ) @ produc1916172923t_char ) ) ) @ A ) ) @ ( hAPP_f1051205629r_bool @ ( hAPP_f987862447r_bool @ cOMBC_1387630958r_bool @ ( hAPP_f1449341487r_bool @ ( hAPP_f1823921107r_bool @ cOMBB_308691073st_val @ cOMBC_818212448l_bool ) @ ( hAPP_f2118054305l_bool @ ( hAPP_f1687138147l_bool @ cOMBB_2078271971st_val @ ( hAPP_f1612138403l_bool @ cOMBB_961360819t_char @ member699351154t_char ) ) @ produc1916172923t_char ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f1314764175l_bool @ ( ord_le1852058257r_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1314764175l_bool @ ( ord_le1852058257r_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1118567467l_bool @ ( ord_le989574145r_bool @ ( hAPP_f1051205629r_bool @ ( hAPP_f987862447r_bool @ cOMBC_1387630958r_bool @ ( hAPP_f1449341487r_bool @ ( hAPP_f1823921107r_bool @ cOMBB_308691073st_val @ cOMBC_818212448l_bool ) @ ( hAPP_f2118054305l_bool @ ( hAPP_f1687138147l_bool @ cOMBB_2078271971st_val @ ( hAPP_f1612138403l_bool @ cOMBB_961360819t_char @ member699351154t_char ) ) @ produc1916172923t_char ) ) ) @ A ) ) @ ( hAPP_f1051205629r_bool @ ( hAPP_f987862447r_bool @ cOMBC_1387630958r_bool @ ( hAPP_f1449341487r_bool @ ( hAPP_f1823921107r_bool @ cOMBB_308691073st_val @ cOMBC_818212448l_bool ) @ ( hAPP_f2118054305l_bool @ ( hAPP_f1687138147l_bool @ cOMBB_2078271971st_val @ ( hAPP_f1612138403l_bool @ cOMBB_961360819t_char @ member699351154t_char ) ) @ produc1916172923t_char ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).

thf(1160,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( red @ G ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1139_red__reds_OCallObj) ).

thf(5714,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( red @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).

thf(230,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_option_val_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__HOL__Obool) ).

thf(2157,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_option_val_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(137,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( cast_list_char @ D @ E ) @ F ) )
     => ~ ( ( F
            = ( hAPP_list_char_ty @ class @ D ) )
         => ! [G: $i] :
              ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ E @ G ) )
             => ( ( hBOOL @ ( is_refT @ G ) )
               => ~ ( hBOOL @ ( hAPP_list_char_bool @ ( is_cla570604648t_char @ A ) @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1062_WTrt__elim__cases_I6_J) ).

thf(1804,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( cast_list_char @ D @ E ) @ F ) )
     => ~ ( ( F
            = ( hAPP_list_char_ty @ class @ D ) )
         => ! [G: $i] :
              ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ E @ G ) )
             => ( ( hBOOL @ ( is_refT @ G ) )
               => ~ ( hBOOL @ ( hAPP_list_char_bool @ ( is_cla570604648t_char @ A ) @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(395,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ B ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ B ) @ ( semila1168318597r_bool @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_870_UnCI) ).

thf(2841,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ B ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ B ) @ ( semila1168318597r_bool @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(1142,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( B
            = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ C ) @ D ) ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_551_splitI2) ).

thf(5635,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( B
            = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ C ) @ D ) ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).

thf(64,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ D ) @ E ) ) ) @ ( transi772168185t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ B ) @ C ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ G ) @ H ) ) ) @ ( transi772168185t_char @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ G ) @ H ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_776_rtrancl__induct2) ).

thf(1498,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ D ) @ E ) ) ) @ ( transi772168185t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ B ) @ C ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ G ) @ H ) ) ) @ ( transi772168185t_char @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ G ) @ H ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(78,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P449474095r_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_It) ).

thf(1540,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P449474095r_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(997,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ E ) ) @ F ) ) ) @ ( red @ G ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_965_red__reds_OBinOpRed2) ).

thf(5081,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ E ) ) @ F ) ) ) @ ( red @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).

thf(617,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hext @ D @ E ) )
     => ( ( ( hAPP_n546249108on_val @ D @ A )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) )
       => ? [F: $i] :
            ( ( hAPP_n546249108on_val @ E @ A )
            = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_566_hext__objD) ).

thf(3650,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hext @ D @ E ) )
     => ( ( ( hAPP_n546249108on_val @ D @ A )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) )
       => ? [F: $i] :
            ( ( hAPP_n546249108on_val @ E @ A )
            = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(692,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ ( hAPP_list_char_ty @ class @ E ) ) )
     => ( ( hBOOL @ ( final_list_char @ D ) )
       => ( ! [F: $i] :
              ( D
             != ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) )
         => ~ ! [F: $i] :
                ( D
               != ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_997_final__addrE) ).

thf(3941,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ ( hAPP_list_char_ty @ class @ E ) ) )
     => ( ( hBOOL @ ( final_list_char @ D ) )
       => ( ! [F: $i] :
              ( D
             != ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) )
         => ~ ! [F: $i] :
                ( D
               != ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).

thf(348,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f678833350l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__fun_It) ).

thf(2638,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f678833350l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(569,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ A ) @ B )
        = ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_Pair__inject) ).

thf(3440,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ A ) @ B )
        = ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(471,axiom,
    ! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( throw_list_char @ ( throw_list_char @ B ) ) @ C ) @ ( throw_list_char @ B ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_911_redp__redsp_OThrowThrow) ).

thf(3105,plain,
    ! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( throw_list_char @ ( throw_list_char @ B ) ) @ C ) @ ( throw_list_char @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(647,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( hAPP_val_option_ty @ ( typeof_h @ C ) @ D )
        = ( hAPP_ty_option_ty @ some_ty @ E ) )
     => ( hBOOL @ ( wTrt_1 @ A @ C @ B @ ( hAPP_v834067052t_char @ val_list_char @ D ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1009_WTrtVal) ).

thf(3784,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( hAPP_val_option_ty @ ( typeof_h @ C ) @ D )
        = ( hAPP_ty_option_ty @ some_ty @ E ) )
     => ( hBOOL @ ( wTrt_1 @ A @ C @ B @ ( hAPP_v834067052t_char @ val_list_char @ D ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).

thf(682,axiom,
    ! [A: $i] :
      ( ( addr @ A )
     != unit ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_947_val_Osimps_I11_J) ).

thf(3909,plain,
    ! [A: $i] :
      ( ( addr @ A )
     != unit ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).

thf(611,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( produc1838470831l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P71593144l_bool @ A @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_505_curryD) ).

thf(3615,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( produc1838470831l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P71593144l_bool @ A @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(1013,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ ( produc2062775566l_bool @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_370_curryI) ).

thf(5145,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ ( produc2062775566l_bool @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).

thf(128,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( hBOOL @ ( hAPP_f82569901l_bool @ ( hAPP_P1293136973l_bool @ member1840112042t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f82569901l_bool @ ( hAPP_P1293136973l_bool @ member1840112042t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_pred__equals__eq2) ).

thf(1762,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f82569901l_bool @ ( hAPP_P1293136973l_bool @ member1840112042t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f82569901l_bool @ ( hAPP_P1293136973l_bool @ member1840112042t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f82569901l_bool @ ( hAPP_P1293136973l_bool @ member1840112042t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f82569901l_bool @ ( hAPP_P1293136973l_bool @ member1840112042t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f82569901l_bool @ ( hAPP_P1293136973l_bool @ member1840112042t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f82569901l_bool @ ( hAPP_P1293136973l_bool @ member1840112042t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f82569901l_bool @ ( hAPP_P1293136973l_bool @ member1840112042t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f82569901l_bool @ ( hAPP_P1293136973l_bool @ member1840112042t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(6,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f258424141l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc_) ).

thf(1270,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f258424141l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(1003,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_990_CastReds) ).

thf(5098,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).

thf(3,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_prod_Oexhaust) ).

thf(1259,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(76,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_list_char_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__HOL__Obool) ).

thf(1534,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_list_char_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(170,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ A ) @ B )
        = ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_Pair__inject) ).

thf(1953,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ A ) @ B )
        = ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(738,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P88824722l_bool @ ( hAPP_f1776493709l_bool @ ( hAPP_f810261999l_bool @ cOMBB_1034324152on_val @ A ) @ B ) @ C )
      = ( hAPP_P126004409l_bool @ A @ ( hAPP_P658340954on_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc_) ).

thf(4108,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P88824722l_bool @ ( hAPP_f1776493709l_bool @ ( hAPP_f810261999l_bool @ cOMBB_1034324152on_val @ A ) @ B ) @ C )
      = ( hAPP_P126004409l_bool @ A @ ( hAPP_P658340954on_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).

thf(836,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ C ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) @ E ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( throw_list_char @ B ) @ C ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_926_Throw) ).

thf(4486,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ C ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) @ E ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( throw_list_char @ B ) @ C ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).

thf(1126,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P1926698759r_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1926698759r_bool @ A @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_split__paired__All) ).

thf(5577,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P1926698759r_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1926698759r_bool @ A @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1926698759r_bool @ A @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P1926698759r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).

thf(1110,axiom,
    ! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( throw_list_char @ A ) ) ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ B ) ) ) @ ( red @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_924_red__reds_OThrowThrow) ).

thf(5502,plain,
    ! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( throw_list_char @ A ) ) ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ B ) ) ) @ ( red @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).

thf(174,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ D ) @ E ) ) ) @ ( transi772168185t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ D ) @ E ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ G ) @ H ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ I ) @ J ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ D ) @ E ) ) ) @ ( transi772168185t_char @ F ) ) )
               => ( ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_760_converse__rtrancl__induct2) ).

thf(1970,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ D ) @ E ) ) ) @ ( transi772168185t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ D ) @ E ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ G ) @ H ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ I ) @ J ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ D ) @ E ) ) ) @ ( transi772168185t_char @ F ) ) )
               => ( ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(505,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1845912621l_bool @ ( hAPP_f1868463117l_bool @ ( hAPP_f1365840271l_bool @ cOMBB_1705938036t_char @ A ) @ B ) @ C )
      = ( hAPP_f1239832973l_bool @ A @ ( hAPP_l1388836853t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__070) ).

thf(3218,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1845912621l_bool @ ( hAPP_f1868463117l_bool @ ( hAPP_f1365840271l_bool @ cOMBB_1705938036t_char @ A ) @ B ) @ C )
      = ( hAPP_f1239832973l_bool @ A @ ( hAPP_l1388836853t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(910,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ ( transi2024712006on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ A ) ) @ D ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ A ) ) @ ( transi2024712006on_val @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_728_rtrancl_Ortrancl__into__rtrancl) ).

thf(4789,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ ( transi2024712006on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ A ) ) @ D ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ A ) ) @ ( transi2024712006on_val @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).

thf(470,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_734_subsetI) ).

thf(3102,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(1088,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ ( dom_list_char_val @ C ) ) @ ( dom_list_char_val @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_593_red__lcl__incr) ).

thf(5428,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ ( dom_list_char_val @ C ) ) @ ( dom_list_char_val @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).

thf(477,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ E ) @ F )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ ( transi1065307915t_char @ ( subcls744239332t_char @ C ) ) @ G ) @ D ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( tryCatch_list_char @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ D @ A @ B ) @ E ) @ ( block_list_char @ A @ ( hAPP_list_char_ty @ class @ D ) @ ( seq_list_char @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ B ) ) ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1053_redp__redsp_ORedTryCatch) ).

thf(3119,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ E ) @ F )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ ( transi1065307915t_char @ ( subcls744239332t_char @ C ) ) @ G ) @ D ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( tryCatch_list_char @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ D @ A @ B ) @ E ) @ ( block_list_char @ A @ ( hAPP_list_char_ty @ class @ D ) @ ( seq_list_char @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ B ) ) ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(1074,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P638161699l_bool @ ( hAPP_f762728813l_bool @ ( hAPP_f1510763001l_bool @ cOMBB_565412073on_val @ A ) @ B ) @ C )
      = ( hAPP_P1303341961l_bool @ A @ ( hAPP_P1886180715on_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_) ).

thf(5373,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P638161699l_bool @ ( hAPP_f762728813l_bool @ ( hAPP_f1510763001l_bool @ cOMBB_565412073on_val @ A ) @ B ) @ C )
      = ( hAPP_P1303341961l_bool @ A @ ( hAPP_P1886180715on_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).

thf(639,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_f1634841927l_bool @ produc1491230096l_bool @ A ) @ B ) )
     => ~ ! [C: $i,D: $i] :
            ( ( B
              = ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) )
           => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_528_splitE) ).

thf(3746,plain,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_f1634841927l_bool @ produc1491230096l_bool @ A ) @ B ) )
     => ~ ! [C: $i,D: $i] :
            ( ( B
              = ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) )
           => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(938,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ A ) ) @ ( transi2024712006on_val @ D ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ A ) ) @ ( transi2024712006on_val @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_724_converse__rtrancl__into__rtrancl) ).

thf(4883,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ A ) ) @ ( transi2024712006on_val @ D ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ A ) ) @ ( transi2024712006on_val @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).

thf(1251,axiom,
    ( ( hAPP_l207779698on_val @ l_a @ v_1 )
    = ( hAPP_val_option_val @ some_val @ v_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_InitBlockRed_I3_J) ).

thf(6111,plain,
    ( ( hAPP_l207779698on_val @ l_a @ v_1 )
    = ( hAPP_val_option_val @ some_val @ v_2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251]) ).

thf(461,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f2050077417l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod__013) ).

thf(3078,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f2050077417l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(1108,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) ) @ ( red @ I ) ) )
     => ( ( hBOOL @ ( wTrt_1 @ I @ D @ A @ C @ B ) )
       => ( ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ I ) @ D ) @ E ) @ A ) )
         => ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ I ) @ G ) @ H ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_red__preserves__lconf) ).

thf(5497,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) ) @ ( red @ I ) ) )
     => ( ( hBOOL @ ( wTrt_1 @ I @ D @ A @ C @ B ) )
       => ( ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ I ) @ D ) @ E ) @ A ) )
         => ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ I ) @ G ) @ H ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).

thf(437,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_693_equalityD2) ).

thf(3001,plain,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(456,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ A ) @ B )
        = ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_Pair__inject) ).

thf(3060,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ A ) @ B )
        = ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(920,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( hBOOL @ ( hAPP_o2007402111l_bool @ ( hAPP_o1968908095l_bool @ fequal1937332960on_val @ A ) @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__St) ).

thf(4817,plain,
    ! [A: $i,B: $i] :
      ( ~ ( hBOOL @ ( hAPP_o2007402111l_bool @ ( hAPP_o1968908095l_bool @ fequal1937332960on_val @ A ) @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).

thf(943,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P378063101l_bool @ B @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ C ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P378063101l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_prod__induct3) ).

thf(4898,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P378063101l_bool @ B @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ C ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P378063101l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).

thf(880,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1450446905l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc) ).

thf(4676,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1450446905l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).

thf(798,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( size_s2113983095t_char @ G )
        = ( size_size_list_ty @ H ) )
     => ( ( ( size_size_list_val @ F )
          = ( size_size_list_ty @ H ) )
       => ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ G ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ H ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ F ) @ D ) ) ) ) @ E ) )
        <=> ( ( hBOOL @ ( wTrt_1 @ A @ B @ ( map_up891053837har_ty @ C @ G @ H ) @ D @ E ) )
            & ? [I: $i] :
                ( ( ( map_val_option_ty @ ( typeof_h @ B ) @ F )
                  = ( map_ty_option_ty @ some_ty @ I ) )
                & ( hBOOL @ ( list_all2_ty_ty @ ( widen_2090681816t_char @ A ) @ I @ H ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1190_wt__blocks) ).

thf(4320,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( size_s2113983095t_char @ G )
        = ( size_size_list_ty @ H ) )
     => ( ( ( size_size_list_val @ F )
          = ( size_size_list_ty @ H ) )
       => ( ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ G ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ H ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ F ) @ D ) ) ) ) @ E ) )
           => ( ( hBOOL @ ( wTrt_1 @ A @ B @ ( map_up891053837har_ty @ C @ G @ H ) @ D @ E ) )
              & ? [I: $i] :
                  ( ( ( map_val_option_ty @ ( typeof_h @ B ) @ F )
                    = ( map_ty_option_ty @ some_ty @ I ) )
                  & ( hBOOL @ ( list_all2_ty_ty @ ( widen_2090681816t_char @ A ) @ I @ H ) ) ) ) )
          & ( ( ( hBOOL @ ( wTrt_1 @ A @ B @ ( map_up891053837har_ty @ C @ G @ H ) @ D @ E ) )
              & ? [I: $i] :
                  ( ( ( map_val_option_ty @ ( typeof_h @ B ) @ F )
                    = ( map_ty_option_ty @ some_ty @ I ) )
                  & ( hBOOL @ ( list_all2_ty_ty @ ( widen_2090681816t_char @ A ) @ I @ H ) ) ) )
           => ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ G ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ H ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ F ) @ D ) ) ) ) @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).

thf(800,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_819_order__trans) ).

thf(4333,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).

thf(190,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wTrt @ C @ D @ E @ F @ G ) )
     => ( ( hBOOL @ ( wTrt @ C @ D @ E @ A @ B ) )
       => ( hBOOL @ ( wTrt @ C @ D @ E @ ( seq_list_char @ F @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1020_WTrt_H__WTrts_H_Ointros_I18_J) ).

thf(2023,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wTrt @ C @ D @ E @ F @ G ) )
     => ( ( hBOOL @ ( wTrt @ C @ D @ E @ A @ B ) )
       => ( hBOOL @ ( wTrt @ C @ D @ E @ ( seq_list_char @ F @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(485,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ A ) @ B )
        = ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_Pair__eq) ).

thf(3143,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ A ) @ B )
          = ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ A ) @ B )
          = ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(12,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i,E: $i] :
          ( A
         != ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_prod__cases4) ).

thf(1292,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i,E: $i] :
          ( A
         != ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(1006,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( transi921647814on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ D ) @ E ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( transi921647814on_val @ F ) ) )
               => ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_771_converse__rtrancl__induct2) ).

thf(5107,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( transi921647814on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ D ) @ E ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( transi921647814on_val @ F ) ) )
               => ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).

thf(400,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) ) @ ( reds @ I ) ) )
     => ( ( hBOOL @ ( wTrts_1 @ I @ D @ A @ C @ B ) )
       => ( ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ I ) @ D ) @ E ) @ A ) )
         => ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ I ) @ G ) @ H ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1176_reds__preserves__lconf) ).

thf(2868,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) ) @ ( reds @ I ) ) )
     => ( ( hBOOL @ ( wTrts_1 @ I @ D @ A @ C @ B ) )
       => ( ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ I ) @ D ) @ E ) @ A ) )
         => ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ I ) @ G ) @ H ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(1178,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) )
     => ( hBOOL @ ( hext @ C @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_856_eval__hext) ).

thf(5786,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) )
     => ( hBOOL @ ( hext @ C @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).

thf(143,axiom,
    ! [A: $i] :
      ( ( map_ad325961431ar_val @ A @ ( hAPP_o538043682on_val @ cOMBK_1097134891t_char @ none_val ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_636_map__add__empty) ).

thf(1842,plain,
    ! [A: $i] :
      ( ( map_ad325961431ar_val @ A @ ( hAPP_o538043682on_val @ cOMBK_1097134891t_char @ none_val ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(1129,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P1221872711l_bool @ B @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1221872711l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_prod__induct3) ).

thf(5588,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P1221872711l_bool @ B @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1221872711l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).

thf(167,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ B ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_prod__cases3) ).

thf(1937,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ B ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(216,axiom,
    ! [A: $i] :
      ( ( bool @ A )
     != null ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1071_val_Osimps_I13_J) ).

thf(2108,plain,
    ! [A: $i] :
      ( ( bool @ A )
     != null ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(934,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ E ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ A @ B ) @ C ) @ D ) )
      <=> ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) )
          & ( hBOOL @ ( final_list_char @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_847_big__iff__small) ).

thf(4867,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ E ) )
     => ( ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ A @ B ) @ C ) @ D ) )
         => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) )
            & ( hBOOL @ ( final_list_char @ C ) ) ) )
        & ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) )
            & ( hBOOL @ ( final_list_char @ C ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ A @ B ) @ C ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).

thf(1199,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
    <=> ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_467_prod_Osimps_I2_J) ).

thf(5905,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) ) )
      & ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).

thf(304,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ ( dom_list_char_val @ C ) ) )
     => ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ C @ A ) @ B )
        = ( hAPP_l207779698on_val @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_431_map__add__dom__app__simps_I2_J) ).

thf(2472,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ ( dom_list_char_val @ C ) ) )
     => ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ C @ A ) @ B )
        = ( hAPP_l207779698on_val @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(1080,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_prod_Oexhaust) ).

thf(5387,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).

thf(1242,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1029_FAccRedsNull) ).

thf(6065,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1242]) ).

thf(484,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_f1534412387l_bool @ produc769963999l_bool @ A ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_449_splitD) ).

thf(3141,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_f1534412387l_bool @ produc769963999l_bool @ A ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(695,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P92196306r_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P92196306r_bool @ A @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_split__paired__All) ).

thf(3952,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P92196306r_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P92196306r_bool @ A @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P92196306r_bool @ A @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P92196306r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).

thf(959,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ H ) ) ) @ I ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
     => ( ( ( hAPP_n546249108on_val @ ( hp @ I ) @ H )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
       => ( ( ( hAPP_P2094403585on_val @ E @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) )
            = ( hAPP_val_option_val @ some_val @ C ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ F @ A @ B ) ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ I ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_903_FAccRedsVal) ).

thf(4951,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ H ) ) ) @ I ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
     => ( ( ( hAPP_n546249108on_val @ ( hp @ I ) @ H )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
       => ( ( ( hAPP_P2094403585on_val @ E @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) )
            = ( hAPP_val_option_val @ some_val @ C ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ F @ A @ B ) ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ I ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).

thf(1186,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_PairE) ).

thf(5818,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).

thf(786,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ! [D: $i] :
          ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ B @ ( hAPP_ty_option_ty @ some_ty @ C ) ) @ D )
          = none_ty ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_641_map__upd__nonempty) ).

thf(4276,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ! [D: $i] :
          ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ B @ ( hAPP_ty_option_ty @ some_ty @ C ) ) @ D )
          = none_ty ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).

thf(556,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1314764175l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__O) ).

thf(3407,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1314764175l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(328,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f82569901l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O) ).

thf(2561,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f82569901l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(757,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hAPP_n546249108on_val @ A @ B )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ C ) )
     => ( ( fun_up2041264236on_val @ A @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ C ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_map__upd__triv) ).

thf(4167,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hAPP_n546249108on_val @ A @ B )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ C ) )
     => ( ( fun_up2041264236on_val @ A @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ C ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).

thf(822,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_e1705922617l_bool @ ( hAPP_f1475571983l_bool @ ( hAPP_f1946480059l_bool @ cOMBB_673739729t_char @ A ) @ B ) @ C )
      = ( hAPP_f101237475l_bool @ A @ ( hAPP_e286792811l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_077) ).

thf(4425,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_e1705922617l_bool @ ( hAPP_f1475571983l_bool @ ( hAPP_f1946480059l_bool @ cOMBB_673739729t_char @ A ) @ B ) @ C )
      = ( hAPP_f101237475l_bool @ A @ ( hAPP_e286792811l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).

thf(821,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ C ) @ D )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ F ) ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ E ) @ A ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ B ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) @ C ) ) ) @ ( red @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_995_red__reds_ORedCast) ).

thf(4421,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ C ) @ D )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ F ) ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ E ) @ A ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ B ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) @ C ) ) ) @ ( red @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).

thf(440,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ ( transi374442731on_val @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_665_r__into__rtrancl) ).

thf(3010,plain,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ ( transi374442731on_val @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(1097,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ D @ A ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_649_SeqReds2) ).

thf(5464,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ D @ A ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).

thf(138,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_list_char_bool @ ( is_cla570604648t_char @ C ) @ D ) )
     => ( hBOOL @ ( wTrt_1 @ C @ A @ B @ ( new_list_char @ D ) @ ( hAPP_list_char_ty @ class @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1125_WTrtNew) ).

thf(1810,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_list_char_bool @ ( is_cla570604648t_char @ C ) @ D ) )
     => ( hBOOL @ ( wTrt_1 @ C @ A @ B @ ( new_list_char @ D ) @ ( hAPP_list_char_ty @ class @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(932,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ H ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ H ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ C ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ E @ A @ B ) ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ C ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_951_BinOpRedsThrow2) ).

thf(4861,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ H ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ H ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ C ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ E @ A @ B ) ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ C ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).

thf(235,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_v1392248405l_bool @ ( hAPP_f198821591l_bool @ ( hAPP_f1880802701l_bool @ cOMBC_1979963740l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1728541444l_bool @ ( hAPP_v1988122071l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Value__Oval_000tc__fun_Itc__prod_Itc__Value__Oval_Mt_034) ).

thf(2172,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_v1392248405l_bool @ ( hAPP_f198821591l_bool @ ( hAPP_f1880802701l_bool @ cOMBC_1979963740l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1728541444l_bool @ ( hAPP_v1988122071l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(876,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ B @ ( hAPP_ty_option_ty @ some_ty @ C ) ) @ D )
        = ( hAPP_ty_option_ty @ some_ty @ E ) )
    <=> ( ( ( D = B )
          & ( C = E ) )
        | ( ( D != B )
          & ( ( hAPP_l512744617ion_ty @ A @ D )
            = ( hAPP_ty_option_ty @ some_ty @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_map__upd__Some__unfold) ).

thf(4648,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ B @ ( hAPP_ty_option_ty @ some_ty @ C ) ) @ D )
          = ( hAPP_ty_option_ty @ some_ty @ E ) )
       => ( ( ( D = B )
            & ( C = E ) )
          | ( ( D != B )
            & ( ( hAPP_l512744617ion_ty @ A @ D )
              = ( hAPP_ty_option_ty @ some_ty @ E ) ) ) ) )
      & ( ( ( ( D = B )
            & ( C = E ) )
          | ( ( D != B )
            & ( ( hAPP_l512744617ion_ty @ A @ D )
              = ( hAPP_ty_option_ty @ some_ty @ E ) ) ) )
       => ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ B @ ( hAPP_ty_option_ty @ some_ty @ C ) ) @ D )
          = ( hAPP_ty_option_ty @ some_ty @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).

thf(1146,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f1889282162l_bool @ ( ord_le1449176264r_bool @ ( hAPP_f2071340985r_bool @ ( hAPP_f133320957r_bool @ cOMBC_1127703214r_bool @ ( hAPP_f1608277885r_bool @ ( hAPP_f1134248971r_bool @ cOMBB_338473166ist_ty @ cOMBC_1365742487l_bool ) @ ( hAPP_f2047757465l_bool @ ( hAPP_f466945179l_bool @ cOMBB_68065882ist_ty @ ( hAPP_f693085049l_bool @ cOMBB_147773915t_char @ member140606439t_char ) ) @ produc1909267824t_char ) ) ) @ A ) ) @ ( hAPP_f2071340985r_bool @ ( hAPP_f133320957r_bool @ cOMBC_1127703214r_bool @ ( hAPP_f1608277885r_bool @ ( hAPP_f1134248971r_bool @ cOMBB_338473166ist_ty @ cOMBC_1365742487l_bool ) @ ( hAPP_f2047757465l_bool @ ( hAPP_f466945179l_bool @ cOMBB_68065882ist_ty @ ( hAPP_f693085049l_bool @ cOMBB_147773915t_char @ member140606439t_char ) ) @ produc1909267824t_char ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1746574980l_bool @ ( ord_le1218729222r_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_809_pred__subset__eq2) ).

thf(5662,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( hAPP_f1889282162l_bool @ ( ord_le1449176264r_bool @ ( hAPP_f2071340985r_bool @ ( hAPP_f133320957r_bool @ cOMBC_1127703214r_bool @ ( hAPP_f1608277885r_bool @ ( hAPP_f1134248971r_bool @ cOMBB_338473166ist_ty @ cOMBC_1365742487l_bool ) @ ( hAPP_f2047757465l_bool @ ( hAPP_f466945179l_bool @ cOMBB_68065882ist_ty @ ( hAPP_f693085049l_bool @ cOMBB_147773915t_char @ member140606439t_char ) ) @ produc1909267824t_char ) ) ) @ A ) ) @ ( hAPP_f2071340985r_bool @ ( hAPP_f133320957r_bool @ cOMBC_1127703214r_bool @ ( hAPP_f1608277885r_bool @ ( hAPP_f1134248971r_bool @ cOMBB_338473166ist_ty @ cOMBC_1365742487l_bool ) @ ( hAPP_f2047757465l_bool @ ( hAPP_f466945179l_bool @ cOMBB_68065882ist_ty @ ( hAPP_f693085049l_bool @ cOMBB_147773915t_char @ member140606439t_char ) ) @ produc1909267824t_char ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f1746574980l_bool @ ( ord_le1218729222r_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1746574980l_bool @ ( ord_le1218729222r_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1889282162l_bool @ ( ord_le1449176264r_bool @ ( hAPP_f2071340985r_bool @ ( hAPP_f133320957r_bool @ cOMBC_1127703214r_bool @ ( hAPP_f1608277885r_bool @ ( hAPP_f1134248971r_bool @ cOMBB_338473166ist_ty @ cOMBC_1365742487l_bool ) @ ( hAPP_f2047757465l_bool @ ( hAPP_f466945179l_bool @ cOMBB_68065882ist_ty @ ( hAPP_f693085049l_bool @ cOMBB_147773915t_char @ member140606439t_char ) ) @ produc1909267824t_char ) ) ) @ A ) ) @ ( hAPP_f2071340985r_bool @ ( hAPP_f133320957r_bool @ cOMBC_1127703214r_bool @ ( hAPP_f1608277885r_bool @ ( hAPP_f1134248971r_bool @ cOMBB_338473166ist_ty @ cOMBC_1365742487l_bool ) @ ( hAPP_f2047757465l_bool @ ( hAPP_f466945179l_bool @ cOMBB_68065882ist_ty @ ( hAPP_f693085049l_bool @ cOMBB_147773915t_char @ member140606439t_char ) ) @ produc1909267824t_char ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).

thf(499,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B )
        = ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_Pair__inject) ).

thf(3194,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B )
        = ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(326,axiom,
    ! [A: $i] :
      ( ? [B: $i] : ( hBOOL @ ( hAPP_P943837928l_bool @ A @ B ) )
    <=> ? [B: $i,C: $i] :
          ( ( is_bop @ B )
          & ( hBOOL @ ( hAPP_P943837928l_bool @ A @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_split__paired__Ex) ).

thf(2551,plain,
    ! [A: $i] :
      ( ( ? [B: $i] : ( hBOOL @ ( hAPP_P943837928l_bool @ A @ B ) )
       => ? [B: $i,C: $i] :
            ( ( is_bop @ B )
            & ( hBOOL @ ( hAPP_P943837928l_bool @ A @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) ) ) )
      & ( ? [B: $i,C: $i] :
            ( ( is_bop @ B )
            & ( hBOOL @ ( hAPP_P943837928l_bool @ A @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) ) )
       => ? [B: $i] : ( hBOOL @ ( hAPP_P943837928l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(210,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f749178132l_bool @ ( hAPP_f1099622285l_bool @ ( hAPP_f919000597l_bool @ cOMBB_1153773871on_val @ A ) @ B ) @ C )
      = ( hAPP_P1217996045l_bool @ A @ ( hAPP_f900686428on_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun__051) ).

thf(2085,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f749178132l_bool @ ( hAPP_f1099622285l_bool @ ( hAPP_f919000597l_bool @ cOMBB_1153773871on_val @ A ) @ B ) @ C )
      = ( hAPP_P1217996045l_bool @ A @ ( hAPP_f900686428on_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(223,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( fv @ ( fAcc_list_char @ A @ B @ C ) )
      = ( fv @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_915_fv__fvs_Osimps_I7_J) ).

thf(2125,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( fv @ ( fAcc_list_char @ A @ B @ C ) )
      = ( fv @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(1041,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_647_LAssReds) ).

thf(5234,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).

thf(1255,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B )
        = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_Pair__eq) ).

thf(6129,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B )
          = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B )
          = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1255]) ).

thf(778,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( d_list_char @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_DefAss_O_092_060D_062_000tc__List__Olist_Itc__String__Ochar_J) ).

thf(4244,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( d_list_char @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).

thf(314,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P929938951l_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P929938951l_bool @ A @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_split__paired__All) ).

thf(2505,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P929938951l_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P929938951l_bool @ A @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P929938951l_bool @ A @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P929938951l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(955,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ ( dom_list_char_val @ F ) ) @ ( semila919158006r_bool @ ( dom_list_char_val @ C ) @ ( fv @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_887_Red__dom__lcl) ).

thf(4934,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ ( dom_list_char_val @ F ) ) @ ( semila919158006r_bool @ ( dom_list_char_val @ C ) @ ( fv @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).

thf(1174,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P527298901l_bool @ ( hAPP_f1204100177l_bool @ ( hAPP_f2026692601l_bool @ cOMBB_1977588741on_val @ A ) @ B ) @ C )
      = ( hAPP_f762728813l_bool @ A @ ( hAPP_P1870962205on_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__) ).

thf(5776,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P527298901l_bool @ ( hAPP_f1204100177l_bool @ ( hAPP_f2026692601l_bool @ cOMBB_1977588741on_val @ A ) @ B ) @ C )
      = ( hAPP_f762728813l_bool @ A @ ( hAPP_P1870962205on_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).

thf(376,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hAPP_l512744617ion_ty @ A @ B )
        = C )
     => ( ( fun_up424764369ion_ty @ A @ B @ C )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_fun__upd__idem) ).

thf(2756,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hAPP_l512744617ion_ty @ A @ B )
        = C )
     => ( ( fun_up424764369ion_ty @ A @ B @ C )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(490,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ E @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) )
     => ( ( ( hAPP_n546249108on_val @ H @ G )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) )
       => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ A ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ D ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ ( cast_list_char @ A @ E ) @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_994_Cast) ).

thf(3162,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ E @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) )
     => ( ( ( hAPP_n546249108on_val @ H @ G )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) )
       => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ A ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ D ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ ( cast_list_char @ A @ E ) @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(1102,axiom,
    ! [A: $i] :
      ( ? [B: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ B ) )
    <=> ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_split__paired__Ex) ).

thf(5479,plain,
    ! [A: $i] :
      ( ( ? [B: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ B ) )
       => ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) )
      & ( ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
       => ? [B: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).

thf(915,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ D ) @ E ) @ F ) @ G ) )
     => ( ( hBOOL @ ( conf_P373316194t_char @ D @ E @ B @ C ) )
       => ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ D ) @ E ) @ ( fun_up1149430426on_val @ F @ A @ ( hAPP_val_option_val @ some_val @ B ) ) ) @ ( fun_up424764369ion_ty @ G @ A @ ( hAPP_ty_option_ty @ some_ty @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_375_lconf__upd2) ).

thf(4804,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ D ) @ E ) @ F ) @ G ) )
     => ( ( hBOOL @ ( conf_P373316194t_char @ D @ E @ B @ C ) )
       => ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ D ) @ E ) @ ( fun_up1149430426on_val @ F @ A @ ( hAPP_val_option_val @ some_val @ B ) ) ) @ ( fun_up424764369ion_ty @ G @ A @ ( hAPP_ty_option_ty @ some_ty @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).

thf(512,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ D @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( fAcc_list_char @ D @ A @ B ) @ E ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1045_FAccNull) ).

thf(3242,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ D @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( fAcc_list_char @ D @ A @ B ) @ E ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(630,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f288221747l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc_) ).

thf(3703,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f288221747l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(21,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ A ) @ B )
        = ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_Pair__eq) ).

thf(1324,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ A ) @ B )
          = ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ A ) @ B )
          = ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P1680401186r_bool @ B @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ D ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P1680401186r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_prod__induct4) ).

thf(1263,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P1680401186r_bool @ B @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ D ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P1680401186r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(610,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i,E: $i,F: $i] :
          ( A
         != ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ B ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ E ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_prod__cases5) ).

thf(3611,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i,E: $i,F: $i] :
          ( A
         != ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ B ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ E ) @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(1163,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( hBOOL @ ( hAPP_f1661305905l_bool @ ( hAPP_P1878549513l_bool @ member490182804on_val @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f1661305905l_bool @ ( hAPP_P1878549513l_bool @ member490182804on_val @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_pred__equals__eq2) ).

thf(5726,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f1661305905l_bool @ ( hAPP_P1878549513l_bool @ member490182804on_val @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1661305905l_bool @ ( hAPP_P1878549513l_bool @ member490182804on_val @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1661305905l_bool @ ( hAPP_P1878549513l_bool @ member490182804on_val @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1661305905l_bool @ ( hAPP_P1878549513l_bool @ member490182804on_val @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f1661305905l_bool @ ( hAPP_P1878549513l_bool @ member490182804on_val @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1661305905l_bool @ ( hAPP_P1878549513l_bool @ member490182804on_val @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1661305905l_bool @ ( hAPP_P1878549513l_bool @ member490182804on_val @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1661305905l_bool @ ( hAPP_P1878549513l_bool @ member490182804on_val @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).

thf(317,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( wTrt_1 @ E @ F @ G @ H @ nt ) )
     => ( ( hBOOL @ ( wTrts_1 @ E @ F @ G @ C @ D ) )
       => ( hBOOL @ ( wTrt_1 @ E @ F @ G @ ( call_list_char @ H @ A @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1173_WTrtCallNT) ).

thf(2519,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( wTrt_1 @ E @ F @ G @ H @ nt ) )
     => ( ( hBOOL @ ( wTrts_1 @ E @ F @ G @ C @ D ) )
       => ( hBOOL @ ( wTrt_1 @ E @ F @ G @ ( call_list_char @ H @ A @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(322,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P92196306r_bool @ B @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P92196306r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_prod__induct4) ).

thf(2536,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P92196306r_bool @ B @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P92196306r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(479,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ E ) @ F ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( fAcc_list_char @ D @ A @ B ) @ E ) @ ( fAcc_list_char @ F @ A @ B ) ) @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_914_redp__redsp_OFAccRed) ).

thf(3126,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ E ) @ F ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( fAcc_list_char @ D @ A @ B ) @ E ) @ ( fAcc_list_char @ F @ A @ B ) ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(648,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f515912112l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_) ).

thf(3787,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f515912112l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(74,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_P1183008383l_bool @ ( produc2053127004l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_506_curryD) ).

thf(1530,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_P1183008383l_bool @ ( produc2053127004l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(309,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ ( produc886919678l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P929938951l_bool @ A @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_507_curryD) ).

thf(2487,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ ( produc886919678l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P929938951l_bool @ A @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(338,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_t708040077har_ty @ ( hAPP_P827589667har_ty @ produc1265154397har_ty @ A ) @ B )
        = ( hAPP_t708040077har_ty @ ( hAPP_P827589667har_ty @ produc1265154397har_ty @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_Pair__eq) ).

thf(2598,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_t708040077har_ty @ ( hAPP_P827589667har_ty @ produc1265154397har_ty @ A ) @ B )
          = ( hAPP_t708040077har_ty @ ( hAPP_P827589667har_ty @ produc1265154397har_ty @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_t708040077har_ty @ ( hAPP_P827589667har_ty @ produc1265154397har_ty @ A ) @ B )
          = ( hAPP_t708040077har_ty @ ( hAPP_P827589667har_ty @ produc1265154397har_ty @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(727,axiom,
    ! [A: $i] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ unit ) @ A ) ) )
      = none_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1007_binop_Osimps_I3_J) ).

thf(4068,plain,
    ! [A: $i] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ unit ) @ A ) ) )
      = none_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).

thf(1077,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ D @ A @ B @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_974_TryRedsVal) ).

thf(5380,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ D @ A @ B @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).

thf(141,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( wTrt @ D @ E @ F @ G @ ( hAPP_list_char_ty @ class @ H ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( has_fi1183600461t_char @ D @ H @ A @ B ) @ C ) )
       => ( hBOOL @ ( wTrt @ D @ E @ F @ ( fAcc_list_char @ G @ A @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1025_WTrt_H__WTrts_H_Ointros_I8_J) ).

thf(1831,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( wTrt @ D @ E @ F @ G @ ( hAPP_list_char_ty @ class @ H ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( has_fi1183600461t_char @ D @ H @ A @ B ) @ C ) )
       => ( hBOOL @ ( wTrt @ D @ E @ F @ ( fAcc_list_char @ G @ A @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(229,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( new_Addr @ F )
        = ( hAPP_nat_option_nat @ some_nat @ G ) )
     => ( ( hBOOL @ ( fields1147507508t_char @ C @ D @ E ) )
       => ( ( B
            = ( fun_up2041264236on_val @ F @ G @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ ( init_fields @ E ) ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( new_list_char @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ A ) ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1133_New) ).

thf(2153,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( new_Addr @ F )
        = ( hAPP_nat_option_nat @ some_nat @ G ) )
     => ( ( hBOOL @ ( fields1147507508t_char @ C @ D @ E ) )
       => ( ( B
            = ( fun_up2041264236on_val @ F @ G @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ ( init_fields @ E ) ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( new_list_char @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ A ) ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(409,axiom,
    ! [A: $i] :
      ( ( fv @ ( throw_list_char @ A ) )
      = ( fv @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_913_fv__fvs_Osimps_I14_J) ).

thf(2900,plain,
    ! [A: $i] :
      ( ( fv @ ( throw_list_char @ A ) )
      = ( fv @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(967,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ ( transi2024712006on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ C ) )
       => ( ! [E: $i,F: $i] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ E ) @ F ) ) @ D ) )
             => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ F ) @ C ) ) @ ( transi2024712006on_val @ D ) ) )
               => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ F ) )
                 => ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ E ) ) ) ) )
         => ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_844_converse__rtrancl__induct) ).

thf(4970,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ ( transi2024712006on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ C ) )
       => ( ! [E: $i,F: $i] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ E ) @ F ) ) @ D ) )
             => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ F ) @ C ) ) @ ( transi2024712006on_val @ D ) ) )
               => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ F ) )
                 => ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ E ) ) ) ) )
         => ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).

thf(1143,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P468446343l_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P468446343l_bool @ A @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_split__paired__All) ).

thf(5639,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P468446343l_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P468446343l_bool @ A @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P468446343l_bool @ A @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P468446343l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).

thf(1010,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( produc1911975310l_bool @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_371_curryI) ).

thf(5134,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( produc1911975310l_bool @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).

thf(334,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( reds @ G ) ) )
     => ( hBOOL @ ( hext @ B @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1149_reds__hext__incr) ).

thf(2581,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( reds @ G ) ) )
     => ( hBOOL @ ( hext @ B @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(303,axiom,
    ! [A: $i,B: $i] :
      ( ( ( hAPP_ty_option_ty @ some_ty @ A )
        = ( hAPP_ty_option_ty @ some_ty @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_354_option_Oinject) ).

thf(2465,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( hAPP_ty_option_ty @ some_ty @ A )
          = ( hAPP_ty_option_ty @ some_ty @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( hAPP_ty_option_ty @ some_ty @ A )
          = ( hAPP_ty_option_ty @ some_ty @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(146,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_pred__equals__eq2) ).

thf(1852,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(389,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( conf_P373316194t_char @ B @ C @ D @ E ) )
     => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ B ) @ E ) @ A ) )
       => ( hBOOL @ ( conf_P373316194t_char @ B @ C @ D @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_439_conf__widen) ).

thf(2813,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( conf_P373316194t_char @ B @ C @ D @ E ) )
     => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ B ) @ E ) @ A ) )
       => ( hBOOL @ ( conf_P373316194t_char @ B @ C @ D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(614,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_671_subsetD) ).

thf(3628,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(475,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P499022727r_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__St) ).

thf(3115,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P499022727r_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(1037,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ ( produc2062775566l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_495_curryE) ).

thf(5217,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ ( produc2062775566l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).

thf(514,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) @ ( transi374442731on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_P71593144l_bool @ A @ B ) )
       => ( ! [E: $i,F: $i] :
              ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ E ) ) @ ( transi374442731on_val @ D ) ) )
             => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ E ) @ F ) ) @ D ) )
               => ( ( hBOOL @ ( hAPP_P71593144l_bool @ A @ E ) )
                 => ( hBOOL @ ( hAPP_P71593144l_bool @ A @ F ) ) ) ) )
         => ( hBOOL @ ( hAPP_P71593144l_bool @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_796_rtrancl__induct) ).

thf(3247,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) @ ( transi374442731on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_P71593144l_bool @ A @ B ) )
       => ( ! [E: $i,F: $i] :
              ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ E ) ) @ ( transi374442731on_val @ D ) ) )
             => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ E ) @ F ) ) @ D ) )
               => ( ( hBOOL @ ( hAPP_P71593144l_bool @ A @ E ) )
                 => ( hBOOL @ ( hAPP_P71593144l_bool @ A @ F ) ) ) ) )
         => ( hBOOL @ ( hAPP_P71593144l_bool @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(557,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( new_Addr @ D )
        = none_nat )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( new_list_char @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ C ) ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ outOfMemory ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1129_NewFail) ).

thf(3409,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( new_Addr @ D )
        = none_nat )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( new_list_char @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ C ) ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ outOfMemory ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(626,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( wf_pro755087577t_char @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_WellForm_Owf__prog_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Stri) ).

thf(3692,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( wf_pro755087577t_char @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(307,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ G @ H ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ I ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ K ) ) )
     => ( ( ( hAPP_n546249108on_val @ J @ I )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
       => ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ C ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ F ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ ( tryCatch_list_char @ G @ C @ A @ B ) @ H ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ I ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ K ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_970_TryThrow) ).

thf(2482,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ G @ H ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ I ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ K ) ) )
     => ( ( ( hAPP_n546249108on_val @ J @ I )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
       => ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ C ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ F ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ ( tryCatch_list_char @ G @ C @ A @ B ) @ H ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ I ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ K ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(751,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P1562529797l_bool @ ( hAPP_f1233028029l_bool @ ( hAPP_f1715733055l_bool @ cOMBB_123628846t_char @ A ) @ B ) @ C )
      = ( hAPP_P1472618637l_bool @ A @ ( hAPP_P767818445t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String___052) ).

thf(4152,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P1562529797l_bool @ ( hAPP_f1233028029l_bool @ ( hAPP_f1715733055l_bool @ cOMBB_123628846t_char @ A ) @ B ) @ C )
      = ( hAPP_P1472618637l_bool @ A @ ( hAPP_P767818445t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).

thf(121,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f595031537l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc_) ).

thf(1720,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f595031537l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(177,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f665343921l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J__018) ).

thf(1979,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f665343921l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(985,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( red @ G ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_961_red__reds_OBinOpRed1) ).

thf(5026,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( red @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).

thf(438,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( throw_list_char @ D ) @ E ) @ F ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ C @ ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ A ) @ ( cons_exp_list_char @ ( throw_list_char @ D ) @ B ) ) @ E ) @ ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ A ) @ ( cons_exp_list_char @ F @ B ) ) ) @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1160_list__eval__Throw) ).

thf(3005,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( throw_list_char @ D ) @ E ) @ F ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ C @ ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ A ) @ ( cons_exp_list_char @ ( throw_list_char @ D ) @ B ) ) @ E ) @ ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ A ) @ ( cons_exp_list_char @ F @ B ) ) ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(22,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_l902158906r_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mt) ).

thf(1333,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_l902158906r_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(850,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_PairE) ).

thf(4535,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).

thf(1056,axiom,
    ! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ B ) ) ) @ ( red @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1038_red__reds_ORedCastNull) ).

thf(5310,plain,
    ! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ B ) ) ) @ ( red @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).

thf(791,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( while_list_char @ B @ C ) @ D ) @ E ) @ F ) )
     => ( ( ( E
            = ( hAPP_v834067052t_char @ val_list_char @ unit ) )
         => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fFalse ) ) ) @ F ) ) )
       => ( ! [G: $i] :
              ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fTrue ) ) ) @ G ) )
             => ! [H: $i,I: $i] :
                  ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ C @ G ) @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ I ) )
                 => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( while_list_char @ B @ C ) @ I ) @ E ) @ F ) ) ) )
         => ( ! [G: $i] :
                ( ( E
                  = ( throw_list_char @ G ) )
               => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( throw_list_char @ G ) ) @ F ) ) )
           => ~ ! [G: $i,H: $i] :
                  ( ( E
                    = ( throw_list_char @ H ) )
                 => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fTrue ) ) ) @ G ) )
                   => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ C @ G ) @ ( throw_list_char @ H ) ) @ F ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1090_eval__cases_I11_J) ).

thf(4288,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( while_list_char @ B @ C ) @ D ) @ E ) @ F ) )
     => ( ( ( E
            = ( hAPP_v834067052t_char @ val_list_char @ unit ) )
         => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fFalse ) ) ) @ F ) ) )
       => ( ! [G: $i] :
              ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fTrue ) ) ) @ G ) )
             => ! [H: $i,I: $i] :
                  ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ C @ G ) @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ I ) )
                 => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( while_list_char @ B @ C ) @ I ) @ E ) @ F ) ) ) )
         => ( ! [G: $i] :
                ( ( E
                  = ( throw_list_char @ G ) )
               => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( throw_list_char @ G ) ) @ F ) ) )
           => ~ ! [G: $i,H: $i] :
                  ( ( E
                    = ( throw_list_char @ H ) )
                 => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fTrue ) ) ) @ G ) )
                   => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ C @ G ) @ ( throw_list_char @ H ) ) @ F ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).

thf(855,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ A ) @ B )
        = ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_Pair__inject) ).

thf(4567,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ A ) @ B )
        = ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).

thf(965,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fTrue ) ) ) @ H ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ H ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) )
       => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( while_list_char @ F @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( while_list_char @ F @ C ) ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1088_WhileTReds) ).

thf(4966,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fTrue ) ) ) @ H ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ H ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) )
       => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( while_list_char @ F @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( while_list_char @ F @ C ) ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).

thf(709,axiom,
    ! [A: $i,B: $i,C: $i] : ( is_bool @ ( fields1147507508t_char @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_TypeRel_OFields_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String_) ).

thf(3999,plain,
    ! [A: $i,B: $i,C: $i] : ( is_bool @ ( fields1147507508t_char @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).

thf(719,axiom,
    unit != null,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1033_val_Osimps_I4_J) ).

thf(4036,plain,
    unit != null,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).

thf(351,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ A @ B @ C ) @ B @ D )
      = ( fun_up424764369ion_ty @ A @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_fun__upd__upd) ).

thf(2645,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ A @ B @ C ) @ B @ D )
      = ( fun_up424764369ion_ty @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(320,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ A ) @ B )
        = ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_Pair__inject) ).

thf(2529,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ A ) @ B )
        = ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(749,axiom,
    ! [A: $i,B: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ B ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1043_redp__redsp_ORedThrowNull) ).

thf(4148,plain,
    ! [A: $i,B: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ B ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).

thf(347,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] :
          ( ( is_bop @ C )
         => ( hBOOL @ ( hAPP_P943837928l_bool @ B @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ E ) ) ) ) )
     => ( hBOOL @ ( hAPP_P943837928l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_prod__induct3) ).

thf(2634,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] :
          ( ( is_bop @ C )
         => ( hBOOL @ ( hAPP_P943837928l_bool @ B @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ E ) ) ) ) )
     => ( hBOOL @ ( hAPP_P943837928l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(1007,axiom,
    ! [A: $i,B: $i] :
      ( ( ( bool @ A )
        = ( bool @ B ) )
    <=> ( ( hBOOL @ A )
      <=> ( hBOOL @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1067_val_Osimps_I1_J) ).

thf(5112,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( bool @ A )
          = ( bool @ B ) )
       => ( ( ( hBOOL @ A )
           => ( hBOOL @ B ) )
          & ( ( hBOOL @ B )
           => ( hBOOL @ A ) ) ) )
      & ( ( ( ( hBOOL @ A )
           => ( hBOOL @ B ) )
          & ( ( hBOOL @ B )
           => ( hBOOL @ A ) ) )
       => ( ( bool @ A )
          = ( bool @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).

thf(42,axiom,
    ! [A: $i] : ( is_bool @ ( finals_list_char @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_BigStep_Ofinals_000tc__List__Olist_Itc__String__Ochar_J) ).

thf(1434,plain,
    ! [A: $i] : ( is_bool @ ( finals_list_char @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(381,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P282169671l_bool @ ( cOMBS_1319864284l_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_P1402001845l_bool @ A @ C ) @ ( hAPP_P282169671l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_) ).

thf(2788,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P282169671l_bool @ ( cOMBS_1319864284l_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_P1402001845l_bool @ A @ C ) @ ( hAPP_P282169671l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(1119,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( throw_list_char @ A ) @ B @ C @ D ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ E ) ) ) @ ( red @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_934_red__reds_OFAssThrow1) ).

thf(5544,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( throw_list_char @ A ) @ B @ C @ D ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ E ) ) ) @ ( red @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).

thf(659,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ E ) @ F )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
     => ( ~ ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ ( transi1065307915t_char @ ( subcls744239332t_char @ C ) ) @ G ) @ D ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( tryCatch_list_char @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ D @ A @ B ) @ E ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1055_redp__redsp_ORedTryFail) ).

thf(3834,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ E ) @ F )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
     => ( ~ ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ ( transi1065307915t_char @ ( subcls744239332t_char @ C ) ) @ G ) @ D ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( tryCatch_list_char @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ D @ A @ B ) @ E ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).

thf(874,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] : ( is_bool @ ( conf_P373316194t_char @ A @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Conform_Oconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O) ).

thf(4644,plain,
    ! [A: $i,B: $i,C: $i,D: $i] : ( is_bool @ ( conf_P373316194t_char @ A @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).

thf(507,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ B @ C ) @ B )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_fun__upd__same) ).

thf(3225,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ B @ C ) @ B )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(199,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f2071159779l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Value__Oval_Mtc__fun_Itc__Value__Oval_Mtc__HOL__Obool) ).

thf(2043,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f2071159779l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(526,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( tryCatch_list_char @ D @ E @ F @ G ) @ H ) )
     => ~ ! [I: $i] :
            ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ I ) )
           => ( ( hBOOL @ ( wTrt_1 @ A @ B @ ( fun_up424764369ion_ty @ C @ F @ ( hAPP_ty_option_ty @ some_ty @ ( hAPP_list_char_ty @ class @ E ) ) ) @ G @ H ) )
             => ~ ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ A ) @ I ) @ H ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_996_WTrt__elim__cases_I5_J) ).

thf(3279,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( tryCatch_list_char @ D @ E @ F @ G ) @ H ) )
     => ~ ! [I: $i] :
            ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ I ) )
           => ( ( hBOOL @ ( wTrt_1 @ A @ B @ ( fun_up424764369ion_ty @ C @ F @ ( hAPP_ty_option_ty @ some_ty @ ( hAPP_list_char_ty @ class @ E ) ) ) @ G @ H ) )
             => ~ ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ A ) @ I ) @ H ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(941,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P2077557811l_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P2077557811l_bool @ A @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_split__paired__All) ).

thf(4889,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P2077557811l_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P2077557811l_bool @ A @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P2077557811l_bool @ A @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P2077557811l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).

thf(606,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( block_list_char @ B @ C @ ( seq_list_char @ ( lAss_list_char @ B @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ E ) ) ) ) ) @ F ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ E ) ) ) ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_943_redp__redsp_OInitBlockThrow) ).

thf(3587,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( block_list_char @ B @ C @ ( seq_list_char @ ( lAss_list_char @ B @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ E ) ) ) ) ) @ F ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ E ) ) ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(496,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l2140727500r_bool @ ( hAPP_f2025561243r_bool @ ( hAPP_f1500560577r_bool @ cOMBC_1784597444r_bool @ A ) @ B ) @ C )
      = ( hAPP_f658521820r_bool @ ( hAPP_l923073979r_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_068) ).

thf(3183,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l2140727500r_bool @ ( hAPP_f2025561243r_bool @ ( hAPP_f1500560577r_bool @ cOMBC_1784597444r_bool @ A ) @ B ) @ C )
      = ( hAPP_f658521820r_bool @ ( hAPP_l923073979r_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(404,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_e53687815l_bool @ ( hAPP_f361629773l_bool @ ( hAPP_f1612138403l_bool @ cOMBB_961360819t_char @ A ) @ B ) @ C )
      = ( hAPP_P845017029l_bool @ A @ ( hAPP_e1752110927t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__) ).

thf(2883,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_e53687815l_bool @ ( hAPP_f361629773l_bool @ ( hAPP_f1612138403l_bool @ cOMBB_961360819t_char @ A ) @ B ) @ C )
      = ( hAPP_P845017029l_bool @ A @ ( hAPP_e1752110927t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(833,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( preallocated @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ sys_xcpts ) )
       => ( ! [D: $i] :
              ( ( ( hAPP_n546249108on_val @ C @ ( addr_of_sys_xcpt @ B ) )
                = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ D ) ) )
             => ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_f388705405r_bool @ A @ C ) @ B ) ) )
         => ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_f388705405r_bool @ A @ C ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1074_preallocatedE) ).

thf(4476,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( preallocated @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ sys_xcpts ) )
       => ( ! [D: $i] :
              ( ( ( hAPP_n546249108on_val @ C @ ( addr_of_sys_xcpt @ B ) )
                = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ D ) ) )
             => ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_f388705405r_bool @ A @ C ) @ B ) ) )
         => ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_f388705405r_bool @ A @ C ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).

thf(383,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( ( hAPP_val_option_ty @ ( typeof_h @ G ) @ H )
        = ( hAPP_ty_option_ty @ some_ty @ I ) )
     => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ E ) @ I ) @ F ) )
       => ( ( hBOOL @ ( wTrt @ E @ G @ ( fun_up424764369ion_ty @ A @ B @ ( hAPP_ty_option_ty @ some_ty @ F ) ) @ C @ D ) )
         => ( hBOOL @ ( wTrt @ E @ G @ A @ ( block_list_char @ B @ F @ ( seq_list_char @ ( lAss_list_char @ B @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ C ) ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1018_WTrt_H__WTrts_H_Ointros_I16_J) ).

thf(2793,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( ( hAPP_val_option_ty @ ( typeof_h @ G ) @ H )
        = ( hAPP_ty_option_ty @ some_ty @ I ) )
     => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ E ) @ I ) @ F ) )
       => ( ( hBOOL @ ( wTrt @ E @ G @ ( fun_up424764369ion_ty @ A @ B @ ( hAPP_ty_option_ty @ some_ty @ F ) ) @ C @ D ) )
         => ( hBOOL @ ( wTrt @ E @ G @ A @ ( block_list_char @ B @ F @ ( seq_list_char @ ( lAss_list_char @ B @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ C ) ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(1207,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ F @ none_val ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) ) @ ( red @ J ) ) )
     => ( ( ( hAPP_l207779698on_val @ I @ F )
          = ( hAPP_val_option_val @ some_val @ B ) )
       => ( ~ ( hBOOL @ ( assigned @ F @ C ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ F @ A @ C ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ F @ A @ ( seq_list_char @ ( lAss_list_char @ F @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ F @ ( hAPP_l207779698on_val @ E @ F ) ) ) ) ) ) @ ( red @ J ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_588_red__reds_OBlockRedSome) ).

thf(5930,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ F @ none_val ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) ) @ ( red @ J ) ) )
     => ( ( ( hAPP_l207779698on_val @ I @ F )
          = ( hAPP_val_option_val @ some_val @ B ) )
       => ( ~ ( hBOOL @ ( assigned @ F @ C ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ F @ A @ C ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ F @ A @ ( seq_list_char @ ( lAss_list_char @ F @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ F @ ( hAPP_l207779698on_val @ E @ F ) ) ) ) ) ) @ ( red @ J ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1207]) ).

thf(973,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ A @ B @ ( seq_list_char @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) ) ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) ) @ E ) ) ) @ ( red @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_907_red__reds_OInitBlockThrow) ).

thf(4995,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ A @ B @ ( seq_list_char @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) ) ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) ) @ E ) ) ) @ ( red @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).

thf(856,axiom,
    ! [A: $i] : ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_795_order__refl) ).

thf(4572,plain,
    ! [A: $i] : ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).

thf(413,axiom,
    ! [A: $i] :
      ( ? [B: $i] : ( hBOOL @ ( hAPP_P929938951l_bool @ A @ B ) )
    <=> ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P929938951l_bool @ A @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_split__paired__Ex) ).

thf(2909,plain,
    ! [A: $i] :
      ( ( ? [B: $i] : ( hBOOL @ ( hAPP_P929938951l_bool @ A @ B ) )
       => ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P929938951l_bool @ A @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) ) )
      & ( ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P929938951l_bool @ A @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) )
       => ? [B: $i] : ( hBOOL @ ( hAPP_P929938951l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(852,axiom,
    ! [A: $i,B: $i] :
      ( ( ( addr @ A )
        = ( addr @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_948_val_Osimps_I3_J) ).

thf(4550,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( addr @ A )
          = ( addr @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( addr @ A )
          = ( addr @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).

thf(653,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_692_equalityD1) ).

thf(3807,plain,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(158,axiom,
    ! [A: $i,B: $i] :
      ( ( ( hAPP_list_char_ty @ class @ A )
        = ( hAPP_list_char_ty @ class @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1060_ty_Oinject) ).

thf(1906,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( hAPP_list_char_ty @ class @ A )
          = ( hAPP_list_char_ty @ class @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( hAPP_list_char_ty @ class @ A )
          = ( hAPP_list_char_ty @ class @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(369,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P468446343l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Optio) ).

thf(2729,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P468446343l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(744,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_P1384137393r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_471_mem__def) ).

thf(4131,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_P1384137393r_bool @ B @ A ) ) )
      & ( ( hBOOL @ ( hAPP_P1384137393r_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).

thf(814,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) @ ( transi935034983cl_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_val_bool @ A @ B ) )
       => ( ! [E: $i,F: $i] :
              ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ E ) ) @ ( transi935034983cl_val @ D ) ) )
             => ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ E ) @ F ) ) @ D ) )
               => ( ( hBOOL @ ( hAPP_val_bool @ A @ E ) )
                 => ( hBOOL @ ( hAPP_val_bool @ A @ F ) ) ) ) )
         => ( hBOOL @ ( hAPP_val_bool @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_799_rtrancl__induct) ).

thf(4380,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) @ ( transi935034983cl_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_val_bool @ A @ B ) )
       => ( ! [E: $i,F: $i] :
              ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ E ) ) @ ( transi935034983cl_val @ D ) ) )
             => ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ E ) @ F ) ) @ D ) )
               => ( ( hBOOL @ ( hAPP_val_bool @ A @ E ) )
                 => ( hBOOL @ ( hAPP_val_bool @ A @ F ) ) ) ) )
         => ( hBOOL @ ( hAPP_val_bool @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).

thf(58,axiom,
    nt != void,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1112_ty_Osimps_I7_J) ).

thf(1483,plain,
    nt != void,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(1247,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ A @ B @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ D ) ) ) @ ( red @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_462_red__reds_ORedBlock) ).

thf(6084,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ A @ B @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ D ) ) ) @ ( red @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247]) ).

thf(707,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) ) @ ( lex_pr1541028704on_val @ E @ F ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1734260017l_bool @ ( hAPP_P53416969l_bool @ member894971540t_char @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ A ) @ C ) ) @ E ) )
        | ( ( A = C )
          & ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ B ) @ D ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_376_in__lex__prod) ).

thf(3985,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) ) @ ( lex_pr1541028704on_val @ E @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f1734260017l_bool @ ( hAPP_P53416969l_bool @ member894971540t_char @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ B ) @ D ) ) @ F ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1734260017l_bool @ ( hAPP_P53416969l_bool @ member894971540t_char @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ B ) @ D ) ) @ F ) ) ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) ) @ ( lex_pr1541028704on_val @ E @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).

thf(519,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ ( produc886919678l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P929938951l_bool @ A @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_491_curryE) ).

thf(3262,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ ( produc886919678l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P929938951l_bool @ A @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(1135,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_prod__cases3) ).

thf(5608,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).

thf(221,axiom,
    produc2128769400l_bool = produc1958875245l_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_519_internal__split__def) ).

thf(2121,plain,
    produc2128769400l_bool = produc1958875245l_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(256,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( fun_up424764369ion_ty @ A @ B @ C )
        = A )
    <=> ( ( hAPP_l512744617ion_ty @ A @ B )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_fun__upd__idem__iff) ).

thf(2235,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( fun_up424764369ion_ty @ A @ B @ C )
          = A )
       => ( ( hAPP_l512744617ion_ty @ A @ B )
          = C ) )
      & ( ( ( hAPP_l512744617ion_ty @ A @ B )
          = C )
       => ( ( fun_up424764369ion_ty @ A @ B @ C )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(632,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_split__paired__All) ).

thf(3707,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(123,axiom,
    ! [A: $i] :
      ( ( hAPP_P1510515380on_val @ some_P948696889on_val @ A )
     != none_P179726773on_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_611_option_Osimps_I3_J) ).

thf(1727,plain,
    ! [A: $i] :
      ( ( hAPP_P1510515380on_val @ some_P948696889on_val @ A )
     != none_P179726773on_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(291,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ C @ D ) @ E ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ ( cast_list_char @ A @ C ) @ D ) @ ( cast_list_char @ A @ E ) ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_983_redp__redsp_OCastRed) ).

thf(2413,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ C @ D ) @ E ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ ( cast_list_char @ A @ C ) @ D ) @ ( cast_list_char @ A @ E ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(481,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P1926698759r_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String___028) ).

thf(3130,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P1926698759r_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(286,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P504978887l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_) ).

thf(2391,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P504978887l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(108,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ A ) @ B )
        = ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_Pair__eq) ).

thf(1680,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ A ) @ B )
          = ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ A ) @ B )
          = ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(1182,axiom,
    hBOOL @ ( wf_pro755087577t_char @ wf_J_mdecl @ p ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_assms) ).

thf(5808,plain,
    hBOOL @ ( wf_pro755087577t_char @ wf_J_mdecl @ p ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).

thf(113,axiom,
    ! [A: $i] :
      ( ( hAPP_val_option_ty @ ( typeof_h @ A ) @ null )
      = ( hAPP_ty_option_ty @ some_ty @ nt ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1119_typeof__h_Osimps_I2_J) ).

thf(1698,plain,
    ! [A: $i] :
      ( ( hAPP_val_option_ty @ ( typeof_h @ A ) @ null )
      = ( hAPP_ty_option_ty @ some_ty @ nt ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(194,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1748390065l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__015) ).

thf(2033,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1748390065l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(863,axiom,
    ! [A: $i,B: $i] :
      ( ( fvs @ ( cons_exp_list_char @ A @ B ) )
      = ( semila919158006r_bool @ ( fv @ A ) @ ( fvs @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1155_fv__fvs_Osimps_I17_J) ).

thf(4613,plain,
    ! [A: $i,B: $i] :
      ( ( fvs @ ( cons_exp_list_char @ A @ B ) )
      = ( semila919158006r_bool @ ( fv @ A ) @ ( fvs @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).

thf(672,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f2106398425l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List_) ).

thf(3871,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f2106398425l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).

thf(517,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1536299231l_bool @ ( hAPP_f935003377l_bool @ ( hAPP_f162154931l_bool @ cOMBB_859890145har_ty @ A ) @ B ) @ C )
      = ( hAPP_f156692813l_bool @ A @ ( hAPP_l352172327t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc_) ).

thf(3257,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1536299231l_bool @ ( hAPP_f935003377l_bool @ ( hAPP_f162154931l_bool @ cOMBB_859890145har_ty @ A ) @ B ) @ C )
      = ( hAPP_f156692813l_bool @ A @ ( hAPP_l352172327t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(1092,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P1632759357r_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1632759357r_bool @ A @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_split__paired__All) ).

thf(5451,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P1632759357r_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1632759357r_bool @ A @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1632759357r_bool @ A @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P1632759357r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).

thf(677,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f742333458l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__) ).

thf(3890,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f742333458l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).

thf(1050,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f2071159779l_bool @ ( ord_le408082617l_bool @ ( hAPP_f198821591l_bool @ ( hAPP_f1880802701l_bool @ cOMBC_1979963740l_bool @ ( hAPP_f1859053709l_bool @ ( hAPP_f400269243l_bool @ cOMBB_1701031980ol_val @ cOMBC_331963401l_bool ) @ ( hAPP_f293485653l_bool @ ( hAPP_f565735867l_bool @ cOMBB_815843940ol_val @ ( hAPP_f183649339l_bool @ cOMBB_2078984970ol_val @ member649088532al_val ) ) @ product_Pair_val_val ) ) ) @ A ) ) @ ( hAPP_f198821591l_bool @ ( hAPP_f1880802701l_bool @ cOMBC_1979963740l_bool @ ( hAPP_f1859053709l_bool @ ( hAPP_f400269243l_bool @ cOMBB_1701031980ol_val @ cOMBC_331963401l_bool ) @ ( hAPP_f293485653l_bool @ ( hAPP_f565735867l_bool @ cOMBB_815843940ol_val @ ( hAPP_f183649339l_bool @ cOMBB_2078984970ol_val @ member649088532al_val ) ) @ product_Pair_val_val ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f2028441009l_bool @ ( ord_le310098611l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_812_pred__subset__eq2) ).

thf(5278,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( hAPP_f2071159779l_bool @ ( ord_le408082617l_bool @ ( hAPP_f198821591l_bool @ ( hAPP_f1880802701l_bool @ cOMBC_1979963740l_bool @ ( hAPP_f1859053709l_bool @ ( hAPP_f400269243l_bool @ cOMBB_1701031980ol_val @ cOMBC_331963401l_bool ) @ ( hAPP_f293485653l_bool @ ( hAPP_f565735867l_bool @ cOMBB_815843940ol_val @ ( hAPP_f183649339l_bool @ cOMBB_2078984970ol_val @ member649088532al_val ) ) @ product_Pair_val_val ) ) ) @ A ) ) @ ( hAPP_f198821591l_bool @ ( hAPP_f1880802701l_bool @ cOMBC_1979963740l_bool @ ( hAPP_f1859053709l_bool @ ( hAPP_f400269243l_bool @ cOMBB_1701031980ol_val @ cOMBC_331963401l_bool ) @ ( hAPP_f293485653l_bool @ ( hAPP_f565735867l_bool @ cOMBB_815843940ol_val @ ( hAPP_f183649339l_bool @ cOMBB_2078984970ol_val @ member649088532al_val ) ) @ product_Pair_val_val ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f2028441009l_bool @ ( ord_le310098611l_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( ord_le310098611l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2071159779l_bool @ ( ord_le408082617l_bool @ ( hAPP_f198821591l_bool @ ( hAPP_f1880802701l_bool @ cOMBC_1979963740l_bool @ ( hAPP_f1859053709l_bool @ ( hAPP_f400269243l_bool @ cOMBB_1701031980ol_val @ cOMBC_331963401l_bool ) @ ( hAPP_f293485653l_bool @ ( hAPP_f565735867l_bool @ cOMBB_815843940ol_val @ ( hAPP_f183649339l_bool @ cOMBB_2078984970ol_val @ member649088532al_val ) ) @ product_Pair_val_val ) ) ) @ A ) ) @ ( hAPP_f198821591l_bool @ ( hAPP_f1880802701l_bool @ cOMBC_1979963740l_bool @ ( hAPP_f1859053709l_bool @ ( hAPP_f400269243l_bool @ cOMBB_1701031980ol_val @ cOMBC_331963401l_bool ) @ ( hAPP_f293485653l_bool @ ( hAPP_f565735867l_bool @ cOMBB_815843940ol_val @ ( hAPP_f183649339l_bool @ cOMBB_2078984970ol_val @ member649088532al_val ) ) @ product_Pair_val_val ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).

thf(331,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) @ ( transi374442731on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ B ) @ C ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ G ) @ H ) ) ) @ ( transi374442731on_val @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ G ) @ H ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_773_rtrancl__induct2) ).

thf(2570,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) @ ( transi374442731on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ B ) @ C ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ G ) @ H ) ) ) @ ( transi374442731on_val @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ G ) @ H ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(421,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ A ) @ B )
        = ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_Pair__eq) ).

thf(2941,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ A ) @ B )
          = ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ A ) @ B )
          = ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(803,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ G @ H ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fTrue ) ) ) @ I ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ C @ I ) @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ ( while_list_char @ G @ C ) @ E ) @ A ) @ B ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ ( while_list_char @ G @ C ) @ H ) @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1084_WhileT) ).

thf(4340,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ G @ H ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fTrue ) ) ) @ I ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ C @ I ) @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ ( while_list_char @ G @ C ) @ E ) @ A ) @ B ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ ( while_list_char @ G @ C ) @ H ) @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).

thf(90,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P71593144l_bool @ ( hAPP_f1317381998l_bool @ ( hAPP_f1734997943l_bool @ cOMBC_1491642377l_bool @ A ) @ B ) @ C )
      = ( hAPP_f458849545l_bool @ ( hAPP_P88824722l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Oli) ).

thf(1595,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P71593144l_bool @ ( hAPP_f1317381998l_bool @ ( hAPP_f1734997943l_bool @ cOMBC_1491642377l_bool @ A ) @ B ) @ C )
      = ( hAPP_f458849545l_bool @ ( hAPP_P88824722l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(589,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( hBOOL @ ( hAPP_f1780084320l_bool @ ( hAPP_P1472618637l_bool @ member133545693t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f1780084320l_bool @ ( hAPP_P1472618637l_bool @ member133545693t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_pred__equals__eq2) ).

thf(3523,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f1780084320l_bool @ ( hAPP_P1472618637l_bool @ member133545693t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1780084320l_bool @ ( hAPP_P1472618637l_bool @ member133545693t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1780084320l_bool @ ( hAPP_P1472618637l_bool @ member133545693t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1780084320l_bool @ ( hAPP_P1472618637l_bool @ member133545693t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f1780084320l_bool @ ( hAPP_P1472618637l_bool @ member133545693t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1780084320l_bool @ ( hAPP_P1472618637l_bool @ member133545693t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1780084320l_bool @ ( hAPP_P1472618637l_bool @ member133545693t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1780084320l_bool @ ( hAPP_P1472618637l_bool @ member133545693t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(1206,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( preallocated @ B ) )
     => ( ( hBOOL @ ( hext @ B @ A ) )
       => ( hBOOL @ ( preallocated @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_993_preallocated__hext) ).

thf(5928,plain,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( preallocated @ B ) )
     => ( ( hBOOL @ ( hext @ B @ A ) )
       => ( hBOOL @ ( preallocated @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).

thf(858,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ F @ G ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ H ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ E @ B @ H ) @ ( map_va1934808527t_char @ val_list_char @ C ) ) @ D ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ ( call_list_char @ F @ A @ B ) @ G ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1144_CallNull) ).

thf(4577,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ F @ G ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ H ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ E @ B @ H ) @ ( map_va1934808527t_char @ val_list_char @ C ) ) @ D ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ ( call_list_char @ F @ A @ B ) @ G ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).

thf(807,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ I @ J @ K ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ L ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ M ) @ N ) ) )
     => ( ( ( hAPP_n546249108on_val @ M @ L )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
       => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ G ) @ F ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ I ) ) ) )
         => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ I @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ M ) @ ( fun_up1149430426on_val @ N @ B @ ( hAPP_val_option_val @ some_val @ ( addr @ L ) ) ) ) ) @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) )
           => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ I @ ( tryCatch_list_char @ J @ F @ B @ A ) @ K ) @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ B @ ( hAPP_l207779698on_val @ N @ B ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_976_TryCatch) ).

thf(4359,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ I @ J @ K ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ L ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ M ) @ N ) ) )
     => ( ( ( hAPP_n546249108on_val @ M @ L )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
       => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ G ) @ F ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ I ) ) ) )
         => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ I @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ M ) @ ( fun_up1149430426on_val @ N @ B @ ( hAPP_val_option_val @ some_val @ ( addr @ L ) ) ) ) ) @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) )
           => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ I @ ( tryCatch_list_char @ J @ F @ B @ A ) @ K ) @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ B @ ( hAPP_l207779698on_val @ N @ B ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).

thf(524,axiom,
    ! [A: $i,B: $i] :
      ( ( is_bool @ B )
     => ( is_bool @ ( hAPP_bool_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) ).

thf(3274,plain,
    ! [A: $i,B: $i] :
      ( ( is_bool @ B )
     => ( is_bool @ ( hAPP_bool_bool @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(1169,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f1520735791l_bool @ ( ord_le1151384881r_bool @ ( hAPP_f719350875r_bool @ ( hAPP_f2133563379r_bool @ cOMBC_1025440566r_bool @ ( hAPP_f1957374161r_bool @ ( hAPP_f304993943r_bool @ cOMBB_847828016t_char @ cOMBC_516637475l_bool ) @ ( hAPP_f1817350437l_bool @ ( hAPP_f614662951l_bool @ cOMBB_1558246132t_char @ ( hAPP_f251669717l_bool @ cOMBB_773661144t_char @ member1771544038t_char ) ) @ produc1483578759t_char ) ) ) @ A ) ) @ ( hAPP_f719350875r_bool @ ( hAPP_f2133563379r_bool @ cOMBC_1025440566r_bool @ ( hAPP_f1957374161r_bool @ ( hAPP_f304993943r_bool @ cOMBB_847828016t_char @ cOMBC_516637475l_bool ) @ ( hAPP_f1817350437l_bool @ ( hAPP_f614662951l_bool @ cOMBB_1558246132t_char @ ( hAPP_f251669717l_bool @ cOMBB_773661144t_char @ member1771544038t_char ) ) @ produc1483578759t_char ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f2050077417l_bool @ ( ord_le725666495r_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_807_pred__subset__eq2) ).

thf(5758,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( hAPP_f1520735791l_bool @ ( ord_le1151384881r_bool @ ( hAPP_f719350875r_bool @ ( hAPP_f2133563379r_bool @ cOMBC_1025440566r_bool @ ( hAPP_f1957374161r_bool @ ( hAPP_f304993943r_bool @ cOMBB_847828016t_char @ cOMBC_516637475l_bool ) @ ( hAPP_f1817350437l_bool @ ( hAPP_f614662951l_bool @ cOMBB_1558246132t_char @ ( hAPP_f251669717l_bool @ cOMBB_773661144t_char @ member1771544038t_char ) ) @ produc1483578759t_char ) ) ) @ A ) ) @ ( hAPP_f719350875r_bool @ ( hAPP_f2133563379r_bool @ cOMBC_1025440566r_bool @ ( hAPP_f1957374161r_bool @ ( hAPP_f304993943r_bool @ cOMBB_847828016t_char @ cOMBC_516637475l_bool ) @ ( hAPP_f1817350437l_bool @ ( hAPP_f614662951l_bool @ cOMBB_1558246132t_char @ ( hAPP_f251669717l_bool @ cOMBB_773661144t_char @ member1771544038t_char ) ) @ produc1483578759t_char ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f2050077417l_bool @ ( ord_le725666495r_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f2050077417l_bool @ ( ord_le725666495r_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1520735791l_bool @ ( ord_le1151384881r_bool @ ( hAPP_f719350875r_bool @ ( hAPP_f2133563379r_bool @ cOMBC_1025440566r_bool @ ( hAPP_f1957374161r_bool @ ( hAPP_f304993943r_bool @ cOMBB_847828016t_char @ cOMBC_516637475l_bool ) @ ( hAPP_f1817350437l_bool @ ( hAPP_f614662951l_bool @ cOMBB_1558246132t_char @ ( hAPP_f251669717l_bool @ cOMBB_773661144t_char @ member1771544038t_char ) ) @ produc1483578759t_char ) ) ) @ A ) ) @ ( hAPP_f719350875r_bool @ ( hAPP_f2133563379r_bool @ cOMBC_1025440566r_bool @ ( hAPP_f1957374161r_bool @ ( hAPP_f304993943r_bool @ cOMBB_847828016t_char @ cOMBC_516637475l_bool ) @ ( hAPP_f1817350437l_bool @ ( hAPP_f614662951l_bool @ cOMBB_1558246132t_char @ ( hAPP_f251669717l_bool @ cOMBB_773661144t_char @ member1771544038t_char ) ) @ produc1483578759t_char ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).

thf(30,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P1384137393r_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1384137393r_bool @ A @ ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_split__paired__All) ).

thf(1374,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P1384137393r_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1384137393r_bool @ A @ ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1384137393r_bool @ A @ ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P1384137393r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(809,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( ( is_bop @ B )
         => ( A
           != ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_prod_Oexhaust) ).

thf(4365,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( ( is_bop @ B )
         => ( A
           != ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).

thf(319,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P1235399154l_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1235399154l_bool @ A @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_split__paired__All) ).

thf(2524,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P1235399154l_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1235399154l_bool @ A @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1235399154l_bool @ A @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P1235399154l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(551,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( wTrt_1 @ E @ F @ G @ H @ I ) )
     => ( ( hBOOL @ ( wTrt_1 @ E @ F @ ( fun_up424764369ion_ty @ G @ A @ ( hAPP_ty_option_ty @ some_ty @ ( hAPP_list_char_ty @ class @ B ) ) ) @ C @ D ) )
       => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ E ) @ I ) @ D ) )
         => ( hBOOL @ ( wTrt_1 @ E @ F @ G @ ( tryCatch_list_char @ H @ B @ A @ C ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_982_WTrtTry) ).

thf(3396,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( wTrt_1 @ E @ F @ G @ H @ I ) )
     => ( ( hBOOL @ ( wTrt_1 @ E @ F @ ( fun_up424764369ion_ty @ G @ A @ ( hAPP_ty_option_ty @ some_ty @ ( hAPP_list_char_ty @ class @ B ) ) ) @ C @ D ) )
       => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ E ) @ I ) @ D ) )
         => ( hBOOL @ ( wTrt_1 @ E @ F @ G @ ( tryCatch_list_char @ H @ B @ A @ C ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(99,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ E ) )
     => ( hBOOL @ ( wTrt @ A @ B @ C @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1021_wt__wt_H) ).

thf(1631,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ E ) )
     => ( hBOOL @ ( wTrt @ A @ B @ C @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(1043,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f861853459l_bool @ ( ord_le1270183657l_bool @ ( hAPP_f447422815l_bool @ ( hAPP_f2052909183l_bool @ cOMBC_766524526l_bool @ ( hAPP_f1427871743l_bool @ ( hAPP_f32926423l_bool @ cOMBB_779086262on_val @ cOMBC_1491642377l_bool ) @ ( hAPP_f1082373989l_bool @ ( hAPP_f869803751l_bool @ cOMBB_555068556on_val @ ( hAPP_f810261999l_bool @ cOMBB_1034324152on_val @ member875476972on_val ) ) @ produc1611380469on_val ) ) ) @ A ) ) @ ( hAPP_f447422815l_bool @ ( hAPP_f2052909183l_bool @ cOMBC_766524526l_bool @ ( hAPP_f1427871743l_bool @ ( hAPP_f32926423l_bool @ cOMBB_779086262on_val @ cOMBC_1491642377l_bool ) @ ( hAPP_f1082373989l_bool @ ( hAPP_f869803751l_bool @ cOMBB_555068556on_val @ ( hAPP_f810261999l_bool @ cOMBB_1034324152on_val @ member875476972on_val ) ) @ produc1611380469on_val ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_802_pred__subset__eq2) ).

thf(5241,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( hAPP_f861853459l_bool @ ( ord_le1270183657l_bool @ ( hAPP_f447422815l_bool @ ( hAPP_f2052909183l_bool @ cOMBC_766524526l_bool @ ( hAPP_f1427871743l_bool @ ( hAPP_f32926423l_bool @ cOMBB_779086262on_val @ cOMBC_1491642377l_bool ) @ ( hAPP_f1082373989l_bool @ ( hAPP_f869803751l_bool @ cOMBB_555068556on_val @ ( hAPP_f810261999l_bool @ cOMBB_1034324152on_val @ member875476972on_val ) ) @ produc1611380469on_val ) ) ) @ A ) ) @ ( hAPP_f447422815l_bool @ ( hAPP_f2052909183l_bool @ cOMBC_766524526l_bool @ ( hAPP_f1427871743l_bool @ ( hAPP_f32926423l_bool @ cOMBB_779086262on_val @ cOMBC_1491642377l_bool ) @ ( hAPP_f1082373989l_bool @ ( hAPP_f869803751l_bool @ cOMBB_555068556on_val @ ( hAPP_f810261999l_bool @ cOMBB_1034324152on_val @ member875476972on_val ) ) @ produc1611380469on_val ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f861853459l_bool @ ( ord_le1270183657l_bool @ ( hAPP_f447422815l_bool @ ( hAPP_f2052909183l_bool @ cOMBC_766524526l_bool @ ( hAPP_f1427871743l_bool @ ( hAPP_f32926423l_bool @ cOMBB_779086262on_val @ cOMBC_1491642377l_bool ) @ ( hAPP_f1082373989l_bool @ ( hAPP_f869803751l_bool @ cOMBB_555068556on_val @ ( hAPP_f810261999l_bool @ cOMBB_1034324152on_val @ member875476972on_val ) ) @ produc1611380469on_val ) ) ) @ A ) ) @ ( hAPP_f447422815l_bool @ ( hAPP_f2052909183l_bool @ cOMBC_766524526l_bool @ ( hAPP_f1427871743l_bool @ ( hAPP_f32926423l_bool @ cOMBB_779086262on_val @ cOMBC_1491642377l_bool ) @ ( hAPP_f1082373989l_bool @ ( hAPP_f869803751l_bool @ cOMBB_555068556on_val @ ( hAPP_f810261999l_bool @ cOMBB_1034324152on_val @ member875476972on_val ) ) @ produc1611380469on_val ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).

thf(1208,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ ( throw_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ D ) ) ) @ ( red @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1101_red__reds_OCondThrow) ).

thf(5933,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ ( throw_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ D ) ) ) @ ( red @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).

thf(510,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] :
          ( ( ( hAPP_n546249108on_val @ B @ C )
            = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
         => ? [F: $i] :
              ( ( hAPP_n546249108on_val @ A @ C )
              = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ F ) ) ) )
     => ( hBOOL @ ( hext @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_591_hextI) ).

thf(3234,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] :
          ( ( ( hAPP_n546249108on_val @ B @ C )
            = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
         => ? [F: $i] :
              ( ( hAPP_n546249108on_val @ A @ C )
              = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ F ) ) ) )
     => ( hBOOL @ ( hext @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(588,axiom,
    ! [A: $i] :
      ( ( hAPP_nat_option_nat @ some_nat @ A )
     != none_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_609_option_Osimps_I3_J) ).

thf(3519,plain,
    ! [A: $i] :
      ( ( hAPP_nat_option_nat @ some_nat @ A )
     != none_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(1190,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fFalse ) ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ E @ A @ B ) ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1109_CondReds2F) ).

thf(5844,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fFalse ) ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ E @ A @ B ) ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).

thf(310,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( cast_list_char @ B @ ( throw_list_char @ C ) ) @ D ) @ ( throw_list_char @ C ) ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_986_redp__redsp_OCastThrow) ).

thf(2489,plain,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( cast_list_char @ B @ ( throw_list_char @ C ) ) @ D ) @ ( throw_list_char @ C ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(287,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( ( is_bop @ B )
         => ( A
           != ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_prod__cases3) ).

thf(2393,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( ( is_bop @ B )
         => ( A
           != ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(1136,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P27757617y_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P27757617y_bool @ A @ ( hAPP_t708040077har_ty @ ( hAPP_P827589667har_ty @ produc1265154397har_ty @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_split__paired__All) ).

thf(5612,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P27757617y_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P27757617y_bool @ A @ ( hAPP_t708040077har_ty @ ( hAPP_P827589667har_ty @ produc1265154397har_ty @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P27757617y_bool @ A @ ( hAPP_t708040077har_ty @ ( hAPP_P827589667har_ty @ produc1265154397har_ty @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P27757617y_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).

thf(388,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P943837928l_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] :
          ( ( is_bop @ B )
         => ( hBOOL @ ( hAPP_P943837928l_bool @ A @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_split__paired__All) ).

thf(2806,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P943837928l_bool @ A @ B ) )
       => ! [B: $i,C: $i] :
            ( ( is_bop @ B )
           => ( hBOOL @ ( hAPP_P943837928l_bool @ A @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) ) ) )
      & ( ! [B: $i,C: $i] :
            ( ( is_bop @ B )
           => ( hBOOL @ ( hAPP_P943837928l_bool @ A @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P943837928l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(173,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P2028072621l_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P2028072621l_bool @ A @ ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_split__paired__All) ).

thf(1965,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P2028072621l_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P2028072621l_bool @ A @ ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P2028072621l_bool @ A @ ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P2028072621l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(958,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f2041029616l_bool @ ( ord_le285175110l_bool @ ( hAPP_f844901525l_bool @ ( hAPP_f348508809l_bool @ cOMBC_622308798l_bool @ ( hAPP_f1149562121l_bool @ ( hAPP_f1850037271l_bool @ cOMBB_773375802t_char @ cOMBC_2141828763l_bool ) @ ( hAPP_f1752856401l_bool @ ( hAPP_f552300311l_bool @ cOMBB_1270208498t_char @ ( hAPP_f1564338425l_bool @ cOMBB_1078680455on_val @ member1972431429on_val ) ) @ produc379668296on_val ) ) ) @ A ) ) @ ( hAPP_f844901525l_bool @ ( hAPP_f348508809l_bool @ cOMBC_622308798l_bool @ ( hAPP_f1149562121l_bool @ ( hAPP_f1850037271l_bool @ cOMBB_773375802t_char @ cOMBC_2141828763l_bool ) @ ( hAPP_f1752856401l_bool @ ( hAPP_f552300311l_bool @ cOMBB_1270208498t_char @ ( hAPP_f1564338425l_bool @ cOMBB_1078680455on_val @ member1972431429on_val ) ) @ produc379668296on_val ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f837795298l_bool @ ( ord_le1461833060l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_811_pred__subset__eq2) ).

thf(4946,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( hAPP_f2041029616l_bool @ ( ord_le285175110l_bool @ ( hAPP_f844901525l_bool @ ( hAPP_f348508809l_bool @ cOMBC_622308798l_bool @ ( hAPP_f1149562121l_bool @ ( hAPP_f1850037271l_bool @ cOMBB_773375802t_char @ cOMBC_2141828763l_bool ) @ ( hAPP_f1752856401l_bool @ ( hAPP_f552300311l_bool @ cOMBB_1270208498t_char @ ( hAPP_f1564338425l_bool @ cOMBB_1078680455on_val @ member1972431429on_val ) ) @ produc379668296on_val ) ) ) @ A ) ) @ ( hAPP_f844901525l_bool @ ( hAPP_f348508809l_bool @ cOMBC_622308798l_bool @ ( hAPP_f1149562121l_bool @ ( hAPP_f1850037271l_bool @ cOMBB_773375802t_char @ cOMBC_2141828763l_bool ) @ ( hAPP_f1752856401l_bool @ ( hAPP_f552300311l_bool @ cOMBB_1270208498t_char @ ( hAPP_f1564338425l_bool @ cOMBB_1078680455on_val @ member1972431429on_val ) ) @ produc379668296on_val ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f837795298l_bool @ ( ord_le1461833060l_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f837795298l_bool @ ( ord_le1461833060l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2041029616l_bool @ ( ord_le285175110l_bool @ ( hAPP_f844901525l_bool @ ( hAPP_f348508809l_bool @ cOMBC_622308798l_bool @ ( hAPP_f1149562121l_bool @ ( hAPP_f1850037271l_bool @ cOMBB_773375802t_char @ cOMBC_2141828763l_bool ) @ ( hAPP_f1752856401l_bool @ ( hAPP_f552300311l_bool @ cOMBB_1270208498t_char @ ( hAPP_f1564338425l_bool @ cOMBB_1078680455on_val @ member1972431429on_val ) ) @ produc379668296on_val ) ) ) @ A ) ) @ ( hAPP_f844901525l_bool @ ( hAPP_f348508809l_bool @ cOMBC_622308798l_bool @ ( hAPP_f1149562121l_bool @ ( hAPP_f1850037271l_bool @ cOMBB_773375802t_char @ cOMBC_2141828763l_bool ) @ ( hAPP_f1752856401l_bool @ ( hAPP_f552300311l_bool @ cOMBB_1270208498t_char @ ( hAPP_f1564338425l_bool @ cOMBB_1078680455on_val @ member1972431429on_val ) ) @ produc379668296on_val ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).

thf(841,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i,E: $i,F: $i] :
          ( A
         != ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ B ) @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_prod__cases5) ).

thf(4505,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i,E: $i,F: $i] :
          ( A
         != ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ B ) @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).

thf(721,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ C ) @ D )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ F ) ) )
     => ( ~ ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ ( transi1065307915t_char @ ( subcls744239332t_char @ A ) ) @ E ) @ B ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( cast_list_char @ B @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) @ C ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) ) ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1056_redp__redsp_ORedCastFail) ).

thf(4041,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ C ) @ D )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ F ) ) )
     => ( ~ ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ ( transi1065307915t_char @ ( subcls744239332t_char @ A ) ) @ E ) @ B ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( cast_list_char @ B @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) @ C ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) ) ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).

thf(748,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ E ) @ F )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ G ) @ C ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ D ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ C @ A @ B ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ A @ ( hAPP_list_char_ty @ class @ C ) @ ( seq_list_char @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ B ) ) ) @ E ) ) ) @ ( red @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_979_red__reds_ORedTryCatch) ).

thf(4144,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ E ) @ F )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ G ) @ C ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ D ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ C @ A @ B ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ A @ ( hAPP_list_char_ty @ class @ C ) @ ( seq_list_char @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ B ) ) ) @ E ) ) ) @ ( red @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).

thf(546,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ A ) @ B ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) ) @ ( lex_pr307591827t_char @ E @ F ) ) )
    <=> ( ( hBOOL @ ( hAPP_f348753975l_bool @ ( hAPP_P1033205013l_bool @ member273646106st_val @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ A ) @ C ) ) @ E ) )
        | ( ( A = C )
          & ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ B ) @ D ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_382_in__lex__prod) ).

thf(3372,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ A ) @ B ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) ) @ ( lex_pr307591827t_char @ E @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f348753975l_bool @ ( hAPP_P1033205013l_bool @ member273646106st_val @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ B ) @ D ) ) @ F ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f348753975l_bool @ ( hAPP_P1033205013l_bool @ member273646106st_val @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ B ) @ D ) ) @ F ) ) ) )
       => ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ A ) @ B ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) ) @ ( lex_pr307591827t_char @ E @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(142,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ A ) @ B )
        = ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_Pair__eq) ).

thf(1833,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ A ) @ B )
          = ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ A ) @ B )
          = ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(1093,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ ( produc1159035454l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_513_curryD) ).

thf(5456,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ ( produc1159035454l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).

thf(1100,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_e286792811l_bool @ ( hAPP_f1614195593l_bool @ ( hAPP_f705562443l_bool @ cOMBB_507006011t_char @ A ) @ B ) @ C )
      = ( hAPP_f826324045l_bool @ A @ ( hAPP_e1659493427on_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O) ).

thf(5474,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_e286792811l_bool @ ( hAPP_f1614195593l_bool @ ( hAPP_f705562443l_bool @ cOMBB_507006011t_char @ A ) @ B ) @ C )
      = ( hAPP_f826324045l_bool @ A @ ( hAPP_e1659493427on_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).

thf(251,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_bool_bool @ ( ord_less_eq_bool @ ( hAPP_list_char_bool @ B @ A ) ) @ ( hAPP_list_char_bool @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_829_le__funD) ).

thf(2225,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_bool_bool @ ( ord_less_eq_bool @ ( hAPP_list_char_bool @ B @ A ) ) @ ( hAPP_list_char_bool @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(1105,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B )
        = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_Pair__inject) ).

thf(5488,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B )
        = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).

thf(516,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_712_set__mp) ).

thf(3255,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(654,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ ( cons_list_char @ A @ B ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ ( cons_ty @ C @ D ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ ( cons_val @ E @ F ) ) @ G ) ) ) )
      = ( block_list_char @ A @ C @ ( seq_list_char @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ E ) ) @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ F ) @ G ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1178_blocks_Osimps_I1_J) ).

thf(3811,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ ( cons_list_char @ A @ B ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ ( cons_ty @ C @ D ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ ( cons_val @ E @ F ) ) @ G ) ) ) )
      = ( block_list_char @ A @ C @ ( seq_list_char @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ E ) ) @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ F ) @ G ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).

thf(382,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1889282162l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Type__Oty_J_Mtc__fun_Itc__prod_Itc__) ).

thf(2791,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1889282162l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(511,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ C ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ D ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( throw_list_char @ B ) @ C ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1042_ThrowNull) ).

thf(3240,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ C ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ D ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( throw_list_char @ B ) @ C ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(463,axiom,
    ! [A: $i] :
      ( ( hAPP_ty_option_ty @ some_ty @ A )
     != none_ty ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_610_option_Osimps_I3_J) ).

thf(3081,plain,
    ! [A: $i] :
      ( ( hAPP_ty_option_ty @ some_ty @ A )
     != none_ty ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(164,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i] :
      ( ( hBOOL @ ( wTrt @ I @ J @ K @ L @ ( hAPP_list_char_ty @ class @ M ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( method1809630380t_char @ I @ M @ C @ D @ E @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ F ) @ G ) ) @ H ) )
       => ( ( hBOOL @ ( wTrts @ I @ J @ K @ A @ B ) )
         => ( ( hBOOL @ ( list_all2_ty_ty @ ( widen_2090681816t_char @ I ) @ B @ D ) )
           => ( hBOOL @ ( wTrt @ I @ J @ K @ ( call_list_char @ L @ C @ A ) @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1192_WTrt_H__WTrts_H_Ointros_I12_J) ).

thf(1929,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i] :
      ( ( hBOOL @ ( wTrt @ I @ J @ K @ L @ ( hAPP_list_char_ty @ class @ M ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( method1809630380t_char @ I @ M @ C @ D @ E @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ F ) @ G ) ) @ H ) )
       => ( ( hBOOL @ ( wTrts @ I @ J @ K @ A @ B ) )
         => ( ( hBOOL @ ( list_all2_ty_ty @ ( widen_2090681816t_char @ I ) @ B @ D ) )
           => ( hBOOL @ ( wTrt @ I @ J @ K @ ( call_list_char @ L @ C @ A ) @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(1210,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( B
            = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) )
         => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ C ) @ D ) ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_552_splitI2) ).

thf(5940,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( B
            = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) )
         => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ C ) @ D ) ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).

thf(693,axiom,
    ! [A: $i] :
      ( ? [B: $i] : ( hBOOL @ ( hAPP_P449474095r_bool @ A @ B ) )
    <=> ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P449474095r_bool @ A @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_split__paired__Ex) ).

thf(3945,plain,
    ! [A: $i] :
      ( ( ? [B: $i] : ( hBOOL @ ( hAPP_P449474095r_bool @ A @ B ) )
       => ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P449474095r_bool @ A @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) ) )
      & ( ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P449474095r_bool @ A @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) )
       => ? [B: $i] : ( hBOOL @ ( hAPP_P449474095r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).

thf(527,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ A ) @ B )
        = ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_Pair__inject) ).

thf(3283,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ A ) @ B )
        = ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(1140,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ A @ B @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) )
     => ( hBOOL @ ( hext @ C @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1148_evals__hext) ).

thf(5627,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ A @ B @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) )
     => ( hBOOL @ ( hext @ C @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).

thf(521,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ E @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fTrue ) ) ) @ G ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ A @ G ) @ ( throw_list_char @ B ) ) @ C ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ ( while_list_char @ E @ A ) @ F ) @ ( throw_list_char @ B ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1085_WhileBodyThrow) ).

thf(3266,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ E @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fTrue ) ) ) @ G ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ A @ G ) @ ( throw_list_char @ B ) ) @ C ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ ( while_list_char @ E @ A ) @ F ) @ ( throw_list_char @ B ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(357,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P2077557811l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It_029) ).

thf(2674,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P2077557811l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(188,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) ) @ ( transi61620055on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ D ) @ E ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ I ) @ J ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) ) @ ( transi61620055on_val @ F ) ) )
               => ( ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_770_converse__rtrancl__induct2) ).

thf(2016,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) ) @ ( transi61620055on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ D ) @ E ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ I ) @ J ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) ) @ ( transi61620055on_val @ F ) ) )
               => ( ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(316,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( E
        = ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ F ) @ ( cons_exp_list_char @ ( throw_list_char @ G ) @ H ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ B ) @ C @ E ) @ D ) @ ( throw_list_char @ G ) ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1159_redp__redsp_OCallThrowParams) ).

thf(2514,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( E
        = ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ F ) @ ( cons_exp_list_char @ ( throw_list_char @ G ) @ H ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ B ) @ C @ E ) @ D ) @ ( throw_list_char @ G ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(742,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ A ) @ B )
        = ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_Pair__inject) ).

thf(4122,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ A ) @ B )
        = ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).

thf(523,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ G @ H ) @ ( hAPP_v834067052t_char @ val_list_char @ I ) ) @ J ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ C @ J ) @ ( throw_list_char @ D ) ) @ E ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ ( fAss_list_char @ G @ A @ B @ C ) @ H ) @ ( throw_list_char @ D ) ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_927_eval__evals_OFAssThrow2) ).

thf(3272,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ G @ H ) @ ( hAPP_v834067052t_char @ val_list_char @ I ) ) @ J ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ C @ J ) @ ( throw_list_char @ D ) ) @ E ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ ( fAss_list_char @ G @ A @ B @ C ) @ H ) @ ( throw_list_char @ D ) ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(914,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f720086610l_bool @ ( hAPP_f292637069l_bool @ ( hAPP_f1168269397l_bool @ cOMBB_1293776864on_val @ A ) @ B ) @ C )
      = ( hAPP_P998768845l_bool @ A @ ( hAPP_f1727192346on_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_060) ).

thf(4801,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f720086610l_bool @ ( hAPP_f292637069l_bool @ ( hAPP_f1168269397l_bool @ cOMBB_1293776864on_val @ A ) @ B ) @ C )
      = ( hAPP_P998768845l_bool @ A @ ( hAPP_f1727192346on_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).

thf(134,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_list_char_bool @ ( hAPP_f335969926r_bool @ ( hAPP_f1367982615r_bool @ cOMBC_1603044337l_bool @ A ) @ B ) @ C )
      = ( hAPP_f2106398425l_bool @ ( hAPP_l553007690l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro) ).

thf(1795,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_list_char_bool @ ( hAPP_f335969926r_bool @ ( hAPP_f1367982615r_bool @ cOMBC_1603044337l_bool @ A ) @ B ) @ C )
      = ( hAPP_f2106398425l_bool @ ( hAPP_l553007690l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(114,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P92196306r_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J__024) ).

thf(1701,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P92196306r_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(288,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f434955681l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_006) ).

thf(2398,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f434955681l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(968,axiom,
    ! [A: $i,B: $i] :
      ( ( ( hAPP_val_option_val @ some_val @ A )
        = ( hAPP_val_option_val @ some_val @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_356_option_Oinject) ).

thf(4975,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( hAPP_val_option_val @ some_val @ A )
          = ( hAPP_val_option_val @ some_val @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( hAPP_val_option_val @ some_val @ A )
          = ( hAPP_val_option_val @ some_val @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).

thf(555,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( fv @ ( call_list_char @ A @ B @ C ) )
      = ( semila919158006r_bool @ ( fv @ A ) @ ( fvs @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1154_fv__fvs_Osimps_I9_J) ).

thf(3404,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( fv @ ( call_list_char @ A @ B @ C ) )
      = ( semila919158006r_bool @ ( fv @ A ) @ ( fvs @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(902,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ A ) @ B )
        = ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_Pair__eq) ).

thf(4758,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ A ) @ B )
          = ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ A ) @ B )
          = ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).

thf(360,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_prod_Oexhaust) ).

thf(2695,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(983,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) ) @ ( red @ I ) ) )
     => ( ( hBOOL @ ( wTrt_1 @ I @ D @ A @ C @ B ) )
       => ( ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ I ) @ D ) )
         => ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ I ) @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_red__preserves__hconf) ).

thf(5022,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) ) @ ( red @ I ) ) )
     => ( ( hBOOL @ ( wTrt_1 @ I @ D @ A @ C @ B ) )
       => ( ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ I ) @ D ) )
         => ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ I ) @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).

thf(60,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f851858423l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_) ).

thf(1488,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f851858423l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(1218,axiom,
    ! [A: $i,B: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) ) @ A ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ A ) ) ) @ ( red @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1048_red__reds_ORedThrowNull) ).

thf(5965,plain,
    ! [A: $i,B: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) ) @ A ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ A ) ) ) @ ( red @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218]) ).

thf(1120,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( new_Addr @ D )
        = none_nat )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( new_list_char @ A ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ B ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ outOfMemory ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ B ) ) ) ) @ ( red @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1124_red__reds_ORedNewFail) ).

thf(5546,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( new_Addr @ D )
        = none_nat )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( new_list_char @ A ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ B ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ outOfMemory ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ B ) ) ) ) @ ( red @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).

thf(646,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ A @ ( cons_exp_list_char @ B @ C ) @ D ) @ E ) @ F ) )
     => ( ! [G: $i,H: $i,I: $i] :
            ( ( E
              = ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ G ) @ I ) )
           => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ H ) )
             => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ A @ C @ H ) @ I ) @ F ) ) ) )
       => ~ ! [G: $i] :
              ( ( E
                = ( cons_exp_list_char @ ( throw_list_char @ G ) @ C ) )
             => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( throw_list_char @ G ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1167_evals__cases_I2_J) ).

thf(3773,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ A @ ( cons_exp_list_char @ B @ C ) @ D ) @ E ) @ F ) )
     => ( ! [G: $i,H: $i,I: $i] :
            ( ( E
              = ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ G ) @ I ) )
           => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ H ) )
             => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ A @ C @ H ) @ I ) @ F ) ) ) )
       => ~ ! [G: $i] :
              ( ( E
                = ( cons_exp_list_char @ ( throw_list_char @ G ) @ C ) )
             => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( throw_list_char @ G ) ) @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(1132,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( transi921647814on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) @ ( transi921647814on_val @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_787_rtrancl__induct2) ).

thf(5595,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( transi921647814on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) @ ( transi921647814on_val @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).

thf(735,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( final_list_char @ C ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ C @ B ) @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_889_eval__finalId) ).

thf(4099,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( final_list_char @ C ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ C @ B ) @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).

thf(478,axiom,
    ! [A: $i,B: $i] :
      ( ( fv @ ( seq_list_char @ A @ B ) )
      = ( semila919158006r_bool @ ( fv @ A ) @ ( fv @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_884_fv__fvs_Osimps_I11_J) ).

thf(3123,plain,
    ! [A: $i,B: $i] :
      ( ( fv @ ( seq_list_char @ A @ B ) )
      = ( semila919158006r_bool @ ( fv @ A ) @ ( fv @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(629,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( fun_up2041264236on_val @ ( fun_up2041264236on_val @ A @ B @ C ) @ B @ D )
      = ( fun_up2041264236on_val @ A @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_fun__upd__upd) ).

thf(3700,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( fun_up2041264236on_val @ ( fun_up2041264236on_val @ A @ B @ C ) @ B @ D )
      = ( fun_up2041264236on_val @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(294,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) @ ( transi935034983cl_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ A ) ) @ D ) )
       => ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ A ) ) @ ( transi935034983cl_val @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_729_rtrancl_Ortrancl__into__rtrancl) ).

thf(2425,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) @ ( transi935034983cl_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ A ) ) @ D ) )
       => ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ A ) ) @ ( transi935034983cl_val @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(531,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1987619678r_bool @ ( hAPP_f2071340985r_bool @ ( hAPP_f133320957r_bool @ cOMBC_1127703214r_bool @ A ) @ B ) @ C )
      = ( hAPP_f1298720864r_bool @ ( hAPP_l96108383r_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Type__Oty_J_000tc__fun_Itc__prod_It) ).

thf(3304,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1987619678r_bool @ ( hAPP_f2071340985r_bool @ ( hAPP_f133320957r_bool @ cOMBC_1127703214r_bool @ A ) @ B ) @ C )
      = ( hAPP_f1298720864r_bool @ ( hAPP_l96108383r_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(466,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hext @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Objects_Ohext) ).

thf(3091,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hext @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(242,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( is_bop @ A )
        & ( is_bop @ B )
        & ( is_bop @ C )
        & ( is_bop @ D ) )
     => ( ( ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ A ) @ B )
          = ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) )
       => ~ ( ( A = C )
           => ( B != D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_Pair__inject) ).

thf(2193,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( is_bop @ A )
        & ( is_bop @ B )
        & ( is_bop @ C )
        & ( is_bop @ D ) )
     => ( ( ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ A ) @ B )
          = ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) )
       => ~ ( ( A = C )
           => ( B != D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(444,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f1033709212l_bool @ ( hAPP_f603925568l_bool @ ( hAPP_f181262431l_bool @ cOMBC_832625297y_bool @ A ) @ B ) @ C )
      = ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Optio) ).

thf(3023,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f1033709212l_bool @ ( hAPP_f603925568l_bool @ ( hAPP_f181262431l_bool @ cOMBC_832625297y_bool @ A ) @ B ) @ C )
      = ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(853,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f348753975l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__List__O) ).

thf(4558,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f348753975l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).

thf(987,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( hBOOL @ ( hAPP_f288221747l_bool @ ( hAPP_P569585933l_bool @ member520253462har_ty @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f288221747l_bool @ ( hAPP_P569585933l_bool @ member520253462har_ty @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_pred__equals__eq2) ).

thf(5033,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f288221747l_bool @ ( hAPP_P569585933l_bool @ member520253462har_ty @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f288221747l_bool @ ( hAPP_P569585933l_bool @ member520253462har_ty @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f288221747l_bool @ ( hAPP_P569585933l_bool @ member520253462har_ty @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f288221747l_bool @ ( hAPP_P569585933l_bool @ member520253462har_ty @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f288221747l_bool @ ( hAPP_P569585933l_bool @ member520253462har_ty @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f288221747l_bool @ ( hAPP_P569585933l_bool @ member520253462har_ty @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f288221747l_bool @ ( hAPP_P569585933l_bool @ member520253462har_ty @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f288221747l_bool @ ( hAPP_P569585933l_bool @ member520253462har_ty @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).

thf(743,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_v834067052t_char @ val_list_char @ A )
     != ( lAss_list_char @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_577_exp_Osimps_I74_J) ).

thf(4127,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_v834067052t_char @ val_list_char @ A )
     != ( lAss_list_char @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).

thf(249,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i,F: $i,G: $i] : ( hBOOL @ ( hAPP_P2028072621l_bool @ B @ ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ C ) @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ D ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) ) ) ) )
     => ( hBOOL @ ( hAPP_P2028072621l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_prod__induct5) ).

thf(2220,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i,F: $i,G: $i] : ( hBOOL @ ( hAPP_P2028072621l_bool @ B @ ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ C ) @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ D ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) ) ) ) )
     => ( hBOOL @ ( hAPP_P2028072621l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(699,axiom,
    ! [A: $i] :
      ( ? [B: $i] : ( hBOOL @ ( hAPP_P71593144l_bool @ A @ B ) )
    <=> ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P71593144l_bool @ A @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_split__paired__Ex) ).

thf(3964,plain,
    ! [A: $i] :
      ( ( ? [B: $i] : ( hBOOL @ ( hAPP_P71593144l_bool @ A @ B ) )
       => ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P71593144l_bool @ A @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) ) )
      & ( ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P71593144l_bool @ A @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) )
       => ? [B: $i] : ( hBOOL @ ( hAPP_P71593144l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).

thf(192,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( wTrt @ E @ F @ G @ H @ nt ) )
     => ( ( hBOOL @ ( wTrts @ E @ F @ G @ C @ D ) )
       => ( hBOOL @ ( wTrt @ E @ F @ G @ ( call_list_char @ H @ A @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1196_WTrt_H__WTrts_H_Ointros_I13_J) ).

thf(2029,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( wTrt @ E @ F @ G @ H @ nt ) )
     => ( ( hBOOL @ ( wTrts @ E @ F @ G @ C @ D ) )
       => ( hBOOL @ ( wTrt @ E @ F @ G @ ( call_list_char @ H @ A @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(764,axiom,
    ! [A: $i] :
      ( ! [B: $i] :
          ( A
         != ( hAPP_ty_option_ty @ some_ty @ B ) )
    <=> ( A = none_ty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_615_not__Some__eq) ).

thf(4186,plain,
    ! [A: $i] :
      ( ( ! [B: $i] :
            ( A
           != ( hAPP_ty_option_ty @ some_ty @ B ) )
       => ( A = none_ty ) )
      & ( ( A = none_ty )
       => ! [B: $i] :
            ( A
           != ( hAPP_ty_option_ty @ some_ty @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).

thf(734,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( ( hAPP_n546249108on_val @ F @ G )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ H ) @ I ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) @ B @ C @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ E ) ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( fun_up2041264236on_val @ F @ G @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ H ) @ ( fun_up204312361on_val @ I @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) @ ( hAPP_val_option_val @ some_val @ D ) ) ) ) ) ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_901_redp__redsp_ORedFAss) ).

thf(4096,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( ( hAPP_n546249108on_val @ F @ G )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ H ) @ I ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) @ B @ C @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ E ) ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( fun_up2041264236on_val @ F @ G @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ H ) @ ( fun_up204312361on_val @ I @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) @ ( hAPP_val_option_val @ some_val @ D ) ) ) ) ) ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).

thf(117,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P2118621157r_bool @ ( hAPP_f1298720864r_bool @ ( hAPP_f225832321r_bool @ cOMBC_1365742487l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1746574980l_bool @ ( hAPP_P2028292026l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__) ).

thf(1707,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P2118621157r_bool @ ( hAPP_f1298720864r_bool @ ( hAPP_f225832321r_bool @ cOMBC_1365742487l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1746574980l_bool @ ( hAPP_P2028292026l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(1072,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ ( throw_list_char @ D ) ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( red @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_937_red__reds_OFAssThrow2) ).

thf(5363,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ ( throw_list_char @ D ) ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( red @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).

thf(452,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f986089162l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__HOL__Obool_J_00) ).

thf(3051,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f986089162l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(407,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ A ) @ B )
        = ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_Pair__inject) ).

thf(2891,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ A ) @ B )
        = ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(979,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ ( fun_up1149430426on_val @ F @ A @ ( hAPP_val_option_val @ some_val @ D ) ) ) ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_590_LAssRedsVal) ).

thf(5011,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ ( fun_up1149430426on_val @ F @ A @ ( hAPP_val_option_val @ some_val @ D ) ) ) ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).

thf(1062,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B )
        = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_Pair__inject) ).

thf(5331,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B )
        = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).

thf(776,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( ( is_bop @ B )
         => ( A
           != ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_PairE) ).

thf(4236,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( ( is_bop @ B )
         => ( A
           != ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).

thf(621,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_f1634841927l_bool @ produc1491230096l_bool @ A ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_399_prod__caseI) ).

thf(3663,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_f1634841927l_bool @ produc1491230096l_bool @ A ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(419,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( cond_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fFalse ) ) @ B @ C ) @ D ) @ C ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1099_redp__redsp_ORedCondF) ).

thf(2935,plain,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( cond_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fFalse ) ) @ B @ C ) @ D ) @ C ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(922,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ ( transi2024712006on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ B ) )
       => ( ! [E: $i,F: $i] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ E ) ) @ ( transi2024712006on_val @ D ) ) )
             => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ E ) @ F ) ) @ D ) )
               => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ E ) )
                 => ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ F ) ) ) ) )
         => ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_798_rtrancl__induct) ).

thf(4822,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ ( transi2024712006on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ B ) )
       => ( ! [E: $i,F: $i] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ E ) ) @ ( transi2024712006on_val @ D ) ) )
             => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ E ) @ F ) ) @ D ) )
               => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ E ) )
                 => ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ F ) ) ) ) )
         => ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).

thf(1028,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) @ A @ B @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ D ) ) ) @ ( red @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1050_red__reds_ORedFAssNull) ).

thf(5190,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) @ A @ B @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ D ) ) ) @ ( red @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).

thf(568,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_823_xt1_I3_J) ).

thf(3436,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(233,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hAPP_l512744617ion_ty @ A @ B )
        = ( hAPP_ty_option_ty @ some_ty @ C ) )
     => ( ( fun_up424764369ion_ty @ A @ B @ ( hAPP_ty_option_ty @ some_ty @ C ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_map__upd__triv) ).

thf(2166,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hAPP_l512744617ion_ty @ A @ B )
        = ( hAPP_ty_option_ty @ some_ty @ C ) )
     => ( ( fun_up424764369ion_ty @ A @ B @ ( hAPP_ty_option_ty @ some_ty @ C ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(613,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ A ) @ B )
        = ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_Pair__eq) ).

thf(3619,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ A ) @ B )
          = ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ A ) @ B )
          = ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(299,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( redsp @ C @ D @ E ) @ F ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ D ) @ E ) @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ F ) ) @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1181_redp__redsp_OCallParams) ).

thf(2457,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( redsp @ C @ D @ E ) @ F ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ D ) @ E ) @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ F ) ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(327,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( block_list_char @ A @ B @ C )
     != ( hAPP_v834067052t_char @ val_list_char @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_581_exp_Osimps_I83_J) ).

thf(2557,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( block_list_char @ A @ B @ C )
     != ( hAPP_v834067052t_char @ val_list_char @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(616,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ A ) @ B )
        = ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_Pair__eq) ).

thf(3641,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ A ) @ B )
          = ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ A ) @ B )
          = ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(1,conjecture,
    hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ea ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( hAPP_val_option_val @ some_val @ v ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ e_a ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ h_a ) @ l_a ) ) ) ) @ ( red @ p ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ea ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( hAPP_val_option_val @ some_val @ v ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ e_a ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ h_a ) @ l_a ) ) ) ) @ ( red @ p ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(1258,plain,
    ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ea ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( hAPP_val_option_val @ some_val @ v ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ e_a ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ h_a ) @ l_a ) ) ) ) @ ( red @ p ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(1018,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_prod__cases3) ).

thf(5158,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).

thf(940,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ ( transi2024712006on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ A ) ) @ ( transi2024712006on_val @ D ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ A ) ) @ ( transi2024712006on_val @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_732_rtrancl__trans) ).

thf(4887,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ ( transi2024712006on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ A ) ) @ ( transi2024712006on_val @ D ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ A ) ) @ ( transi2024712006on_val @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).

thf(542,axiom,
    ! [A: $i] : ( is_bool @ ( final_list_char @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_BigStep_Ofinal_000tc__List__Olist_Itc__String__Ochar_J) ).

thf(3355,plain,
    ! [A: $i] : ( is_bool @ ( final_list_char @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(635,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( D != E )
     => ( ( fun_up2041264236on_val @ ( fun_up2041264236on_val @ A @ D @ B ) @ E @ C )
        = ( fun_up2041264236on_val @ ( fun_up2041264236on_val @ A @ E @ C ) @ D @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_fun__upd__twist) ).

thf(3719,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( D != E )
     => ( ( fun_up2041264236on_val @ ( fun_up2041264236on_val @ A @ D @ B ) @ E @ C )
        = ( fun_up2041264236on_val @ ( fun_up2041264236on_val @ A @ E @ C ) @ D @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(278,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ ( semila1168318597r_bool @ B @ C ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_863_UnE) ).

thf(2358,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ ( semila1168318597r_bool @ B @ C ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(273,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_pred__equals__eq2) ).

thf(2319,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(824,axiom,
    ! [A: $i,B: $i] :
      ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ ( hAPP_o1269033393on_val @ cOMBK_1867744698t_char @ none_val ) @ A @ none_val ) @ B )
      = none_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_632_empty__upd__none) ).

thf(4433,plain,
    ! [A: $i,B: $i] :
      ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ ( hAPP_o1269033393on_val @ cOMBK_1867744698t_char @ none_val ) @ A @ none_val ) @ B )
      = none_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).

thf(315,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_PairE) ).

thf(2510,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(891,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ A ) @ B )
        = ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_Pair__eq) ).

thf(4716,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ A ) @ B )
          = ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ A ) @ B )
          = ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).

thf(318,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f1145256474l_bool @ ( hAPP_f1452292669l_bool @ ( hAPP_f1977633121l_bool @ cOMBB_1303934920on_val @ A ) @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_f61040418l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_038) ).

thf(2521,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f1145256474l_bool @ ( hAPP_f1452292669l_bool @ ( hAPP_f1977633121l_bool @ cOMBB_1303934920on_val @ A ) @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_f61040418l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(323,axiom,
    ! [A: $i] :
      ( ( A != none_f478147469r_bool )
    <=> ? [B: $i] :
          ( A
          = ( hAPP_f363827556r_bool @ some_f80346385r_bool @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_623_not__None__eq) ).

thf(2538,plain,
    ! [A: $i] :
      ( ( ( A != none_f478147469r_bool )
       => ? [B: $i] :
            ( A
            = ( hAPP_f363827556r_bool @ some_f80346385r_bool @ B ) ) )
      & ( ? [B: $i] :
            ( A
            = ( hAPP_f363827556r_bool @ some_f80346385r_bool @ B ) )
       => ( A != none_f478147469r_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(253,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ F @ G ) @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ I ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ B @ I ) @ ( throw_list_char @ C ) ) @ D ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ ( binOp_list_char @ F @ A @ B ) @ G ) @ ( throw_list_char @ C ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_962_eval__evals_OBinOpThrow2) ).

thf(2229,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ F @ G ) @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ I ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ B @ I ) @ ( throw_list_char @ C ) ) @ D ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ ( binOp_list_char @ F @ A @ B ) @ G ) @ ( throw_list_char @ C ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(84,axiom,
    ! [A: $i] :
      ( ( A != none_P179726773on_val )
     => ~ ! [B: $i] :
            ( A
           != ( hAPP_P1510515380on_val @ some_P948696889on_val @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_792_option_Oexhaust) ).

thf(1574,plain,
    ! [A: $i] :
      ( ( A != none_P179726773on_val )
     => ~ ! [B: $i] :
            ( A
           != ( hAPP_P1510515380on_val @ some_P948696889on_val @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(561,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ ( fun_up424764369ion_ty @ C @ D @ ( hAPP_ty_option_ty @ some_ty @ E ) ) @ F @ G ) )
     => ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( block_list_char @ D @ E @ F ) @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_520_WTrtBlock) ).

thf(3419,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ ( fun_up424764369ion_ty @ C @ D @ ( hAPP_ty_option_ty @ some_ty @ E ) ) @ F @ G ) )
     => ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( block_list_char @ D @ E @ F ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(1054,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f1409772418l_bool @ ( ord_le458107652r_bool @ ( hAPP_f306469557r_bool @ ( hAPP_f197435839r_bool @ cOMBC_886773442r_bool @ ( hAPP_f1749915625r_bool @ ( hAPP_f842743203r_bool @ cOMBB_657296617har_ty @ cOMBC_1407716098l_bool ) @ ( hAPP_f935003377l_bool @ ( hAPP_f162154931l_bool @ cOMBB_859890145har_ty @ ( hAPP_f1847120981l_bool @ cOMBB_1035649854t_char @ member1379348767t_char ) ) @ produc1152259904t_char ) ) ) @ A ) ) @ ( hAPP_f306469557r_bool @ ( hAPP_f197435839r_bool @ cOMBC_886773442r_bool @ ( hAPP_f1749915625r_bool @ ( hAPP_f842743203r_bool @ cOMBB_657296617har_ty @ cOMBC_1407716098l_bool ) @ ( hAPP_f935003377l_bool @ ( hAPP_f162154931l_bool @ cOMBB_859890145har_ty @ ( hAPP_f1847120981l_bool @ cOMBB_1035649854t_char @ member1379348767t_char ) ) @ produc1152259904t_char ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1161798306l_bool @ ( ord_le1734858744r_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_806_pred__subset__eq2) ).

thf(5303,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( hAPP_f1409772418l_bool @ ( ord_le458107652r_bool @ ( hAPP_f306469557r_bool @ ( hAPP_f197435839r_bool @ cOMBC_886773442r_bool @ ( hAPP_f1749915625r_bool @ ( hAPP_f842743203r_bool @ cOMBB_657296617har_ty @ cOMBC_1407716098l_bool ) @ ( hAPP_f935003377l_bool @ ( hAPP_f162154931l_bool @ cOMBB_859890145har_ty @ ( hAPP_f1847120981l_bool @ cOMBB_1035649854t_char @ member1379348767t_char ) ) @ produc1152259904t_char ) ) ) @ A ) ) @ ( hAPP_f306469557r_bool @ ( hAPP_f197435839r_bool @ cOMBC_886773442r_bool @ ( hAPP_f1749915625r_bool @ ( hAPP_f842743203r_bool @ cOMBB_657296617har_ty @ cOMBC_1407716098l_bool ) @ ( hAPP_f935003377l_bool @ ( hAPP_f162154931l_bool @ cOMBB_859890145har_ty @ ( hAPP_f1847120981l_bool @ cOMBB_1035649854t_char @ member1379348767t_char ) ) @ produc1152259904t_char ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f1161798306l_bool @ ( ord_le1734858744r_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1161798306l_bool @ ( ord_le1734858744r_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1409772418l_bool @ ( ord_le458107652r_bool @ ( hAPP_f306469557r_bool @ ( hAPP_f197435839r_bool @ cOMBC_886773442r_bool @ ( hAPP_f1749915625r_bool @ ( hAPP_f842743203r_bool @ cOMBB_657296617har_ty @ cOMBC_1407716098l_bool ) @ ( hAPP_f935003377l_bool @ ( hAPP_f162154931l_bool @ cOMBB_859890145har_ty @ ( hAPP_f1847120981l_bool @ cOMBB_1035649854t_char @ member1379348767t_char ) ) @ produc1152259904t_char ) ) ) @ A ) ) @ ( hAPP_f306469557r_bool @ ( hAPP_f197435839r_bool @ cOMBC_886773442r_bool @ ( hAPP_f1749915625r_bool @ ( hAPP_f842743203r_bool @ cOMBB_657296617har_ty @ cOMBC_1407716098l_bool ) @ ( hAPP_f935003377l_bool @ ( hAPP_f162154931l_bool @ cOMBB_859890145har_ty @ ( hAPP_f1847120981l_bool @ cOMBB_1035649854t_char @ member1379348767t_char ) ) @ produc1152259904t_char ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).

thf(79,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ A ) @ B )
        = ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_Pair__eq) ).

thf(1542,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ A ) @ B )
          = ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ A ) @ B )
          = ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(394,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P1002912327r_bool @ B @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ C ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1002912327r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_prod__induct3) ).

thf(2839,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P1002912327r_bool @ B @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ C ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1002912327r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(408,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_prod_Oexhaust) ).

thf(2896,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(548,axiom,
    ! [A: $i] :
      ( ( bool @ A )
     != unit ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1069_val_Osimps_I7_J) ).

thf(3384,plain,
    ! [A: $i] :
      ( ( bool @ A )
     != unit ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(842,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D = C )
       => ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ C @ B ) @ D )
          = B ) )
      & ( ( D != C )
       => ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ C @ B ) @ D )
          = ( hAPP_n546249108on_val @ A @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_fun__upd__def) ).

thf(4509,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D = C )
       => ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ C @ B ) @ D )
          = B ) )
      & ( ( D != C )
       => ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ C @ B ) @ D )
          = ( hAPP_n546249108on_val @ A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).

thf(220,axiom,
    ! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( hAPP_v834067052t_char @ val_list_char @ B ) @ C ) @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_886_Val) ).

thf(2119,plain,
    ! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( hAPP_v834067052t_char @ val_list_char @ B ) @ C ) @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(995,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D = C )
       => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ C @ B ) @ D )
          = B ) )
      & ( ( D != C )
       => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ C @ B ) @ D )
          = ( hAPP_l207779698on_val @ A @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_fun__upd__def) ).

thf(5071,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D = C )
       => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ C @ B ) @ D )
          = B ) )
      & ( ( D != C )
       => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ C @ B ) @ D )
          = ( hAPP_l207779698on_val @ A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).

thf(541,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ C ) @ D ) @ E ) )
     => ( hBOOL @ ( final_list_char @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_888_eval__final) ).

thf(3352,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ C ) @ D ) @ E ) )
     => ( hBOOL @ ( final_list_char @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(802,axiom,
    ! [A: $i,B: $i] :
      ( ( semila919158006r_bool @ A @ B )
      = ( semila919158006r_bool @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_883_Un__commute) ).

thf(4337,plain,
    ! [A: $i,B: $i] :
      ( ( semila919158006r_bool @ A @ B )
      = ( semila919158006r_bool @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).

thf(1240,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hAPP_l207779698on_val @ A @ B )
        = ( hAPP_val_option_val @ some_val @ C ) )
     => ( ( fun_up1149430426on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_map__upd__triv) ).

thf(6059,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hAPP_l207779698on_val @ A @ B )
        = ( hAPP_val_option_val @ some_val @ C ) )
     => ( ( fun_up1149430426on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1240]) ).

thf(1035,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ ( dom_list_char_val @ B ) ) )
     => ? [C: $i] :
          ( ( hAPP_l207779698on_val @ B @ A )
          = ( hAPP_val_option_val @ some_val @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_560_domD) ).

thf(5212,plain,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ ( dom_list_char_val @ B ) ) )
     => ? [C: $i] :
          ( ( hAPP_l207779698on_val @ B @ A )
          = ( hAPP_val_option_val @ some_val @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).

thf(954,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f1776419603l_bool @ ( ord_le1871967977r_bool @ ( hAPP_f344506159r_bool @ ( hAPP_f447563647r_bool @ cOMBC_389248878r_bool @ ( hAPP_f1032444159r_bool @ ( hAPP_f254182519r_bool @ cOMBB_1551681790t_char @ cOMBC_1603044337l_bool ) @ ( hAPP_f1764180741l_bool @ ( hAPP_f247798919l_bool @ cOMBB_526805108t_char @ ( hAPP_f144783951l_bool @ cOMBB_1586673472t_char @ member1251428284t_char ) ) @ produc5062597t_char ) ) ) @ A ) ) @ ( hAPP_f344506159r_bool @ ( hAPP_f447563647r_bool @ cOMBC_389248878r_bool @ ( hAPP_f1032444159r_bool @ ( hAPP_f254182519r_bool @ cOMBB_1551681790t_char @ cOMBC_1603044337l_bool ) @ ( hAPP_f1764180741l_bool @ ( hAPP_f247798919l_bool @ cOMBB_526805108t_char @ ( hAPP_f144783951l_bool @ cOMBB_1586673472t_char @ member1251428284t_char ) ) @ produc5062597t_char ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_803_pred__subset__eq2) ).

thf(4929,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( hAPP_f1776419603l_bool @ ( ord_le1871967977r_bool @ ( hAPP_f344506159r_bool @ ( hAPP_f447563647r_bool @ cOMBC_389248878r_bool @ ( hAPP_f1032444159r_bool @ ( hAPP_f254182519r_bool @ cOMBB_1551681790t_char @ cOMBC_1603044337l_bool ) @ ( hAPP_f1764180741l_bool @ ( hAPP_f247798919l_bool @ cOMBB_526805108t_char @ ( hAPP_f144783951l_bool @ cOMBB_1586673472t_char @ member1251428284t_char ) ) @ produc5062597t_char ) ) ) @ A ) ) @ ( hAPP_f344506159r_bool @ ( hAPP_f447563647r_bool @ cOMBC_389248878r_bool @ ( hAPP_f1032444159r_bool @ ( hAPP_f254182519r_bool @ cOMBB_1551681790t_char @ cOMBC_1603044337l_bool ) @ ( hAPP_f1764180741l_bool @ ( hAPP_f247798919l_bool @ cOMBB_526805108t_char @ ( hAPP_f144783951l_bool @ cOMBB_1586673472t_char @ member1251428284t_char ) ) @ produc5062597t_char ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1776419603l_bool @ ( ord_le1871967977r_bool @ ( hAPP_f344506159r_bool @ ( hAPP_f447563647r_bool @ cOMBC_389248878r_bool @ ( hAPP_f1032444159r_bool @ ( hAPP_f254182519r_bool @ cOMBB_1551681790t_char @ cOMBC_1603044337l_bool ) @ ( hAPP_f1764180741l_bool @ ( hAPP_f247798919l_bool @ cOMBB_526805108t_char @ ( hAPP_f144783951l_bool @ cOMBB_1586673472t_char @ member1251428284t_char ) ) @ produc5062597t_char ) ) ) @ A ) ) @ ( hAPP_f344506159r_bool @ ( hAPP_f447563647r_bool @ cOMBC_389248878r_bool @ ( hAPP_f1032444159r_bool @ ( hAPP_f254182519r_bool @ cOMBB_1551681790t_char @ cOMBC_1603044337l_bool ) @ ( hAPP_f1764180741l_bool @ ( hAPP_f247798919l_bool @ cOMBB_526805108t_char @ ( hAPP_f144783951l_bool @ cOMBB_1586673472t_char @ member1251428284t_char ) ) @ produc5062597t_char ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).

thf(840,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ~ ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
         => ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_716_equalityE) ).

thf(4498,plain,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ~ ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
         => ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).

thf(306,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ C ) @ D )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ F ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ ( transi1065307915t_char @ ( subcls744239332t_char @ A ) ) @ E ) @ B ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( cast_list_char @ B @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) @ C ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1054_redp__redsp_ORedCast) ).

thf(2478,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ C ) @ D )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ F ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ ( transi1065307915t_char @ ( subcls744239332t_char @ A ) ) @ E ) @ B ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( cast_list_char @ B @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) @ C ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(285,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( C = D )
       => ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ D @ B ) @ C )
          = B ) )
      & ( ( C != D )
       => ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ D @ B ) @ C )
          = ( hAPP_l512744617ion_ty @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_fun__upd__apply) ).

thf(2383,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( C = D )
       => ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ D @ B ) @ C )
          = B ) )
      & ( ( C != D )
       => ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ D @ B ) @ C )
          = ( hAPP_l512744617ion_ty @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(344,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1297673713l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O) ).

thf(2624,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1297673713l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(292,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ A ) @ B )
        = ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Pair__inject) ).

thf(2415,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ A ) @ B )
        = ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(432,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_670_subsetD) ).

thf(2987,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(1116,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hAPP_P2094403585on_val @ A @ B )
        = ( hAPP_val_option_val @ some_val @ C ) )
     => ( ( fun_up204312361on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_map__upd__triv) ).

thf(5520,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hAPP_P2094403585on_val @ A @ B )
        = ( hAPP_val_option_val @ some_val @ C ) )
     => ( ( fun_up204312361on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).

thf(448,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1661305905l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M) ).

thf(3038,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1661305905l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(1060,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ C ) @ ( dom_Pr695701035ar_val @ D ) ) )
     => ( ( map_ad1185064968ar_val @ ( fun_up204312361on_val @ A @ C @ ( hAPP_val_option_val @ some_val @ B ) ) @ D )
        = ( fun_up204312361on_val @ ( map_ad1185064968ar_val @ A @ D ) @ C @ ( hAPP_val_option_val @ some_val @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_460_map__add__upd__left) ).

thf(5325,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ C ) @ ( dom_Pr695701035ar_val @ D ) ) )
     => ( ( map_ad1185064968ar_val @ ( fun_up204312361on_val @ A @ C @ ( hAPP_val_option_val @ some_val @ B ) ) @ D )
        = ( fun_up204312361on_val @ ( map_ad1185064968ar_val @ A @ D ) @ C @ ( hAPP_val_option_val @ some_val @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).

thf(594,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ A ) ) @ ( transi935034983cl_val @ D ) ) )
       => ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ A ) ) @ ( transi935034983cl_val @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_725_converse__rtrancl__into__rtrancl) ).

thf(3551,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ A ) ) @ ( transi935034983cl_val @ D ) ) )
       => ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ A ) ) @ ( transi935034983cl_val @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(792,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ D @ E ) @ ( throw_list_char @ F ) ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( binOp_list_char @ D @ A @ B ) @ E ) @ ( throw_list_char @ F ) ) @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_955_eval__evals_OBinOpThrow1) ).

thf(4305,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ D @ E ) @ ( throw_list_char @ F ) ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( binOp_list_char @ D @ A @ B ) @ E ) @ ( throw_list_char @ F ) ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).

thf(696,axiom,
    ! [A: $i] :
      ( ( transi1395422419t_char @ ( transi1395422419t_char @ A ) )
      = ( transi1395422419t_char @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_719_rtrancl__idemp) ).

thf(3957,plain,
    ! [A: $i] :
      ( ( transi1395422419t_char @ ( transi1395422419t_char @ A ) )
      = ( transi1395422419t_char @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).

thf(923,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ G ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ ( dom_list_char_val @ F ) ) @ ( semila919158006r_bool @ ( dom_list_char_val @ C ) @ ( fv @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_858_Reds__dom__lcl) ).

thf(4828,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ G ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ ( dom_list_char_val @ F ) ) @ ( semila919158006r_bool @ ( dom_list_char_val @ C ) @ ( fv @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).

thf(88,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_PairE) ).

thf(1589,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(269,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_list_char_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_476_mem__def) ).

thf(2284,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_list_char_bool @ B @ A ) ) )
      & ( ( hBOOL @ ( hAPP_list_char_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(166,axiom,
    ! [A: $i] :
      ( ( hBOOL @ ( is_refT @ A ) )
     => ( ( A != nt )
       => ~ ! [B: $i] :
              ( A
             != ( hAPP_list_char_ty @ class @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1122_refTE) ).

thf(1933,plain,
    ! [A: $i] :
      ( ( hBOOL @ ( is_refT @ A ) )
     => ( ( A != nt )
       => ~ ! [B: $i] :
              ( A
             != ( hAPP_list_char_ty @ class @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(423,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1117138611l_bool @ ( hAPP_f2047757465l_bool @ ( hAPP_f466945179l_bool @ cOMBB_68065882ist_ty @ A ) @ B ) @ C )
      = ( hAPP_f921434893l_bool @ A @ ( hAPP_l14371579t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mt) ).

thf(2955,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1117138611l_bool @ ( hAPP_f2047757465l_bool @ ( hAPP_f466945179l_bool @ cOMBB_68065882ist_ty @ A ) @ B ) @ C )
      = ( hAPP_f921434893l_bool @ A @ ( hAPP_l14371579t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(62,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f1715346603l_bool @ ( hAPP_f1579743228l_bool @ ( hAPP_f1166017719l_bool @ cOMBC_317789649l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1134950784l_bool @ ( hAPP_f749178132l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_) ).

thf(1492,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f1715346603l_bool @ ( hAPP_f1579743228l_bool @ ( hAPP_f1166017719l_bool @ cOMBC_317789649l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1134950784l_bool @ ( hAPP_f749178132l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(122,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ A ) @ B )
        = ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_Pair__inject) ).

thf(1722,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ A ) @ B )
        = ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(1039,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( lex_pr69619957on_val @ E @ F ) ) )
    <=> ( ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ A ) @ C ) ) @ E ) )
        | ( ( A = C )
          & ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ B ) @ D ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_377_in__lex__prod) ).

thf(5222,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( lex_pr69619957on_val @ E @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ B ) @ D ) ) @ F ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ B ) @ D ) ) @ F ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( lex_pr69619957on_val @ E @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).

thf(772,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_826_order__eq__refl) ).

thf(4213,plain,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).

thf(864,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
      | ( hBOOL @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).

thf(4616,plain,
    ! [A: $i,B: $i] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
      | ( hBOOL @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).

thf(1067,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( fun_up1149430426on_val @ D @ E @ none_val ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) ) @ ( red @ I ) ) )
     => ( ( ( hAPP_l207779698on_val @ H @ E )
          = none_val )
       => ( ~ ( hBOOL @ ( assigned @ E @ B ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ E @ A @ B ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ E @ A @ F ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ ( fun_up1149430426on_val @ H @ E @ ( hAPP_l207779698on_val @ D @ E ) ) ) ) ) ) @ ( red @ I ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_653_red__reds_OBlockRedNone) ).

thf(5346,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( fun_up1149430426on_val @ D @ E @ none_val ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) ) @ ( red @ I ) ) )
     => ( ( ( hAPP_l207779698on_val @ H @ E )
          = none_val )
       => ( ~ ( hBOOL @ ( assigned @ E @ B ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ E @ A @ B ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ E @ A @ F ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ ( fun_up1149430426on_val @ H @ E @ ( hAPP_l207779698on_val @ D @ E ) ) ) ) ) ) @ ( red @ I ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).

thf(398,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_824_ord__eq__le__trans) ).

thf(2856,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(386,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P2053453961y_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__) ).

thf(2802,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P2053453961y_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(1122,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) ) @ D )
        = ( hAPP_val_option_val @ some_val @ E ) )
    <=> ( ( ( D = B )
          & ( C = E ) )
        | ( ( D != B )
          & ( ( hAPP_P2094403585on_val @ A @ D )
            = ( hAPP_val_option_val @ some_val @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_map__upd__Some__unfold) ).

thf(5552,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) ) @ D )
          = ( hAPP_val_option_val @ some_val @ E ) )
       => ( ( ( D = B )
            & ( C = E ) )
          | ( ( D != B )
            & ( ( hAPP_P2094403585on_val @ A @ D )
              = ( hAPP_val_option_val @ some_val @ E ) ) ) ) )
      & ( ( ( ( D = B )
            & ( C = E ) )
          | ( ( D != B )
            & ( ( hAPP_P2094403585on_val @ A @ D )
              = ( hAPP_val_option_val @ some_val @ E ) ) ) )
       => ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) ) @ D )
          = ( hAPP_val_option_val @ some_val @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).

thf(1128,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i,E: $i] :
          ( A
         != ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ B ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_prod__cases4) ).

thf(5584,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i,E: $i] :
          ( A
         != ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ B ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).

thf(1202,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_421_splitI) ).

thf(5920,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).

thf(717,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ A ) @ B )
        = ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_Pair__inject) ).

thf(4028,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ A ) @ B )
        = ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).

thf(297,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_706_set__rev__mp) ).

thf(2446,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(290,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P1680401186r_bool @ ( hAPP_f1666729379r_bool @ ( hAPP_f1020753317r_bool @ cOMBC_1297648632l_bool @ A ) @ B ) @ C )
      = ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_069) ).

thf(2410,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P1680401186r_bool @ ( hAPP_f1666729379r_bool @ ( hAPP_f1020753317r_bool @ cOMBC_1297648632l_bool @ A ) @ B ) @ C )
      = ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(403,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ A ) @ B )
        = ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_Pair__eq) ).

thf(2874,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ A ) @ B )
          = ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ A ) @ B )
          = ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(1098,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( red @ G ) ) )
     => ( ( hBOOL @ ( wTrt_1 @ G @ ( hp @ D ) @ A @ C @ B ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1700205512_sconf @ G @ A ) @ D ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1700205512_sconf @ G @ A ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_red__preserves__sconf) ).

thf(5466,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( red @ G ) ) )
     => ( ( hBOOL @ ( wTrt_1 @ G @ ( hp @ D ) @ A @ C @ B ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1700205512_sconf @ G @ A ) @ D ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1700205512_sconf @ G @ A ) @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).

thf(1176,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ B @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_prod__induct4) ).

thf(5780,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ B @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).

thf(105,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_prod_Oexhaust) ).

thf(1667,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(238,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P2118621157r_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P2118621157r_bool @ A @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_split__paired__All) ).

thf(2180,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P2118621157r_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P2118621157r_bool @ A @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P2118621157r_bool @ A @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P2118621157r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(871,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( seq_list_char @ A @ B )
     != ( hAPP_v834067052t_char @ val_list_char @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_578_exp_Osimps_I85_J) ).

thf(4635,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( seq_list_char @ A @ B )
     != ( hAPP_v834067052t_char @ val_list_char @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).

thf(1227,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( while_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1087_WhileRedsThrow) ).

thf(6004,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( while_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227]) ).

thf(454,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ B ) @ C @ ( throw_list_char @ D ) ) @ E ) @ ( throw_list_char @ D ) ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_963_redp__redsp_OBinOpThrow2) ).

thf(3055,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ B ) @ C @ ( throw_list_char @ D ) ) @ E ) @ ( throw_list_char @ D ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(712,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_PairE) ).

thf(4009,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).

thf(726,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_PairE) ).

thf(4064,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).

thf(181,axiom,
    ! [A: $i] :
      ( ( A != none_P179726773on_val )
    <=> ? [B: $i] :
          ( A
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_621_not__None__eq) ).

thf(1993,plain,
    ! [A: $i] :
      ( ( ( A != none_P179726773on_val )
       => ? [B: $i] :
            ( A
            = ( hAPP_P1510515380on_val @ some_P948696889on_val @ B ) ) )
      & ( ? [B: $i] :
            ( A
            = ( hAPP_P1510515380on_val @ some_P948696889on_val @ B ) )
       => ( A != none_P179726773on_val ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(1091,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ A @ B ) @ C )
        = ( hAPP_val_option_val @ some_val @ D ) )
    <=> ( ( ( hAPP_l207779698on_val @ B @ C )
          = ( hAPP_val_option_val @ some_val @ D ) )
        | ( ( ( hAPP_l207779698on_val @ B @ C )
            = none_val )
          & ( ( hAPP_l207779698on_val @ A @ C )
            = ( hAPP_val_option_val @ some_val @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_645_map__add__Some__iff) ).

thf(5439,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ A @ B ) @ C )
          = ( hAPP_val_option_val @ some_val @ D ) )
       => ( ( ( hAPP_l207779698on_val @ B @ C )
            = ( hAPP_val_option_val @ some_val @ D ) )
          | ( ( ( hAPP_l207779698on_val @ B @ C )
              = none_val )
            & ( ( hAPP_l207779698on_val @ A @ C )
              = ( hAPP_val_option_val @ some_val @ D ) ) ) ) )
      & ( ( ( ( hAPP_l207779698on_val @ B @ C )
            = ( hAPP_val_option_val @ some_val @ D ) )
          | ( ( ( hAPP_l207779698on_val @ B @ C )
              = none_val )
            & ( ( hAPP_l207779698on_val @ A @ C )
              = ( hAPP_val_option_val @ some_val @ D ) ) ) )
       => ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ A @ B ) @ C )
          = ( hAPP_val_option_val @ some_val @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).

thf(140,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ A ) @ B ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) ) @ ( lex_pr1588300168t_char @ E @ F ) ) )
    <=> ( ( hBOOL @ ( hAPP_f433445541l_bool @ ( hAPP_P1019319281l_bool @ member104734088ist_ty @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ A ) @ C ) ) @ E ) )
        | ( ( A = C )
          & ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ B ) @ D ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_383_in__lex__prod) ).

thf(1821,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ A ) @ B ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) ) @ ( lex_pr1588300168t_char @ E @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f433445541l_bool @ ( hAPP_P1019319281l_bool @ member104734088ist_ty @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ B ) @ D ) ) @ F ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f433445541l_bool @ ( hAPP_P1019319281l_bool @ member104734088ist_ty @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ B ) @ D ) ) @ F ) ) ) )
       => ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ A ) @ B ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) ) @ ( lex_pr1588300168t_char @ E @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(124,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ A ) @ B )
        = ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_Pair__eq) ).

thf(1731,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ A ) @ B )
          = ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ A ) @ B )
          = ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(784,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ A ) @ B ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) ) @ ( lex_pr213428520t_char @ E @ F ) ) )
    <=> ( ( hBOOL @ ( hAPP_f288221747l_bool @ ( hAPP_P569585933l_bool @ member520253462har_ty @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ A ) @ C ) ) @ E ) )
        | ( ( A = C )
          & ( hBOOL @ ( hAPP_f1748390065l_bool @ ( hAPP_P1503283977l_bool @ member1580476948t_char @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ B ) @ D ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_379_in__lex__prod) ).

thf(4264,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ A ) @ B ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) ) @ ( lex_pr213428520t_char @ E @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f288221747l_bool @ ( hAPP_P569585933l_bool @ member520253462har_ty @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f1748390065l_bool @ ( hAPP_P1503283977l_bool @ member1580476948t_char @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ B ) @ D ) ) @ F ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f288221747l_bool @ ( hAPP_P569585933l_bool @ member520253462har_ty @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f1748390065l_bool @ ( hAPP_P1503283977l_bool @ member1580476948t_char @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ B ) @ D ) ) @ F ) ) ) )
       => ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ A ) @ B ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) ) @ ( lex_pr213428520t_char @ E @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).

thf(602,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_val_bool @ ( hAPP_f1728541444l_bool @ ( hAPP_f1764548711l_bool @ cOMBC_331963401l_bool @ A ) @ B ) @ C )
      = ( hAPP_f2028441009l_bool @ ( hAPP_v3604996l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Value__Oval_000tc__fun_Itc__prod_Itc__Value__Oval_Mt) ).

thf(3572,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_val_bool @ ( hAPP_f1728541444l_bool @ ( hAPP_f1764548711l_bool @ cOMBC_331963401l_bool @ A ) @ B ) @ C )
      = ( hAPP_f2028441009l_bool @ ( hAPP_v3604996l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(689,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( is_bool @ ( wTrts @ A @ B @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Progress_OWTrts_H) ).

thf(3932,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( is_bool @ ( wTrts @ A @ B @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).

thf(491,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ B ) )
      <=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_427_split__weak__cong) ).

thf(3165,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ B ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ C ) ) )
        & ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ C ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(762,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) ) @ ( reds @ I ) ) )
     => ( ( hBOOL @ ( wTrts_1 @ I @ D @ A @ C @ B ) )
       => ( ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ I ) @ D ) )
         => ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ I ) @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1175_reds__preserves__hconf) ).

thf(4181,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) ) @ ( reds @ I ) ) )
     => ( ( hBOOL @ ( wTrts_1 @ I @ D @ A @ C @ B ) )
       => ( ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ I ) @ D ) )
         => ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ I ) @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).

thf(336,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P1333315679l_bool @ B @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P1333315679l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_prod__induct4) ).

thf(2593,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P1333315679l_bool @ B @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P1333315679l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(572,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ G ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ E ) @ F ) ) ) @ ( transi374442731on_val @ ( reds @ G ) ) ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ G @ E @ F ) @ A ) @ B ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ G @ C @ D ) @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1146_extend__evals) ).

thf(3451,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ G ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ E ) @ F ) ) ) @ ( transi374442731on_val @ ( reds @ G ) ) ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ G @ E @ F ) @ A ) @ B ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ G @ C @ D ) @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(701,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1795246582l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_I) ).

thf(3971,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1795246582l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).

thf(25,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ A ) @ B )
        = ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_Pair__eq) ).

thf(1344,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ A ) @ B )
          = ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ A ) @ B )
          = ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(270,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ sys_xcpts ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ A @ nullPointer ) )
       => ( ( hBOOL @ ( hAPP_list_char_bool @ A @ outOfMemory ) )
         => ( ( hBOOL @ ( hAPP_list_char_bool @ A @ classCast ) )
           => ( hBOOL @ ( hAPP_list_char_bool @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1063_sys__xcpts__cases) ).

thf(2289,plain,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ sys_xcpts ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ A @ nullPointer ) )
       => ( ( hBOOL @ ( hAPP_list_char_bool @ A @ outOfMemory ) )
         => ( ( hBOOL @ ( hAPP_list_char_bool @ A @ classCast ) )
           => ( hBOOL @ ( hAPP_list_char_bool @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(1023,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ B @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_prod__induct3) ).

thf(5180,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ B @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).

thf(260,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( fAss_list_char @ ( throw_list_char @ B ) @ C @ D @ E ) @ F ) @ ( throw_list_char @ B ) ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_923_redp__redsp_OFAssThrow1) ).

thf(2252,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( fAss_list_char @ ( throw_list_char @ B ) @ C @ D @ E ) @ F ) @ ( throw_list_char @ B ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(353,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1342015621r_bool @ ( hAPP_f719350875r_bool @ ( hAPP_f2133563379r_bool @ cOMBC_1025440566r_bool @ A ) @ B ) @ C )
      = ( hAPP_f764724814r_bool @ ( hAPP_l1988620845r_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_063) ).

thf(2664,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1342015621r_bool @ ( hAPP_f719350875r_bool @ ( hAPP_f2133563379r_bool @ cOMBC_1025440566r_bool @ A ) @ B ) @ C )
      = ( hAPP_f764724814r_bool @ ( hAPP_l1988620845r_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(667,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1118567467l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Value__Oval_J_Mtc__fun_Itc__Expr__Oe) ).

thf(3861,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1118567467l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).

thf(267,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1591404153l_bool @ ( hAPP_f333583909l_bool @ ( hAPP_f1407048615l_bool @ cOMBB_741416308t_char @ A ) @ B ) @ C )
      = ( hAPP_f1107475085l_bool @ A @ ( hAPP_l902950593t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_) ).

thf(2278,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1591404153l_bool @ ( hAPP_f333583909l_bool @ ( hAPP_f1407048615l_bool @ cOMBB_741416308t_char @ A ) @ B ) @ C )
      = ( hAPP_f1107475085l_bool @ A @ ( hAPP_l902950593t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(977,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_422_splitI) ).

thf(5007,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).

thf(301,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P124632071l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_) ).

thf(2461,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P124632071l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(428,axiom,
    ! [A: $i,B: $i] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ ( addr @ A ) ) @ B ) ) )
      = none_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1013_binop_Osimps_I6_J) ).

thf(2974,plain,
    ! [A: $i,B: $i] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ ( addr @ A ) ) @ B ) ) )
      = none_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(1085,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( lAss_list_char @ B @ C ) @ D ) @ E ) @ F ) )
     => ( ( ( E
            = ( hAPP_v834067052t_char @ val_list_char @ unit ) )
         => ! [G: $i,H: $i,I: $i] :
              ( ( F
                = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ B @ ( hAPP_val_option_val @ some_val @ G ) ) ) )
             => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ C @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) ) )
       => ~ ! [G: $i] :
              ( ( E
                = ( throw_list_char @ G ) )
             => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ C @ D ) @ ( throw_list_char @ G ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_944_eval__cases_I4_J) ).

thf(5410,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( lAss_list_char @ B @ C ) @ D ) @ E ) @ F ) )
     => ( ( ( E
            = ( hAPP_v834067052t_char @ val_list_char @ unit ) )
         => ! [G: $i,H: $i,I: $i] :
              ( ( F
                = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ B @ ( hAPP_val_option_val @ some_val @ G ) ) ) )
             => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ C @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) ) )
       => ~ ! [G: $i] :
              ( ( E
                = ( throw_list_char @ G ) )
             => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ C @ D ) @ ( throw_list_char @ G ) ) @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).

thf(1095,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_707_set__rev__mp) ).

thf(5459,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).

thf(883,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_prod_Oexhaust) ).

thf(4684,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).

thf(1188,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_prod__cases3) ).

thf(5838,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).

thf(1065,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P378063101l_bool @ B @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ C ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P378063101l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_prod__induct4) ).

thf(5340,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P378063101l_bool @ B @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ C ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P378063101l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).

thf(1164,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ ( fun_up1149430426on_val @ F @ G @ ( hAPP_val_option_val @ some_val @ H ) ) ) ) @ I ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ K ) ) )
     => ( ( ( hAPP_l207779698on_val @ K @ G )
          = ( hAPP_val_option_val @ some_val @ B ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( block_list_char @ G @ A @ ( seq_list_char @ ( lAss_list_char @ G @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ D ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) @ ( block_list_char @ G @ A @ ( seq_list_char @ ( lAss_list_char @ G @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ I ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ ( fun_up1149430426on_val @ K @ G @ ( hAPP_l207779698on_val @ F @ G ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_587_redp__redsp_OInitBlockRed) ).

thf(5742,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ ( fun_up1149430426on_val @ F @ G @ ( hAPP_val_option_val @ some_val @ H ) ) ) ) @ I ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ K ) ) )
     => ( ( ( hAPP_l207779698on_val @ K @ G )
          = ( hAPP_val_option_val @ some_val @ B ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( block_list_char @ G @ A @ ( seq_list_char @ ( lAss_list_char @ G @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ D ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) @ ( block_list_char @ G @ A @ ( seq_list_char @ ( lAss_list_char @ G @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ I ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ ( fun_up1149430426on_val @ K @ G @ ( hAPP_l207779698on_val @ F @ G ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).

thf(473,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ E ) @ F ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( cond_list_char @ D @ A @ B ) @ E ) @ ( cond_list_char @ F @ A @ B ) ) @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1092_redp__redsp_OCondRed) ).

thf(3110,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ E ) @ F ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( cond_list_char @ D @ A @ B ) @ E ) @ ( cond_list_char @ F @ A @ B ) ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(375,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i,E: $i] :
          ( A
         != ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ B ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_prod__cases4) ).

thf(2752,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i,E: $i] :
          ( A
         != ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ B ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(533,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l810309945l_bool @ ( hAPP_f1817350437l_bool @ ( hAPP_f614662951l_bool @ cOMBB_1558246132t_char @ A ) @ B ) @ C )
      = ( hAPP_f2037329933l_bool @ A @ ( hAPP_l309186817t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__) ).

thf(3310,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l810309945l_bool @ ( hAPP_f1817350437l_bool @ ( hAPP_f614662951l_bool @ cOMBB_1558246132t_char @ A ) @ B ) @ C )
      = ( hAPP_f2037329933l_bool @ A @ ( hAPP_l309186817t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(960,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ C ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_930_ThrowReds) ).

thf(4954,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ C ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).

thf(1107,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_423_splitI) ).

thf(5495,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).

thf(206,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( B
            = ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) )
         => ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ C ) @ D ) ) )
     => ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_f1534412387l_bool @ produc769963999l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_546_splitI2) ).

thf(2069,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( B
            = ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) )
         => ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ C ) @ D ) ) )
     => ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_f1534412387l_bool @ produc769963999l_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(590,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hAPP_n546249108on_val @ A @ B )
        = C )
     => ( ( fun_up2041264236on_val @ A @ B @ C )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_fun__upd__idem) ).

thf(3539,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hAPP_n546249108on_val @ A @ B )
        = C )
     => ( ( fun_up2041264236on_val @ A @ B @ C )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(925,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1141_CallRedsObj) ).

thf(4832,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).

thf(643,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( assigned @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_SmallStep_Oassigned) ).

thf(3759,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( assigned @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(660,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ A ) @ B )
        = ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_Pair__inject) ).

thf(3838,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ A ) @ B )
        = ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

thf(1030,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1142_CallRedsThrowObj) ).

thf(5197,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).

thf(1002,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( B
            = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) )
         => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ C ) @ D ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_550_splitI2) ).

thf(5094,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( B
            = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) )
         => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ C ) @ D ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).

thf(563,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ B @ C ) @ B )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_fun__upd__same) ).

thf(3423,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ B @ C ) @ B )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(46,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_P1183008383l_bool @ ( produc2053127004l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_490_curryE) ).

thf(1445,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_P1183008383l_bool @ ( produc2053127004l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(343,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ E ) @ F )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ G ) @ C ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ D ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ C @ A @ B ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) ) @ E ) ) ) @ ( red @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_975_red__reds_ORedTryFail) ).

thf(2620,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ E ) @ F )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ G ) @ C ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ D ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ C @ A @ B ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) ) @ E ) ) ) @ ( red @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(1145,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( hBOOL @ ( hAPP_f91506671l_bool @ ( hAPP_P2015860941l_bool @ member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f91506671l_bool @ ( hAPP_P2015860941l_bool @ member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_pred__equals__eq2) ).

thf(5646,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f91506671l_bool @ ( hAPP_P2015860941l_bool @ member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f91506671l_bool @ ( hAPP_P2015860941l_bool @ member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f91506671l_bool @ ( hAPP_P2015860941l_bool @ member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f91506671l_bool @ ( hAPP_P2015860941l_bool @ member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f91506671l_bool @ ( hAPP_P2015860941l_bool @ member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f91506671l_bool @ ( hAPP_P2015860941l_bool @ member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f91506671l_bool @ ( hAPP_P2015860941l_bool @ member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f91506671l_bool @ ( hAPP_P2015860941l_bool @ member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).

thf(811,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_list_char_bool @ B @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_list_char_bool @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_595_rev__predicate1D) ).

thf(4373,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_list_char_bool @ B @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_list_char_bool @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).

thf(625,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P71593144l_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P71593144l_bool @ A @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_split__paired__All) ).

thf(3687,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P71593144l_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P71593144l_bool @ A @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P71593144l_bool @ A @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P71593144l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(1045,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) ) @ D )
        = ( hAPP_val_option_val @ some_val @ E ) )
    <=> ( ( ( D = B )
          & ( C = E ) )
        | ( ( D != B )
          & ( ( hAPP_l207779698on_val @ A @ D )
            = ( hAPP_val_option_val @ some_val @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_map__upd__Some__unfold) ).

thf(5248,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) ) @ D )
          = ( hAPP_val_option_val @ some_val @ E ) )
       => ( ( ( D = B )
            & ( C = E ) )
          | ( ( D != B )
            & ( ( hAPP_l207779698on_val @ A @ D )
              = ( hAPP_val_option_val @ some_val @ E ) ) ) ) )
      & ( ( ( ( D = B )
            & ( C = E ) )
          | ( ( D != B )
            & ( ( hAPP_l207779698on_val @ A @ D )
              = ( hAPP_val_option_val @ some_val @ E ) ) ) )
       => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) ) @ D )
          = ( hAPP_val_option_val @ some_val @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).

thf(730,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_prod__cases3) ).

thf(4085,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).

thf(489,axiom,
    ! [A: $i] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ unit ) ) )
      = none_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1006_binop_Osimps_I7_J) ).

thf(3159,plain,
    ! [A: $i] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ unit ) ) )
      = none_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(204,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ E ) @ F ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ D ) @ E ) @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ F ) ) @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_956_redp__redsp_OBinOpRed2) ).

thf(2064,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ E ) @ F ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ D ) @ E ) @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ F ) ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(808,axiom,
    ! [A: $i,B: $i] :
      ( ( fv @ ( cast_list_char @ A @ B ) )
      = ( fv @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_984_fv__fvs_Osimps_I2_J) ).

thf(4362,plain,
    ! [A: $i,B: $i] :
      ( ( fv @ ( cast_list_char @ A @ B ) )
      = ( fv @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).

thf(417,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P92196306r_bool @ B @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P92196306r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_prod__induct3) ).

thf(2931,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P92196306r_bool @ B @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P92196306r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(1125,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( produc1911975310l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_496_curryE) ).

thf(5575,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( produc1911975310l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).

thf(55,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P824029447r_bool @ B @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ C ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ D ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P824029447r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_prod__induct4) ).

thf(1477,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P824029447r_bool @ B @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ C ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ D ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P824029447r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(536,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f433445541l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__List__Oli) ).

thf(3325,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f433445541l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(889,axiom,
    ! [A: $i] :
      ( ( A != none_f478147469r_bool )
     => ~ ! [B: $i] :
            ( A
           != ( hAPP_f363827556r_bool @ some_f80346385r_bool @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_794_option_Oexhaust) ).

thf(4703,plain,
    ! [A: $i] :
      ( ( A != none_f478147469r_bool )
     => ~ ! [B: $i] :
            ( A
           != ( hAPP_f363827556r_bool @ some_f80346385r_bool @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).

thf(214,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( redsp @ A @ B @ C ) @ D ) @ E ) )
    <=> ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) @ ( reds @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1177_redsp__reds__eq) ).

thf(2101,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( redsp @ A @ B @ C ) @ D ) @ E ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) @ ( reds @ A ) ) ) )
      & ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) @ ( reds @ A ) ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( redsp @ A @ B @ C ) @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(1147,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ E ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) )
       => ( ( hBOOL @ ( final_list_char @ C ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ A @ B ) @ C ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_852_small__by__big) ).

thf(5667,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ E ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) )
       => ( ( hBOOL @ ( final_list_char @ C ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ A @ B ) @ C ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).

thf(766,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_735_subsetI) ).

thf(4196,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).

thf(1234,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ ( hAPP_f1666729379r_bool @ ( hAPP_f1020753317r_bool @ cOMBC_1297648632l_bool @ member1467889965t_char ) @ A ) ) @ ( hAPP_f1666729379r_bool @ ( hAPP_f1020753317r_bool @ cOMBC_1297648632l_bool @ member1467889965t_char ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_598_pred__subset__eq) ).

thf(6027,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ ( hAPP_f1666729379r_bool @ ( hAPP_f1020753317r_bool @ cOMBC_1297648632l_bool @ member1467889965t_char ) @ A ) ) @ ( hAPP_f1666729379r_bool @ ( hAPP_f1020753317r_bool @ cOMBC_1297648632l_bool @ member1467889965t_char ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ ( hAPP_f1666729379r_bool @ ( hAPP_f1020753317r_bool @ cOMBC_1297648632l_bool @ member1467889965t_char ) @ A ) ) @ ( hAPP_f1666729379r_bool @ ( hAPP_f1020753317r_bool @ cOMBC_1297648632l_bool @ member1467889965t_char ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1234]) ).

thf(494,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hext @ C @ D ) )
     => ( ( ( hAPP_val_option_ty @ ( typeof_h @ C ) @ A )
          = ( hAPP_ty_option_ty @ some_ty @ B ) )
       => ( ( hAPP_val_option_ty @ ( typeof_h @ D ) @ A )
          = ( hAPP_ty_option_ty @ some_ty @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1010_hext__typeof__mono) ).

thf(3178,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hext @ C @ D ) )
     => ( ( ( hAPP_val_option_ty @ ( typeof_h @ C ) @ A )
          = ( hAPP_ty_option_ty @ some_ty @ B ) )
       => ( ( hAPP_val_option_ty @ ( typeof_h @ D ) @ A )
          = ( hAPP_ty_option_ty @ some_ty @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(788,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P1002912327r_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__) ).

thf(4282,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P1002912327r_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).

thf(868,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_v1988122071l_bool @ ( hAPP_f1859053709l_bool @ ( hAPP_f400269243l_bool @ cOMBB_1701031980ol_val @ A ) @ B ) @ C )
      = ( hAPP_f1764548711l_bool @ A @ ( hAPP_v417179479l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Value__Oval_Mtc__fun_Itc__fun_Itc__prod_Itc) ).

thf(4626,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_v1988122071l_bool @ ( hAPP_f1859053709l_bool @ ( hAPP_f400269243l_bool @ cOMBB_1701031980ol_val @ A ) @ B ) @ C )
      = ( hAPP_f1764548711l_bool @ A @ ( hAPP_v417179479l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).

thf(436,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P71593144l_bool @ A @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( produc1838470831l_bool @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_364_curryI) ).

thf(2999,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P71593144l_bool @ A @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( produc1838470831l_bool @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(540,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hAPP_v834067052t_char @ val_list_char @ A )
     != ( block_list_char @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_580_exp_Osimps_I82_J) ).

thf(3348,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hAPP_v834067052t_char @ val_list_char @ A )
     != ( block_list_char @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(1000,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f1033709212l_bool @ ( hAPP_f1008932791l_bool @ ( hAPP_f2057883639l_bool @ cOMBB_1750801836on_val @ A ) @ B ) @ C )
      = ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It) ).

thf(5089,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f1033709212l_bool @ ( hAPP_f1008932791l_bool @ ( hAPP_f2057883639l_bool @ cOMBB_1750801836on_val @ A ) @ B ) @ C )
      = ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).

thf(111,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P2118621157r_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc__) ).

thf(1694,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P2118621157r_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(359,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( wTrt_1 @ B @ C @ D @ E @ F ) )
     => ( ( hBOOL @ ( hext @ C @ A ) )
       => ( hBOOL @ ( wTrt_1 @ B @ A @ D @ E @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_563_WTrt__hext__mono) ).

thf(2693,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( wTrt_1 @ B @ C @ D @ E @ F ) )
     => ( ( hBOOL @ ( hext @ C @ A ) )
       => ( hBOOL @ ( wTrt_1 @ B @ A @ D @ E @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(771,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i,F: $i] :
          ( ( is_bop @ D )
         => ( hBOOL @ ( hAPP_P738987199l_bool @ B @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ C ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ D ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ E ) @ F ) ) ) ) ) )
     => ( hBOOL @ ( hAPP_P738987199l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_prod__induct4) ).

thf(4209,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i,F: $i] :
          ( ( is_bop @ D )
         => ( hBOOL @ ( hAPP_P738987199l_bool @ B @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ C ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ D ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ E ) @ F ) ) ) ) ) )
     => ( hBOOL @ ( hAPP_P738987199l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).

thf(834,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ B @ C ) @ D ) @ E ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( throw_list_char @ B ) @ C ) @ ( throw_list_char @ D ) ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_912_redp__redsp_OThrowRed) ).

thf(4481,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ B @ C ) @ D ) @ E ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( throw_list_char @ B ) @ C ) @ ( throw_list_char @ D ) ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).

thf(753,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wTrt_1 @ D @ E @ F @ G @ nt ) )
     => ( hBOOL @ ( wTrt_1 @ D @ E @ F @ ( fAcc_list_char @ G @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1114_WTrtFAccNT) ).

thf(4158,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wTrt_1 @ D @ E @ F @ G @ nt ) )
     => ( hBOOL @ ( wTrt_1 @ D @ E @ F @ ( fAcc_list_char @ G @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).

thf(580,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1931964053l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_I_003) ).

thf(3490,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1931964053l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(82,axiom,
    ! [A: $i] :
      ( ( hBOOL @ ( is_refT @ A ) )
    <=> ( ( A = nt )
        | ? [B: $i] :
            ( A
            = ( hAPP_list_char_ty @ class @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1116_is__refT__def) ).

thf(1562,plain,
    ! [A: $i] :
      ( ( ( hBOOL @ ( is_refT @ A ) )
       => ( ( A = nt )
          | ? [B: $i] :
              ( A
              = ( hAPP_list_char_ty @ class @ B ) ) ) )
      & ( ( ( A = nt )
          | ? [B: $i] :
              ( A
              = ( hAPP_list_char_ty @ class @ B ) ) )
       => ( hBOOL @ ( is_refT @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(184,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ A ) @ B )
        = ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_Pair__inject) ).

thf(2005,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ A ) @ B )
        = ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(1118,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( hBOOL @ ( hAPP_f479632753l_bool @ ( hAPP_P153687689l_bool @ member817832404t_char @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f479632753l_bool @ ( hAPP_P153687689l_bool @ member817832404t_char @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_pred__equals__eq2) ).

thf(5528,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f479632753l_bool @ ( hAPP_P153687689l_bool @ member817832404t_char @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f479632753l_bool @ ( hAPP_P153687689l_bool @ member817832404t_char @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f479632753l_bool @ ( hAPP_P153687689l_bool @ member817832404t_char @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f479632753l_bool @ ( hAPP_P153687689l_bool @ member817832404t_char @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f479632753l_bool @ ( hAPP_P153687689l_bool @ member817832404t_char @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f479632753l_bool @ ( hAPP_P153687689l_bool @ member817832404t_char @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f479632753l_bool @ ( hAPP_P153687689l_bool @ member817832404t_char @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f479632753l_bool @ ( hAPP_P153687689l_bool @ member817832404t_char @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).

thf(896,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i,O: $i,P: $i,Q: $i,R: $i,S: $i,T: $i,U: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ Q @ R @ S ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ T ) ) ) @ U ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ Q @ M @ U ) @ ( map_va1934808527t_char @ val_list_char @ N ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ O ) @ P ) ) )
       => ( ( ( hAPP_n546249108on_val @ O @ T )
            = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ K ) @ L ) ) )
         => ( ( hBOOL @ ( hAPP_list_char_bool @ ( method1809630380t_char @ Q @ K @ E @ F @ G @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ H ) @ I ) ) @ J ) )
           => ( ( ( size_size_list_val @ N )
                = ( size_s2113983095t_char @ H ) )
             => ( ( D
                  = ( map_up1085636310ar_val @ ( fun_up1149430426on_val @ ( hAPP_o538043682on_val @ cOMBK_1097134891t_char @ none_val ) @ this @ ( hAPP_val_option_val @ some_val @ ( addr @ T ) ) ) @ H @ N ) )
               => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ Q @ I @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ O ) @ D ) ) @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
                 => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ Q @ ( call_list_char @ R @ E @ M ) @ S ) @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ P ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1184_Call) ).

thf(4735,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i,O: $i,P: $i,Q: $i,R: $i,S: $i,T: $i,U: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ Q @ R @ S ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ T ) ) ) @ U ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ Q @ M @ U ) @ ( map_va1934808527t_char @ val_list_char @ N ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ O ) @ P ) ) )
       => ( ( ( hAPP_n546249108on_val @ O @ T )
            = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ K ) @ L ) ) )
         => ( ( hBOOL @ ( hAPP_list_char_bool @ ( method1809630380t_char @ Q @ K @ E @ F @ G @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ H ) @ I ) ) @ J ) )
           => ( ( ( size_size_list_val @ N )
                = ( size_s2113983095t_char @ H ) )
             => ( ( D
                  = ( map_up1085636310ar_val @ ( fun_up1149430426on_val @ ( hAPP_o538043682on_val @ cOMBK_1097134891t_char @ none_val ) @ this @ ( hAPP_val_option_val @ some_val @ ( addr @ T ) ) ) @ H @ N ) )
               => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ Q @ I @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ O ) @ D ) ) @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
                 => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ Q @ ( call_list_char @ R @ E @ M ) @ S ) @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ P ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).

thf(1213,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( wTrts @ A @ B @ C @ D @ E ) )
     => ( hBOOL @ ( wTrts_1 @ A @ B @ C @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1194_wts_H__wts) ).

thf(5952,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( wTrts @ A @ B @ C @ D @ E ) )
     => ( hBOOL @ ( wTrts_1 @ A @ B @ C @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1213]) ).

thf(346,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_t708040077har_ty @ ( hAPP_P827589667har_ty @ produc1265154397har_ty @ A ) @ B )
        = ( hAPP_t708040077har_ty @ ( hAPP_P827589667har_ty @ produc1265154397har_ty @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_Pair__inject) ).

thf(2629,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_t708040077har_ty @ ( hAPP_P827589667har_ty @ produc1265154397har_ty @ A ) @ B )
        = ( hAPP_t708040077har_ty @ ( hAPP_P827589667har_ty @ produc1265154397har_ty @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(54,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_P1680401186r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_472_mem__def) ).

thf(1472,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_P1680401186r_bool @ B @ A ) ) )
      & ( ( hBOOL @ ( hAPP_P1680401186r_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(1170,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1039_CastRedsNull) ).

thf(5763,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).

thf(1229,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_973_BinOpRedsThrow1) ).

thf(6008,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1229]) ).

thf(80,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wTrt @ C @ D @ E @ F @ G ) )
     => ( ( hBOOL @ ( wTrts @ C @ D @ E @ A @ B ) )
       => ( hBOOL @ ( wTrts @ C @ D @ E @ ( cons_exp_list_char @ F @ A ) @ ( cons_ty @ G @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1197_WTrt_H__WTrts_H_Ointros_I15_J) ).

thf(1551,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wTrt @ C @ D @ E @ F @ G ) )
     => ( ( hBOOL @ ( wTrts @ C @ D @ E @ A @ B ) )
       => ( hBOOL @ ( wTrts @ C @ D @ E @ ( cons_exp_list_char @ F @ A ) @ ( cons_ty @ G @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(202,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( fun_up2041264236on_val @ A @ B @ C )
        = A )
    <=> ( ( hAPP_n546249108on_val @ A @ B )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_fun__upd__idem__iff) ).

thf(2054,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( fun_up2041264236on_val @ A @ B @ C )
          = A )
       => ( ( hAPP_n546249108on_val @ A @ B )
          = C ) )
      & ( ( ( hAPP_n546249108on_val @ A @ B )
          = C )
       => ( ( fun_up2041264236on_val @ A @ B @ C )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(770,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ A ) @ ( transi1395422419t_char @ B ) ) )
     => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ ( transi1395422419t_char @ A ) ) @ ( transi1395422419t_char @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_683_rtrancl__subset__rtrancl) ).

thf(4207,plain,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ A ) @ ( transi1395422419t_char @ B ) ) )
     => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ ( transi1395422419t_char @ A ) ) @ ( transi1395422419t_char @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).

thf(898,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f2028441009l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc__HOL__Ob) ).

thf(4741,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f2028441009l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).

thf(1215,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_967_BinOp1Reds) ).

thf(5959,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).

thf(946,axiom,
    ! [A: $i] :
      ( ( hAPP_option_val_val @ the_val @ ( hAPP_val_option_val @ some_val @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_685_the_Osimps) ).

thf(4907,plain,
    ! [A: $i] :
      ( ( hAPP_option_val_val @ the_val @ ( hAPP_val_option_val @ some_val @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).

thf(414,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ A ) @ B )
        = ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_Pair__inject) ).

thf(2914,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ A ) @ B )
        = ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(86,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f126445617l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__) ).

thf(1583,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f126445617l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(745,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_prod__cases3) ).

thf(4136,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).

thf(213,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B ) ) @ ( transi935034983cl_val @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: $i] :
              ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ D ) ) @ C ) )
             => ~ ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ B ) ) @ ( transi935034983cl_val @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_841_converse__rtranclE) ).

thf(2096,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B ) ) @ ( transi935034983cl_val @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: $i] :
              ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ D ) ) @ C ) )
             => ~ ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ B ) ) @ ( transi935034983cl_val @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(16,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P1183499705r_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__) ).

thf(1304,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P1183499705r_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(149,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P929938951l_bool @ ( hAPP_f1335946228l_bool @ ( hAPP_f263393637l_bool @ cOMBC_813705475l_bool @ A ) @ B ) @ C )
      = ( hAPP_f742333458l_bool @ ( hAPP_P1614880106l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__fun_) ).

thf(1873,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P929938951l_bool @ ( hAPP_f1335946228l_bool @ ( hAPP_f263393637l_bool @ cOMBC_813705475l_bool @ A ) @ B ) @ C )
      = ( hAPP_f742333458l_bool @ ( hAPP_P1614880106l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(713,axiom,
    ! [A: $i] :
      ( ! [B: $i] :
          ( A
         != ( hAPP_f363827556r_bool @ some_f80346385r_bool @ B ) )
    <=> ( A = none_f478147469r_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_618_not__Some__eq) ).

thf(4013,plain,
    ! [A: $i] :
      ( ( ! [B: $i] :
            ( A
           != ( hAPP_f363827556r_bool @ some_f80346385r_bool @ B ) )
       => ( A = none_f478147469r_bool ) )
      & ( ( A = none_f478147469r_bool )
       => ! [B: $i] :
            ( A
           != ( hAPP_f363827556r_bool @ some_f80346385r_bool @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).

thf(127,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_prod__cases3) ).

thf(1758,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(1195,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P1085566419p_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] :
          ( ( ( is_bop @ B )
            & ( is_bop @ C ) )
         => ( hBOOL @ ( hAPP_P1085566419p_bool @ A @ ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_split__paired__All) ).

thf(5886,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P1085566419p_bool @ A @ B ) )
       => ! [B: $i,C: $i] :
            ( ( ( is_bop @ B )
              & ( is_bop @ C ) )
           => ( hBOOL @ ( hAPP_P1085566419p_bool @ A @ ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ B ) @ C ) ) ) ) )
      & ( ! [B: $i,C: $i] :
            ( ( ( is_bop @ B )
              & ( is_bop @ C ) )
           => ( hBOOL @ ( hAPP_P1085566419p_bool @ A @ ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ B ) @ C ) ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P1085566419p_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).

thf(918,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fFalse ) ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( while_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1078_WhileFReds) ).

thf(4813,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fFalse ) ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( while_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).

thf(434,axiom,
    null != unit,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1032_val_Osimps_I5_J) ).

thf(2994,plain,
    null != unit,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(831,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_pred__equals__eq2) ).

thf(4456,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).

thf(502,axiom,
    ! [A: $i,B: $i] :
      ( ( fun_up204312361on_val @ A @ B @ ( hAPP_P2094403585on_val @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_fun__upd__triv) ).

thf(3206,plain,
    ! [A: $i,B: $i] :
      ( ( fun_up204312361on_val @ A @ B @ ( hAPP_P2094403585on_val @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(847,axiom,
    ! [A: $i,B: $i] : ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ A ) @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_widen__refl) ).

thf(4529,plain,
    ! [A: $i,B: $i] : ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ A ) @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).

thf(196,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) @ B @ ( map_va1934808527t_char @ val_list_char @ C ) ) @ D ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1135_redp__redsp_ORedCallNull) ).

thf(2037,plain,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) @ B @ ( map_va1934808527t_char @ val_list_char @ C ) ) @ D ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(1151,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ ( transi2024712006on_val @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_667_r__into__rtrancl) ).

thf(5678,plain,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ ( transi2024712006on_val @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).

thf(931,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( map_ad325961431ar_val @ A @ D ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ ( map_ad325961431ar_val @ A @ G ) ) ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_654_Red__lcl__add) ).

thf(4859,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( map_ad325961431ar_val @ A @ D ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ ( map_ad325961431ar_val @ A @ G ) ) ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).

thf(245,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ! [D: $i] :
          ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ C ) ) @ D )
          = none_P179726773on_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_640_map__upd__nonempty) ).

thf(2202,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ! [D: $i] :
          ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ C ) ) @ D )
          = none_P179726773on_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(1245,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ I ) @ J ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ K ) ) ) @ L ) ) ) @ ( transi2024712006on_val @ ( red @ M ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ L ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) ) @ ( transi2024712006on_val @ ( red @ M ) ) ) )
       => ( ( ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) )
            = ( hAPP_n546249108on_val @ G @ K ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ I @ A @ B @ E ) ) @ J ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( fun_up2041264236on_val @ G @ K @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ ( fun_up204312361on_val @ D @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) @ ( hAPP_val_option_val @ some_val @ F ) ) ) ) ) ) @ H ) ) ) ) @ ( transi2024712006on_val @ ( red @ M ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_892_FAssRedsVal) ).

thf(6076,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ I ) @ J ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ K ) ) ) @ L ) ) ) @ ( transi2024712006on_val @ ( red @ M ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ L ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) ) @ ( transi2024712006on_val @ ( red @ M ) ) ) )
       => ( ( ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) )
            = ( hAPP_n546249108on_val @ G @ K ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ I @ A @ B @ E ) ) @ J ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( fun_up2041264236on_val @ G @ K @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ ( fun_up204312361on_val @ D @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) @ ( hAPP_val_option_val @ some_val @ F ) ) ) ) ) ) @ H ) ) ) ) @ ( transi2024712006on_val @ ( red @ M ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245]) ).

thf(685,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f1175813647l_bool @ ( hAPP_f550652027l_bool @ ( hAPP_f838396643l_bool @ cOMBC_2027949654l_bool @ A ) @ B ) @ C )
      = ( hAPP_f603925568l_bool @ ( hAPP_f1617787571l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It) ).

thf(3921,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f1175813647l_bool @ ( hAPP_f550652027l_bool @ ( hAPP_f838396643l_bool @ cOMBC_2027949654l_bool @ A ) @ B ) @ C )
      = ( hAPP_f603925568l_bool @ ( hAPP_f1617787571l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).

thf(24,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_prod_Oexhaust) ).

thf(1340,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(884,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( lAss_list_char @ A @ B )
     != ( block_list_char @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_571_exp_Osimps_I142_J) ).

thf(4688,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( lAss_list_char @ A @ B )
     != ( block_list_char @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).

thf(262,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( is_bop @ A )
        & ( is_bop @ C ) )
     => ( ( ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ A ) @ B )
          = ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) )
       => ~ ( ( A = C )
           => ( B != D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_Pair__inject) ).

thf(2256,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( is_bop @ A )
        & ( is_bop @ C ) )
     => ( ( ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ A ) @ B )
          = ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) )
       => ~ ( ( A = C )
           => ( B != D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(171,axiom,
    ! [A: $i] :
      ( nt
     != ( hAPP_list_char_ty @ class @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1110_ty_Osimps_I20_J) ).

thf(1958,plain,
    ! [A: $i] :
      ( nt
     != ( hAPP_list_char_ty @ class @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(1159,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ! [D: $i] :
          ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) ) @ D )
          = none_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_642_map__upd__nonempty) ).

thf(5710,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ! [D: $i] :
          ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) ) @ D )
          = none_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).

thf(722,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
    <=> ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
        & ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_691_set__eq__subset) ).

thf(4045,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
       => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).

thf(1123,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ E ) ) )
        = ( hAPP_val_option_val @ some_val @ F ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ D ) @ C @ ( hAPP_v834067052t_char @ val_list_char @ E ) ) ) @ A ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ A ) ) ) @ ( red @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1004_red__reds_ORedBinOp) ).

thf(5570,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ E ) ) )
        = ( hAPP_val_option_val @ some_val @ F ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ D ) @ C @ ( hAPP_v834067052t_char @ val_list_char @ E ) ) ) @ A ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ A ) ) ) @ ( red @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).

thf(366,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ B ) @ ( transi1395422419t_char @ A ) ) )
       => ( ( transi1395422419t_char @ B )
          = ( transi1395422419t_char @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_680_rtrancl__subset) ).

thf(2715,plain,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ B ) @ ( transi1395422419t_char @ A ) ) )
       => ( ( transi1395422419t_char @ B )
          = ( transi1395422419t_char @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(683,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ B ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) ) @ ( transi61620055on_val @ E ) ) )
     => ( ( ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ B )
         != ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) )
       => ~ ! [F: $i,G: $i] :
              ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ B ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ F ) @ G ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) ) @ ( transi61620055on_val @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_754_converse__rtranclE2) ).

thf(3913,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ B ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) ) @ ( transi61620055on_val @ E ) ) )
     => ( ( ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ B )
         != ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) )
       => ~ ! [F: $i,G: $i] :
              ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ B ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ F ) @ G ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) ) @ ( transi61620055on_val @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).

thf(474,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
      | ( hBOOL @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).

thf(3112,plain,
    ! [A: $i,B: $i] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
      | ( hBOOL @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(957,axiom,
    ! [A: $i] :
      ( ( A != none_val )
    <=> ? [B: $i] :
          ( A
          = ( hAPP_val_option_val @ some_val @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_622_not__None__eq) ).

thf(4939,plain,
    ! [A: $i] :
      ( ( ( A != none_val )
       => ? [B: $i] :
            ( A
            = ( hAPP_val_option_val @ some_val @ B ) ) )
      & ( ? [B: $i] :
            ( A
            = ( hAPP_val_option_val @ some_val @ B ) )
       => ( A != none_val ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).

thf(1131,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C != D )
     => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ D @ B ) @ C )
        = ( hAPP_l207779698on_val @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_fun__upd__other) ).

thf(5592,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C != D )
     => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ D @ B ) @ C )
        = ( hAPP_l207779698on_val @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).

thf(1117,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f539072365l_bool @ ( ord_le176694639r_bool @ ( hAPP_f2091926485r_bool @ ( hAPP_f1820115955r_bool @ cOMBC_790582442r_bool @ ( hAPP_f2059406941r_bool @ ( hAPP_f108089737r_bool @ cOMBB_2143526097t_char @ cOMBC_220519196l_bool ) @ ( hAPP_f165071409l_bool @ ( hAPP_f1174637065l_bool @ cOMBB_33167485t_char @ ( hAPP_f380623487l_bool @ cOMBB_1033145403t_char @ member1840112042t_char ) ) @ produc1147572817t_char ) ) ) @ A ) ) @ ( hAPP_f2091926485r_bool @ ( hAPP_f1820115955r_bool @ cOMBC_790582442r_bool @ ( hAPP_f2059406941r_bool @ ( hAPP_f108089737r_bool @ cOMBB_2143526097t_char @ cOMBC_220519196l_bool ) @ ( hAPP_f165071409l_bool @ ( hAPP_f1174637065l_bool @ cOMBB_33167485t_char @ ( hAPP_f380623487l_bool @ cOMBB_1033145403t_char @ member1840112042t_char ) ) @ produc1147572817t_char ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f82569901l_bool @ ( ord_le715555971r_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_805_pred__subset__eq2) ).

thf(5523,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( hAPP_f539072365l_bool @ ( ord_le176694639r_bool @ ( hAPP_f2091926485r_bool @ ( hAPP_f1820115955r_bool @ cOMBC_790582442r_bool @ ( hAPP_f2059406941r_bool @ ( hAPP_f108089737r_bool @ cOMBB_2143526097t_char @ cOMBC_220519196l_bool ) @ ( hAPP_f165071409l_bool @ ( hAPP_f1174637065l_bool @ cOMBB_33167485t_char @ ( hAPP_f380623487l_bool @ cOMBB_1033145403t_char @ member1840112042t_char ) ) @ produc1147572817t_char ) ) ) @ A ) ) @ ( hAPP_f2091926485r_bool @ ( hAPP_f1820115955r_bool @ cOMBC_790582442r_bool @ ( hAPP_f2059406941r_bool @ ( hAPP_f108089737r_bool @ cOMBB_2143526097t_char @ cOMBC_220519196l_bool ) @ ( hAPP_f165071409l_bool @ ( hAPP_f1174637065l_bool @ cOMBB_33167485t_char @ ( hAPP_f380623487l_bool @ cOMBB_1033145403t_char @ member1840112042t_char ) ) @ produc1147572817t_char ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f82569901l_bool @ ( ord_le715555971r_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f82569901l_bool @ ( ord_le715555971r_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f539072365l_bool @ ( ord_le176694639r_bool @ ( hAPP_f2091926485r_bool @ ( hAPP_f1820115955r_bool @ cOMBC_790582442r_bool @ ( hAPP_f2059406941r_bool @ ( hAPP_f108089737r_bool @ cOMBB_2143526097t_char @ cOMBC_220519196l_bool ) @ ( hAPP_f165071409l_bool @ ( hAPP_f1174637065l_bool @ cOMBB_33167485t_char @ ( hAPP_f380623487l_bool @ cOMBB_1033145403t_char @ member1840112042t_char ) ) @ produc1147572817t_char ) ) ) @ A ) ) @ ( hAPP_f2091926485r_bool @ ( hAPP_f1820115955r_bool @ cOMBC_790582442r_bool @ ( hAPP_f2059406941r_bool @ ( hAPP_f108089737r_bool @ cOMBB_2143526097t_char @ cOMBC_220519196l_bool ) @ ( hAPP_f165071409l_bool @ ( hAPP_f1174637065l_bool @ cOMBB_33167485t_char @ ( hAPP_f380623487l_bool @ cOMBB_1033145403t_char @ member1840112042t_char ) ) @ produc1147572817t_char ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).

thf(996,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_407_prod__caseI) ).

thf(5079,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).

thf(609,axiom,
    ! [A: $i] :
      ( ( hAPP_option_ty_ty @ the_ty @ ( hAPP_ty_option_ty @ some_ty @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_688_the_Osimps) ).

thf(3608,plain,
    ! [A: $i] :
      ( ( hAPP_option_ty_ty @ the_ty @ ( hAPP_ty_option_ty @ some_ty @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(144,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ A ) @ B )
        = ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_Pair__inject) ).

thf(1845,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ A ) @ B )
        = ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(782,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ E ) @ F ) ) ) @ ( reds @ G ) ) )
     => ( ( hBOOL @ ( wTrts_1 @ G @ ( hp @ D ) @ A @ C @ B ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1700205512_sconf @ G @ A ) @ D ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1700205512_sconf @ G @ A ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1170_reds__preserves__sconf) ).

thf(4255,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ E ) @ F ) ) ) @ ( reds @ G ) ) )
     => ( ( hBOOL @ ( wTrts_1 @ G @ ( hp @ D ) @ A @ C @ B ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1700205512_sconf @ G @ A ) @ D ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1700205512_sconf @ G @ A ) @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).

thf(135,axiom,
    ! [A: $i] :
      ( void
     != ( hAPP_list_char_ty @ class @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1059_ty_Osimps_I8_J) ).

thf(1798,plain,
    ! [A: $i] :
      ( void
     != ( hAPP_list_char_ty @ class @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(1139,axiom,
    ! [A: $i,B: $i] :
      ( ( semila751111325l_bool @ A @ B )
      = ( collec718040978on_val @ ( cOMBS_1319864284l_bool @ ( hAPP_f379976829l_bool @ ( hAPP_f606945057l_bool @ cOMBB_705522285on_val @ fdisj ) @ ( hAPP_f2036784149l_bool @ ( hAPP_f1720452391l_bool @ cOMBC_1021753250l_bool @ member773094996on_val ) @ A ) ) @ ( hAPP_f2036784149l_bool @ ( hAPP_f1720452391l_bool @ cOMBC_1021753250l_bool @ member773094996on_val ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_882_Un__def) ).

thf(5624,plain,
    ! [A: $i,B: $i] :
      ( ( semila751111325l_bool @ A @ B )
      = ( collec718040978on_val @ ( cOMBS_1319864284l_bool @ ( hAPP_f379976829l_bool @ ( hAPP_f606945057l_bool @ cOMBB_705522285on_val @ fdisj ) @ ( hAPP_f2036784149l_bool @ ( hAPP_f1720452391l_bool @ cOMBC_1021753250l_bool @ member773094996on_val ) @ A ) ) @ ( hAPP_f2036784149l_bool @ ( hAPP_f1720452391l_bool @ cOMBC_1021753250l_bool @ member773094996on_val ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).

thf(1161,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f570766339l_bool @ ( ord_le1080391173l_bool @ ( hAPP_f989077673l_bool @ ( hAPP_f40682957l_bool @ cOMBC_562612496l_bool @ ( hAPP_f1475571983l_bool @ ( hAPP_f1946480059l_bool @ cOMBB_673739729t_char @ cOMBC_1585774710l_bool ) @ ( hAPP_f1614195593l_bool @ ( hAPP_f705562443l_bool @ cOMBB_507006011t_char @ ( hAPP_f1639555093l_bool @ cOMBB_985659173on_val @ member840932460on_val ) ) @ produc1259058957on_val ) ) ) @ A ) ) @ ( hAPP_f989077673l_bool @ ( hAPP_f40682957l_bool @ cOMBC_562612496l_bool @ ( hAPP_f1475571983l_bool @ ( hAPP_f1946480059l_bool @ cOMBB_673739729t_char @ cOMBC_1585774710l_bool ) @ ( hAPP_f1614195593l_bool @ ( hAPP_f705562443l_bool @ cOMBB_507006011t_char @ ( hAPP_f1639555093l_bool @ cOMBB_985659173on_val @ member840932460on_val ) ) @ produc1259058957on_val ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f91506671l_bool @ ( ord_le1668954565l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_816_pred__subset__eq2) ).

thf(5716,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( hAPP_f570766339l_bool @ ( ord_le1080391173l_bool @ ( hAPP_f989077673l_bool @ ( hAPP_f40682957l_bool @ cOMBC_562612496l_bool @ ( hAPP_f1475571983l_bool @ ( hAPP_f1946480059l_bool @ cOMBB_673739729t_char @ cOMBC_1585774710l_bool ) @ ( hAPP_f1614195593l_bool @ ( hAPP_f705562443l_bool @ cOMBB_507006011t_char @ ( hAPP_f1639555093l_bool @ cOMBB_985659173on_val @ member840932460on_val ) ) @ produc1259058957on_val ) ) ) @ A ) ) @ ( hAPP_f989077673l_bool @ ( hAPP_f40682957l_bool @ cOMBC_562612496l_bool @ ( hAPP_f1475571983l_bool @ ( hAPP_f1946480059l_bool @ cOMBB_673739729t_char @ cOMBC_1585774710l_bool ) @ ( hAPP_f1614195593l_bool @ ( hAPP_f705562443l_bool @ cOMBB_507006011t_char @ ( hAPP_f1639555093l_bool @ cOMBB_985659173on_val @ member840932460on_val ) ) @ produc1259058957on_val ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f91506671l_bool @ ( ord_le1668954565l_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f91506671l_bool @ ( ord_le1668954565l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f570766339l_bool @ ( ord_le1080391173l_bool @ ( hAPP_f989077673l_bool @ ( hAPP_f40682957l_bool @ cOMBC_562612496l_bool @ ( hAPP_f1475571983l_bool @ ( hAPP_f1946480059l_bool @ cOMBB_673739729t_char @ cOMBC_1585774710l_bool ) @ ( hAPP_f1614195593l_bool @ ( hAPP_f705562443l_bool @ cOMBB_507006011t_char @ ( hAPP_f1639555093l_bool @ cOMBB_985659173on_val @ member840932460on_val ) ) @ produc1259058957on_val ) ) ) @ A ) ) @ ( hAPP_f989077673l_bool @ ( hAPP_f40682957l_bool @ cOMBC_562612496l_bool @ ( hAPP_f1475571983l_bool @ ( hAPP_f1946480059l_bool @ cOMBB_673739729t_char @ cOMBC_1585774710l_bool ) @ ( hAPP_f1614195593l_bool @ ( hAPP_f705562443l_bool @ cOMBB_507006011t_char @ ( hAPP_f1639555093l_bool @ cOMBB_985659173on_val @ member840932460on_val ) ) @ produc1259058957on_val ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).

thf(1187,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( hBOOL @ ( hAPP_f966411375l_bool @ ( hAPP_P998768845l_bool @ member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f966411375l_bool @ ( hAPP_P998768845l_bool @ member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_pred__equals__eq2) ).

thf(5822,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f966411375l_bool @ ( hAPP_P998768845l_bool @ member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f966411375l_bool @ ( hAPP_P998768845l_bool @ member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f966411375l_bool @ ( hAPP_P998768845l_bool @ member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f966411375l_bool @ ( hAPP_P998768845l_bool @ member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f966411375l_bool @ ( hAPP_P998768845l_bool @ member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f966411375l_bool @ ( hAPP_P998768845l_bool @ member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f966411375l_bool @ ( hAPP_P998768845l_bool @ member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f966411375l_bool @ ( hAPP_P998768845l_bool @ member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).

thf(69,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( wTrt @ A @ B @ C @ D @ E ) )
     => ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1022_wt_H__wt) ).

thf(1516,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( wTrt @ A @ B @ C @ D @ E ) )
     => ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(91,axiom,
    void != nt,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1113_ty_Osimps_I6_J) ).

thf(1598,plain,
    void != nt,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(1114,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_bool_bool @ A @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ B ) @ C ) ) )
     => ~ ! [D: $i,E: $i] :
            ( ( C
              = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) )
           => ~ ( hBOOL @ ( hAPP_bool_bool @ A @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ B @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_562_splitE2) ).

thf(5514,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_bool_bool @ A @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ B ) @ C ) ) )
     => ~ ! [D: $i,E: $i] :
            ( ( C
              = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) )
           => ~ ( hBOOL @ ( hAPP_bool_bool @ A @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ B @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).

thf(586,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_PairE) ).

thf(3507,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(956,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ F ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ D @ A @ B @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ F ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_940_FAssRedsThrow1) ).

thf(4937,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ F ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ D @ A @ B @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ F ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).

thf(429,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ ( transi1395422419t_char @ D ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ A @ B ) )
       => ( ! [E: $i,F: $i] :
              ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ E ) ) @ ( transi1395422419t_char @ D ) ) )
             => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ E ) @ F ) ) @ D ) )
               => ( ( hBOOL @ ( hAPP_list_char_bool @ A @ E ) )
                 => ( hBOOL @ ( hAPP_list_char_bool @ A @ F ) ) ) ) )
         => ( hBOOL @ ( hAPP_list_char_bool @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_797_rtrancl__induct) ).

thf(2977,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ ( transi1395422419t_char @ D ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ A @ B ) )
       => ( ! [E: $i,F: $i] :
              ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ E ) ) @ ( transi1395422419t_char @ D ) ) )
             => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ E ) @ F ) ) @ D ) )
               => ( ( hBOOL @ ( hAPP_list_char_bool @ A @ E ) )
                 => ( hBOOL @ ( hAPP_list_char_bool @ A @ F ) ) ) ) )
         => ( hBOOL @ ( hAPP_list_char_bool @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(283,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_t1875766236har_ty @ ( hAPP_l1948972481har_ty @ produc251930284har_ty @ A ) @ B )
        = ( hAPP_t1875766236har_ty @ ( hAPP_l1948972481har_ty @ produc251930284har_ty @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Pair__inject) ).

thf(2375,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_t1875766236har_ty @ ( hAPP_l1948972481har_ty @ produc251930284har_ty @ A ) @ B )
        = ( hAPP_t1875766236har_ty @ ( hAPP_l1948972481har_ty @ produc251930284har_ty @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(186,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_P1183008383l_bool @ ( produc2053127004l_bool @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_365_curryI) ).

thf(2012,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_P1183008383l_bool @ ( produc2053127004l_bool @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(680,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f893576377l_bool @ ( hAPP_f1250221913l_bool @ ( hAPP_f1860331535l_bool @ cOMBB_2084052674on_val @ A ) @ B ) @ C )
      = ( hAPP_f510152537l_bool @ A @ ( hAPP_f613075253l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_073) ).

thf(3904,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f893576377l_bool @ ( hAPP_f1250221913l_bool @ ( hAPP_f1860331535l_bool @ cOMBB_2084052674on_val @ A ) @ B ) @ C )
      = ( hAPP_f510152537l_bool @ A @ ( hAPP_f613075253l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).

thf(518,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( wTrt @ E @ F @ G @ H @ I ) )
     => ( ( hBOOL @ ( wTrt @ E @ F @ ( fun_up424764369ion_ty @ G @ A @ ( hAPP_ty_option_ty @ some_ty @ ( hAPP_list_char_ty @ class @ B ) ) ) @ C @ D ) )
       => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ E ) @ I ) @ D ) )
         => ( hBOOL @ ( wTrt @ E @ F @ G @ ( tryCatch_list_char @ H @ B @ A @ C ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1027_WTrt_H__WTrts_H_Ointros_I22_J) ).

thf(3260,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( wTrt @ E @ F @ G @ H @ I ) )
     => ( ( hBOOL @ ( wTrt @ E @ F @ ( fun_up424764369ion_ty @ G @ A @ ( hAPP_ty_option_ty @ some_ty @ ( hAPP_list_char_ty @ class @ B ) ) ) @ C @ D ) )
       => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ E ) @ I ) @ D ) )
         => ( hBOOL @ ( wTrt @ E @ F @ G @ ( tryCatch_list_char @ H @ B @ A @ C ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(1109,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( D != E )
     => ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ A @ D @ B ) @ E @ C )
        = ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ A @ E @ C ) @ D @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_fun__upd__twist) ).

thf(5499,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( D != E )
     => ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ A @ D @ B ) @ E @ C )
        = ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ A @ E @ C ) @ D @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).

thf(1211,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ E ) ) )
     => ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B )
         != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) )
       => ~ ! [F: $i,G: $i] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_742_converse__rtranclE2) ).

thf(5944,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ E ) ) )
     => ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B )
         != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) )
       => ~ ! [F: $i,G: $i] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).

thf(620,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ C ) @ D )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ F ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ E ) @ A ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ B ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) ) ) ) @ C ) ) ) @ ( red @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1003_red__reds_ORedCastFail) ).

thf(3659,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ C ) @ D )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ F ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ E ) @ A ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ B ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) ) ) ) @ C ) ) ) @ ( red @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(168,axiom,
    ! [A: $i,B: $i] :
      ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ ( hAPP_o538043682on_val @ cOMBK_1097134891t_char @ none_val ) @ A @ none_val ) @ B )
      = none_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_635_empty__upd__none) ).

thf(1941,plain,
    ! [A: $i,B: $i] :
      ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ ( hAPP_o538043682on_val @ cOMBK_1097134891t_char @ none_val ) @ A @ none_val ) @ B )
      = none_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(1103,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ H ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ H ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ F @ A @ B @ C ) ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1030_FAssRedsNull) ).

thf(5484,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ H ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ H ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ F @ A @ B @ C ) ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).

thf(843,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( is_bool @ ( wTrts_1 @ A @ B @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_WellTypeRT_OWTrts) ).

thf(4517,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( is_bool @ ( wTrts_1 @ A @ B @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).

thf(508,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_v834067052t_char @ val_list_char @ A )
     != ( seq_list_char @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_576_exp_Osimps_I84_J) ).

thf(3228,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_v834067052t_char @ val_list_char @ A )
     != ( seq_list_char @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(873,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_b1257035143l_bool @ ( hAPP_f2100207721l_bool @ ( hAPP_f1374595987l_bool @ cOMBB_761748254ol_bop @ A ) @ B ) @ C )
      = ( hAPP_f263393637l_bool @ A @ ( hAPP_b406740087l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mt_040) ).

thf(4641,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_b1257035143l_bool @ ( hAPP_f2100207721l_bool @ ( hAPP_f1374595987l_bool @ cOMBB_761748254ol_bop @ A ) @ B ) @ C )
      = ( hAPP_f263393637l_bool @ A @ ( hAPP_b406740087l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).

thf(1162,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( transi2024712006on_val @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: $i] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ D ) ) @ ( transi2024712006on_val @ C ) ) )
             => ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ B ) ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_836_rtranclE) ).

thf(5721,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( transi2024712006on_val @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: $i] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ D ) ) @ ( transi2024712006on_val @ C ) ) )
             => ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ B ) ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).

thf(236,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1734260017l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olis) ).

thf(2175,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1734260017l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(130,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( wTrt @ A @ B @ C @ D @ E ) )
    <=> ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1023_wt_H__iff__wt) ).

thf(1780,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( hBOOL @ ( wTrt @ A @ B @ C @ D @ E ) )
       => ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ E ) ) )
      & ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ E ) )
       => ( hBOOL @ ( wTrt @ A @ B @ C @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(503,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ ( transi1395422419t_char @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ A ) ) @ ( transi1395422419t_char @ D ) ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ A ) ) @ ( transi1395422419t_char @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_731_rtrancl__trans) ).

thf(3209,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ ( transi1395422419t_char @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ A ) ) @ ( transi1395422419t_char @ D ) ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ A ) ) @ ( transi1395422419t_char @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(942,axiom,
    ! [A: $i,B: $i] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_o2007402111l_bool @ ( hAPP_o1968908095l_bool @ fequal1937332960on_val @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__St) ).

thf(4894,plain,
    ! [A: $i,B: $i] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_o2007402111l_bool @ ( hAPP_o1968908095l_bool @ fequal1937332960on_val @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).

thf(963,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( fun_up1149430426on_val @ D @ E @ ( hAPP_val_option_val @ some_val @ F ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
     => ( ( hBOOL @ ( final_list_char @ G ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ E @ A @ ( seq_list_char @ ( lAss_list_char @ E @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ B ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ E @ ( hAPP_l207779698on_val @ D @ E ) ) ) ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_657_InitBlockRedsFinal) ).

thf(4961,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( fun_up1149430426on_val @ D @ E @ ( hAPP_val_option_val @ some_val @ F ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
     => ( ( hBOOL @ ( final_list_char @ G ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ E @ A @ ( seq_list_char @ ( lAss_list_char @ E @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ B ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ E @ ( hAPP_l207779698on_val @ D @ E ) ) ) ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).

thf(1089,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f1450446905l_bool @ ( ord_le125655867l_bool @ ( hAPP_f47713631l_bool @ ( hAPP_f77033475l_bool @ cOMBC_1317565126l_bool @ ( hAPP_f1250221913l_bool @ ( hAPP_f1860331535l_bool @ cOMBB_2084052674on_val @ cOMBC_1518234801l_bool ) @ ( hAPP_f1670595613l_bool @ ( hAPP_f1472899487l_bool @ cOMBB_588525814on_val @ ( hAPP_f1168269397l_bool @ cOMBB_1293776864on_val @ member763590124on_val ) ) @ produc899768717on_val ) ) ) @ A ) ) @ ( hAPP_f47713631l_bool @ ( hAPP_f77033475l_bool @ cOMBC_1317565126l_bool @ ( hAPP_f1250221913l_bool @ ( hAPP_f1860331535l_bool @ cOMBB_2084052674on_val @ cOMBC_1518234801l_bool ) @ ( hAPP_f1670595613l_bool @ ( hAPP_f1472899487l_bool @ cOMBB_588525814on_val @ ( hAPP_f1168269397l_bool @ cOMBB_1293776864on_val @ member763590124on_val ) ) @ produc899768717on_val ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f966411375l_bool @ ( ord_le1908998213l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_815_pred__subset__eq2) ).

thf(5431,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( hAPP_f1450446905l_bool @ ( ord_le125655867l_bool @ ( hAPP_f47713631l_bool @ ( hAPP_f77033475l_bool @ cOMBC_1317565126l_bool @ ( hAPP_f1250221913l_bool @ ( hAPP_f1860331535l_bool @ cOMBB_2084052674on_val @ cOMBC_1518234801l_bool ) @ ( hAPP_f1670595613l_bool @ ( hAPP_f1472899487l_bool @ cOMBB_588525814on_val @ ( hAPP_f1168269397l_bool @ cOMBB_1293776864on_val @ member763590124on_val ) ) @ produc899768717on_val ) ) ) @ A ) ) @ ( hAPP_f47713631l_bool @ ( hAPP_f77033475l_bool @ cOMBC_1317565126l_bool @ ( hAPP_f1250221913l_bool @ ( hAPP_f1860331535l_bool @ cOMBB_2084052674on_val @ cOMBC_1518234801l_bool ) @ ( hAPP_f1670595613l_bool @ ( hAPP_f1472899487l_bool @ cOMBB_588525814on_val @ ( hAPP_f1168269397l_bool @ cOMBB_1293776864on_val @ member763590124on_val ) ) @ produc899768717on_val ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f966411375l_bool @ ( ord_le1908998213l_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f966411375l_bool @ ( ord_le1908998213l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1450446905l_bool @ ( ord_le125655867l_bool @ ( hAPP_f47713631l_bool @ ( hAPP_f77033475l_bool @ cOMBC_1317565126l_bool @ ( hAPP_f1250221913l_bool @ ( hAPP_f1860331535l_bool @ cOMBB_2084052674on_val @ cOMBC_1518234801l_bool ) @ ( hAPP_f1670595613l_bool @ ( hAPP_f1472899487l_bool @ cOMBB_588525814on_val @ ( hAPP_f1168269397l_bool @ cOMBB_1293776864on_val @ member763590124on_val ) ) @ produc899768717on_val ) ) ) @ A ) ) @ ( hAPP_f47713631l_bool @ ( hAPP_f77033475l_bool @ cOMBC_1317565126l_bool @ ( hAPP_f1250221913l_bool @ ( hAPP_f1860331535l_bool @ cOMBB_2084052674on_val @ cOMBC_1518234801l_bool ) @ ( hAPP_f1670595613l_bool @ ( hAPP_f1472899487l_bool @ cOMBB_588525814on_val @ ( hAPP_f1168269397l_bool @ cOMBB_1293776864on_val @ member763590124on_val ) ) @ produc899768717on_val ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).

thf(119,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P92196306r_bool @ A @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P1907982426r_bool @ ( hAPP_l217977712r_bool @ ( produc1574020101r_bool @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_363_curryI) ).

thf(1716,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P92196306r_bool @ A @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P1907982426r_bool @ ( hAPP_l217977712r_bool @ ( produc1574020101r_bool @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(41,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P1333315679l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Oli) ).

thf(1432,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P1333315679l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(1237,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( red @ F ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ D ) ) @ E ) ) ) @ ( red @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_988_red__reds_OCastRed) ).

thf(6037,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( red @ F ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ D ) ) @ E ) ) ) @ ( red @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1237]) ).

thf(1168,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P748443392y_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P748443392y_bool @ A @ ( hAPP_t1875766236har_ty @ ( hAPP_l1948972481har_ty @ produc251930284har_ty @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_split__paired__All) ).

thf(5753,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P748443392y_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P748443392y_bool @ A @ ( hAPP_t1875766236har_ty @ ( hAPP_l1948972481har_ty @ produc251930284har_ty @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P748443392y_bool @ A @ ( hAPP_t1875766236har_ty @ ( hAPP_l1948972481har_ty @ produc251930284har_ty @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P748443392y_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).

thf(501,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( lAss_list_char @ A @ B )
     != ( hAPP_v834067052t_char @ val_list_char @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_579_exp_Osimps_I75_J) ).

thf(3202,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( lAss_list_char @ A @ B )
     != ( hAPP_v834067052t_char @ val_list_char @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(275,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ D @ E @ F ) @ G ) @ H ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ D @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ E ) @ F ) @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ G ) ) @ H ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_894_redp__redsp_OFAssRed2) ).

thf(2337,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ D @ E @ F ) @ G ) @ H ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ D @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ E ) @ F ) @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ G ) ) @ H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(1224,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f1776070952l_bool @ ( ord_le1725884030l_bool @ ( hAPP_f257113085l_bool @ ( hAPP_f1100052969l_bool @ cOMBC_199425070l_bool @ ( hAPP_f2100207721l_bool @ ( hAPP_f1374595987l_bool @ cOMBB_761748254ol_bop @ cOMBC_813705475l_bool ) @ ( hAPP_f866074145l_bool @ ( hAPP_f877616419l_bool @ cOMBB_1458388806ol_bop @ ( hAPP_f62511709l_bool @ cOMBB_2139740953al_val @ member1417904245al_val ) ) @ produc621191550al_val ) ) ) @ A ) ) @ ( hAPP_f257113085l_bool @ ( hAPP_f1100052969l_bool @ cOMBC_199425070l_bool @ ( hAPP_f2100207721l_bool @ ( hAPP_f1374595987l_bool @ cOMBB_761748254ol_bop @ cOMBC_813705475l_bool ) @ ( hAPP_f866074145l_bool @ ( hAPP_f877616419l_bool @ cOMBB_1458388806ol_bop @ ( hAPP_f62511709l_bool @ cOMBB_2139740953al_val @ member1417904245al_val ) ) @ produc621191550al_val ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f742333458l_bool @ ( ord_le1467847572l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_813_pred__subset__eq2) ).

thf(5995,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( hAPP_f1776070952l_bool @ ( ord_le1725884030l_bool @ ( hAPP_f257113085l_bool @ ( hAPP_f1100052969l_bool @ cOMBC_199425070l_bool @ ( hAPP_f2100207721l_bool @ ( hAPP_f1374595987l_bool @ cOMBB_761748254ol_bop @ cOMBC_813705475l_bool ) @ ( hAPP_f866074145l_bool @ ( hAPP_f877616419l_bool @ cOMBB_1458388806ol_bop @ ( hAPP_f62511709l_bool @ cOMBB_2139740953al_val @ member1417904245al_val ) ) @ produc621191550al_val ) ) ) @ A ) ) @ ( hAPP_f257113085l_bool @ ( hAPP_f1100052969l_bool @ cOMBC_199425070l_bool @ ( hAPP_f2100207721l_bool @ ( hAPP_f1374595987l_bool @ cOMBB_761748254ol_bop @ cOMBC_813705475l_bool ) @ ( hAPP_f866074145l_bool @ ( hAPP_f877616419l_bool @ cOMBB_1458388806ol_bop @ ( hAPP_f62511709l_bool @ cOMBB_2139740953al_val @ member1417904245al_val ) ) @ produc621191550al_val ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f742333458l_bool @ ( ord_le1467847572l_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f742333458l_bool @ ( ord_le1467847572l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1776070952l_bool @ ( ord_le1725884030l_bool @ ( hAPP_f257113085l_bool @ ( hAPP_f1100052969l_bool @ cOMBC_199425070l_bool @ ( hAPP_f2100207721l_bool @ ( hAPP_f1374595987l_bool @ cOMBB_761748254ol_bop @ cOMBC_813705475l_bool ) @ ( hAPP_f866074145l_bool @ ( hAPP_f877616419l_bool @ cOMBB_1458388806ol_bop @ ( hAPP_f62511709l_bool @ cOMBB_2139740953al_val @ member1417904245al_val ) ) @ produc621191550al_val ) ) ) @ A ) ) @ ( hAPP_f257113085l_bool @ ( hAPP_f1100052969l_bool @ cOMBC_199425070l_bool @ ( hAPP_f2100207721l_bool @ ( hAPP_f1374595987l_bool @ cOMBB_761748254ol_bop @ cOMBC_813705475l_bool ) @ ( hAPP_f866074145l_bool @ ( hAPP_f877616419l_bool @ cOMBB_1458388806ol_bop @ ( hAPP_f62511709l_bool @ cOMBB_2139740953al_val @ member1417904245al_val ) ) @ produc621191550al_val ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).

thf(741,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
    <=> ! [C: $i] : ( hBOOL @ ( hAPP_bool_bool @ ( ord_less_eq_bool @ ( hAPP_list_char_bool @ A @ C ) ) @ ( hAPP_list_char_bool @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_830_le__fun__def) ).

thf(4117,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
       => ! [C: $i] : ( hBOOL @ ( hAPP_bool_bool @ ( ord_less_eq_bool @ ( hAPP_list_char_bool @ A @ C ) ) @ ( hAPP_list_char_bool @ B @ C ) ) ) )
      & ( ! [C: $i] : ( hBOOL @ ( hAPP_bool_bool @ ( ord_less_eq_bool @ ( hAPP_list_char_bool @ A @ C ) ) @ ( hAPP_list_char_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).

thf(10,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P801803911r_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc) ).

thf(1285,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P801803911r_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(1026,axiom,
    ! [A: $i] :
      ( ( hBOOL @ A )
      | ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).

thf(5186,plain,
    ! [A: $i] :
      ( ( hBOOL @ A )
      | ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).

thf(443,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_prod_Oexhaust) ).

thf(3019,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(462,axiom,
    is_bool @ fTrue,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_fTrue) ).

thf(3080,plain,
    is_bool @ fTrue,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(845,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P378063101l_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P378063101l_bool @ A @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_split__paired__All) ).

thf(4522,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P378063101l_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P378063101l_bool @ A @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P378063101l_bool @ A @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P378063101l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).

thf(796,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ B ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_prod__cases3) ).

thf(4314,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ B ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).

thf(732,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P71593144l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__St_022) ).

thf(4092,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P71593144l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).

thf(945,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ ( produc1159035454l_bool @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_372_curryI) ).

thf(4905,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ ( produc1159035454l_bool @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).

thf(15,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_PairE) ).

thf(1300,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(103,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ A ) @ B ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) ) @ ( transi1789604888t_char @ E ) ) )
     => ( ( ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ A ) @ B )
         != ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) )
       => ~ ! [F: $i,G: $i] :
              ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ A ) @ B ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ F ) @ G ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) ) @ ( transi1789604888t_char @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_747_converse__rtranclE2) ).

thf(1637,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ A ) @ B ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) ) @ ( transi1789604888t_char @ E ) ) )
     => ( ( ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ A ) @ B )
         != ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) )
       => ~ ! [F: $i,G: $i] :
              ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ A ) @ B ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ F ) @ G ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) ) @ ( transi1789604888t_char @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(650,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( fv @ ( cond_list_char @ A @ B @ C ) )
      = ( semila919158006r_bool @ ( semila919158006r_bool @ ( fv @ A ) @ ( fv @ B ) ) @ ( fv @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1095_fv__fvs_Osimps_I12_J) ).

thf(3791,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( fv @ ( cond_list_char @ A @ B @ C ) )
      = ( semila919158006r_bool @ ( semila919158006r_bool @ ( fv @ A ) @ ( fv @ B ) ) @ ( fv @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).

thf(714,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_708_set__mp) ).

thf(4020,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).

thf(981,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P2115985549l_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P2115985549l_bool @ A @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_split__paired__All) ).

thf(5015,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P2115985549l_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P2115985549l_bool @ A @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P2115985549l_bool @ A @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P2115985549l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).

thf(636,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1842007287l_bool @ ( hAPP_f2118054305l_bool @ ( hAPP_f1687138147l_bool @ cOMBB_2078271971st_val @ A ) @ B ) @ C )
      = ( hAPP_f361629773l_bool @ A @ ( hAPP_l1859255743t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc) ).

thf(3722,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1842007287l_bool @ ( hAPP_f2118054305l_bool @ ( hAPP_f1687138147l_bool @ cOMBB_2078271971st_val @ A ) @ B ) @ C )
      = ( hAPP_f361629773l_bool @ A @ ( hAPP_l1859255743t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(1049,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ G ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) ) @ ( transi374442731on_val @ ( reds @ H ) ) ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ D @ A ) ) @ E ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ F ) @ B ) ) @ C ) ) ) @ ( transi374442731on_val @ ( reds @ H ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1166_ListRedsVal) ).

thf(5276,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ G ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) ) @ ( transi374442731on_val @ ( reds @ H ) ) ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ D @ A ) ) @ E ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ F ) @ B ) ) @ C ) ) ) @ ( transi374442731on_val @ ( reds @ H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).

thf(131,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i] :
      ( ( hBOOL @ ( wTrt_1 @ I @ J @ K @ L @ ( hAPP_list_char_ty @ class @ M ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( method1809630380t_char @ I @ M @ C @ D @ E @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ F ) @ G ) ) @ H ) )
       => ( ( hBOOL @ ( wTrts_1 @ I @ J @ K @ A @ B ) )
         => ( ( hBOOL @ ( list_all2_ty_ty @ ( widen_2090681816t_char @ I ) @ B @ D ) )
           => ( hBOOL @ ( wTrt_1 @ I @ J @ K @ ( call_list_char @ L @ C @ A ) @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1191_WTrtCall) ).

thf(1785,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i] :
      ( ( hBOOL @ ( wTrt_1 @ I @ J @ K @ L @ ( hAPP_list_char_ty @ class @ M ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( method1809630380t_char @ I @ M @ C @ D @ E @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ F ) @ G ) ) @ H ) )
       => ( ( hBOOL @ ( wTrts_1 @ I @ J @ K @ A @ B ) )
         => ( ( hBOOL @ ( list_all2_ty_ty @ ( widen_2090681816t_char @ I ) @ B @ D ) )
           => ( hBOOL @ ( wTrt_1 @ I @ J @ K @ ( call_list_char @ L @ C @ A ) @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(577,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f1617787571l_bool @ ( hAPP_f857351829l_bool @ ( hAPP_f348318673l_bool @ cOMBB_1518282696on_val @ A ) @ B ) @ C )
      = ( hAPP_f181262431l_bool @ A @ ( hAPP_f1213370163y_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_053) ).

thf(3475,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f1617787571l_bool @ ( hAPP_f857351829l_bool @ ( hAPP_f348318673l_bool @ cOMBB_1518282696on_val @ A ) @ B ) @ C )
      = ( hAPP_f181262431l_bool @ A @ ( hAPP_f1213370163y_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(445,axiom,
    ! [A: $i] :
      ( ( semila919158006r_bool @ A @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_875_Un__absorb) ).

thf(3026,plain,
    ! [A: $i] :
      ( ( semila919158006r_bool @ A @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(266,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ C @ D ) @ E ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ ( seq_list_char @ C @ A ) @ D ) @ ( seq_list_char @ E @ A ) ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_625_redp__redsp_OSeqRed) ).

thf(2276,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ C @ D ) @ E ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ ( seq_list_char @ C @ A ) @ D ) @ ( seq_list_char @ E @ A ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(224,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ ( semila449273525l_bool @ B @ C ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_861_UnE) ).

thf(2128,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ ( semila449273525l_bool @ B @ C ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(1016,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) @ A @ ( map_va1934808527t_char @ val_list_char @ B ) ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ C ) ) ) @ ( red @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1134_red__reds_ORedCallNull) ).

thf(5154,plain,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) @ A @ ( map_va1934808527t_char @ val_list_char @ B ) ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ C ) ) ) @ ( red @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).

thf(362,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( block_list_char @ A @ B @ C )
     != ( seq_list_char @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_570_exp_Osimps_I196_J) ).

thf(2701,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( block_list_char @ A @ B @ C )
     != ( seq_list_char @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(777,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1062423959r_bool @ ( hAPP_f1051205629r_bool @ ( hAPP_f987862447r_bool @ cOMBC_1387630958r_bool @ A ) @ B ) @ C )
      = ( hAPP_f1724656343r_bool @ ( hAPP_l296209613r_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Value__Oval_J_000tc__fun_Itc__prod_) ).

thf(4241,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1062423959r_bool @ ( hAPP_f1051205629r_bool @ ( hAPP_f987862447r_bool @ cOMBC_1387630958r_bool @ A ) @ B ) @ C )
      = ( hAPP_f1724656343r_bool @ ( hAPP_l296209613r_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).

thf(324,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fFalse ) ) ) @ E ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ ( while_list_char @ C @ A ) @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1086_WhileF) ).

thf(2545,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fFalse ) ) ) @ E ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ ( while_list_char @ C @ A ) @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(410,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ D ) @ ( throw_list_char @ E ) ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ ( cast_list_char @ A @ C ) @ D ) @ ( throw_list_char @ E ) ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_985_eval__evals_OCastThrow) ).

thf(2903,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ D ) @ ( throw_list_char @ E ) ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ ( cast_list_char @ A @ C ) @ D ) @ ( throw_list_char @ E ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(969,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) ) @ ( red @ H ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ D ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ F ) ) @ G ) ) ) @ ( red @ H ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_897_red__reds_OFAssRed2) ).

thf(4982,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) ) @ ( red @ H ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ D ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ F ) ) @ G ) ) ) @ ( red @ H ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).

thf(558,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l296209613r_bool @ ( hAPP_f1449341487r_bool @ ( hAPP_f1823921107r_bool @ cOMBB_308691073st_val @ A ) @ B ) @ C )
      = ( hAPP_f388097003r_bool @ A @ ( hAPP_l1842007287l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_044) ).

thf(3412,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l296209613r_bool @ ( hAPP_f1449341487r_bool @ ( hAPP_f1823921107r_bool @ cOMBB_308691073st_val @ A ) @ B ) @ C )
      = ( hAPP_f388097003r_bool @ A @ ( hAPP_l1842007287l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(906,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1780084320l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O_010) ).

thf(4781,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1780084320l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).

thf(493,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ B ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_prod__cases3) ).

thf(3174,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ B ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(756,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( ( size_s2113983095t_char @ I )
        = ( size_size_list_ty @ J ) )
     => ( ( ( size_s2113983095t_char @ I )
          = ( size_size_list_val @ H ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ I ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ J ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ H ) @ B ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) )
         => ? [K: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( map_up1085636310ar_val @ D @ I @ H ) ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ K ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1189_blocksEval) ).

thf(4164,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( ( size_s2113983095t_char @ I )
        = ( size_size_list_ty @ J ) )
     => ( ( ( size_s2113983095t_char @ I )
          = ( size_size_list_val @ H ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ I ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ J ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ H ) @ B ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) )
         => ? [K: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( map_up1085636310ar_val @ D @ I @ H ) ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ K ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).

thf(634,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_PairE) ).

thf(3715,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(472,axiom,
    ! [A: $i] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ null ) ) )
      = none_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1040_binop_Osimps_I8_J) ).

thf(3107,plain,
    ! [A: $i] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ null ) ) )
      = none_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(962,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ ( semila751111325l_bool @ B @ C ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_865_UnE) ).

thf(4959,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ ( semila751111325l_bool @ B @ C ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).

thf(136,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P1907982426r_bool @ ( hAPP_l217977712r_bool @ ( produc1574020101r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P92196306r_bool @ A @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_488_curryE) ).

thf(1802,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P1907982426r_bool @ ( hAPP_l217977712r_bool @ ( produc1574020101r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P92196306r_bool @ A @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(867,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_694_in__mono) ).

thf(4624,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).

thf(837,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f1033709212l_bool @ ( hAPP_f33142364l_bool @ ( hAPP_f510152537l_bool @ cOMBC_1518234801l_bool @ A ) @ B ) @ C )
      = ( hAPP_f966411375l_bool @ ( hAPP_f720086610l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Optio_042) ).

thf(4488,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f1033709212l_bool @ ( hAPP_f33142364l_bool @ ( hAPP_f510152537l_bool @ cOMBC_1518234801l_bool @ A ) @ B ) @ C )
      = ( hAPP_f966411375l_bool @ ( hAPP_f720086610l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).

thf(66,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_list_char_bool @ ( semila919158006r_bool @ A @ B ) @ C ) )
     => ( ~ ( hBOOL @ ( hAPP_list_char_bool @ A @ C ) )
       => ( hBOOL @ ( hAPP_list_char_bool @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_873_sup1E) ).

thf(1506,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_list_char_bool @ ( semila919158006r_bool @ A @ B ) @ C ) )
     => ( ~ ( hBOOL @ ( hAPP_list_char_bool @ A @ C ) )
       => ( hBOOL @ ( hAPP_list_char_bool @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(333,axiom,
    ! [A: $i,B: $i] : ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ A ) ) @ ( transi1395422419t_char @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_660_rtrancl_Ortrancl__refl) ).

thf(2579,plain,
    ! [A: $i,B: $i] : ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ A ) ) @ ( transi1395422419t_char @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(1183,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f678833350l_bool @ ( ord_le188521288l_bool @ ( hAPP_f2080627739l_bool @ ( hAPP_f350189921l_bool @ cOMBC_1535683812l_bool @ ( hAPP_f1094343359l_bool @ ( hAPP_f876671127l_bool @ cOMBB_1200577438t_char @ cOMBC_317789649l_bool ) @ ( hAPP_f1370205989l_bool @ ( hAPP_f1406462375l_bool @ cOMBB_109816436t_char @ ( hAPP_f919000597l_bool @ cOMBB_1153773871on_val @ member1542417277on_val ) ) @ produc823076510on_val ) ) ) @ A ) ) @ ( hAPP_f2080627739l_bool @ ( hAPP_f350189921l_bool @ cOMBC_1535683812l_bool @ ( hAPP_f1094343359l_bool @ ( hAPP_f876671127l_bool @ cOMBB_1200577438t_char @ cOMBC_317789649l_bool ) @ ( hAPP_f1370205989l_bool @ ( hAPP_f1406462375l_bool @ cOMBB_109816436t_char @ ( hAPP_f919000597l_bool @ cOMBB_1153773871on_val @ member1542417277on_val ) ) @ produc823076510on_val ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1134950784l_bool @ ( ord_le1744419030l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_814_pred__subset__eq2) ).

thf(5809,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( hAPP_f678833350l_bool @ ( ord_le188521288l_bool @ ( hAPP_f2080627739l_bool @ ( hAPP_f350189921l_bool @ cOMBC_1535683812l_bool @ ( hAPP_f1094343359l_bool @ ( hAPP_f876671127l_bool @ cOMBB_1200577438t_char @ cOMBC_317789649l_bool ) @ ( hAPP_f1370205989l_bool @ ( hAPP_f1406462375l_bool @ cOMBB_109816436t_char @ ( hAPP_f919000597l_bool @ cOMBB_1153773871on_val @ member1542417277on_val ) ) @ produc823076510on_val ) ) ) @ A ) ) @ ( hAPP_f2080627739l_bool @ ( hAPP_f350189921l_bool @ cOMBC_1535683812l_bool @ ( hAPP_f1094343359l_bool @ ( hAPP_f876671127l_bool @ cOMBB_1200577438t_char @ cOMBC_317789649l_bool ) @ ( hAPP_f1370205989l_bool @ ( hAPP_f1406462375l_bool @ cOMBB_109816436t_char @ ( hAPP_f919000597l_bool @ cOMBB_1153773871on_val @ member1542417277on_val ) ) @ produc823076510on_val ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f1134950784l_bool @ ( ord_le1744419030l_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1134950784l_bool @ ( ord_le1744419030l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f678833350l_bool @ ( ord_le188521288l_bool @ ( hAPP_f2080627739l_bool @ ( hAPP_f350189921l_bool @ cOMBC_1535683812l_bool @ ( hAPP_f1094343359l_bool @ ( hAPP_f876671127l_bool @ cOMBB_1200577438t_char @ cOMBC_317789649l_bool ) @ ( hAPP_f1370205989l_bool @ ( hAPP_f1406462375l_bool @ cOMBB_109816436t_char @ ( hAPP_f919000597l_bool @ cOMBB_1153773871on_val @ member1542417277on_val ) ) @ produc823076510on_val ) ) ) @ A ) ) @ ( hAPP_f2080627739l_bool @ ( hAPP_f350189921l_bool @ cOMBC_1535683812l_bool @ ( hAPP_f1094343359l_bool @ ( hAPP_f876671127l_bool @ cOMBB_1200577438t_char @ cOMBC_317789649l_bool ) @ ( hAPP_f1370205989l_bool @ ( hAPP_f1406462375l_bool @ cOMBB_109816436t_char @ ( hAPP_f919000597l_bool @ cOMBB_1153773871on_val @ member1542417277on_val ) ) @ produc823076510on_val ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).

thf(804,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_e1833980889l_bool @ ( hAPP_f989077673l_bool @ ( hAPP_f40682957l_bool @ cOMBC_562612496l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1175362209l_bool @ ( hAPP_e1705922617l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_0_062) ).

thf(4342,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_e1833980889l_bool @ ( hAPP_f989077673l_bool @ ( hAPP_f40682957l_bool @ cOMBC_562612496l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1175362209l_bool @ ( hAPP_e1705922617l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).

thf(459,axiom,
    ! [A: $i] :
      ( unit
     != ( addr @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_946_val_Osimps_I10_J) ).

thf(3071,plain,
    ! [A: $i] :
      ( unit
     != ( addr @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(544,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) )
      | ( hBOOL @ A )
      | ( hBOOL @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).

thf(3366,plain,
    ! [A: $i,B: $i] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) )
      | ( hBOOL @ A )
      | ( hBOOL @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(739,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ I ) @ J )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ K ) @ L ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( method1809630380t_char @ B @ K @ C @ D @ E @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ F ) @ G ) ) @ H ) )
       => ( ( ( size_size_list_val @ A )
            = ( size_s2113983095t_char @ F ) )
         => ( ( ( size_size_list_ty @ D )
              = ( size_s2113983095t_char @ F ) )
           => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ J ) ) @ C @ ( map_va1934808527t_char @ val_list_char @ A ) ) @ I ) @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ ( cons_list_char @ this @ F ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ ( cons_ty @ ( hAPP_list_char_ty @ class @ H ) @ D ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ ( cons_val @ ( addr @ J ) @ A ) ) @ G ) ) ) ) ) @ I ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1186_redp__redsp_ORedCall) ).

thf(4111,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ I ) @ J )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ K ) @ L ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( method1809630380t_char @ B @ K @ C @ D @ E @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ F ) @ G ) ) @ H ) )
       => ( ( ( size_size_list_val @ A )
            = ( size_s2113983095t_char @ F ) )
         => ( ( ( size_size_list_ty @ D )
              = ( size_s2113983095t_char @ F ) )
           => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ J ) ) @ C @ ( map_va1934808527t_char @ val_list_char @ A ) ) @ I ) @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ ( cons_list_char @ this @ F ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ ( cons_ty @ ( hAPP_list_char_ty @ class @ H ) @ D ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ ( cons_val @ ( addr @ J ) @ A ) ) @ G ) ) ) ) ) @ I ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).

thf(27,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ A ) @ B )
        = ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_Pair__eq) ).

thf(1358,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ A ) @ B )
          = ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ A ) @ B )
          = ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(258,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ A ) ) @ ( transi374442731on_val @ D ) ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ A ) ) @ ( transi374442731on_val @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_722_converse__rtrancl__into__rtrancl) ).

thf(2247,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ A ) ) @ ( transi374442731on_val @ D ) ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ A ) ) @ ( transi374442731on_val @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(1014,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
      ( ( ( size_s2113983095t_char @ J )
        = ( size_size_list_ty @ K ) )
     => ( ( ( size_size_list_val @ I )
          = ( size_size_list_ty @ K ) )
       => ( ( hBOOL @ ( distinct_list_char @ J ) )
         => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( map_up1085636310ar_val @ D @ J @ I ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
           => ( ( hBOOL @ ( final_list_char @ E ) )
             => ( ( A
                  = ( overri2012515291on_val @ G @ D @ ( set_list_char @ J ) ) )
               => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ J ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ K ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ I ) @ B ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ A ) ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1198_blocksRedsFinal) ).

thf(5147,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
      ( ( ( size_s2113983095t_char @ J )
        = ( size_size_list_ty @ K ) )
     => ( ( ( size_size_list_val @ I )
          = ( size_size_list_ty @ K ) )
       => ( ( hBOOL @ ( distinct_list_char @ J ) )
         => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( map_up1085636310ar_val @ D @ J @ I ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
           => ( ( hBOOL @ ( final_list_char @ E ) )
             => ( ( A
                  = ( overri2012515291on_val @ G @ D @ ( set_list_char @ J ) ) )
               => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ J ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ K ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ I ) @ B ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ A ) ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).

thf(1034,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hAPP_l207779698on_val @ A @ B )
        = C )
     => ( ( fun_up1149430426on_val @ A @ B @ C )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_fun__upd__idem) ).

thf(5208,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hAPP_l207779698on_val @ A @ B )
        = C )
     => ( ( fun_up1149430426on_val @ A @ B @ C )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).

thf(1212,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ I ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ I ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
       => ( ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ A ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ H ) @ D ) ) )
            = ( hAPP_val_option_val @ some_val @ B ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ F @ A @ C ) ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_998_BinOpRedsVal) ).

thf(5949,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ I ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ I ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
       => ( ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ A ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ H ) @ D ) ) )
            = ( hAPP_val_option_val @ some_val @ B ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ F @ A @ C ) ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1212]) ).

thf(559,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_f1534412387l_bool @ produc769963999l_bool @ A ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_417_splitI) ).

thf(3415,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_f1534412387l_bool @ produc769963999l_bool @ A ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(658,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_P449474095r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_475_mem__def) ).

thf(3829,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_P449474095r_bool @ B @ A ) ) )
      & ( ( hBOOL @ ( hAPP_P449474095r_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

thf(77,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] :
          ( ( is_bop @ D )
         => ( hBOOL @ ( hAPP_P738987199l_bool @ B @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ C ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ D ) @ E ) ) ) ) )
     => ( hBOOL @ ( hAPP_P738987199l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_prod__induct3) ).

thf(1536,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] :
          ( ( is_bop @ D )
         => ( hBOOL @ ( hAPP_P738987199l_bool @ B @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ C ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ D ) @ E ) ) ) ) )
     => ( hBOOL @ ( hAPP_P738987199l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(178,axiom,
    ! [A: $i] :
      ( ( hAPP_list_char_ty @ class @ A )
     != void ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1058_ty_Osimps_I9_J) ).

thf(1981,plain,
    ! [A: $i] :
      ( ( hAPP_list_char_ty @ class @ A )
     != void ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(825,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ B ) @ ( transi374442731on_val @ A ) ) )
       => ( ( transi374442731on_val @ B )
          = ( transi374442731on_val @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_679_rtrancl__subset) ).

thf(4436,plain,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ B ) @ ( transi374442731on_val @ A ) ) )
       => ( ( transi374442731on_val @ B )
          = ( transi374442731on_val @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).

thf(779,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( hAPP_n546249108on_val @ B @ C )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
     => ( hBOOL @ ( hext @ B @ ( fun_up2041264236on_val @ B @ C @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_564_hext__upd__obj) ).

thf(4246,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( hAPP_n546249108on_val @ B @ C )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
     => ( hBOOL @ ( hext @ B @ ( fun_up2041264236on_val @ B @ C @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).

thf(26,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ A ) @ B )
        = ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_Pair__inject) ).

thf(1353,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ A ) @ B )
        = ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(900,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_b406740087l_bool @ ( hAPP_f866074145l_bool @ ( hAPP_f877616419l_bool @ cOMBB_1458388806ol_bop @ A ) @ B ) @ C )
      = ( hAPP_f1646911885l_bool @ A @ ( hAPP_b1229254591al_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mt) ).

thf(4748,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_b406740087l_bool @ ( hAPP_f866074145l_bool @ ( hAPP_f877616419l_bool @ cOMBB_1458388806ol_bop @ A ) @ B ) @ C )
      = ( hAPP_f1646911885l_bool @ A @ ( hAPP_b1229254591al_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).

thf(1111,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P2053453961y_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P2053453961y_bool @ A @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_split__paired__All) ).

thf(5504,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P2053453961y_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P2053453961y_bool @ A @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P2053453961y_bool @ A @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P2053453961y_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).

thf(549,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ B )
        = ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_Pair__inject) ).

thf(3388,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ B )
        = ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(65,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ ( produc95371820r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P449474095r_bool @ A @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_493_curryE) ).

thf(1504,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ ( produc95371820r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P449474095r_bool @ A @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(768,axiom,
    ! [A: $i,B: $i] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ ( bool @ B ) ) ) )
      = none_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1064_binop_Osimps_I9_J) ).

thf(4202,plain,
    ! [A: $i,B: $i] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ ( bool @ B ) ) ) )
      = none_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).

thf(87,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_prod_Oexhaust) ).

thf(1585,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(1248,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( hBOOL @ ( hAPP_f1748390065l_bool @ ( hAPP_P1503283977l_bool @ member1580476948t_char @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f1748390065l_bool @ ( hAPP_P1503283977l_bool @ member1580476948t_char @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_pred__equals__eq2) ).

thf(6086,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f1748390065l_bool @ ( hAPP_P1503283977l_bool @ member1580476948t_char @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1748390065l_bool @ ( hAPP_P1503283977l_bool @ member1580476948t_char @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1748390065l_bool @ ( hAPP_P1503283977l_bool @ member1580476948t_char @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1748390065l_bool @ ( hAPP_P1503283977l_bool @ member1580476948t_char @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f1748390065l_bool @ ( hAPP_P1503283977l_bool @ member1580476948t_char @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1748390065l_bool @ ( hAPP_P1503283977l_bool @ member1580476948t_char @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1748390065l_bool @ ( hAPP_P1503283977l_bool @ member1580476948t_char @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1748390065l_bool @ ( hAPP_P1503283977l_bool @ member1580476948t_char @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248]) ).

thf(476,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_674_subsetD) ).

thf(3117,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(399,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D = C )
       => ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ C @ B ) @ D )
          = B ) )
      & ( ( D != C )
       => ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ C @ B ) @ D )
          = ( hAPP_P2094403585on_val @ A @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_fun__upd__def) ).

thf(2860,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D = C )
       => ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ C @ B ) @ D )
          = B ) )
      & ( ( D != C )
       => ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ C @ B ) @ D )
          = ( hAPP_P2094403585on_val @ A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(368,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( lAss_list_char @ D @ E ) @ F ) )
     => ~ ( ( F = void )
         => ! [G: $i] :
              ( ( ( hAPP_l512744617ion_ty @ C @ D )
                = ( hAPP_ty_option_ty @ some_ty @ G ) )
             => ! [H: $i] :
                  ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ E @ H ) )
                 => ~ ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ A ) @ H ) @ G ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_655_WTrt__elim__cases_I1_J) ).

thf(2722,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( lAss_list_char @ D @ E ) @ F ) )
     => ~ ( ( F = void )
         => ! [G: $i] :
              ( ( ( hAPP_l512744617ion_ty @ C @ D )
                = ( hAPP_ty_option_ty @ some_ty @ G ) )
             => ! [H: $i] :
                  ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ E @ H ) )
                 => ~ ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ A ) @ H ) @ G ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(29,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P1240100515r_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc) ).

thf(1372,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P1240100515r_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(928,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ E ) @ F )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
     => ( ( ( hAPP_P2094403585on_val @ H @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) )
          = ( hAPP_val_option_val @ some_val @ D ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) @ B @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) ) ) @ ( red @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_904_red__reds_ORedFAcc) ).

thf(4838,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ E ) @ F )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
     => ( ( ( hAPP_P2094403585on_val @ H @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) )
          = ( hAPP_val_option_val @ some_val @ D ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) @ B @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) ) ) @ ( red @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).

thf(998,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ ( throw_list_char @ C ) ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ C ) ) @ D ) ) ) @ ( red @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_971_red__reds_OBinOpThrow2) ).

thf(5083,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ ( throw_list_char @ C ) ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ C ) ) @ D ) ) ) @ ( red @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).

thf(151,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ ( produc156891095r_bool @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_362_curryI) ).

thf(1881,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ ( produc156891095r_bool @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(7,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1715346603l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__011) ).

thf(1272,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1715346603l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(488,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_668_equalityI) ).

thf(3156,plain,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(1004,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( while_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ A @ ( seq_list_char @ B @ ( while_list_char @ A @ B ) ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) ) @ C ) ) ) @ ( red @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1091_red__reds_ORedWhile) ).

thf(5100,plain,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( while_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ A @ ( seq_list_char @ B @ ( while_list_char @ A @ B ) ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) ) @ C ) ) ) @ ( red @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).

thf(439,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l2053770731r_bool @ ( hAPP_f732843907r_bool @ ( hAPP_f1563448447r_bool @ cOMBB_1490692730t_char @ A ) @ B ) @ C )
      = ( hAPP_f1419180947r_bool @ A @ ( hAPP_l1845912621l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__071) ).

thf(3007,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l2053770731r_bool @ ( hAPP_f732843907r_bool @ ( hAPP_f1563448447r_bool @ cOMBB_1490692730t_char @ A ) @ B ) @ C )
      = ( hAPP_f1419180947r_bool @ A @ ( hAPP_l1845912621l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(750,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_list_char_bool @ ( has_fi1183600461t_char @ D @ E @ F @ G ) @ H ) )
     => ( ( hBOOL @ ( conf_P373316194t_char @ D @ B @ C @ G ) )
       => ( ( hBOOL @ ( hAPP_P1235399154l_bool @ ( oconf_1869808039t_char @ D @ B ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ A ) ) )
         => ( hBOOL @ ( hAPP_P1235399154l_bool @ ( oconf_1869808039t_char @ D @ B ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ ( fun_up204312361on_val @ A @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ F ) @ H ) @ ( hAPP_val_option_val @ some_val @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_664_oconf__fupd) ).

thf(4150,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_list_char_bool @ ( has_fi1183600461t_char @ D @ E @ F @ G ) @ H ) )
     => ( ( hBOOL @ ( conf_P373316194t_char @ D @ B @ C @ G ) )
       => ( ( hBOOL @ ( hAPP_P1235399154l_bool @ ( oconf_1869808039t_char @ D @ B ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ A ) ) )
         => ( hBOOL @ ( hAPP_P1235399154l_bool @ ( oconf_1869808039t_char @ D @ B ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ ( fun_up204312361on_val @ A @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ F ) @ H ) @ ( hAPP_val_option_val @ some_val @ C ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).

thf(1196,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ ( fun_up1149430426on_val @ F @ G @ none_val ) ) ) @ H ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) )
     => ( ( ( hAPP_l207779698on_val @ J @ G )
          = ( hAPP_val_option_val @ some_val @ B ) )
       => ( ~ ( hBOOL @ ( assigned @ G @ D ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( block_list_char @ G @ A @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) @ ( block_list_char @ G @ A @ ( seq_list_char @ ( lAss_list_char @ G @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ H ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ ( fun_up1149430426on_val @ J @ G @ ( hAPP_l207779698on_val @ F @ G ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_648_redp__redsp_OBlockRedSome) ).

thf(5895,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ ( fun_up1149430426on_val @ F @ G @ none_val ) ) ) @ H ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) )
     => ( ( ( hAPP_l207779698on_val @ J @ G )
          = ( hAPP_val_option_val @ some_val @ B ) )
       => ( ~ ( hBOOL @ ( assigned @ G @ D ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( block_list_char @ G @ A @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) @ ( block_list_char @ G @ A @ ( seq_list_char @ ( lAss_list_char @ G @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ H ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ ( fun_up1149430426on_val @ J @ G @ ( hAPP_l207779698on_val @ F @ G ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).

thf(335,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ A ) @ B )
        = ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_Pair__eq) ).

thf(2584,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ A ) @ B )
          = ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ A ) @ B )
          = ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(783,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( seq_list_char @ B @ C ) @ D ) @ E ) @ F ) )
     => ( ! [G: $i,H: $i] :
            ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ H ) )
           => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ C @ H ) @ E ) @ F ) ) )
       => ~ ! [G: $i] :
              ( ( E
                = ( throw_list_char @ G ) )
             => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( throw_list_char @ G ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_945_eval__cases_I9_J) ).

thf(4257,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( seq_list_char @ B @ C ) @ D ) @ E ) @ F ) )
     => ( ! [G: $i,H: $i] :
            ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ H ) )
           => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ C @ H ) @ E ) @ F ) ) )
       => ~ ! [G: $i] :
              ( ( E
                = ( throw_list_char @ G ) )
             => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( throw_list_char @ G ) ) @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).

thf(878,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1335043179r_bool @ ( hAPP_f1032444159r_bool @ ( hAPP_f254182519r_bool @ cOMBB_1551681790t_char @ A ) @ B ) @ C )
      = ( hAPP_f1367982615r_bool @ A @ ( hAPP_l1425867561l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_I) ).

thf(4671,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1335043179r_bool @ ( hAPP_f1032444159r_bool @ ( hAPP_f254182519r_bool @ cOMBB_1551681790t_char @ A ) @ B ) @ C )
      = ( hAPP_f1367982615r_bool @ A @ ( hAPP_l1425867561l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).

thf(552,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).

thf(3398,plain,
    ! [A: $i,B: $i] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(817,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ A ) @ B )
        = ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Pair__inject) ).

thf(4392,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ A ) @ B )
        = ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).

thf(528,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( while_list_char @ B @ C ) @ D ) @ ( cond_list_char @ B @ ( seq_list_char @ C @ ( while_list_char @ B @ C ) ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1107_redp__redsp_ORedWhile) ).

thf(3288,plain,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( while_list_char @ B @ C ) @ D ) @ ( cond_list_char @ B @ ( seq_list_char @ C @ ( while_list_char @ B @ C ) ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(773,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B )
        = ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_Pair__eq) ).

thf(4217,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B )
          = ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B )
          = ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).

thf(95,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ ( produc95371820r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P449474095r_bool @ A @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_509_curryD) ).

thf(1617,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ ( produc95371820r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P449474095r_bool @ A @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(1173,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
    <=> ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_469_split__conv) ).

thf(5771,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) ) )
      & ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).

thf(567,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l214204733r_bool @ ( hAPP_f2091926485r_bool @ ( hAPP_f1820115955r_bool @ cOMBC_790582442r_bool @ A ) @ B ) @ C )
      = ( hAPP_f1466436665r_bool @ ( hAPP_l753659065r_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_) ).

thf(3433,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l214204733r_bool @ ( hAPP_f2091926485r_bool @ ( hAPP_f1820115955r_bool @ cOMBC_790582442r_bool @ A ) @ B ) @ C )
      = ( hAPP_f1466436665r_bool @ ( hAPP_l753659065r_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(605,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l2111308793l_bool @ ( hAPP_f1370205989l_bool @ ( hAPP_f1406462375l_bool @ cOMBB_109816436t_char @ A ) @ B ) @ C )
      = ( hAPP_f1099622285l_bool @ A @ ( hAPP_l1786340417on_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__057) ).

thf(3584,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l2111308793l_bool @ ( hAPP_f1370205989l_bool @ ( hAPP_f1406462375l_bool @ cOMBB_109816436t_char @ A ) @ B ) @ C )
      = ( hAPP_f1099622285l_bool @ A @ ( hAPP_l1786340417on_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(861,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C != D )
     => ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ D @ B ) @ C )
        = ( hAPP_n546249108on_val @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_fun__upd__other) ).

thf(4606,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C != D )
     => ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ D @ B ) @ C )
        = ( hAPP_n546249108on_val @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).

thf(391,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ B ) @ C ) @ D ) @ E ) )
     => ( ( hBOOL @ ( hext @ C @ A ) )
       => ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ B ) @ A ) @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_456_lconf__hext) ).

thf(2818,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ B ) @ C ) @ D ) @ E ) )
     => ( ( hBOOL @ ( hext @ C @ A ) )
       => ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ B ) @ A ) @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(81,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ A ) @ B )
        = ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_Pair__eq) ).

thf(1553,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ A ) @ B )
          = ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ A ) @ B )
          = ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(401,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f2041029616l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str) ).

thf(2870,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f2041029616l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(425,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ A ) @ B )
        = ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_Pair__inject) ).

thf(2960,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ A ) @ B )
        = ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(571,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( C = A )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_822_ord__le__eq__trans) ).

thf(3447,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( C = A )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(1124,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) @ ( red @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_457_red__reds_ORedSeq) ).

thf(5573,plain,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) @ ( red @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).

thf(341,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) ) @ ( transi1095029602t_char @ E ) ) )
     => ( ( ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B )
         != ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) )
       => ~ ! [F: $i,G: $i] :
              ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ F ) @ G ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) ) @ ( transi1095029602t_char @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_753_converse__rtranclE2) ).

thf(2611,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) ) @ ( transi1095029602t_char @ E ) ) )
     => ( ( ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B )
         != ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) )
       => ~ ! [F: $i,G: $i] :
              ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ F ) @ G ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) ) @ ( transi1095029602t_char @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(350,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_f1534412387l_bool @ produc769963999l_bool @ A ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_401_prod__caseI) ).

thf(2643,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_f1534412387l_bool @ produc769963999l_bool @ A ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(688,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f1175813647l_bool @ ( cOMBS_570216337l_bool @ A @ B ) @ C )
      = ( hAPP_f1074020887l_bool @ ( hAPP_f1492320500l_bool @ A @ C ) @ ( hAPP_f1175813647l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It) ).

thf(3929,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f1175813647l_bool @ ( cOMBS_570216337l_bool @ A @ B ) @ C )
      = ( hAPP_f1074020887l_bool @ ( hAPP_f1492320500l_bool @ A @ C ) @ ( hAPP_f1175813647l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).

thf(857,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_738_subsetI) ).

thf(4574,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).

thf(872,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f483496539l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod__012) ).

thf(4639,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f483496539l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).

thf(377,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ ( dom_list_char_val @ B ) ) )
    <=> ( ( hAPP_l207779698on_val @ B @ A )
       != none_val ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_629_domIff) ).

thf(2760,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ ( dom_list_char_val @ B ) ) )
       => ( ( hAPP_l207779698on_val @ B @ A )
         != none_val ) )
      & ( ( ( hAPP_l207779698on_val @ B @ A )
         != none_val )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ ( dom_list_char_val @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(553,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( binOp_list_char @ ( throw_list_char @ B ) @ C @ D ) @ E ) @ ( throw_list_char @ B ) ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_957_redp__redsp_OBinOpThrow1) ).

thf(3400,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( binOp_list_char @ ( throw_list_char @ B ) @ C @ D ) @ E ) @ ( throw_list_char @ B ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(578,axiom,
    ! [A: $i,B: $i] :
      ( ( ( hAPP_v834067052t_char @ val_list_char @ A )
        = ( hAPP_v834067052t_char @ val_list_char @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_572_exp_Osimps_I3_J) ).

thf(3478,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( hAPP_v834067052t_char @ val_list_char @ A )
          = ( hAPP_v834067052t_char @ val_list_char @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( hAPP_v834067052t_char @ val_list_char @ A )
          = ( hAPP_v834067052t_char @ val_list_char @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(345,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1571522437l_bool @ ( hAPP_f1136362289l_bool @ ( hAPP_f1736484361l_bool @ cOMBB_2042763133t_char @ A ) @ B ) @ C )
      = ( hAPP_f1233028029l_bool @ A @ ( hAPP_l1873467853t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc_) ).

thf(2626,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1571522437l_bool @ ( hAPP_f1136362289l_bool @ ( hAPP_f1736484361l_bool @ cOMBB_2042763133t_char @ A ) @ B ) @ C )
      = ( hAPP_f1233028029l_bool @ A @ ( hAPP_l1873467853t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(160,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P1240100515r_bool @ B @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ C ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1240100515r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_prod__induct3) ).

thf(1918,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P1240100515r_bool @ B @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ C ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1240100515r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(574,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( is_bop @ A )
        & ( is_bop @ C ) )
     => ( ( ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ A ) @ B )
          = ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) )
      <=> ( ( A = C )
          & ( B = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_Pair__eq) ).

thf(3457,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( is_bop @ A )
        & ( is_bop @ C ) )
     => ( ( ( ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ A ) @ B )
            = ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) )
         => ( ( A = C )
            & ( B = D ) ) )
        & ( ( ( A = C )
            & ( B = D ) )
         => ( ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ A ) @ B )
            = ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(887,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ E @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) )
     => ( ( ( hAPP_n546249108on_val @ H @ G )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) )
       => ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ A ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ D ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ ( cast_list_char @ A @ E ) @ F ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1002_CastFail) ).

thf(4698,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ E @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) )
     => ( ( ( hAPP_n546249108on_val @ H @ G )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) )
       => ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ A ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ D ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ ( cast_list_char @ A @ E ) @ F ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).

thf(599,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f479632753l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O_009) ).

thf(3565,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f479632753l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(211,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ A ) @ B )
        = ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_Pair__inject) ).

thf(2088,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ A ) @ B )
        = ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(607,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( hBOOL @ ( hAPP_f837795298l_bool @ ( hAPP_P483670507l_bool @ member1972431429on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f837795298l_bool @ ( hAPP_P483670507l_bool @ member1972431429on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_pred__equals__eq2) ).

thf(3589,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f837795298l_bool @ ( hAPP_P483670507l_bool @ member1972431429on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f837795298l_bool @ ( hAPP_P483670507l_bool @ member1972431429on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f837795298l_bool @ ( hAPP_P483670507l_bool @ member1972431429on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f837795298l_bool @ ( hAPP_P483670507l_bool @ member1972431429on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f837795298l_bool @ ( hAPP_P483670507l_bool @ member1972431429on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f837795298l_bool @ ( hAPP_P483670507l_bool @ member1972431429on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f837795298l_bool @ ( hAPP_P483670507l_bool @ member1972431429on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f837795298l_bool @ ( hAPP_P483670507l_bool @ member1972431429on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(200,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( while_list_char @ B @ C ) @ D ) @ E ) @ F ) )
    <=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( cond_list_char @ B @ ( seq_list_char @ C @ ( while_list_char @ B @ C ) ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ D ) @ E ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1106_unfold__while) ).

thf(2045,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( while_list_char @ B @ C ) @ D ) @ E ) @ F ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( cond_list_char @ B @ ( seq_list_char @ C @ ( while_list_char @ B @ C ) ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ D ) @ E ) @ F ) ) )
      & ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( cond_list_char @ B @ ( seq_list_char @ C @ ( while_list_char @ B @ C ) ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ D ) @ E ) @ F ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( while_list_char @ B @ C ) @ D ) @ E ) @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(208,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ A ) @ B )
        = ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_Pair__inject) ).

thf(2078,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ A ) @ B )
        = ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(159,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P801803911r_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P801803911r_bool @ A @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_split__paired__All) ).

thf(1913,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P801803911r_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P801803911r_bool @ A @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P801803911r_bool @ A @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P801803911r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(974,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ C ) ) ) @ ( red @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1031_red__reds_ORedFAccNull) ).

thf(4997,plain,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ C ) ) ) @ ( red @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).

thf(593,axiom,
    ! [A: $i,B: $i] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ ( bool @ A ) ) @ B ) ) )
      = none_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1073_binop_Osimps_I5_J) ).

thf(3548,plain,
    ! [A: $i,B: $i] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ ( bool @ A ) ) @ B ) ) )
      = none_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(875,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wTrt @ A @ B @ ( fun_up424764369ion_ty @ C @ D @ ( hAPP_ty_option_ty @ some_ty @ E ) ) @ F @ G ) )
     => ( ~ ( hBOOL @ ( assigned @ D @ F ) )
       => ( hBOOL @ ( wTrt @ A @ B @ C @ ( block_list_char @ D @ E @ F ) @ G ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1026_WTrt_H__WTrts_H_Ointros_I17_J) ).

thf(4646,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wTrt @ A @ B @ ( fun_up424764369ion_ty @ C @ D @ ( hAPP_ty_option_ty @ some_ty @ E ) ) @ F @ G ) )
     => ( ~ ( hBOOL @ ( assigned @ D @ F ) )
       => ( hBOOL @ ( wTrt @ A @ B @ C @ ( block_list_char @ D @ E @ F ) @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).

thf(637,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B ) ) @ ( transi935034983cl_val @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: $i] :
              ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ D ) ) @ ( transi935034983cl_val @ C ) ) )
             => ~ ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ B ) ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_837_rtranclE) ).

thf(3725,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B ) ) @ ( transi935034983cl_val @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: $i] :
              ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ D ) ) @ ( transi935034983cl_val @ C ) ) )
             => ~ ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ B ) ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(1055,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( red @ F ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ D ) ) @ E ) ) ) @ ( red @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_480_red__reds_OLAssRed) ).

thf(5308,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( red @ F ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ D ) ) @ E ) ) ) @ ( red @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).

thf(435,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ D ) @ ( throw_list_char @ E ) ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ B @ ( cons_exp_list_char @ C @ A ) @ D ) @ ( cons_exp_list_char @ ( throw_list_char @ E ) @ A ) ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1157_ConsThrow) ).

thf(2997,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ D ) @ ( throw_list_char @ E ) ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ B @ ( cons_exp_list_char @ C @ A ) @ D ) @ ( cons_exp_list_char @ ( throw_list_char @ E ) @ A ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(240,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ B ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_prod__cases3) ).

thf(2187,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ B ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(711,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1988620845r_bool @ ( hAPP_f1957374161r_bool @ ( hAPP_f304993943r_bool @ cOMBB_847828016t_char @ A ) @ B ) @ C )
      = ( hAPP_f1410576713r_bool @ A @ ( hAPP_l810309945l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List___080) ).

thf(4006,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1988620845r_bool @ ( hAPP_f1957374161r_bool @ ( hAPP_f304993943r_bool @ cOMBB_847828016t_char @ A ) @ B ) @ C )
      = ( hAPP_f1410576713r_bool @ A @ ( hAPP_l810309945l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).

thf(415,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P76086873l_bool @ ( hAPP_f1082373989l_bool @ ( hAPP_f869803751l_bool @ cOMBB_555068556on_val @ A ) @ B ) @ C )
      = ( hAPP_f1776493709l_bool @ A @ ( hAPP_P1526035745on_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__) ).

thf(2919,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P76086873l_bool @ ( hAPP_f1082373989l_bool @ ( hAPP_f869803751l_bool @ cOMBB_555068556on_val @ A ) @ B ) @ C )
      = ( hAPP_f1776493709l_bool @ A @ ( hAPP_P1526035745on_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(758,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P929938951l_bool @ A @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ ( produc886919678l_bool @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_366_curryI) ).

thf(4170,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P929938951l_bool @ A @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ ( produc886919678l_bool @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).

thf(994,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( fun_up204312361on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) )
        = ( fun_up204312361on_val @ D @ B @ ( hAPP_val_option_val @ some_val @ E ) ) )
     => ( C = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_map__upd__eqD1) ).

thf(5068,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( fun_up204312361on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) )
        = ( fun_up204312361on_val @ D @ B @ ( hAPP_val_option_val @ some_val @ E ) ) )
     => ( C = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).

thf(794,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) @ ( transi935034983cl_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ A ) ) @ ( transi935034983cl_val @ D ) ) )
       => ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ A ) ) @ ( transi935034983cl_val @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_733_rtrancl__trans) ).

thf(4310,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) @ ( transi935034983cl_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ A ) ) @ ( transi935034983cl_val @ D ) ) )
       => ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ A ) ) @ ( transi935034983cl_val @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).

thf(725,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( preallocated @ C ) )
     => ( ( ( hAPP_n546249108on_val @ C @ B )
          = none_P179726773on_val )
       => ( hBOOL @ ( preallocated @ ( fun_up2041264236on_val @ C @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_978_preallocated__new) ).

thf(4061,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( preallocated @ C ) )
     => ( ( ( hAPP_n546249108on_val @ C @ B )
          = none_P179726773on_val )
       => ( hBOOL @ ( preallocated @ ( fun_up2041264236on_val @ C @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).

thf(1025,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( red @ G ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1096_red__reds_OCondRed) ).

thf(5184,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( red @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).

thf(412,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P1221872711l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It) ).

thf(2907,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P1221872711l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(881,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_prod_Oexhaust) ).

thf(4678,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).

thf(622,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wTrt_1 @ C @ D @ E @ F @ G ) )
     => ( ( hBOOL @ ( wTrts_1 @ C @ D @ E @ A @ B ) )
       => ( hBOOL @ ( wTrts_1 @ C @ D @ E @ ( cons_exp_list_char @ F @ A ) @ ( cons_ty @ G @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1171_WTrtCons) ).

thf(3665,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wTrt_1 @ C @ D @ E @ F @ G ) )
     => ( ( hBOOL @ ( wTrts_1 @ C @ D @ E @ A @ B ) )
       => ( hBOOL @ ( wTrts_1 @ C @ D @ E @ ( cons_exp_list_char @ F @ A ) @ ( cons_ty @ G @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(894,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ A ) ) @ ( transi1395422419t_char @ D ) ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ A ) ) @ ( transi1395422419t_char @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_723_converse__rtrancl__into__rtrancl) ).

thf(4730,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ A ) ) @ ( transi1395422419t_char @ D ) ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ A ) ) @ ( transi1395422419t_char @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).

thf(990,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_PairE) ).

thf(5055,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).

thf(1058,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ E ) ) ) @ ( transi910771962on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ G ) @ H ) ) ) @ ( transi910771962on_val @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ G ) @ H ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_788_rtrancl__induct2) ).

thf(5315,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ E ) ) ) @ ( transi910771962on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ G ) @ H ) ) ) @ ( transi910771962on_val @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ G ) @ H ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).

thf(364,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) @ ( transi935034983cl_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_val_bool @ A @ C ) )
       => ( ! [E: $i,F: $i] :
              ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ E ) @ F ) ) @ D ) )
             => ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ F ) @ C ) ) @ ( transi935034983cl_val @ D ) ) )
               => ( ( hBOOL @ ( hAPP_val_bool @ A @ F ) )
                 => ( hBOOL @ ( hAPP_val_bool @ A @ E ) ) ) ) )
         => ( hBOOL @ ( hAPP_val_bool @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_845_converse__rtrancl__induct) ).

thf(2707,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) @ ( transi935034983cl_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_val_bool @ A @ C ) )
       => ( ! [E: $i,F: $i] :
              ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ E ) @ F ) ) @ D ) )
             => ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ F ) @ C ) ) @ ( transi935034983cl_val @ D ) ) )
               => ( ( hBOOL @ ( hAPP_val_bool @ A @ F ) )
                 => ( hBOOL @ ( hAPP_val_bool @ A @ E ) ) ) ) )
         => ( hBOOL @ ( hAPP_val_bool @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(265,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ A @ B @ C ) @ D ) @ E ) )
     => ( hBOOL @ ( finals_list_char @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1168_evals__final) ).

thf(2273,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ A @ B @ C ) @ D ) @ E ) )
     => ( hBOOL @ ( finals_list_char @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(916,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ G ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ G @ E @ F ) @ A ) @ B ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ G @ C @ D ) @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_851_extend__eval) ).

thf(4806,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ G ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ G @ E @ F ) @ A ) @ B ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ G @ C @ D ) @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).

thf(397,axiom,
    ! [A: $i,B: $i] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ c_Expr_Obop_OEq ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B ) ) )
      = ( hAPP_val_option_val @ some_val @ ( bool @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ fequal_val @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1077_binop_Osimps_I1_J) ).

thf(2853,plain,
    ! [A: $i,B: $i] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ c_Expr_Obop_OEq ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B ) ) )
      = ( hAPP_val_option_val @ some_val @ ( bool @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ fequal_val @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(877,axiom,
    ! [A: $i] :
      ( ? [B: $i] : ( hBOOL @ ( hAPP_P92196306r_bool @ A @ B ) )
    <=> ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P92196306r_bool @ A @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_split__paired__Ex) ).

thf(4666,plain,
    ! [A: $i] :
      ( ( ? [B: $i] : ( hBOOL @ ( hAPP_P92196306r_bool @ A @ B ) )
       => ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P92196306r_bool @ A @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) ) )
      & ( ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P92196306r_bool @ A @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) )
       => ? [B: $i] : ( hBOOL @ ( hAPP_P92196306r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).

thf(57,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( wTrt @ E @ F @ G @ H @ nt ) )
     => ( ( hBOOL @ ( wTrt @ E @ F @ G @ C @ D ) )
       => ( hBOOL @ ( wTrt @ E @ F @ G @ ( fAss_list_char @ H @ A @ B @ C ) @ void ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1118_WTrt_H__WTrts_H_Ointros_I11_J) ).

thf(1481,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( wTrt @ E @ F @ G @ H @ nt ) )
     => ( ( hBOOL @ ( wTrt @ E @ F @ G @ C @ D ) )
       => ( hBOOL @ ( wTrt @ E @ F @ G @ ( fAss_list_char @ H @ A @ B @ C ) @ void ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(780,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( finals_list_char @ C ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ A @ C @ B ) @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1169_eval__finalsId) ).

thf(4250,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( finals_list_char @ C ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ A @ C @ B ) @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).

thf(538,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ A ) @ B )
        = ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_Pair__eq) ).

thf(3336,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ A ) @ B )
          = ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ A ) @ B )
          = ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(393,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_pred__equals__eq2) ).

thf(2823,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(846,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ C ) @ ( throw_list_char @ D ) ) @ E ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( throw_list_char @ B ) @ C ) @ ( throw_list_char @ D ) ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_910_eval__evals_OThrowThrow) ).

thf(4527,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ C ) @ ( throw_list_char @ D ) ) @ E ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( throw_list_char @ B ) @ C ) @ ( throw_list_char @ D ) ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).

thf(107,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ E ) ) ) @ ( transi1095029602t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ B ) @ C ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ G ) @ H ) ) ) @ ( transi1095029602t_char @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ G ) @ H ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_785_rtrancl__induct2) ).

thf(1674,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ E ) ) ) @ ( transi1095029602t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ B ) @ C ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ G ) @ H ) ) ) @ ( transi1095029602t_char @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ G ) @ H ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(649,axiom,
    ! [A: $i] : ( is_bool @ ( preallocated @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Exceptions_Opreallocated) ).

thf(3789,plain,
    ! [A: $i] : ( is_bool @ ( preallocated @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(731,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ B @ C ) @ B )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_fun__upd__same) ).

thf(4089,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ B @ C ) @ B )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).

thf(1078,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( fun_up1149430426on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) )
        = ( fun_up1149430426on_val @ D @ B @ ( hAPP_val_option_val @ some_val @ E ) ) )
     => ( C = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_map__upd__eqD1) ).

thf(5382,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( fun_up1149430426on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) )
        = ( fun_up1149430426on_val @ D @ B @ ( hAPP_val_option_val @ some_val @ E ) ) )
     => ( C = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).

thf(67,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ A ) @ B ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) ) @ ( transi772168185t_char @ E ) ) )
     => ( ( ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ A ) @ B )
         != ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) )
       => ~ ! [F: $i,G: $i] :
              ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ A ) @ B ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ F ) @ G ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) ) @ ( transi772168185t_char @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_744_converse__rtranclE2) ).

thf(1508,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ A ) @ B ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) ) @ ( transi772168185t_char @ E ) ) )
     => ( ( ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ A ) @ B )
         != ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) )
       => ~ ! [F: $i,G: $i] :
              ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ A ) @ B ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ F ) @ G ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) ) @ ( transi772168185t_char @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(1009,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ D @ A ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_646_SeqReds) ).

thf(5132,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ D @ A ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).

thf(911,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P1609485901l_bool @ ( hAPP_f826324045l_bool @ ( hAPP_f1639555093l_bool @ cOMBB_985659173on_val @ A ) @ B ) @ C )
      = ( hAPP_P2015860941l_bool @ A @ ( hAPP_P604205461on_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O) ).

thf(4791,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P1609485901l_bool @ ( hAPP_f826324045l_bool @ ( hAPP_f1639555093l_bool @ cOMBB_985659173on_val @ A ) @ B ) @ C )
      = ( hAPP_P2015860941l_bool @ A @ ( hAPP_P604205461on_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).

thf(98,axiom,
    ! [A: $i] : ( is_bool @ ( is_refT @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Type_Ois__refT) ).

thf(1629,plain,
    ! [A: $i] : ( is_bool @ ( is_refT @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(191,axiom,
    ! [A: $i] :
      ( ( hBOOL @ ( preallocated @ A ) )
     => ( ( hAPP_val_option_ty @ ( typeof_h @ A ) @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) )
        = ( hAPP_ty_option_ty @ some_ty @ ( hAPP_list_char_ty @ class @ classCast ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1008_typeof__ClassCast) ).

thf(2026,plain,
    ! [A: $i] :
      ( ( hBOOL @ ( preallocated @ A ) )
     => ( ( hAPP_val_option_ty @ ( typeof_h @ A ) @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) )
        = ( hAPP_ty_option_ty @ some_ty @ ( hAPP_list_char_ty @ class @ classCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(615,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
    <=> ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
        & ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_827_order__eq__iff) ).

thf(3630,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
       => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(584,axiom,
    ! [A: $i] : ( is_bool @ ( distinct_list_char @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_List_Odistinct_000tc__List__Olist_Itc__String__Ochar_J) ).

thf(3501,plain,
    ! [A: $i] : ( is_bool @ ( distinct_list_char @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(1082,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( lex_pr731210613on_val @ E @ F ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1754555101l_bool @ ( hAPP_P1679186017l_bool @ member1337019328on_val @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ A ) @ C ) ) @ E ) )
        | ( ( A = C )
          & ( hBOOL @ ( hAPP_f1661305905l_bool @ ( hAPP_P1878549513l_bool @ member490182804on_val @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ B ) @ D ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_390_in__lex__prod) ).

thf(5394,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( lex_pr731210613on_val @ E @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f1754555101l_bool @ ( hAPP_P1679186017l_bool @ member1337019328on_val @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f1661305905l_bool @ ( hAPP_P1878549513l_bool @ member490182804on_val @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ B ) @ D ) ) @ F ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1754555101l_bool @ ( hAPP_P1679186017l_bool @ member1337019328on_val @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f1661305905l_bool @ ( hAPP_P1878549513l_bool @ member490182804on_val @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ B ) @ D ) ) @ F ) ) ) )
       => ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( lex_pr731210613on_val @ E @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).

thf(926,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ A @ B @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ C ) ) ) ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ C ) ) ) ) @ D ) ) ) @ ( red @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_942_red__reds_OBlockThrow) ).

thf(4834,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ A @ B @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ C ) ) ) ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ C ) ) ) ) @ D ) ) ) @ ( red @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).

thf(839,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ E ) @ F ) )
     => ( ( ( hAPP_n546249108on_val @ F @ B )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) )
       => ( ( hBOOL @ ( hAPP_P1235399154l_bool @ ( oconf_1869808039t_char @ E @ F ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ A ) ) )
         => ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ E ) @ ( fun_up2041264236on_val @ F @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_586_hconf__upd__obj) ).

thf(4495,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ E ) @ F ) )
     => ( ( ( hAPP_n546249108on_val @ F @ B )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) )
       => ( ( hBOOL @ ( hAPP_P1235399154l_bool @ ( oconf_1869808039t_char @ E @ F ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ A ) ) )
         => ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ E ) @ ( fun_up2041264236on_val @ F @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ A ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).

thf(72,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_PairE) ).

thf(1523,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(225,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_701_set__rev__mp) ).

thf(2130,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(937,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_405_prod__caseI) ).

thf(4881,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).

thf(545,axiom,
    ! [A: $i] :
      ( unit
     != ( bool @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1068_val_Osimps_I6_J) ).

thf(3368,plain,
    ! [A: $i] :
      ( unit
     != ( bool @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(944,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P476431815r_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P476431815r_bool @ A @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_split__paired__All) ).

thf(4900,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P476431815r_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P476431815r_bool @ A @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P476431815r_bool @ A @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P476431815r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).

thf(263,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( C = D )
       => ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ D @ B ) @ C )
          = B ) )
      & ( ( C != D )
       => ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ D @ B ) @ C )
          = ( hAPP_n546249108on_val @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_fun__upd__apply) ).

thf(2262,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( C = D )
       => ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ D @ B ) @ C )
          = B ) )
      & ( ( C != D )
       => ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ D @ B ) @ C )
          = ( hAPP_n546249108on_val @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(829,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f1033709212l_bool @ ( hAPP_f1074020887l_bool @ ( hAPP_f1863694447l_bool @ cOMBB_383678192on_val @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_f1033709212l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__List__O) ).

thf(4451,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_f1033709212l_bool @ ( hAPP_f1074020887l_bool @ ( hAPP_f1863694447l_bool @ cOMBB_383678192on_val @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_f1033709212l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).

thf(1203,axiom,
    ! [A: $i] : ( hBOOL @ ( hext @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_556_hext__refl) ).

thf(5922,plain,
    ! [A: $i] : ( hBOOL @ ( hext @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).

thf(464,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l465799708l_bool @ ( hAPP_f2080627739l_bool @ ( hAPP_f350189921l_bool @ cOMBC_1535683812l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1579743228l_bool @ ( hAPP_l1739862107l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_041) ).

thf(3085,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l465799708l_bool @ ( hAPP_f2080627739l_bool @ ( hAPP_f350189921l_bool @ cOMBC_1535683812l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1579743228l_bool @ ( hAPP_l1739862107l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(1217,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fTrue ) ) @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ C ) ) ) @ ( red @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1104_red__reds_ORedCondT) ).

thf(5963,plain,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fTrue ) ) @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ C ) ) ) @ ( red @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217]) ).

thf(198,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ E ) @ F ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( binOp_list_char @ D @ A @ B ) @ E ) @ ( binOp_list_char @ F @ A @ B ) ) @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_953_redp__redsp_OBinOpRed1) ).

thf(2041,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ E ) @ F ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( binOp_list_char @ D @ A @ B ) @ E ) @ ( binOp_list_char @ F @ A @ B ) ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(760,axiom,
    ! [A: $i] :
      ( none_ty
     != ( hAPP_ty_option_ty @ some_ty @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_605_option_Osimps_I2_J) ).

thf(4175,plain,
    ! [A: $i] :
      ( none_ty
     != ( hAPP_ty_option_ty @ some_ty @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).

thf(904,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_f1634841927l_bool @ produc1491230096l_bool @ A ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_447_splitD) ).

thf(4774,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_f1634841927l_bool @ produc1491230096l_bool @ A ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).

thf(44,axiom,
    ! [A: $i] :
      ( ( map_ad325961431ar_val @ ( hAPP_o538043682on_val @ cOMBK_1097134891t_char @ none_val ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_637_empty__map__add) ).

thf(1440,plain,
    ! [A: $i] :
      ( ( map_ad325961431ar_val @ ( hAPP_o538043682on_val @ cOMBK_1097134891t_char @ none_val ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(243,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_817_xt1_I6_J) ).

thf(2198,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(68,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P1907982426r_bool @ ( hAPP_f1874697593r_bool @ ( hAPP_f1707979241r_bool @ cOMBC_407285762l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1780084320l_bool @ ( hAPP_P1562529797l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc) ).

thf(1513,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P1907982426r_bool @ ( hAPP_f1874697593r_bool @ ( hAPP_f1707979241r_bool @ cOMBC_407285762l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1780084320l_bool @ ( hAPP_P1562529797l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(155,axiom,
    ! [A: $i] :
      ( ! [B: $i] :
          ( A
         != ( hAPP_P1510515380on_val @ some_P948696889on_val @ B ) )
    <=> ( A = none_P179726773on_val ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_616_not__Some__eq) ).

thf(1893,plain,
    ! [A: $i] :
      ( ( ! [B: $i] :
            ( A
           != ( hAPP_P1510515380on_val @ some_P948696889on_val @ B ) )
       => ( A = none_P179726773on_val ) )
      & ( ( A = none_P179726773on_val )
       => ! [B: $i] :
            ( A
           != ( hAPP_P1510515380on_val @ some_P948696889on_val @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(644,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ A ) @ B ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) ) @ ( lex_pr1787105337t_char @ E @ F ) ) )
    <=> ( ( hBOOL @ ( hAPP_f479632753l_bool @ ( hAPP_P153687689l_bool @ member817832404t_char @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ A ) @ C ) ) @ E ) )
        | ( ( A = C )
          & ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ B ) @ D ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_378_in__lex__prod) ).

thf(3761,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ A ) @ B ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) ) @ ( lex_pr1787105337t_char @ E @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f479632753l_bool @ ( hAPP_P153687689l_bool @ member817832404t_char @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ B ) @ D ) ) @ F ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f479632753l_bool @ ( hAPP_P153687689l_bool @ member817832404t_char @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ B ) @ D ) ) @ F ) ) ) )
       => ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ A ) @ B ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) ) @ ( lex_pr1787105337t_char @ E @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

thf(953,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( red @ F ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ D @ A ) ) @ E ) ) ) @ ( red @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_481_red__reds_OSeqRed) ).

thf(4927,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( red @ F ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ D @ A ) ) @ E ) ) ) @ ( red @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).

thf(1063,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_714_set__mp) ).

thf(5336,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).

thf(1053,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( hBOOL @ ( hAPP_f433445541l_bool @ ( hAPP_P1019319281l_bool @ member104734088ist_ty @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f433445541l_bool @ ( hAPP_P1019319281l_bool @ member104734088ist_ty @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_pred__equals__eq2) ).

thf(5287,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f433445541l_bool @ ( hAPP_P1019319281l_bool @ member104734088ist_ty @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f433445541l_bool @ ( hAPP_P1019319281l_bool @ member104734088ist_ty @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f433445541l_bool @ ( hAPP_P1019319281l_bool @ member104734088ist_ty @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f433445541l_bool @ ( hAPP_P1019319281l_bool @ member104734088ist_ty @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f433445541l_bool @ ( hAPP_P1019319281l_bool @ member104734088ist_ty @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f433445541l_bool @ ( hAPP_P1019319281l_bool @ member104734088ist_ty @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f433445541l_bool @ ( hAPP_P1019319281l_bool @ member104734088ist_ty @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f433445541l_bool @ ( hAPP_P1019319281l_bool @ member104734088ist_ty @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).

thf(109,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_list_char_bool @ B @ C ) )
       => ( hBOOL @ ( hAPP_list_char_bool @ A @ C ) ) )
     => ( hBOOL @ ( hAPP_list_char_bool @ ( semila919158006r_bool @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_874_sup1CI) ).

thf(1689,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_list_char_bool @ B @ C ) )
       => ( hBOOL @ ( hAPP_list_char_bool @ A @ C ) ) )
     => ( hBOOL @ ( hAPP_list_char_bool @ ( semila919158006r_bool @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(703,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_val_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Value__Oval_000tc__HOL__Obool) ).

thf(3978,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_val_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).

thf(495,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P1384137393r_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List_025) ).

thf(3181,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P1384137393r_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(305,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( preallocated @ E ) )
     => ( ( ( hAPP_n546249108on_val @ E @ B )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) )
       => ( hBOOL @ ( preallocated @ ( fun_up2041264236on_val @ E @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_980_preallocated__upd__obj) ).

thf(2475,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( preallocated @ E ) )
     => ( ( ( hAPP_n546249108on_val @ E @ B )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) )
       => ( hBOOL @ ( preallocated @ ( fun_up2041264236on_val @ E @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(627,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_prod_Oexhaust) ).

thf(3694,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(384,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ ( dom_list_char_val @ C ) ) )
     => ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ A @ C ) @ B )
        = ( hAPP_l207779698on_val @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_425_map__add__dom__app__simps_I1_J) ).

thf(2796,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ ( dom_list_char_val @ C ) ) )
     => ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ A @ C ) @ B )
        = ( hAPP_l207779698on_val @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(1019,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( E
        = ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ F ) @ ( cons_exp_list_char @ ( throw_list_char @ G ) @ H ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ E ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ G ) ) @ C ) ) ) @ ( red @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1164_red__reds_OCallThrowParams) ).

thf(5162,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( E
        = ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ F ) @ ( cons_exp_list_char @ ( throw_list_char @ G ) @ H ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ E ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ G ) ) @ C ) ) ) @ ( red @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).

thf(352,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( hBOOL @ ( hAPP_f1134950784l_bool @ ( hAPP_P1217996045l_bool @ member1542417277on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f1134950784l_bool @ ( hAPP_P1217996045l_bool @ member1542417277on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_pred__equals__eq2) ).

thf(2648,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f1134950784l_bool @ ( hAPP_P1217996045l_bool @ member1542417277on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1134950784l_bool @ ( hAPP_P1217996045l_bool @ member1542417277on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1134950784l_bool @ ( hAPP_P1217996045l_bool @ member1542417277on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1134950784l_bool @ ( hAPP_P1217996045l_bool @ member1542417277on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f1134950784l_bool @ ( hAPP_P1217996045l_bool @ member1542417277on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1134950784l_bool @ ( hAPP_P1217996045l_bool @ member1542417277on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1134950784l_bool @ ( hAPP_P1217996045l_bool @ member1542417277on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1134950784l_bool @ ( hAPP_P1217996045l_bool @ member1542417277on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(1154,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( size_s2113983095t_char @ F )
        = ( size_size_list_ty @ G ) )
     => ( ( ( size_size_list_val @ E )
          = ( size_size_list_ty @ G ) )
       => ( ( hBOOL @ ( final_list_char @ D ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ F ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ G ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ E ) @ D ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B ) ) ) ) @ ( transi2024712006on_val @ ( red @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1188_blocksFinal) ).

thf(5692,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( size_s2113983095t_char @ F )
        = ( size_size_list_ty @ G ) )
     => ( ( ( size_size_list_val @ E )
          = ( size_size_list_ty @ G ) )
       => ( ( hBOOL @ ( final_list_char @ D ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ F ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ G ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ E ) @ D ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B ) ) ) ) @ ( transi2024712006on_val @ ( red @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).

thf(332,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1739862107l_bool @ ( hAPP_f1094343359l_bool @ ( hAPP_f876671127l_bool @ cOMBB_1200577438t_char @ A ) @ B ) @ C )
      = ( hAPP_f1166017719l_bool @ A @ ( hAPP_l2111308793l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__061) ).

thf(2576,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1739862107l_bool @ ( hAPP_f1094343359l_bool @ ( hAPP_f876671127l_bool @ cOMBB_1200577438t_char @ A ) @ B ) @ C )
      = ( hAPP_f1166017719l_bool @ A @ ( hAPP_l2111308793l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(205,axiom,
    ! [A: $i,B: $i] :
      ( ( fv @ ( while_list_char @ A @ B ) )
      = ( semila919158006r_bool @ ( fv @ A ) @ ( fv @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1083_fv__fvs_Osimps_I13_J) ).

thf(2066,plain,
    ! [A: $i,B: $i] :
      ( ( fv @ ( while_list_char @ A @ B ) )
      = ( semila919158006r_bool @ ( fv @ A ) @ ( fv @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(280,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) @ ( transi374442731on_val @ ( reds @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B ) ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ D ) ) @ E ) ) ) @ ( transi374442731on_val @ ( reds @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1161_ListReds2) ).

thf(2362,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) @ ( transi374442731on_val @ ( reds @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B ) ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ D ) ) @ E ) ) ) @ ( transi374442731on_val @ ( reds @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(1121,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1700205512_sconf @ p @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( hAPP_val_option_val @ some_val @ v ) ) ) ) )
     => ( ( hBOOL @ ( wTrt_1 @ p @ ha @ B @ ea @ A ) )
       => ? [C: $i] :
            ( ( hBOOL @ ( wTrt_1 @ p @ h_a @ B @ e_a @ C ) )
            & ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ p ) @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_InitBlockRed_I2_J) ).

thf(5549,plain,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1700205512_sconf @ p @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( hAPP_val_option_val @ some_val @ v ) ) ) ) )
     => ( ( hBOOL @ ( wTrt_1 @ p @ ha @ B @ ea @ A ) )
       => ? [C: $i] :
            ( ( hBOOL @ ( wTrt_1 @ p @ h_a @ B @ e_a @ C ) )
            & ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ p ) @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).

thf(1241,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P282169671l_bool @ ( hAPP_f2036784149l_bool @ ( hAPP_f1720452391l_bool @ cOMBC_1021753250l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_) ).

thf(6062,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P282169671l_bool @ ( hAPP_f2036784149l_bool @ ( hAPP_f1720452391l_bool @ cOMBC_1021753250l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241]) ).

thf(1130,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( fun_up1149430426on_val @ D @ A @ ( hAPP_val_option_val @ some_val @ B ) ) ) ) ) ) @ ( red @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_555_red__reds_ORedLAss) ).

thf(5590,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( fun_up1149430426on_val @ D @ A @ ( hAPP_val_option_val @ some_val @ B ) ) ) ) ) ) @ ( red @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).

thf(827,axiom,
    ! [A: $i] :
      ( ( produc2062775566l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_436_curry__split) ).

thf(4446,plain,
    ! [A: $i] :
      ( ( produc2062775566l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).

thf(720,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P1632759357r_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_M) ).

thf(4039,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P1632759357r_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).

thf(1070,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ I ) @ J ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ K ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ L ) @ M ) ) ) ) @ ( transi2024712006on_val @ ( red @ N ) ) ) )
     => ( ( ( hAPP_n546249108on_val @ L @ K )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
       => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ G ) @ F ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ N ) ) ) )
         => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ L ) @ ( fun_up1149430426on_val @ M @ B @ ( hAPP_val_option_val @ some_val @ ( addr @ K ) ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) ) @ ( transi2024712006on_val @ ( red @ N ) ) ) )
           => ( ( hBOOL @ ( final_list_char @ C ) )
             => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ I @ F @ B @ A ) ) @ J ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ B @ ( hAPP_l207779698on_val @ M @ B ) ) ) ) ) ) @ ( transi2024712006on_val @ ( red @ N ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_949_TryCatchRedsFinal) ).

thf(5357,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ I ) @ J ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ K ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ L ) @ M ) ) ) ) @ ( transi2024712006on_val @ ( red @ N ) ) ) )
     => ( ( ( hAPP_n546249108on_val @ L @ K )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
       => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ G ) @ F ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ N ) ) ) )
         => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ L ) @ ( fun_up1149430426on_val @ M @ B @ ( hAPP_val_option_val @ some_val @ ( addr @ K ) ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) ) @ ( transi2024712006on_val @ ( red @ N ) ) ) )
           => ( ( hBOOL @ ( final_list_char @ C ) )
             => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ I @ F @ B @ A ) ) @ J ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ B @ ( hAPP_l207779698on_val @ M @ B ) ) ) ) ) ) @ ( transi2024712006on_val @ ( red @ N ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).

thf(104,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( fAss_list_char @ D @ E @ F @ G ) @ H ) )
     => ( ( ( H = void )
         => ! [I: $i] :
              ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ ( hAPP_list_char_ty @ class @ I ) ) )
             => ! [J: $i] :
                  ( ( hBOOL @ ( hAPP_list_char_bool @ ( has_fi1183600461t_char @ A @ I @ E @ J ) @ F ) )
                 => ! [K: $i] :
                      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ G @ K ) )
                     => ~ ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ A ) @ K ) @ J ) ) ) ) ) )
       => ~ ( ( H = void )
           => ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ nt ) )
             => ! [I: $i] :
                  ~ ( hBOOL @ ( wTrt_1 @ A @ B @ C @ G @ I ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1121_WTrt__elim__cases_I8_J) ).

thf(1642,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( fAss_list_char @ D @ E @ F @ G ) @ H ) )
     => ( ( ( H = void )
         => ! [I: $i] :
              ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ ( hAPP_list_char_ty @ class @ I ) ) )
             => ! [J: $i] :
                  ( ( hBOOL @ ( hAPP_list_char_bool @ ( has_fi1183600461t_char @ A @ I @ E @ J ) @ F ) )
                 => ! [K: $i] :
                      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ G @ K ) )
                     => ~ ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ A ) @ K ) @ J ) ) ) ) ) )
       => ~ ( ( H = void )
           => ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ nt ) )
             => ! [I: $i] :
                  ~ ( hBOOL @ ( wTrt_1 @ A @ B @ C @ G @ I ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(681,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1261741735l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__O) ).

thf(3907,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1261741735l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).

thf(976,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( wTrts_1 @ A @ B @ C @ D @ E ) )
     => ( ( size_s1143674878t_char @ D )
        = ( size_size_list_ty @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1187_WTrts__same__length) ).

thf(5004,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( wTrts_1 @ A @ B @ C @ D @ E ) )
     => ( ( size_s1143674878t_char @ D )
        = ( size_size_list_ty @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).

thf(255,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( cond_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fTrue ) ) @ B @ C ) @ D ) @ B ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1100_redp__redsp_ORedCondT) ).

thf(2233,plain,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( cond_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fTrue ) ) @ B @ C ) @ D ) @ B ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(678,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hext @ A @ B ) )
    <=> ! [C: $i,D: $i,E: $i] :
          ( ( ( hAPP_n546249108on_val @ A @ C )
            = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
         => ? [F: $i] :
              ( ( hAPP_n546249108on_val @ B @ C )
              = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_567_hext__def) ).

thf(3892,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( hext @ A @ B ) )
       => ! [C: $i,D: $i,E: $i] :
            ( ( ( hAPP_n546249108on_val @ A @ C )
              = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
           => ? [F: $i] :
                ( ( hAPP_n546249108on_val @ B @ C )
                = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ F ) ) ) ) )
      & ( ! [C: $i,D: $i,E: $i] :
            ( ( ( hAPP_n546249108on_val @ A @ C )
              = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
           => ? [F: $i] :
                ( ( hAPP_n546249108on_val @ B @ C )
                = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ F ) ) ) )
       => ( hBOOL @ ( hext @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).

thf(520,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ E @ F ) @ ( throw_list_char @ G ) ) @ H ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ ( fAss_list_char @ E @ A @ B @ C ) @ F ) @ ( throw_list_char @ G ) ) @ H ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_920_eval__evals_OFAssThrow1) ).

thf(3264,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ E @ F ) @ ( throw_list_char @ G ) ) @ H ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ ( fAss_list_char @ E @ A @ B @ C ) @ F ) @ ( throw_list_char @ G ) ) @ H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(89,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P943837928l_bool @ A @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_b97269396l_bool @ ( produc1555310053l_bool @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_367_curryI) ).

thf(1593,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P943837928l_bool @ A @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_b97269396l_bool @ ( produc1555310053l_bool @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(73,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_e544220455r_bool @ ( hAPP_f1724656343r_bool @ ( hAPP_f388097003r_bool @ cOMBC_818212448l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1314764175l_bool @ ( hAPP_e53687815l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_0) ).

thf(1527,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_e544220455r_bool @ ( hAPP_f1724656343r_bool @ ( hAPP_f388097003r_bool @ cOMBC_818212448l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1314764175l_bool @ ( hAPP_e53687815l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(860,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ A ) @ B )
        = ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_Pair__eq) ).

thf(4597,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ A ) @ B )
          = ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ A ) @ B )
          = ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).

thf(1205,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) ) @ ( red @ H ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ D @ A @ B @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ F @ A @ B @ C ) ) @ G ) ) ) @ ( red @ H ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_896_red__reds_OFAssRed1) ).

thf(5926,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) ) @ ( red @ H ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ D @ A @ B @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ F @ A @ B @ C ) ) @ G ) ) ) @ ( red @ H ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205]) ).

thf(222,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ E ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ ( cast_list_char @ A @ C ) @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1036_CastNull) ).

thf(2123,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ E ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ ( cast_list_char @ A @ C ) @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(248,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_696_in__mono) ).

thf(2218,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(989,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ B ) )
     => ~ ! [C: $i,D: $i] :
            ( ( B
              = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) )
           => ~ ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_534_splitE) ).

thf(5051,plain,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ B ) )
     => ~ ! [C: $i,D: $i] :
            ( ( B
              = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) )
           => ~ ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).

thf(978,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ C ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ C ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_931_ThrowRedsThrow) ).

thf(5009,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ C ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ C ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).

thf(912,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P1574824955y_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1574824955y_bool @ A @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_split__paired__All) ).

thf(4794,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P1574824955y_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1574824955y_bool @ A @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1574824955y_bool @ A @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P1574824955y_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).

thf(631,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1746574980l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc_) ).

thf(3705,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1746574980l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ? [B: $i] : ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ B ) )
    <=> ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_split__paired__Ex) ).

thf(1280,plain,
    ! [A: $i] :
      ( ( ? [B: $i] : ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ B ) )
       => ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ C ) ) ) )
      & ( ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ C ) ) )
       => ? [B: $i] : ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(85,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P1183499705r_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1183499705r_bool @ A @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_split__paired__All) ).

thf(1578,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P1183499705r_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1183499705r_bool @ A @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1183499705r_bool @ A @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P1183499705r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(832,axiom,
    ! [A: $i,B: $i] :
      ( ( bool @ A )
     != ( addr @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1066_val_Osimps_I20_J) ).

thf(4472,plain,
    ! [A: $i,B: $i] :
      ( ( bool @ A )
     != ( addr @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).

thf(819,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i,E: $i] :
          ( A
         != ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_prod__cases4) ).

thf(4399,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i,E: $i] :
          ( A
         != ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).

thf(587,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D = C )
       => ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ C @ B ) @ D )
          = B ) )
      & ( ( D != C )
       => ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ C @ B ) @ D )
          = ( hAPP_l512744617ion_ty @ A @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_fun__upd__def) ).

thf(3511,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D = C )
       => ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ C @ B ) @ D )
          = B ) )
      & ( ( D != C )
       => ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ C @ B ) @ D )
          = ( hAPP_l512744617ion_ty @ A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(1134,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ G ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( red @ G ) ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ G @ E @ F ) @ A ) @ B ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ G @ C @ D ) @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_849_extend__1__eval) ).

thf(5606,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ G ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( red @ G ) ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ G @ E @ F ) @ A ) @ B ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ G @ C @ D ) @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).

thf(813,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_713_set__mp) ).

thf(4378,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).

thf(321,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_703_set__rev__mp) ).

thf(2534,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(509,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f588675559l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc) ).

thf(3232,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f588675559l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(430,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( cond_list_char @ ( throw_list_char @ B ) @ C @ D ) @ E ) @ ( throw_list_char @ B ) ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1094_redp__redsp_OCondThrow) ).

thf(2983,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( cond_list_char @ ( throw_list_char @ B ) @ C @ D ) @ E ) @ ( throw_list_char @ B ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(669,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P2010574925r_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List_031) ).

thf(3865,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P2010574925r_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).

thf(674,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P2115985549l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__List__Olist_Itc_) ).

thf(3882,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P2115985549l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).

thf(1214,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f434955681l_bool @ ( ord_le1050317687l_bool @ ( hAPP_f1200025813l_bool @ ( hAPP_f1089788553l_bool @ cOMBC_967917532l_bool @ ( hAPP_f2095325577l_bool @ ( hAPP_f1135930489l_bool @ cOMBB_1223415373on_val @ cOMBC_1608987946l_bool ) @ ( hAPP_f1204100177l_bool @ ( hAPP_f2026692601l_bool @ cOMBB_1977588741on_val @ ( hAPP_f1510763001l_bool @ cOMBB_565412073on_val @ member773094996on_val ) ) @ produc1441475159on_val ) ) ) @ A ) ) @ ( hAPP_f1200025813l_bool @ ( hAPP_f1089788553l_bool @ cOMBC_967917532l_bool @ ( hAPP_f2095325577l_bool @ ( hAPP_f1135930489l_bool @ cOMBB_1223415373on_val @ cOMBC_1608987946l_bool ) @ ( hAPP_f1204100177l_bool @ ( hAPP_f2026692601l_bool @ cOMBB_1977588741on_val @ ( hAPP_f1510763001l_bool @ cOMBB_565412073on_val @ member773094996on_val ) ) @ produc1441475159on_val ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_804_pred__subset__eq2) ).

thf(5954,plain,
    ! [A: $i,B: $i] :
      ( ( ( hBOOL @ ( hAPP_f434955681l_bool @ ( ord_le1050317687l_bool @ ( hAPP_f1200025813l_bool @ ( hAPP_f1089788553l_bool @ cOMBC_967917532l_bool @ ( hAPP_f2095325577l_bool @ ( hAPP_f1135930489l_bool @ cOMBB_1223415373on_val @ cOMBC_1608987946l_bool ) @ ( hAPP_f1204100177l_bool @ ( hAPP_f2026692601l_bool @ cOMBB_1977588741on_val @ ( hAPP_f1510763001l_bool @ cOMBB_565412073on_val @ member773094996on_val ) ) @ produc1441475159on_val ) ) ) @ A ) ) @ ( hAPP_f1200025813l_bool @ ( hAPP_f1089788553l_bool @ cOMBC_967917532l_bool @ ( hAPP_f2095325577l_bool @ ( hAPP_f1135930489l_bool @ cOMBB_1223415373on_val @ cOMBC_1608987946l_bool ) @ ( hAPP_f1204100177l_bool @ ( hAPP_f2026692601l_bool @ cOMBB_1977588741on_val @ ( hAPP_f1510763001l_bool @ cOMBB_565412073on_val @ member773094996on_val ) ) @ produc1441475159on_val ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f434955681l_bool @ ( ord_le1050317687l_bool @ ( hAPP_f1200025813l_bool @ ( hAPP_f1089788553l_bool @ cOMBC_967917532l_bool @ ( hAPP_f2095325577l_bool @ ( hAPP_f1135930489l_bool @ cOMBB_1223415373on_val @ cOMBC_1608987946l_bool ) @ ( hAPP_f1204100177l_bool @ ( hAPP_f2026692601l_bool @ cOMBB_1977588741on_val @ ( hAPP_f1510763001l_bool @ cOMBB_565412073on_val @ member773094996on_val ) ) @ produc1441475159on_val ) ) ) @ A ) ) @ ( hAPP_f1200025813l_bool @ ( hAPP_f1089788553l_bool @ cOMBC_967917532l_bool @ ( hAPP_f2095325577l_bool @ ( hAPP_f1135930489l_bool @ cOMBB_1223415373on_val @ cOMBC_1608987946l_bool ) @ ( hAPP_f1204100177l_bool @ ( hAPP_f2026692601l_bool @ cOMBB_1977588741on_val @ ( hAPP_f1510763001l_bool @ cOMBB_565412073on_val @ member773094996on_val ) ) @ produc1441475159on_val ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).

thf(35,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ B ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_prod__cases3) ).

thf(1395,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ B ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(1040,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_675_subsetD) ).

thf(5232,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).

thf(930,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( hBOOL @ ( hAPP_f348753975l_bool @ ( hAPP_P1033205013l_bool @ member273646106st_val @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f348753975l_bool @ ( hAPP_P1033205013l_bool @ member273646106st_val @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_pred__equals__eq2) ).

thf(4843,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f348753975l_bool @ ( hAPP_P1033205013l_bool @ member273646106st_val @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f348753975l_bool @ ( hAPP_P1033205013l_bool @ member273646106st_val @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f348753975l_bool @ ( hAPP_P1033205013l_bool @ member273646106st_val @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f348753975l_bool @ ( hAPP_P1033205013l_bool @ member273646106st_val @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f348753975l_bool @ ( hAPP_P1033205013l_bool @ member273646106st_val @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f348753975l_bool @ ( hAPP_P1033205013l_bool @ member273646106st_val @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f348753975l_bool @ ( hAPP_P1033205013l_bool @ member273646106st_val @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f348753975l_bool @ ( hAPP_P1033205013l_bool @ member273646106st_val @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).

thf(150,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P738987199l_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P738987199l_bool @ A @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_split__paired__All) ).

thf(1876,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P738987199l_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P738987199l_bool @ A @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P738987199l_bool @ A @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P738987199l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(390,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l551544901l_bool @ ( hAPP_f165071409l_bool @ ( hAPP_f1174637065l_bool @ cOMBB_33167485t_char @ A ) @ B ) @ C )
      = ( hAPP_f901718717l_bool @ A @ ( hAPP_l796364813t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_046) ).

thf(2815,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l551544901l_bool @ ( hAPP_f165071409l_bool @ ( hAPP_f1174637065l_bool @ cOMBB_33167485t_char @ A ) @ B ) @ C )
      = ( hAPP_f901718717l_bool @ A @ ( hAPP_l796364813t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(372,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ A ) @ B )
        = ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_Pair__eq) ).

thf(2736,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ A ) @ B )
          = ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ A ) @ B )
          = ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(909,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ ( throw_list_char @ B ) ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ B ) ) @ C ) ) ) @ ( red @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_932_red__reds_OLAssThrow) ).

thf(4787,plain,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ ( throw_list_char @ B ) ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ B ) ) @ C ) ) ) @ ( red @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).

thf(929,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P1384137393r_bool @ ( hAPP_l2054741776r_bool @ ( hAPP_l2138409430r_bool @ wf_J_mdecl @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1384137393r_bool @ ( hAPP_l2054741776r_bool @ ( hAPP_l2138409430r_bool @ wwf_J_mdecl @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_832_wf__mdecl__wwf__mdecl) ).

thf(4841,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P1384137393r_bool @ ( hAPP_l2054741776r_bool @ ( hAPP_l2138409430r_bool @ wf_J_mdecl @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1384137393r_bool @ ( hAPP_l2054741776r_bool @ ( hAPP_l2138409430r_bool @ wwf_J_mdecl @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).

thf(1101,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( fun_up1149430426on_val @ D @ E @ ( hAPP_val_option_val @ some_val @ F ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ E @ A @ ( seq_list_char @ ( lAss_list_char @ E @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ B ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ E @ A @ ( seq_list_char @ ( lAss_list_char @ E @ ( hAPP_v834067052t_char @ val_list_char @ ( hAPP_option_val_val @ the_val @ ( hAPP_l207779698on_val @ I @ E ) ) ) ) @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ E @ ( hAPP_l207779698on_val @ D @ E ) ) ) ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_656_InitBlockReds) ).

thf(5477,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( fun_up1149430426on_val @ D @ E @ ( hAPP_val_option_val @ some_val @ F ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ E @ A @ ( seq_list_char @ ( lAss_list_char @ E @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ B ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ E @ A @ ( seq_list_char @ ( lAss_list_char @ E @ ( hAPP_v834067052t_char @ val_list_char @ ( hAPP_option_val_val @ the_val @ ( hAPP_l207779698on_val @ I @ E ) ) ) ) @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ E @ ( hAPP_l207779698on_val @ D @ E ) ) ) ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).

thf(482,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) @ B @ C @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1046_redp__redsp_ORedFAssNull) ).

thf(3132,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) @ B @ C @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(201,axiom,
    ! [A: $i] :
      ( null
     != ( addr @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1034_val_Osimps_I16_J) ).

thf(2050,plain,
    ! [A: $i] :
      ( null
     != ( addr @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(1133,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) ) @ ( transi910771962on_val @ E ) ) )
     => ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B )
         != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) )
       => ~ ! [F: $i,G: $i] :
              ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ F ) @ G ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) ) @ ( transi910771962on_val @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_756_converse__rtranclE2) ).

thf(5601,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) ) @ ( transi910771962on_val @ E ) ) )
     => ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B )
         != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) )
       => ~ ! [F: $i,G: $i] :
              ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ F ) @ G ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) ) @ ( transi910771962on_val @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).

thf(838,axiom,
    ! [A: $i] :
      ( ( A != none_ty )
     => ~ ! [B: $i] :
            ( A
           != ( hAPP_ty_option_ty @ some_ty @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_791_option_Oexhaust) ).

thf(4491,plain,
    ! [A: $i] :
      ( ( A != none_ty )
     => ~ ! [B: $i] :
            ( A
           != ( hAPP_ty_option_ty @ some_ty @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).

thf(859,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( is_bop @ C )
         => ( ( hBOOL @ ( hAPP_f742333458l_bool @ ( hAPP_P1653675595l_bool @ member1417904245al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) @ B ) )
          <=> ( hBOOL @ ( hAPP_f742333458l_bool @ ( hAPP_P1653675595l_bool @ member1417904245al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) @ A ) ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_pred__equals__eq2) ).

thf(4579,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( is_bop @ C )
           => ( ( ( hBOOL @ ( hAPP_f742333458l_bool @ ( hAPP_P1653675595l_bool @ member1417904245al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) @ B ) )
               => ( hBOOL @ ( hAPP_f742333458l_bool @ ( hAPP_P1653675595l_bool @ member1417904245al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) @ A ) ) )
              & ( ( hBOOL @ ( hAPP_f742333458l_bool @ ( hAPP_P1653675595l_bool @ member1417904245al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) @ A ) )
               => ( hBOOL @ ( hAPP_f742333458l_bool @ ( hAPP_P1653675595l_bool @ member1417904245al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) @ B ) ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: $i,D: $i] :
            ( ( is_bop @ C )
           => ( ( ( hBOOL @ ( hAPP_f742333458l_bool @ ( hAPP_P1653675595l_bool @ member1417904245al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) @ B ) )
               => ( hBOOL @ ( hAPP_f742333458l_bool @ ( hAPP_P1653675595l_bool @ member1417904245al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) @ A ) ) )
              & ( ( hBOOL @ ( hAPP_f742333458l_bool @ ( hAPP_P1653675595l_bool @ member1417904245al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) @ A ) )
               => ( hBOOL @ ( hAPP_f742333458l_bool @ ( hAPP_P1653675595l_bool @ member1417904245al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).

thf(939,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_406_prod__caseI) ).

thf(4885,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).

thf(705,axiom,
    is_bool @ fFalse,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_fFalse) ).

thf(3982,plain,
    is_bool @ fFalse,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).

thf(43,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ B ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_prod__cases3) ).

thf(1436,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ B ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(180,axiom,
    ! [A: $i] :
      ( ( hAPP_list_char_ty @ class @ A )
     != nt ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1111_ty_Osimps_I21_J) ).

thf(1989,plain,
    ! [A: $i] :
      ( ( hAPP_list_char_ty @ class @ A )
     != nt ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(63,axiom,
    ! [A: $i] :
      ( ( hAPP_val_option_ty @ ( typeof_h @ A ) @ unit )
      = ( hAPP_ty_option_ty @ some_ty @ void ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1012_typeof__h_Osimps_I1_J) ).

thf(1495,plain,
    ! [A: $i] :
      ( ( hAPP_val_option_ty @ ( typeof_h @ A ) @ unit )
      = ( hAPP_ty_option_ty @ some_ty @ void ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(790,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_705_set__rev__mp) ).

thf(4286,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).

thf(1223,axiom,
    ! [A: $i] :
      ( ? [B: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ B ) )
    <=> ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_split__paired__Ex) ).

thf(5990,plain,
    ! [A: $i] :
      ( ( ? [B: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ B ) )
       => ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) )
      & ( ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) )
       => ? [B: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223]) ).

thf(966,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hext @ B @ C ) )
     => ( ( hBOOL @ ( hext @ C @ A ) )
       => ( hBOOL @ ( hext @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_565_hext__trans) ).

thf(4968,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hext @ B @ C ) )
     => ( ( hBOOL @ ( hext @ C @ A ) )
       => ( hBOOL @ ( hext @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).

thf(23,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ A ) @ B ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) ) @ ( transi1257872013t_char @ E ) ) )
     => ( ( ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ A ) @ B )
         != ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) )
       => ~ ! [F: $i,G: $i] :
              ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ A ) @ B ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ F ) @ G ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) ) @ ( transi1257872013t_char @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_748_converse__rtranclE2) ).

thf(1335,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ A ) @ B ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) ) @ ( transi1257872013t_char @ E ) ) )
     => ( ( ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ A ) @ B )
         != ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) )
       => ~ ! [F: $i,G: $i] :
              ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ A ) @ B ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ F ) @ G ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) ) @ ( transi1257872013t_char @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(663,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_715_subset__trans) ).

thf(3850,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).

thf(38,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_pred__equals__eq2) ).

thf(1410,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(118,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ B ) @ C ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ D ) @ E ) ) ) @ ( transi198989188t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ B ) @ C ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ B ) @ C ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ G ) @ H ) ) ) @ ( transi198989188t_char @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ G ) @ H ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_775_rtrancl__induct2) ).

thf(1710,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ B ) @ C ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ D ) @ E ) ) ) @ ( transi198989188t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ B ) @ C ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ B ) @ C ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ G ) @ H ) ) ) @ ( transi198989188t_char @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ G ) @ H ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(1076,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ D @ A ) ) @ E ) ) ) @ ( transi374442731on_val @ ( reds @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1165_ListReds1) ).

thf(5378,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ D @ A ) ) @ E ) ) ) @ ( transi374442731on_val @ ( reds @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).

thf(1036,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fTrue ) ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ B ) ) @ C ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( while_list_char @ D @ A ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ B ) ) @ C ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1089_WhileTRedsThrow) ).

thf(5215,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( bool @ fTrue ) ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ B ) ) @ C ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( while_list_char @ D @ A ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ B ) ) @ C ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).

thf(797,axiom,
    ! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( cast_list_char @ B @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ C ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1037_redp__redsp_ORedCastNull) ).

thf(4318,plain,
    ! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( cast_list_char @ B @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ C ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).

thf(1083,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ ( throw_list_char @ A ) @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ C ) ) ) @ ( red @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_933_red__reds_OSeqThrow) ).

thf(5404,plain,
    ! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ ( throw_list_char @ A ) @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ C ) ) ) @ ( red @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).

thf(1001,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ ( dom_list_char_val @ D ) ) @ ( dom_list_char_val @ G ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_855_eval__lcl__incr) ).

thf(5092,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ ( dom_list_char_val @ D ) ) @ ( dom_list_char_val @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).

thf(1193,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_pred__equals__eq2) ).

thf(5867,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).

thf(564,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_739_subsetI) ).

thf(3426,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(154,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P801803911r_bool @ B @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ C ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P801803911r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_prod__induct3) ).

thf(1891,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P801803911r_bool @ B @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ C ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P801803911r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(765,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ C ) @ ( dom_list_char_ty @ D ) ) )
     => ( ( map_add_list_char_ty @ ( fun_up424764369ion_ty @ A @ C @ ( hAPP_ty_option_ty @ some_ty @ B ) ) @ D )
        = ( fun_up424764369ion_ty @ ( map_add_list_char_ty @ A @ D ) @ C @ ( hAPP_ty_option_ty @ some_ty @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_461_map__add__upd__left) ).

thf(4193,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ C ) @ ( dom_list_char_ty @ D ) ) )
     => ( ( map_add_list_char_ty @ ( fun_up424764369ion_ty @ A @ C @ ( hAPP_ty_option_ty @ some_ty @ B ) ) @ D )
        = ( fun_up424764369ion_ty @ ( map_add_list_char_ty @ A @ D ) @ C @ ( hAPP_ty_option_ty @ some_ty @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).

thf(948,axiom,
    ! [A: $i,B: $i] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_option_val_bool @ ( hAPP_o586881855l_bool @ fequal_option_val @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Option__Ooption_Itc__Value__Oval_J_T) ).

thf(4912,plain,
    ! [A: $i,B: $i] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_option_val_bool @ ( hAPP_o586881855l_bool @ fequal_option_val @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).

thf(450,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ D @ E @ F ) @ G ) @ H ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ D @ ( fAss_list_char @ E @ A @ B @ C ) @ F ) @ ( fAss_list_char @ G @ A @ B @ C ) ) @ H ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_893_redp__redsp_OFAssRed1) ).

thf(3045,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ D @ E @ F ) @ G ) @ H ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ D @ ( fAss_list_char @ E @ A @ B @ C ) @ F ) @ ( fAss_list_char @ G @ A @ B @ C ) ) @ H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(1021,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( throw_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ D ) ) ) @ ( red @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1140_red__reds_OCallThrowObj) ).

thf(5176,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( throw_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ D ) ) ) @ ( red @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).

thf(661,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ B ) ) @ ( transi374442731on_val @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: $i] :
              ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ D ) ) @ ( transi374442731on_val @ C ) ) )
             => ~ ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ D ) @ B ) ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_834_rtranclE) ).

thf(3843,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ B ) ) @ ( transi374442731on_val @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: $i] :
              ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ D ) ) @ ( transi374442731on_val @ C ) ) )
             => ~ ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ D ) @ B ) ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).

thf(1051,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ B @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_prod__induct3) ).

thf(5283,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ B @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).

thf(189,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P2028072621l_bool @ B @ ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ C ) @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P2028072621l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_prod__induct3) ).

thf(2021,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P2028072621l_bool @ B @ ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ C ) @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P2028072621l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(277,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ A ) @ B )
        = ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Pair__inject) ).

thf(2353,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ A ) @ B )
        = ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(313,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ C ) @ D ) )
     => ( ( ( hAPP_n546249108on_val @ D @ A )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ B ) )
       => ( hBOOL @ ( hAPP_P1235399154l_bool @ ( oconf_1869808039t_char @ C @ D ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_651_hconfD) ).

thf(2502,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ C ) @ D ) )
     => ( ( ( hAPP_n546249108on_val @ D @ A )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ B ) )
       => ( hBOOL @ ( hAPP_P1235399154l_bool @ ( oconf_1869808039t_char @ C @ D ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(1015,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hext @ B @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_red__hext__incr) ).

thf(5151,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hext @ B @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).

thf(1012,axiom,
    ! [A: $i] :
      ( ? [B: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ B ) )
    <=> ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_split__paired__Ex) ).

thf(5140,plain,
    ! [A: $i] :
      ( ( ? [B: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ B ) )
       => ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) )
      & ( ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) )
       => ? [B: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).

thf(671,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( call_list_char @ ( throw_list_char @ B ) @ C @ D ) @ E ) @ ( throw_list_char @ B ) ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1138_redp__redsp_OCallThrowObj) ).

thf(3869,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( call_list_char @ ( throw_list_char @ B ) @ C @ D ) @ E ) @ ( throw_list_char @ B ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).

thf(936,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ E ) ) ) @ ( transi910771962on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ D ) @ E ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ G ) @ H ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ I ) @ J ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ E ) ) ) @ ( transi910771962on_val @ F ) ) )
               => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_772_converse__rtrancl__induct2) ).

thf(4876,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ E ) ) ) @ ( transi910771962on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ D ) @ E ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ G ) @ H ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ I ) @ J ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ E ) ) ) @ ( transi910771962on_val @ F ) ) )
               => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).

thf(656,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( fv @ ( binOp_list_char @ A @ B @ C ) )
      = ( semila919158006r_bool @ ( fv @ A ) @ ( fv @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_960_fv__fvs_Osimps_I4_J) ).

thf(3817,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( fv @ ( binOp_list_char @ A @ B @ C ) )
      = ( semila919158006r_bool @ ( fv @ A ) @ ( fv @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

thf(1042,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( hBOOL @ ( hAPP_P2010574925r_bool @ A @ B ) )
    <=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P2010574925r_bool @ A @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_split__paired__All) ).

thf(5236,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( hBOOL @ ( hAPP_P2010574925r_bool @ A @ B ) )
       => ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P2010574925r_bool @ A @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ B ) @ C ) ) ) )
      & ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P2010574925r_bool @ A @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ B ) @ C ) ) )
       => ! [B: $i] : ( hBOOL @ ( hAPP_P2010574925r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).

thf(805,axiom,
    ! [A: $i] :
      ( none_nat
     != ( hAPP_nat_option_nat @ some_nat @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_604_option_Osimps_I2_J) ).

thf(4345,plain,
    ! [A: $i] :
      ( none_nat
     != ( hAPP_nat_option_nat @ some_nat @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).

thf(282,axiom,
    ! [A: $i,B: $i] :
      ( ( ( new_Addr @ A )
        = ( hAPP_nat_option_nat @ some_nat @ B ) )
     => ( ( hAPP_n546249108on_val @ A @ B )
        = none_P179726773on_val ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1127_new__Addr__SomeD) ).

thf(2372,plain,
    ! [A: $i,B: $i] :
      ( ( ( new_Addr @ A )
        = ( hAPP_nat_option_nat @ some_nat @ B ) )
     => ( ( hAPP_n546249108on_val @ A @ B )
        = none_P179726773on_val ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(879,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_bool_bool @ ( ord_less_eq_bool @ ( hAPP_list_char_bool @ B @ A ) ) @ ( hAPP_list_char_bool @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_828_le__funE) ).

thf(4674,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_bool_bool @ ( ord_less_eq_bool @ ( hAPP_list_char_bool @ B @ A ) ) @ ( hAPP_list_char_bool @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).

thf(951,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_992_CastRedsThrow) ).

thf(4923,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).

thf(513,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ G @ H ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ I ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ K ) ) )
     => ( ( ( hAPP_n546249108on_val @ J @ I )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
       => ( ( ( hAPP_P2094403585on_val @ E @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) )
            = ( hAPP_val_option_val @ some_val @ C ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ ( fAcc_list_char @ G @ A @ B ) @ H ) @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ K ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_906_FAcc) ).

thf(3244,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ G @ H ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ I ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ K ) ) )
     => ( ( ( hAPP_n546249108on_val @ J @ I )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
       => ( ( ( hAPP_P2094403585on_val @ E @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) )
            = ( hAPP_val_option_val @ some_val @ C ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ ( fAcc_list_char @ G @ A @ B ) @ H ) @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ K ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(231,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B )
        = ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_Pair__inject) ).

thf(2159,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B )
        = ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(370,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_698_in__mono) ).

thf(2731,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(480,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_699_in__mono) ).

thf(3128,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(176,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P738987199l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc_) ).

thf(1977,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_P738987199l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(296,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_pred__equals__eq2) ).

thf(2430,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: $i,D: $i] :
            ( ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(591,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ B ) @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ B ) @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ B ) @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_widen__trans) ).

thf(3543,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ B ) @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ B ) @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ B ) @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(455,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C != D )
     => ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ D @ B ) @ C )
        = ( hAPP_l512744617ion_ty @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_fun__upd__other) ).

thf(3057,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C != D )
     => ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ D @ B ) @ C )
        = ( hAPP_l512744617ion_ty @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(75,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( wTrt_1 @ B @ C @ D @ E @ F ) )
     => ( ( hBOOL @ ( is_refT @ F ) )
       => ( ( hBOOL @ ( hAPP_list_char_bool @ ( is_cla570604648t_char @ B ) @ A ) )
         => ( hBOOL @ ( wTrt_1 @ B @ C @ D @ ( cast_list_char @ A @ E ) @ ( hAPP_list_char_ty @ class @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1057_WTrtCast) ).

thf(1532,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( wTrt_1 @ B @ C @ D @ E @ F ) )
     => ( ( hBOOL @ ( is_refT @ F ) )
       => ( ( hBOOL @ ( hAPP_list_char_bool @ ( is_cla570604648t_char @ B ) @ A ) )
         => ( hBOOL @ ( wTrt_1 @ B @ C @ D @ ( cast_list_char @ A @ E ) @ ( hAPP_list_char_ty @ class @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(913,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( produc1911975310l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_512_curryD) ).

thf(4799,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( produc1911975310l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).

thf(601,axiom,
    ! [A: $i] : ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_690_subset__refl) ).

thf(3570,plain,
    ! [A: $i] : ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(308,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ B ) @ C @ D @ ( throw_list_char @ E ) ) @ F ) @ ( throw_list_char @ E ) ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_929_redp__redsp_OFAssThrow2) ).

thf(2485,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ B ) @ C @ D @ ( throw_list_char @ E ) ) @ F ) @ ( throw_list_char @ E ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(32,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wf_J_mdecl @ F ) )
     => ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ D ) @ E ) ) ) ) @ ( set_Pr1494163115t_char @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ ( set_Pr2033386304t_char @ E ) ) )
         => ( hBOOL @ ( hAPP_P1384137393r_bool @ ( hAPP_l2054741776r_bool @ ( hAPP_l2138409430r_bool @ wf_J_mdecl @ F ) @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1182_wf__J__prog__wf__J__mdecl) ).

thf(1384,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wf_J_mdecl @ F ) )
     => ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ D ) @ E ) ) ) ) @ ( set_Pr1494163115t_char @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ ( set_Pr2033386304t_char @ E ) ) )
         => ( hBOOL @ ( hAPP_P1384137393r_bool @ ( hAPP_l2054741776r_bool @ ( hAPP_l2138409430r_bool @ wf_J_mdecl @ F ) @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(608,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1129005983r_bool @ ( hAPP_f1749915625r_bool @ ( hAPP_f842743203r_bool @ cOMBB_657296617har_ty @ A ) @ B ) @ C )
      = ( hAPP_f841257045r_bool @ A @ ( hAPP_l1536299231l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__076) ).

thf(3605,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l1129005983r_bool @ ( hAPP_f1749915625r_bool @ ( hAPP_f842743203r_bool @ cOMBB_657296617har_ty @ A ) @ B ) @ C )
      = ( hAPP_f841257045r_bool @ A @ ( hAPP_l1536299231l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(1038,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ C @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ F @ none_val ) ) ) @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) )
     => ( ( ( hAPP_l207779698on_val @ I @ F )
          = none_val )
       => ( ~ ( hBOOL @ ( assigned @ F @ C ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ ( block_list_char @ F @ A @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) @ ( block_list_char @ F @ A @ G ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ F @ ( hAPP_l207779698on_val @ E @ F ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_630_redp__redsp_OBlockRedNone) ).

thf(5219,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ C @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ F @ none_val ) ) ) @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) )
     => ( ( ( hAPP_l207779698on_val @ I @ F )
          = none_val )
       => ( ~ ( hBOOL @ ( assigned @ F @ C ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ ( block_list_char @ F @ A @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) @ ( block_list_char @ F @ A @ G ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ F @ ( hAPP_l207779698on_val @ E @ F ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).

thf(1099,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( transi2024712006on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ H ) ) ) @ ( transi2024712006on_val @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ H ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_774_rtrancl__induct2) ).

thf(5468,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( transi2024712006on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ H ) ) ) @ ( transi2024712006on_val @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ H ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).

thf(1069,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( map_ad1185064968ar_val @ A @ ( fun_up204312361on_val @ B @ C @ ( hAPP_val_option_val @ some_val @ D ) ) )
      = ( fun_up204312361on_val @ ( map_ad1185064968ar_val @ A @ B ) @ C @ ( hAPP_val_option_val @ some_val @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_514_map__add__upd) ).

thf(5354,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( map_ad1185064968ar_val @ A @ ( fun_up204312361on_val @ B @ C @ ( hAPP_val_option_val @ some_val @ D ) ) )
      = ( fun_up204312361on_val @ ( map_ad1185064968ar_val @ A @ B ) @ C @ ( hAPP_val_option_val @ some_val @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).

thf(728,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( seq_list_char @ A @ B )
        = ( seq_list_char @ C @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_573_exp_Osimps_I11_J) ).

thf(4071,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( seq_list_char @ A @ B )
          = ( seq_list_char @ C @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( seq_list_char @ A @ B )
          = ( seq_list_char @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).

thf(1075,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ D ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ F ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_899_FAssReds2) ).

thf(5376,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ D ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ F ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).

thf(361,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1134950784l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_I) ).

thf(2699,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1134950784l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(582,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i,O: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ K @ L @ M ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ N ) ) ) @ O ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ K @ G @ O ) @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) )
       => ( ( ( hAPP_n546249108on_val @ I @ N )
            = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ F ) ) )
         => ( ( B
              = ( fun_up204312361on_val @ F @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) @ ( hAPP_val_option_val @ some_val @ H ) ) )
           => ( ( A
                = ( fun_up2041264236on_val @ I @ N @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ B ) ) ) )
             => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ K @ ( fAss_list_char @ L @ C @ D @ G ) @ M ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ J ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_900_FAss) ).

thf(3494,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i,O: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ K @ L @ M ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ N ) ) ) @ O ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ K @ G @ O ) @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) )
       => ( ( ( hAPP_n546249108on_val @ I @ N )
            = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ F ) ) )
         => ( ( B
              = ( fun_up204312361on_val @ F @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) @ ( hAPP_val_option_val @ some_val @ H ) ) )
           => ( ( A
                = ( fun_up2041264236on_val @ I @ N @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ B ) ) ) )
             => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ K @ ( fAss_list_char @ L @ C @ D @ G ) @ M ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ J ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(36,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) ) @ ( transi61620055on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ B ) @ C ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) ) @ ( transi61620055on_val @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_786_rtrancl__induct2) ).

thf(1399,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) ) @ ( transi61620055on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ B ) @ C ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) ) @ ( transi61620055on_val @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(684,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_v417179479l_bool @ ( hAPP_f293485653l_bool @ ( hAPP_f565735867l_bool @ cOMBB_815843940ol_val @ A ) @ B ) @ C )
      = ( hAPP_f1394668591l_bool @ A @ ( hAPP_v1519391al_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Value__Oval_Mtc__prod_Itc__Value__Oval_Mtc_) ).

thf(3918,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_v417179479l_bool @ ( hAPP_f293485653l_bool @ ( hAPP_f565735867l_bool @ cOMBB_815843940ol_val @ A ) @ B ) @ C )
      = ( hAPP_f1394668591l_bool @ A @ ( hAPP_v1519391al_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).

thf(264,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l217977712r_bool @ ( hAPP_f1044627221r_bool @ ( hAPP_f308875635r_bool @ cOMBC_1718404842r_bool @ A ) @ B ) @ C )
      = ( hAPP_f1874697593r_bool @ ( hAPP_l1783480313r_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J__043) ).

thf(2270,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_l217977712r_bool @ ( hAPP_f1044627221r_bool @ ( hAPP_f308875635r_bool @ cOMBC_1718404842r_bool @ A ) @ B ) @ C )
      = ( hAPP_f1874697593r_bool @ ( hAPP_l1783480313r_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(93,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( wTrt @ B @ C @ D @ E @ F ) )
     => ( ( hBOOL @ ( is_refT @ F ) )
       => ( hBOOL @ ( wTrt @ B @ C @ D @ ( throw_list_char @ E ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1024_WTrt_H__WTrts_H_Ointros_I21_J) ).

thf(1606,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( wTrt @ B @ C @ D @ E @ F ) )
     => ( ( hBOOL @ ( is_refT @ F ) )
       => ( hBOOL @ ( wTrt @ B @ C @ D @ ( throw_list_char @ E ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(801,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1520735791l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_I_004) ).

thf(4335,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1520735791l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).

thf(694,axiom,
    ! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ A ) @ B ) @ ( hAPP_o538043682on_val @ cOMBK_1097134891t_char @ none_val ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_594_lconf__empty) ).

thf(3950,plain,
    ! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ A ) @ B ) @ ( hAPP_o538043682on_val @ cOMBK_1097134891t_char @ none_val ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).

thf(604,axiom,
    ! [A: $i] :
      ( ( A != none_nat )
     => ~ ! [B: $i] :
            ( A
           != ( hAPP_nat_option_nat @ some_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_790_option_Oexhaust) ).

thf(3580,plain,
    ! [A: $i] :
      ( ( A != none_nat )
     => ~ ! [B: $i] :
            ( A
           != ( hAPP_nat_option_nat @ some_nat @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(785,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ D ) @ ( throw_list_char @ E ) ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ ( while_list_char @ C @ A ) @ D ) @ ( throw_list_char @ E ) ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1079_WhileCondThrow) ).

thf(4274,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ D ) @ ( throw_list_char @ E ) ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ ( while_list_char @ C @ A ) @ D ) @ ( throw_list_char @ E ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).

thf(172,axiom,
    add != c_Expr_Obop_OEq,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1081_bop_Osimps_I2_J) ).

thf(1962,plain,
    add != c_Expr_Obop_OEq,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(1158,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_l207779698on_val @ B @ C )
        = ( hAPP_val_option_val @ some_val @ D ) )
     => ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ A @ B ) @ C )
        = ( hAPP_val_option_val @ some_val @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_470_map__add__find__right) ).

thf(5707,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_l207779698on_val @ B @ C )
        = ( hAPP_val_option_val @ some_val @ D ) )
     => ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ A @ B ) @ C )
        = ( hAPP_val_option_val @ some_val @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).

thf(530,axiom,
    ! [A: $i] :
      ( ? [B: $i] : ( hBOOL @ ( hAPP_P2118621157r_bool @ A @ B ) )
    <=> ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P2118621157r_bool @ A @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_split__paired__Ex) ).

thf(3299,plain,
    ! [A: $i] :
      ( ( ? [B: $i] : ( hBOOL @ ( hAPP_P2118621157r_bool @ A @ B ) )
       => ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P2118621157r_bool @ A @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ) ) )
      & ( ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P2118621157r_bool @ A @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ) )
       => ? [B: $i] : ( hBOOL @ ( hAPP_P2118621157r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(903,axiom,
    ! [A: $i] :
      ( ( A != none_nat )
    <=> ? [B: $i] :
          ( A
          = ( hAPP_nat_option_nat @ some_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_619_not__None__eq) ).

thf(4767,plain,
    ! [A: $i] :
      ( ( ( A != none_nat )
       => ? [B: $i] :
            ( A
            = ( hAPP_nat_option_nat @ some_nat @ B ) ) )
      & ( ? [B: $i] :
            ( A
            = ( hAPP_nat_option_nat @ some_nat @ B ) )
       => ( A != none_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).

thf(51,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wTrt @ D @ E @ F @ G @ nt ) )
     => ( hBOOL @ ( wTrt @ D @ E @ F @ ( fAcc_list_char @ G @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1115_WTrt_H__WTrts_H_Ointros_I9_J) ).

thf(1463,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wTrt @ D @ E @ F @ G @ nt ) )
     => ( hBOOL @ ( wTrt @ D @ E @ F @ ( fAcc_list_char @ G @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(1090,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( ( hAPP_n546249108on_val @ F @ G )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ H ) @ I ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) @ A @ B @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( fun_up2041264236on_val @ F @ G @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ H ) @ ( fun_up204312361on_val @ I @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) @ ( hAPP_val_option_val @ some_val @ C ) ) ) ) ) ) @ D ) ) ) ) @ ( red @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_902_red__reds_ORedFAss) ).

thf(5436,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( ( hAPP_n546249108on_val @ F @ G )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ H ) @ I ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) @ A @ B @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( fun_up2041264236on_val @ F @ G @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ H ) @ ( fun_up204312361on_val @ I @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) @ ( hAPP_val_option_val @ some_val @ C ) ) ) ) ) ) @ D ) ) ) ) @ ( red @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).

thf(61,axiom,
    ! [A: $i,B: $i,C: $i] : ( is_bool @ ( list_all2_ty_ty @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_List_Olist__all2_000tc__Type__Oty_000tc__Type__Oty) ).

thf(1490,plain,
    ! [A: $i,B: $i,C: $i] : ( is_bool @ ( list_all2_ty_ty @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(535,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ A ) @ B )
        = ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_Pair__eq) ).

thf(3316,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ A ) @ B )
          = ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ A ) @ B )
          = ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(603,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ ( transi1395422419t_char @ D ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ A @ C ) )
       => ( ! [E: $i,F: $i] :
              ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ E ) @ F ) ) @ D ) )
             => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ F ) @ C ) ) @ ( transi1395422419t_char @ D ) ) )
               => ( ( hBOOL @ ( hAPP_list_char_bool @ A @ F ) )
                 => ( hBOOL @ ( hAPP_list_char_bool @ A @ E ) ) ) ) )
         => ( hBOOL @ ( hAPP_list_char_bool @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_843_converse__rtrancl__induct) ).

thf(3575,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ ( transi1395422419t_char @ D ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ A @ C ) )
       => ( ! [E: $i,F: $i] :
              ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ E ) @ F ) ) @ D ) )
             => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ F ) @ C ) ) @ ( transi1395422419t_char @ D ) ) )
               => ( ( hBOOL @ ( hAPP_list_char_bool @ A @ F ) )
                 => ( hBOOL @ ( hAPP_list_char_bool @ A @ E ) ) ) ) )
         => ( hBOOL @ ( hAPP_list_char_bool @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

thf(237,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wTrt_1 @ C @ D @ E @ F @ G ) )
     => ( ( hBOOL @ ( wTrt_1 @ C @ D @ E @ A @ B ) )
       => ( hBOOL @ ( wTrt_1 @ C @ D @ E @ ( seq_list_char @ F @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_553_WTrtSeq) ).

thf(2177,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( wTrt_1 @ C @ D @ E @ F @ G ) )
     => ( ( hBOOL @ ( wTrt_1 @ C @ D @ E @ A @ B ) )
       => ( hBOOL @ ( wTrt_1 @ C @ D @ E @ ( seq_list_char @ F @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(1243,axiom,
    ! [A: $i] :
      ( ! [B: $i] :
          ( A
         != ( hAPP_val_option_val @ some_val @ B ) )
    <=> ( A = none_val ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_617_not__Some__eq) ).

thf(6067,plain,
    ! [A: $i] :
      ( ( ! [B: $i] :
            ( A
           != ( hAPP_val_option_val @ some_val @ B ) )
       => ( A = none_val ) )
      & ( ( A = none_val )
       => ! [B: $i] :
            ( A
           != ( hAPP_val_option_val @ some_val @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1243]) ).

thf(641,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P1116729363l_bool @ ( hAPP_f1200025813l_bool @ ( hAPP_f1089788553l_bool @ cOMBC_967917532l_bool @ A ) @ B ) @ C )
      = ( hAPP_f973018659l_bool @ ( hAPP_P609938901l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O_079) ).

thf(3753,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P1116729363l_bool @ ( hAPP_f1200025813l_bool @ ( hAPP_f1089788553l_bool @ cOMBC_967917532l_bool @ A ) @ B ) @ C )
      = ( hAPP_f973018659l_bool @ ( hAPP_P609938901l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(849,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( redsp @ B @ C @ D ) @ E ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( redsp @ B @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ C ) @ D ) @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ E ) ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1179_redp__redsp_OListRed2) ).

thf(4533,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( redsp @ B @ C @ D ) @ E ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( redsp @ B @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ C ) @ D ) @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ E ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).

thf(697,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1001225811y_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption) ).

thf(3960,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1001225811y_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).

thf(356,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ A ) @ ( transi374442731on_val @ B ) ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ ( transi374442731on_val @ A ) ) @ ( transi374442731on_val @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_682_rtrancl__subset__rtrancl) ).

thf(2672,plain,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ A ) @ ( transi374442731on_val @ B ) ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ ( transi374442731on_val @ A ) ) @ ( transi374442731on_val @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(349,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ E ) @ F )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
     => ( ( ( hAPP_P2094403585on_val @ H @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) )
          = ( hAPP_val_option_val @ some_val @ D ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( fAcc_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) @ B @ C ) @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_905_redp__redsp_ORedFAcc) ).

thf(2640,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ E ) @ F )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
     => ( ( ( hAPP_P2094403585on_val @ H @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) )
          = ( hAPP_val_option_val @ some_val @ D ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( fAcc_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) @ B @ C ) @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(169,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ A ) @ B )
        = ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_Pair__eq) ).

thf(1944,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ A ) @ B )
          = ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ A ) @ B )
          = ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(28,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ A ) @ B )
        = ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_Pair__inject) ).

thf(1367,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ A ) @ B )
        = ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(329,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).

thf(2563,plain,
    ! [A: $i,B: $i] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(686,axiom,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f61040418l_bool @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__O) ).

thf(3924,plain,
    ! [A: $i,B: $i] : ( is_bool @ ( hAPP_f61040418l_bool @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(1221,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ ( throw_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ D ) ) ) @ ( red @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_916_red__reds_OFAccThrow) ).

thf(5986,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ ( throw_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ D ) ) ) @ ( red @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1221]) ).

thf(1057,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ C ) @ ( dom_list_char_val @ D ) ) )
     => ( ( map_ad325961431ar_val @ ( fun_up1149430426on_val @ A @ C @ ( hAPP_val_option_val @ some_val @ B ) ) @ D )
        = ( fun_up1149430426on_val @ ( map_ad325961431ar_val @ A @ D ) @ C @ ( hAPP_val_option_val @ some_val @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_459_map__add__upd__left) ).

thf(5312,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ C ) @ ( dom_list_char_val @ D ) ) )
     => ( ( map_ad325961431ar_val @ ( fun_up1149430426on_val @ A @ C @ ( hAPP_val_option_val @ some_val @ B ) ) @ D )
        = ( fun_up1149430426on_val @ ( map_ad325961431ar_val @ A @ D ) @ C @ ( hAPP_val_option_val @ some_val @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).

thf(1094,axiom,
    hBOOL @ fTrue,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).

thf(5458,plain,
    hBOOL @ fTrue,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).

thf(1179,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ A @ B ) @ C )
        = ( hAPP_val_option_val @ some_val @ D ) )
     => ( ( ( hAPP_l207779698on_val @ B @ C )
          = ( hAPP_val_option_val @ some_val @ D ) )
        | ( ( ( hAPP_l207779698on_val @ B @ C )
            = none_val )
          & ( ( hAPP_l207779698on_val @ A @ C )
            = ( hAPP_val_option_val @ some_val @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_644_map__add__SomeD) ).

thf(5789,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ A @ B ) @ C )
        = ( hAPP_val_option_val @ some_val @ D ) )
     => ( ( ( hAPP_l207779698on_val @ B @ C )
          = ( hAPP_val_option_val @ some_val @ D ) )
        | ( ( ( hAPP_l207779698on_val @ B @ C )
            = none_val )
          & ( ( hAPP_l207779698on_val @ A @ C )
            = ( hAPP_val_option_val @ some_val @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).

thf(468,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P1384137393r_bool @ ( hAPP_f1853572245r_bool @ ( hAPP_f1933376467r_bool @ cOMBC_36589090l_bool @ A ) @ B ) @ C )
      = ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod) ).

thf(3096,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_P1384137393r_bool @ ( hAPP_f1853572245r_bool @ ( hAPP_f1933376467r_bool @ cOMBC_36589090l_bool @ A ) @ B ) @ C )
      = ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(246,axiom,
    ! [A: $i,B: $i] :
      ( ( ( hAPP_f363827556r_bool @ some_f80346385r_bool @ A )
        = ( hAPP_f363827556r_bool @ some_f80346385r_bool @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_355_option_Oinject) ).

thf(2206,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( hAPP_f363827556r_bool @ some_f80346385r_bool @ A )
          = ( hAPP_f363827556r_bool @ some_f80346385r_bool @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( hAPP_f363827556r_bool @ some_f80346385r_bool @ A )
          = ( hAPP_f363827556r_bool @ some_f80346385r_bool @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(723,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_v3604996l_bool @ ( hAPP_f1394668591l_bool @ ( hAPP_f183649339l_bool @ cOMBB_2078984970ol_val @ A ) @ B ) @ C )
      = ( hAPP_P530382601l_bool @ A @ ( hAPP_v852496844al_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__fun_) ).

thf(4056,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP_v3604996l_bool @ ( hAPP_f1394668591l_bool @ ( hAPP_f183649339l_bool @ cOMBB_2078984970ol_val @ A ) @ B ) @ C )
      = ( hAPP_P530382601l_bool @ A @ ( hAPP_v852496844al_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).

thf(933,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ B ) )
     => ~ ! [C: $i,D: $i] :
            ( ( B
              = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) )
           => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_535_splitE) ).

thf(4863,plain,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ B ) )
     => ~ ! [C: $i,D: $i] :
            ( ( B
              = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) )
           => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).

thf(1236,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ ( throw_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ D ) ) ) @ ( red @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_966_red__reds_OBinOpThrow1) ).

thf(6035,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ ( throw_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ D ) ) ) @ ( red @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1236]) ).

thf(241,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( produc1838470831l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P71593144l_bool @ A @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_489_curryE) ).

thf(2191,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( produc1838470831l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P71593144l_bool @ A @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(48,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ E ) ) ) @ ( transi1095029602t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ D ) @ E ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ G ) @ H ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ I ) @ J ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ E ) ) ) @ ( transi1095029602t_char @ F ) ) )
               => ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_769_converse__rtrancl__induct2) ).

thf(1449,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ E ) ) ) @ ( transi1095029602t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ D ) @ E ) )
       => ( ! [G: $i,H: $i,I: $i,J: $i] :
              ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ G ) @ H ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ I ) @ J ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ E ) ) ) @ ( transi1095029602t_char @ F ) ) )
               => ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(139,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ A ) @ B )
        = ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_Pair__eq) ).

thf(1812,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ A ) @ B )
          = ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ A ) @ B )
          = ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(215,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ ( transi1395422419t_char @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_666_r__into__rtrancl) ).

thf(2106,plain,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ ( transi1395422419t_char @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(595,axiom,
    ! [A: $i,B: $i] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ ( addr @ B ) ) ) )
      = none_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1014_binop_Osimps_I10_J) ).

thf(3553,plain,
    ! [A: $i,B: $i] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ ( addr @ B ) ) ) )
      = none_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(53,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i,E: $i] :
          ( A
         != ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ B ) @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_prod__cases4) ).

thf(1468,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i,E: $i] :
          ( A
         != ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ B ) @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(451,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hAPP_P2094403585on_val @ A @ B )
        = C )
     => ( ( fun_up204312361on_val @ A @ B @ C )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_fun__upd__idem) ).

thf(3047,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hAPP_P2094403585on_val @ A @ B )
        = C )
     => ( ( fun_up204312361on_val @ A @ B @ C )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(6162,plain,
    $false,
    inference(e,[status(thm)],[5385,5365,4094,2889,3798,4022,2463,4682,3172,5509,3873,4560,3962,5422,1718,3345,3053,4101,1454,2031,5136,1633,4183,3698,5676,2595,1850,1315,3863,2427,3969,5205,6074,5028,4728,5582,4992,5898,1924,2117,4226,2495,3040,3012,5669,2114,3402,1692,6017,3382,2231,3858,5644,5842,1443,3417,2676,2014,3498,2380,1486,4105,1426,3429,4739,2607,2035,4026,2141,2712,3562,1458,3276,3848,1705,3017,5967,5425,5814,4234,1671,3794,1608,4633,4403,1756,1310,2448,2933,5674,3253,2459,3313,5782,5178,2844,5192,2360,6138,3545,5518,5745,2010,3730,6102,5269,4386,2972,4142,2491,5486,2985,5935,2227,4618,3088,2886,4916,5903,1601,1386,3466,2400,4963,5750,1904,1518,1265,1703,5024,5342,3820,4539,1985,2667,5910,1871,5188,3617,3653,3485,4349,6006,4984,2745,5461,5765,4439,1287,3221,3938,3029,4743,1792,1430,2039,6039,4956,1298,5883,2339,4692,5064,5274,5130,2185,6113,5182,4428,3855,2420,1379,2169,5199,1319,1479,4830,3470,2989,4390,5617,3268,1922,6010,3099,5338,4179,2767,5622,4622,1572,3902,3657,1931,5020,5493,6025,1778,2222,6002,3431,3075,4001,4820,3453,3983,5680,4815,5914,5156,4871,2073,2950,4696,4205,4988,2616,1465,4329,3887,3199,3934,3393,5013,4454,2782,3973,5804,2291,3357,2254,3290,3093,4115,2335,5360,4783,3152,3771,4162,5059,4751,3068,3421,3712,1447,1886,4707,3559,5328,1696,4033,3189,2281,5246,3676,5846,5321,4307,2002,3756,6021,2242,2799,3327,4701,2750,1405,2804,2965,4519,3211,1521,3492,2718,5970,1975,4082,4483,5695,2922,5961,5406,3567,5167,3995,2093,4370,4910,4925,3503,4199,4629,5751,3852,1306,4531,2364,2164,5697,3186,5862,2307,2083,4312,4059,2905,1868,2061,4172,2773,4999,2000,1636,1274,5049,2705,1900,6124,5512,5266,4785,4160,6079,6122,5630,2733,2249,6000,3867,4397,4920,6032,4375,5794,4609,5349,4252,5815,3884,2937,3154,4449,3134,5085,4284,1619,2150,6107,5102,3814,2132,4836,5924,1883,5769,3980,4140,2670,1920,5690,2872,1296,4776,1787,5201,2213,3926,2547,2112,2958,3307,4280,5391,5702,4725,2565,6043,4155,2820,3065,3750,3556,5988,5779,1624,6143,2200,2609,1634,1392,3667,4732,3033,1740,3445,5285,5066,4808,5714,2157,1804,2841,5635,1498,1540,5081,3650,3941,2638,3440,3105,3784,3909,3615,5145,1762,1270,5098,1259,1534,1953,4108,4486,5577,5502,1970,3218,4789,3102,5428,3119,5373,3746,4883,6111,3078,5497,3001,3060,4817,4898,4676,4320,4333,2023,3143,1292,5107,2868,5786,1842,5588,1937,2108,4867,5905,2472,5387,6065,3141,3952,4951,5818,4276,3407,2561,4167,4425,4421,3010,5464,1810,4861,2172,4648,5662,3194,2551,2085,2125,5234,6129,4244,2505,4934,5776,2756,3162,5479,4804,3242,3703,1324,1263,3611,5726,2519,2536,3126,3787,1530,2487,2598,4068,5380,1831,2153,2900,4970,5639,5134,2581,2465,1852,2813,3628,3115,5217,3247,3409,3692,2482,4152,1720,1979,5026,3005,1333,4535,5310,4288,4567,4966,3999,4036,2645,2529,4148,2634,5112,1434,2788,5544,3834,4644,3225,2043,3279,4889,3587,3183,2883,4476,2793,5930,4995,4572,2909,4550,3807,1906,2729,4131,4380,1483,6084,3985,3262,5608,2121,2235,3707,1727,2413,3130,2391,1680,5808,1698,2033,4613,3871,3257,5451,3890,5278,2570,2941,4340,1595,3523,5928,4577,4359,3274,5758,1374,4365,2524,3396,1631,5241,5933,3234,3519,5844,2489,2393,5612,2806,1965,4946,4505,4041,4144,3372,1833,5456,5474,2225,5488,3255,3811,2791,3240,3081,1929,5940,3945,3283,5627,3266,2674,2016,2514,4122,3272,4801,1795,1701,2398,4975,3404,4758,2695,5022,1488,5965,5546,3773,5595,4099,3123,3700,2425,3304,3091,2193,3023,4558,5033,4127,2220,3964,2029,4186,4096,1707,5363,3051,2891,5011,5331,4236,3663,2935,4822,5190,3436,2166,3619,2457,2557,3641,1258,5158,4887,3355,3719,2358,2319,4433,2510,4716,2521,2538,2229,1574,3419,5303,1542,2839,2896,3384,4509,2119,5071,3352,4337,6059,5212,4929,4498,2478,2383,2624,2415,2987,5520,3038,5325,3551,4305,3957,4828,1589,2284,1933,2955,1492,1722,5222,4213,4616,5346,2856,2802,5552,5584,5920,4028,2446,2410,2874,5466,5780,1667,2180,4635,6004,3055,4009,4064,1993,5439,1821,1731,4264,3572,3932,3165,4181,2593,3451,3971,1344,2289,5180,2252,2664,3861,2278,5007,2461,2974,5410,5459,4684,5838,5340,5742,3110,2752,3310,4954,5495,2069,3539,4832,3759,3838,5197,5094,3423,1445,2620,5646,4373,3687,5248,4085,3159,2064,4362,2931,5575,1477,3325,4703,2101,5667,4196,6027,3178,4282,4626,2999,3348,5089,1694,2693,4209,4481,4158,3490,1562,2005,5528,4735,5952,2629,1472,5763,6008,1551,2054,4207,4741,5959,4907,2914,1583,4136,2096,1304,1873,4013,1758,5886,4813,2994,4456,3206,4529,2037,5678,4859,2202,6076,3921,1340,4688,2256,1958,5710,4045,5570,2715,3913,3112,4939,5592,5523,5079,3608,1845,4255,1798,5624,5716,5822,1516,1598,5514,3507,4937,2977,2375,2012,3904,3260,5499,5944,3659,1941,5484,4517,3228,4641,5721,2175,1780,3209,4894,4961,5431,1716,1432,6037,5753,3202,2337,5995,4117,1285,5186,3019,3080,4522,4314,4092,4905,1300,1637,3791,4020,5015,3722,5276,1785,3475,3026,2276,2128,5154,2701,4241,2545,2903,4982,3412,4781,3174,4164,3715,3107,4959,1802,4624,4488,1506,2579,5809,4342,3071,3366,4111,1358,2247,5147,5208,5949,3415,3829,1536,1981,4436,4246,1353,4748,5504,3388,1504,4202,1585,6086,3117,2860,2722,1372,4838,5083,1881,1272,3156,5100,3007,4150,5895,2584,4257,4671,3398,4392,3288,4217,1617,5771,3433,3584,4606,2818,1553,2870,2960,3447,5573,2611,2643,3929,4574,4639,2760,3400,3478,2626,1918,3457,4698,3565,2088,3589,2045,2078,1913,4997,3548,4646,3725,5308,2997,2187,4006,2919,4170,5068,4310,4061,5184,2907,4678,3665,4730,5055,5315,2707,2273,4806,2853,4666,1481,4250,3336,2823,4527,1674,3789,4089,5382,1508,5132,4791,1629,2026,3630,3501,5394,4834,4495,1523,2130,4881,3368,4900,2262,4451,5922,3085,5963,2041,4175,4774,1440,2198,1513,1893,3761,4927,5336,5287,1689,3978,3181,2475,3694,2796,5162,2648,5692,2576,2066,2362,5549,6062,5590,4446,4039,5357,1642,3907,5004,2233,3892,3264,1593,1527,4597,5926,2123,2218,5051,5009,4794,3705,1280,1578,4472,4399,3511,5606,4378,2534,3232,2983,3865,3882,5954,1395,5232,4843,1876,2815,2736,4787,4841,5477,3132,2050,5601,4491,4579,4885,3982,1436,1989,1495,4286,5990,4968,1335,3850,1410,1710,5378,5215,4318,5404,5092,5867,3426,1891,4193,4912,3045,5176,3843,5283,2021,2353,2502,5151,5140,3869,4876,3817,5236,4345,2372,4674,4923,3244,2159,2731,3128,1977,2430,3543,3057,1532,4799,3570,2485,1384,3605,5219,5468,5354,4071,5376,2699,3494,1399,3918,2270,1606,4335,3950,3580,4274,1962,5707,3299,4767,1463,5436,1490,3316,3575,2177,6067,3753,4533,3960,2672,2640,1944,1367,2563,3924,5986,5312,5458,5789,3096,2206,4056,4863,6035,2191,1449,1812,2106,3553,1468,3047]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWW478+3 : TPTP v8.1.2. Released v5.3.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n013.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu May 18 22:01:22 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.96/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.15/1.16  % [INFO] 	 Parsing done (322ms). 
% 2.15/1.17  % [INFO] 	 Running in sequential loop mode. 
% 2.75/1.37  % [INFO] 	 eprover registered as external prover. 
% 2.75/1.37  % [INFO] 	 cvc4 registered as external prover. 
% 2.75/1.38  % [INFO] 	 Scanning for conjecture ... 
% 3.55/1.58  % [INFO] 	 Found a conjecture and 1490 axioms. Running axiom selection ... 
% 5.27/2.25  % [INFO] 	 Axiom selection finished. Selected 1255 axioms (removed 235 axioms). 
% 7.60/2.94  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 7.60/2.98  % [INFO] 	 Type checking passed. 
% 7.60/2.98  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 32.87/10.97  % External prover 'e' found a proof!
% 32.87/10.97  % [INFO] 	 Killing All external provers ... 
% 32.87/10.97  % Time passed: 10453ms (effective reasoning time: 9796ms)
% 32.87/10.97  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 32.87/10.98  % Axioms used in derivation (1255): gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olis_008, gsy_c_hAPP_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__HOL__Obool, fact_707_set__rev__mp, gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__O, fact_780_rtrancl__induct2, fact_382_in__lex__prod, fact_1193_wts_H__iff__wts, gsy_c_hAPP_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O, fact_808_pred__subset__eq2, fact_353_option_Oinject, fact_617_not__Some__eq, fact_278_pred__equals__eq2, fact_152_split__paired__All, gsy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It, fact_1049_ThrowRedsNull, fact_604_option_Osimps_I2_J, fact_642_map__upd__nonempty, fact_929_redp__redsp_OFAssThrow2, fact_279_pred__equals__eq2, fact_1189_blocksEval, fact_214_fun__upd__upd, fact_653_red__reds_OBlockRedNone, gsy_c_WellTypeRT_OWTrts, fact_285_pred__equals__eq2, fact_1005_eval__cases_I3_J, gsy_c_TypeRel_OFields_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String_, fact_436_curry__split, fact_957_redp__redsp_OBinOpThrow1, fact_123_Pair__eq, fact_350_red__hext__incr, help_COMBC_1_1_COMBC_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O, gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__St_022, help_COMBB_1_1_COMBB_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc, fact_120_Pair__eq, fact_218_fun__upd__idem__iff, fact_294_pred__equals__eq2, fact_321_PairE, fact_974_TryRedsVal, help_COMBB_1_1_COMBB_000tc__fun_Itc__Value__Oval_Mtc__prod_Itc__Value__Oval_Mtc_, fact_681_rtrancl__subset, fact_893_redp__redsp_OFAssRed1, fact_1065_val_Osimps_I21_J, fact_459_map__add__upd__left, fact_1090_eval__cases_I11_J, fact_1197_WTrt_H__WTrts_H_Ointros_I15_J, fact_1081_bop_Osimps_I2_J, fact_830_le__fun__def, fact_64_Pair__inject, fact_1031_red__reds_ORedFAccNull, fact_792_option_Oexhaust, fact_67_Pair__inject, fact_1062_WTrt__elim__cases_I6_J, fact_487_curryE, fact_9_map__upd__Some__unfold, fact_861_UnE, fact_1059_ty_Osimps_I8_J, fact_834_rtranclE, fact_1070_val_Osimps_I12_J, gsy_c_Expr_Obop_OAdd, fact_1172_WTrts__hext__mono, fact_1032_val_Osimps_I5_J, fact_889_eval__finalId, fact_1146_extend__evals, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc___084, fact_809_pred__subset__eq2, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__011, fact_44_prod__cases4, fact_145_split__paired__All, fact_1019_WTrt_H__WTrts_H_Ointros_I3_J, fact_94_Pair__inject, fact_48_prod__cases4, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__070, fact_1170_reds__preserves__sconf, fact_669_subsetD, fact_554_lconf__def, fact_735_subsetI, fact_300_prod_Oexhaust, fact_618_not__Some__eq, fact_265_prod__induct3, fact_1098_CondT, fact_850_big__by__small, fact_196_fun__upd__other, fact_1002_CastFail, fact_415_splitI, fact_1080_bop_Oexhaust, fact_189_fun__upd__def, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_, fact_635_empty__upd__none, help_fconj_3_1_U, fact_177_split__paired__All, fact_622_not__None__eq, fact_870_UnCI, fact_102_Pair__eq, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_077, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc_, fact_1033_val_Osimps_I4_J, fact_140_Pair__eq, gsy_c_WellTypeRT_OWTrt, fact_366_curryI, fact_963_redp__redsp_OBinOpThrow2, fact_1096_red__reds_OCondRed, fact_609_option_Osimps_I3_J, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O_010, fact_666_r__into__rtrancl, fact_1042_ThrowNull, fact_739_subsetI, fact_799_rtrancl__induct, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__, fact_470_map__add__find__right, help_COMBB_1_1_COMBB_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_050, fact_374_lconf__upd, fact_899_FAssReds2, fact_496_curryE, fact_15_map__upd__eqD1, help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It_055, fact_1123_eval__cases_I10_J, fact_103_Pair__eq, fact_759_converse__rtrancl__induct2, help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Value__Oval_J_000tc__fun_Itc__prod_, fact_287_pred__equals__eq2, fact_827_order__eq__iff, fact_654_Red__lcl__add, fact_17_map__upd__eqD1, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O, fact_927_eval__evals_OFAssThrow2, fact_490_curryE, fact_1134_red__reds_ORedCallNull, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__067, fact_79_Pair__inject, fact_1034_val_Osimps_I16_J, fact_755_converse__rtranclE2, fact_56_Pair__inject, fact_113_Pair__eq, fact_1154_fv__fvs_Osimps_I9_J, fact_519_internal__split__def, fact_302_prod_Oexhaust, fact_702_set__rev__mp, fact_970_TryThrow, fact_848_eval__notfree__unchanged, fact_818_xt1_I5_J, fact_46_prod__cases4, fact_95_Pair__inject, fact_80_Pair__inject, fact_912_redp__redsp_OThrowRed, fact_1068_val_Osimps_I6_J, fact_643_redp__redsp_ORedBlock, fact_984_fv__fvs_Osimps_I2_J, fact_1142_CallRedsThrowObj, fact_995_red__reds_ORedCast, fact_179_split__paired__All, fact_1110_ty_Osimps_I20_J, help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod, fact_115_Pair__eq, help_COMBB_1_1_COMBB_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_044, fact_75_Pair__inject, fact_295_pred__equals__eq2, help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It, gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List, fact_563_WTrt__hext__mono, fact_488_curryE, fact_135_Pair__eq, fact_1027_WTrt_H__WTrts_H_Ointros_I22_J, fact_993_preallocated__hext, fact_283_pred__equals__eq2, fact_86_Pair__inject, fact_788_rtrancl__induct2, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc, fact_457_red__reds_ORedSeq, fact_50_prod__cases4, fact_506_curryD, gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__fun_It, fact_738_subsetI, fact_918_eval__evals_OSeqThrow, fact_961_red__reds_OBinOpRed1, fact_231_prod__cases3, fact_36_prod__induct4, fact_273_pred__equals__eq2, fact_111_Pair__eq, fact_741_converse__rtranclE2, fact_803_pred__subset__eq2, fact_477_mem__def, fact_1060_ty_Oinject, fact_0_InitBlockRed_I3_J, fact_323_PairE, fact_118_Pair__eq, fact_639_map__upd__nonempty, fact_2_fun__upd__triv, fact_164_split__paired__All, fact_1111_ty_Osimps_I21_J, fact_1053_redp__redsp_ORedTryCatch, fact_489_curryE, fact_205_fun__upd__apply, fact_269_prod__induct3, fact_968_red__reds_ORedTry, gsy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mt, fact_1151_red__reds_OCallParams, fact_1130_redp__redsp_ORedNewFail, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_006, fact_655_WTrt__elim__cases_I1_J, fact_775_rtrancl__induct2, fact_272_pred__equals__eq2, fact_1171_WTrtCons, fact_570_exp_Osimps_I196_J, fact_284_pred__equals__eq2, fact_96_Pair__inject, gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__List__Olist_Itc_, fact_326_PairE, fact_219_widen__refl, fact_343_split__paired__Ex, fact_1136_CallObjThrow, help_COMBC_1_1_COMBC_000tc__Value__Oval_000tc__fun_Itc__prod_Itc__Value__Oval_Mt, fact_461_map__add__upd__left, fact_5_fun__upd__triv, fact_92_Pair__inject, fact_312_prod_Oexhaust, fact_1191_WTrtCall, fact_197_fun__upd__other, fact_85_Pair__inject, fact_199_fun__upd__twist, fact_107_Pair__eq, fact_282_pred__equals__eq2, fact_171_split__paired__All, help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_073, fact_913_fv__fvs_Osimps_I14_J, fact_1161_ListReds2, help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Oli, fact_427_split__weak__cong, fact_35_prod__induct4, fact_1006_binop_Osimps_I7_J, fact_449_splitD, fact_1127_new__Addr__SomeD, fact_226_prod__cases3, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mt, fact_13_map__upd__triv, fact_503_curryD, help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc_, fact_958_Try, fact_417_splitI, fact_157_split__paired__All, fact_630_redp__redsp_OBlockRedNone, fact_786_rtrancl__induct2, fact_161_split__paired__All, fact_578_exp_Osimps_I85_J, fact_301_prod_Oexhaust, fact_938_LAssRedsThrow, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc_, fact_38_prod__induct4, fact_1104_red__reds_ORedCondT, fact_318_PairE, help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__prod_Itc__, fact_462_red__reds_ORedBlock, fact_1114_WTrtFAccNT, help_fTrue_1_1_T, fact_530_splitE, fact_583_exp_Osimps_I145_J, gsy_c_hAPP_000tc__fun_Itc__Value__Oval_Mtc__fun_Itc__Value__Oval_Mtc__HOL__Obool, fact_194_fun__upd__idem, fact_824_ord__eq__le__trans, fact_665_r__into__rtrancl, fact_947_val_Osimps_I11_J, help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_, fact_1046_redp__redsp_ORedFAssNull, fact_250_prod__induct3, fact_999_CastRedsFail, help_fequal_2_1_fequal_000tc__Value__Oval_T, help_fequal_1_1_fequal_000tc__Value__Oval_T, fact_508_curryD, fact_262_prod__induct3, fact_980_preallocated__upd__obj, help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_060, fact_1020_WTrt_H__WTrts_H_Ointros_I18_J, fact_619_not__None__eq, fact_244_prod__cases3, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O_009, fact_432_map__add__assoc, fact_898_FAssReds1, fact_967_BinOp1Reds, fact_753_converse__rtranclE2, fact_978_preallocated__new, fact_290_pred__equals__eq2, fact_725_converse__rtrancl__into__rtrancl, fact_1044_FAssNull, fact_1156_eval__evals_OCons, fact_863_UnE, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O, fact_960_fv__fvs_Osimps_I4_J, gsy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__, help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_041, fact_1147_bigs__by__smalls, fact_509_curryD, fact_812_pred__subset__eq2, fact_76_Pair__inject, fact_616_not__Some__eq, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__015, fact_78_Pair__inject, fact_988_red__reds_OCastRed, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List___080, fact_181_split__paired__All, fact_689_the_Osimps, fact_251_prod__induct3, fact_935_redp__redsp_OBlockThrow, fact_155_split__paired__All, fact_1126_WTrt__elim__cases_I10_J, help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List, fact_223_prod__cases3, fact_347_widen__trans, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_081, gsy_c_fFalse, fact_298_pred__equals__eq2, fact_464_domI, fact_324_PairE, fact_875_Un__absorb, fact_975_red__reds_ORedTryFail, fact_1198_blocksRedsFinal, fact_756_converse__rtranclE2, fact_572_exp_Osimps_I3_J, fact_238_prod__cases3, fact_116_Pair__eq, fact_610_option_Osimps_I3_J, fact_97_Pair__inject, fact_297_pred__equals__eq2, help_fTrue_1_1_U, fact_1099_redp__redsp_ORedCondF, fact_969_TryReds, gsy_c_hAPP_000tc__prod_Itc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc_, fact_842_converse__rtrancl__induct, fact_229_prod__cases3, fact_636_map__add__empty, fact_651_hconfD, help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro, fact_330_PairE, fact_814_pred__subset__eq2, fact_1116_is__refT__def, fact_717_hext__new, fact_160_split__paired__All, fact_613_option_Osimps_I3_J, fact_703_set__rev__mp, gsy_c_fTrue, fact_211_fun__upd__upd, fact_51_prod__cases4, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M, gsy_c_hAPP_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__HOL__Obool, fact_1088_WhileTReds, fact_528_splitE, fact_32_prod__induct4, fact_894_redp__redsp_OFAssRed2, fact_1001_redp__redsp_ORedBinOp, help_fNot_2_1_U, fact_1183_CallRedsFinal, gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc__, fact_852_small__by__big, fact_585_exp_Osimps_I197_J, gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_I_003, gsy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc, fact_296_pred__equals__eq2, fact_252_prod__induct3, fact_286_pred__equals__eq2, fact_63_Pair__inject, gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc, fact_1051_finalRefE, fact_644_map__add__SomeD, fact_1163_CallParamsThrow, fact_646_SeqReds, fact_823_xt1_I3_J, gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__, fact_178_split__paired__All, fact_888_eval__final, fact_299_prod_Oexhaust, gsy_c_Conform_Oconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O, help_fNot_1_1_U, fact_841_converse__rtranclE, fact_577_exp_Osimps_I74_J, fact_754_converse__rtranclE2, fact_1035_val_Osimps_I17_J, fact_1079_WhileCondThrow, fact_33_prod__induct4, fact_203_fun__upd__apply, gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__HOL__Obool_J_00, fact_1055_redp__redsp_ORedTryFail, help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_, help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_068, fact_997_final__addrE, fact_906_FAcc, fact_1094_redp__redsp_OCondThrow, fact_785_rtrancl__induct2, fact_1097_CondF, help_fFalse_1_1_T, fact_564_hext__upd__obj, fact_693_equalityD2, fact_210_fun__upd__same, fact_908_redp__redsp_OFAccThrow, fact_6_assms, fact_389_in__lex__prod, fact_673_subsetD, gsy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List_031, help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J__043, fact_54_InitBlockRed_I4_J, fact_1121_WTrt__elim__cases_I8_J, fact_456_lconf__hext, fact_802_pred__subset__eq2, gsy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String___030, fact_304_prod_Oexhaust, fact_748_converse__rtranclE2, fact_1014_binop_Osimps_I10_J, fact_337_split__paired__Ex, fact_638_redp__redsp_ORedSeq, fact_1131_red__reds_ORedNew, fact_165_split__paired__All, fact_254_prod__induct3, fact_335_split__paired__Ex, fact_469_split__conv, fact_884_fv__fvs_Osimps_I11_J, help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_I, fact_1164_red__reds_OCallThrowParams, fact_740_subsetI, fact_1007_binop_Osimps_I3_J, fact_1047_redp__redsp_ORedFAccNull, fact_1052_eval__cases_I12_J, fact_421_splitI, fact_308_prod_Oexhaust, fact_589_WTrtLAss, fact_1182_wf__J__prog__wf__J__mdecl, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__List__Oli, fact_143_split__paired__All, gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__List__Olist_Itc__T, fact_987_WTrtFAcc, fact_648_redp__redsp_OBlockRedSome, fact_313_prod_Oexhaust, fact_678_rtrancl__mono, fact_902_red__reds_ORedFAss, fact_718_rtrancl__idemp, fact_292_pred__equals__eq2, gsy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__, fact_657_InitBlockRedsFinal, fact_431_map__add__dom__app__simps_I2_J, fact_724_converse__rtrancl__into__rtrancl, gsy_c_hAPP_000tc__prod_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Optio, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod__012, fact_534_splitE, fact_274_pred__equals__eq2, fact_831_wf__prog__wwf__prog, fact_1037_redp__redsp_ORedCastNull, fact_176_split__paired__All, gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J__023, fact_706_set__rev__mp, help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_049, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mt, fact_840_converse__rtranclE, gsy_c_hAPP_000tc__fun_Itc__Expr__Obop_Mtc__fun_Itc__prod_Itc__Value__Oval_Mtc__V, fact_873_sup1E, fact_712_set__mp, fact_1112_ty_Osimps_I7_J, fact_277_pred__equals__eq2, fact_836_rtranclE, help_COMBS_1_1_COMBS_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_, fact_921_redp__redsp_OSeqThrow, fact_714_set__mp, fact_668_equalityI, fact_705_set__rev__mp, fact_744_converse__rtranclE2, fact_943_redp__redsp_OInitBlockThrow, fact_71_Pair__inject, fact_965_red__reds_OBinOpRed2, fact_994_Cast, fact_175_split__paired__All, fact_507_curryD, fact_234_prod__cases3, fact_62_Pair__inject, fact_1129_NewFail, fact_1185_red__reds_ORedCall, fact_806_pred__subset__eq2, fact_887_Red__dom__lcl, fact_1199_blocksReds, fact_355_option_Oinject, fact_632_empty__upd__none, fact_454_splitD, fact_985_eval__evals_OCastThrow, fact_268_prod__induct3, fact_694_in__mono, fact_1015_typeof__OutOfMemory, fact_406_prod__caseI, fact_109_Pair__eq, fact_656_InitBlockReds, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J__083, fact_4_fun__upd__triv, fact_900_FAss, fact_890_eval__cases_I8_J, fact_903_FAccRedsVal, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Obop_Mtc__Expr__Obop_J_Mtc__HOL__Oboo, gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List_025, fact_715_subset__trans, help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Oli_082, fact_1022_wt_H__wt, help_COMBC_1_1_COMBC_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O_079, fact_215_fun__upd__idem__iff, fact_1138_redp__redsp_OCallThrowObj, fact_660_rtrancl_Ortrancl__refl, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__, fact_1039_CastRedsNull, fact_733_rtrancl__trans, fact_170_split__paired__All, fact_797_rtrancl__induct, help_COMBC_1_1_COMBC_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Optio_042, fact_315_PairE, fact_565_hext__trans, help_fdisj_1_1_U, fact_26_prod__cases5, fact_1064_binop_Osimps_I9_J, fact_429_map__add__dom__app__simps_I3_J, fact_826_order__eq__refl, fact_88_Pair__inject, fact_1013_binop_Osimps_I6_J, help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_053, fact_1145_extend__1__evals, fact_348_InitBlockRed_I5_J, fact_688_the_Osimps, fact_855_eval__lcl__incr, fact_147_split__paired__All, fact_674_subsetD, fact_303_prod_Oexhaust, help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc_, fact_591_hextI, fact_954_redp__redsp_OTryRed, gsy_c_BigStep_Ofinals_000tc__List__Olist_Itc__String__Ochar_J, fact_142_Pair__eq, gsy_c_List_Olist__all2_000tc__Type__Oty_000tc__Type__Oty, fact_1128_WTrt_H__WTrts_H_Ointros_I1_J, fact_371_curryI, fact_159_split__paired__All, fact_551_splitI2, fact_1168_evals__final, fact_690_subset__refl, fact_128_Pair__eq, fact_864_UnE, gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str, fact_492_curryE, fact_1083_fv__fvs_Osimps_I13_J, fact_334_split__paired__Ex, fact_516_map__add__upd, fact_816_pred__subset__eq2, fact_611_option_Osimps_I3_J, fact_734_subsetI, fact_973_BinOpRedsThrow1, fact_202_fun__upd__twist, fact_1150_evals__lcl__incr, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olis, fact_1179_redp__redsp_OListRed2, fact_256_prod__induct3, fact_1135_redp__redsp_ORedCallNull, fact_798_rtrancl__induct, fact_701_set__rev__mp, fact_804_pred__subset__eq2, gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String___028, fact_936_FAccReds, fact_945_eval__cases_I9_J, fact_390_in__lex__prod, fact_1165_ListReds1, fact_658_assigned__def, fact_439_conf__widen, fact_314_prod_Oexhaust, fact_757_converse__rtrancl__induct2, fact_169_split__paired__All, fact_209_fun__upd__same, gsy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_, fact_623_not__None__eq, fact_937_red__reds_OFAssThrow2, fact_1071_val_Osimps_I13_J, fact_773_rtrancl__induct2, fact_615_not__Some__eq, fact_481_red__reds_OSeqRed, help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Type__Oty_J_000tc__fun_Itc__prod_It, help_fconj_2_1_U, fact_621_not__None__eq, help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun__051, fact_1178_blocks_Osimps_I1_J, fact_956_redp__redsp_OBinOpRed2, fact_162_split__paired__All, fact_240_prod__cases3, fact_801_pred__subset__eq2, fact_1181_redp__redsp_OCallParams, fact_811_pred__subset__eq2, fact_1186_redp__redsp_ORedCall, fact_375_lconf__upd2, gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_I_004, fact_971_red__reds_OBinOpThrow2, help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_072, fact_401_prod__caseI, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__, fact_1086_WhileF, fact_1009_WTrtVal, fact_47_prod__cases4, fact_124_Pair__eq, fact_710_set__mp, fact_972_BinOp2Reds, help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_069, fact_720_rtrancl__idemp, gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_, fact_675_subsetD, fact_1023_wt_H__iff__wt, fact_1010_hext__typeof__mono, help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_, fact_156_split__paired__All, fact_535_splitE, fact_721_hconf__new, fact_794_option_Oexhaust, fact_641_map__upd__nonempty, gsy_c_List_Odistinct_000tc__List__Olist_Itc__String__Ochar_J, fact_769_converse__rtrancl__induct2, fact_117_Pair__eq, fact_89_Pair__inject, fact_138_Pair__eq, gsy_c_Objects_Ohext, fact_1069_val_Osimps_I7_J, fact_346_split__paired__Ex, help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String___052, fact_289_pred__equals__eq2, fact_25_prod__cases5, fact_592_redp__redsp_ORedLAss, fact_364_curryI, fact_989_red__reds_OCastThrow, fact_513_curryD, fact_270_red__preserves__sconf, fact_378_in__lex__prod, fact_87_Pair__inject, fact_336_split__paired__Ex, fact_911_redp__redsp_OThrowThrow, fact_568__092_060D_062___092_060D_062s_Osimps_I6_J, fact_129_Pair__eq, fact_1100_redp__redsp_ORedCondT, fact_307_prod_Oexhaust, fact_924_red__reds_OThrowThrow, fact_1107_redp__redsp_ORedWhile, fact_264_prod__induct3, fact_1089_WhileTRedsThrow, fact_150_split__paired__All, fact_425_map__add__dom__app__simps_I1_J, fact_514_map__add__upd, fact_1149_reds__hext__incr, fact_941_FAssRedsThrow2, fact_69_Pair__inject, fact_139_Pair__eq, fact_224_prod__cases3, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J__018, fact_691_set__eq__subset, fact_57_Pair__inject, fact_695_in__mono, fact_1105_red__reds_ORedCondF, fact_106_Pair__eq, fact_587_redp__redsp_OInitBlockRed, fact_709_set__mp, gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__Ol, gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__St, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String_, fact_1174_WTrts__Val, fact_1000_BinOp, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_, fact_966_red__reds_OBinOpThrow1, fact_1082_bop_Osimps_I1_J, fact_872_UnCI, fact_838_converse__rtranclE, fact_624_redp__redsp_OLAssRed, fact_319_PairE, fact_58_Pair__inject, fact_731_rtrancl__trans, fact_233_prod__cases3, fact_580_exp_Osimps_I82_J, fact_940_FAssRedsThrow1, fact_280_pred__equals__eq2, fact_986_redp__redsp_OCastThrow, fact_793_option_Oexhaust, fact_722_converse__rtrancl__into__rtrancl, fact_504_curryD, fact_944_eval__cases_I4_J, fact_1103_CondRedsThrow, fact_845_converse__rtrancl__induct, fact_1085_WhileBodyThrow, fact_671_subsetD, fact_1067_val_Osimps_I1_J, fact_1076_preallocated__def, fact_1004_red__reds_ORedBinOp, fact_772_converse__rtrancl__induct2, fact_55_Pair__inject, fact_253_prod__induct3, fact_65_Pair__inject, fact_341_split__paired__Ex, fact_228_prod__cases3, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc_016, fact_180_split__paired__All, fact_1113_ty_Osimps_I6_J, fact_586_hconf__upd__obj, fact_1074_preallocatedE, fact_576_exp_Osimps_I84_J, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_064, help_COMBB_1_1_COMBB_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_046, fact_248_prod__induct3, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod__013, fact_815_pred__subset__eq2, fact_1148_evals__hext, fact_949_TryCatchRedsFinal, fact_472_mem__def, fact_844_converse__rtrancl__induct, gsy_c_hAPP_000tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_, fact_787_rtrancl__induct2, fact_819_order__trans, fact_552_splitI2, fact_134_Pair__eq, fact_562_splitE2, fact_356_option_Oinject, fact_391_in__lex__prod, fact_843_converse__rtrancl__induct, fact_166_split__paired__All, fact_996_WTrt__elim__cases_I5_J, gsy_c_hAPP_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt, fact_948_val_Osimps_I3_J, fact_892_FAssRedsVal, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc_, fact_729_rtrancl_Ortrancl__into__rtrancl, fact_858_Reds__dom__lcl, fact_770_converse__rtrancl__induct2, fact_895_fv__fvs_Osimps_I8_J, fact_760_converse__rtrancl__induct2, fact_136_Pair__eq, fact_1024_WTrt_H__WTrts_H_Ointros_I21_J, fact_1087_WhileRedsThrow, fact_399_prod__caseI, help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Oli, fact_84_Pair__inject, help_COMBC_1_1_COMBC_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It, fact_992_CastRedsThrow, fact_68_Pair__inject, fact_605_option_Osimps_I2_J, gsy_c_hAPP_000tc__prod_Itc__Expr__Obop_Mtc__Expr__Obop_J_000tc__HOL__Obool, fact_679_rtrancl__subset, fact_14_map__upd__triv, fact_249_prod__induct3, fact_1188_blocksFinal, fact_1057_WTrtCast, help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O, fact_807_pred__subset__eq2, fact_683_rtrancl__subset__rtrancl, fact_566_hext__objD, fact_607_option_Osimps_I2_J, fact_512_curryD, fact_868_UnCI, fact_771_converse__rtrancl__induct2, fact_212_fun__upd__upd, fact_182_split__paired__All, fact_764_converse__rtrancl__induct2, gsy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_M, fact_736_subsetI, fact_909_eval__evals_OFAccThrow, fact_1166_ListRedsVal, fact_49_prod__cases4, fact_758_converse__rtrancl__induct2, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__, fact_247_prod__induct3, gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_M_001, fact_1169_eval__finalsId, fact_594_lconf__empty, help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__List__Olis, fact_983_redp__redsp_OCastRed, fact_1140_red__reds_OCallThrowObj, fact_682_rtrancl__subset__rtrancl, fact_925_red__reds_OThrowRed, fact_491_curryE, fact_915_fv__fvs_Osimps_I7_J, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_078, fact_891_eval__restrict__lcl, fact_730_rtrancl__trans, fact_871_UnCI, fact_241_prod__cases3, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc_, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc_, fact_220_red__preserves__hconf, fact_1141_CallRedsObj, gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_M, fact_763_converse__rtrancl__induct2, gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Type__Oty_J_00, fact_625_redp__redsp_OSeqRed, fact_1153_CallRedsThrowParams, fact_1061_WTrt_H__WTrts_H_Ointros_I2_J, gsy_c_hAPP_000tc__Type__Oty_000tc__HOL__Obool, fact_774_rtrancl__induct2, fact_131_Pair__eq, fact_854_Block, fact_747_converse__rtranclE2, fact_847_big__iff__small, fact_791_option_Oexhaust, fact_931_ThrowRedsThrow, gsy_c_Progress_OWTrts_H, fact_964_red__reds_OTryRed, fact_839_converse__rtranclE, fact_198_fun__upd__other, fact_1192_WTrt_H__WTrts_H_Ointros_I12_J, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mt_040, fact_376_in__lex__prod, fact_833_Red__fv, fact_885_eval__cases_I2_J, fact_158_split__paired__All, fact_645_map__add__Some__iff, fact_942_red__reds_OBlockThrow, fact_21_prod__induct5, fact_629_domIff, fact_81_Pair__inject, help_fdisj_2_1_U, fact_1160_list__eval__Throw, gsy_c_BigStep_Ofinal_000tc__List__Olist_Itc__String__Ochar_J, fact_743_converse__rtranclE2, fact_659_rtrancl_Ortrancl__refl, fact_790_option_Oexhaust, fact_77_Pair__inject, help_COMBC_1_1_COMBC_000tc__Value__Oval_000tc__fun_Itc__prod_Itc__Value__Oval_Mt_034, fact_405_prod__caseI, fact_1091_red__reds_ORedWhile, fact_575_exp_Osimps_I10_J, fact_83_Pair__inject, fact_221_red__preserves__lconf, fact_101_Pair__eq, fact_370_curryI, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc__HOL__Ob, fact_598_pred__subset__eq, fact_1012_typeof__h_Osimps_I1_J, fact_112_Pair__eq, fact_206_fun__upd__apply, fact_550_splitI2, fact_835_rtranclE, fact_732_rtrancl__trans, fact_1157_ConsThrow, gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__O, fact_1167_evals__cases_I2_J, fact_133_Pair__eq, fact_959_redp__redsp_ORedTry, fact_1093_eval__evals_OCondThrow, fact_1196_WTrt_H__WTrts_H_Ointros_I13_J, fact_1143_CallRedsNull, help_COMBC_1_1_COMBC_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Optio, fact_471_mem__def, fact_800_pred__subset__eq2, fact_810_pred__subset__eq2, help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It, fact_45_prod__cases4, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__, fact_227_prod__cases3, fact_946_val_Osimps_I10_J, fact_305_prod_Oexhaust, fact_982_WTrtTry, fact_1045_FAccNull, fact_857_Seq, fact_320_PairE, fact_345_split__paired__Ex, gsy_c_hAPP_000tc__prod_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_, fact_281_pred__equals__eq2, fact_480_red__reds_OLAssRed, fact_1115_WTrt_H__WTrts_H_Ointros_I9_J, fact_825_order__antisym__conv, fact_573_exp_Osimps_I11_J, fact_822_ord__le__eq__trans, fact_438_red__reds_ORedInitBlock, gsy_c_Expr_Obop_OEq, fact_700_in__mono, fact_167_split__paired__All, fact_905_redp__redsp_ORedFAcc, fact_377_in__lex__prod, fact_31_prod__induct4, fact_856_eval__hext, fact_520_WTrtBlock, fact_597_pred__subset__eq, fact_108_Pair__eq, fact_259_prod__induct3, fact_141_Pair__eq, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mt, fact_146_split__paired__All, fact_1133_New, fact_351_red__preserves__defass, fact_962_eval__evals_OBinOpThrow2, fact_1018_WTrt_H__WTrts_H_Ointros_I16_J, fact_338_split__paired__Ex, fact_837_rtranclE, fact_325_PairE, fact_216_fun__upd__idem__iff, gsy_c_hAPP_000tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc_, fact_163_split__paired__All, fact_932_red__reds_OLAssThrow, fact_1029_FAccRedsNull, fact_953_redp__redsp_OBinOpRed1, fact_10_map__upd__Some__unfold, fact_579_exp_Osimps_I75_J, help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__, fact_1028_WTrt_H__WTrts_H_Ointros_I10_J, fact_90_Pair__inject, fact_910_eval__evals_OThrowThrow, fact_603_pred__subset__eq, fact_727_rtrancl_Ortrancl__into__rtrancl, fact_692_equalityD1, fact_130_Pair__eq, fact_684_rtrancl__subset__rtrancl, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__O, gsy_c_hAPP_000tc__Value__Oval_000tc__HOL__Obool, fact_631_map__add__None, fact_453_splitD, fact_1102_CondReds, fact_1173_WTrtCallNT, fact_191_fun__upd__idem, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__071, fact_713_set__mp, fact_22_prod__induct5, fact_515_map__add__upd, fact_98_Pair__inject, fact_952_TryRedsFail, fact_497_curryE, fact_950_WTrtThrow, fact_817_xt1_I6_J, fact_569_exp_Osimps_I143_J, fact_567_hext__def, fact_813_pred__subset__eq2, fact_546_splitI2, gsy_c_DefAss_O_092_060D_062_000tc__List__Olist_Itc__String__Ochar_J, fact_571_exp_Osimps_I142_J, fact_955_eval__evals_OBinOpThrow1, fact_407_prod__caseI, fact_342_split__paired__Ex, fact_362_curryI, fact_1063_sys__xcpts__cases, fact_1175_reds__preserves__hconf, fact_1158_red__reds_OListRed2, fact_1118_WTrt_H__WTrts_H_Ointros_I11_J, fact_12_map__upd__triv, fact_596_predicate1D, fact_59_Pair__inject, fact_368_curryI, fact_232_prod__cases3, fact_1194_wts_H__wts, fact_1021_wt__wt_H, fact_225_prod__cases3, fact_829_le__funD, fact_352_option_Oinject, fact_309_prod_Oexhaust, fact_904_red__reds_ORedFAcc, fact_1054_redp__redsp_ORedCast, fact_708_set__mp, gsy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It_029, help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__057, fact_127_Pair__eq, fact_372_curryI, fact_1187_WTrts__same__length, fact_388_in__lex__prod, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__List__O, help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc_, fact_1030_FAssRedsNull, fact_933_red__reds_OSeqThrow, fact_311_prod_Oexhaust, fact_1190_wt__blocks, fact_1120_WTrt__elim__cases_I7_J, fact_423_splitI, fact_495_curryE, help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_058, gsy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Oli, fact_1077_binop_Osimps_I1_J, fact_153_split__paired__All, help_fdisj_3_1_U, fact_173_split__paired__All, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O, fact_37_prod__induct4, fact_119_Pair__eq, help_COMBC_1_1_COMBC_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_, help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List_, help_fconj_1_1_U, fact_606_option_Osimps_I2_J, fact_517_map__add__upd, fact_114_Pair__eq, fact_1066_val_Osimps_I20_J, fact_245_prod__cases3, fact_849_extend__1__eval, fact_680_rtrancl__subset, gsy_c_hAPP_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__HOL_, fact_16_map__upd__eqD1, fact_192_fun__upd__idem, fact_726_rtrancl_Ortrancl__into__rtrancl, fact_213_fun__upd__upd, gsy_c_Type_Ois__refT, fact_821_xt1_I4_J, fact_742_converse__rtranclE2, fact_275_pred__equals__eq2, fact_939_SeqRedsThrow, fact_183_split__paired__All, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_I, fact_998_BinOpRedsVal, help_fequal_1_1_fequal_000tc__Option__Ooption_Itc__Value__Oval_J_T, fact_1095_fv__fvs_Osimps_I12_J, fact_663_BlockRedsFinal, fact_917_FAccRedsThrow, fact_422_splitI, fact_1144_CallNull, fact_3_fun__upd__triv, help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_063, fact_930_ThrowReds, fact_235_prod__cases3, gsy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_M_021, fact_1132_redp__redsp_ORedNew, fact_979_red__reds_ORedTryCatch, fact_556_hext__refl, fact_590_LAssRedsVal, fact_18_map__upd__eqD1, fact_467_prod_Osimps_I2_J, fact_322_PairE, fact_172_split__paired__All, fact_795_order__refl, gsy_c_hAPP_000tc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It, help_COMBC_1_1_COMBC_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_0, fact_1003_red__reds_ORedCastFail, fact_1078_WhileFReds, fact_365_curryI, fact_698_in__mono, fact_677_rtrancl__mono, fact_1108_CondReds2T, fact_662_rtrancl_Ortrancl__refl, fact_20_prod__induct5, fact_43_prod__cases4, fact_1180_redp__redsp_OListRed1, fact_1101_red__reds_OCondThrow, fact_1_InitBlockRed_I1_J, help_COMBB_1_1_COMBB_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc, fact_74_Pair__inject, fact_93_Pair__inject, gsy_c_WellForm_Owf__prog_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Stri, fact_271_pred__equals__eq2, help_fFalse_1_1_U, fact_882_Un__def, gsy_c_Progress_OWTrt_H, fact_276_pred__equals__eq2, fact_536_splitE, help_fequal_2_1_fequal_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__St, fact_239_prod__cases3, help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__061, fact_349_sconf__def, fact_293_pred__equals__eq2, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_038, fact_465_red__reds_OInitBlockRed, fact_647_LAssReds, fact_990_CastReds, fact_719_rtrancl__idemp, help_COMBB_1_1_COMBB_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__fun_, fact_685_the_Osimps, fact_1184_Call, fact_260_prod__induct3, fact_1048_red__reds_ORedThrowNull, fact_344_split__paired__Ex, fact_505_curryD, help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It, fact_339_split__paired__Ex, fact_896_red__reds_OFAssRed1, fact_511_curryD, fact_920_eval__evals_OFAssThrow1, fact_204_fun__upd__apply, help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__, fact_8_map__upd__Some__unfold, fact_257_prod__induct3, fact_832_wf__mdecl__wwf__mdecl, fact_934_red__reds_OFAssThrow1, fact_916_red__reds_OFAccThrow, fact_208_fun__upd__same, fact_99_Pair__eq, fact_640_map__upd__nonempty, fact_796_rtrancl__induct, fact_588_red__reds_OBlockRedSome, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__014, fact_914_redp__redsp_OFAccRed, fact_151_split__paired__All, fact_193_fun__upd__idem, help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__076, help_fequal_2_1_fequal_000tc__Option__Ooption_Itc__Value__Oval_J_T, fact_923_redp__redsp_OFAssThrow1, fact_1139_red__reds_OCallObj, gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_It, fact_897_red__reds_OFAssRed2, fact_373_red__lcl__add, fact_317_PairE, fact_230_prod__cases3, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc___085, fact_327_PairE, fact_919_eval__evals_OLAssThrow, fact_310_prod_Oexhaust, fact_73_Pair__inject, fact_455_splitD, fact_288_pred__equals__eq2, fact_340_split__paired__Ex, fact_853_LAss, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mt_054, fact_316_PairE, fact_574_exp_Osimps_I6_J, fact_1073_binop_Osimps_I5_J, fact_789_progress, fact_664_oconf__fupd, fact_676_rtrancl__mono, fact_122_Pair__eq, fact_91_Pair__inject, fact_1040_binop_Osimps_I8_J, help_COMBC_1_1_COMBC_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_0_062, gsy_c_hAPP_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__Value__Ov, fact_981_CastRedsAddr, fact_200_fun__upd__twist, fact_883_Un__commute, gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption_002, help_COMBC_1_1_COMBC_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_059, fact_637_empty__map__add, gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Value__Oval_J_Mtc__fun_Itc__Expr__Oe, gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J__024, fact_1058_ty_Osimps_I9_J, fact_201_fun__upd__twist, gsy_c_hAPP_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__String__Ochar_, fact_363_curryI, fact_195_fun__upd__other, help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String___056, fact_928_red__reds_OFAccRed, fact_1036_CastNull, fact_1056_redp__redsp_ORedCastFail, gsy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc, fact_1152_CallRedsParams, fact_329_PairE, fact_1122_refTE, fact_447_splitD, fact_1008_typeof__ClassCast, fact_620_not__None__eq, fact_126_Pair__eq, fact_7_map__upd__Some__unfold, fact_1195_wts__wts_H, fact_865_UnE, fact_1050_red__reds_ORedFAssNull, fact_1177_redsp__reds__eq, help_COMBB_1_1_COMBB_000tc__fun_Itc__Value__Oval_Mtc__fun_Itc__fun_Itc__prod_Itc, fact_383_in__lex__prod, fact_805_pred__subset__eq2, fact_728_rtrancl_Ortrancl__into__rtrancl, fact_1125_WTrtNew, fact_1124_red__reds_ORedNewFail, fact_379_in__lex__prod, fact_1016_typeof__NullPointer, fact_1041_binop_Osimps_I4_J, fact_475_mem__def, fact_951_BinOpRedsThrow2, fact_70_Pair__inject, fact_1106_unfold__while, fact_1075_preallocatedD, fact_558_cond__split__eta, fact_1117_WTrtFAssNT, fact_27_prod__cases5, fact_976_TryCatch, fact_132_Pair__eq, help_fequal_1_1_fequal_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__St, fact_991_WTrtFAss, fact_649_SeqReds2, fact_907_red__reds_OInitBlockThrow, fact_696_in__mono, fact_874_sup1CI, fact_168_split__paired__All, fact_926_Throw, fact_1092_redp__redsp_OCondRed, fact_553_WTrtSeq, fact_1043_redp__redsp_ORedThrowNull, fact_922_redp__redsp_OLAssThrow, fact_886_Val, fact_1176_reds__preserves__lconf, fact_125_Pair__eq, gsy_c_Exceptions_Opreallocated, gsy_c_SmallStep_Oassigned, fact_100_Pair__eq, fact_608_option_Osimps_I2_J, fact_1109_CondReds2F, fact_1162_red__reds_OListRed1, gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Type__Oty_J_Mtc__fun_Itc__prod_Itc__, fact_1084_WhileT, fact_846_le__funI, gsy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__HOL__Obool, fact_581_exp_Osimps_I83_J, help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__St, fact_779_rtrancl__induct2, fact_1155_fv__fvs_Osimps_I17_J, fact_187_fun__upd__def, fact_1025_WTrt_H__WTrts_H_Ointros_I8_J, fact_174_split__paired__All, fact_555_red__reds_ORedLAss, fact_593_red__lcl__incr, fact_828_le__funE, fact_614_not__Some__eq, gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_I, help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_036, fact_217_fun__upd__idem__iff, fact_34_prod__induct4, fact_667_r__into__rtrancl, fact_820_order__antisym, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__O, fact_121_Pair__eq, help_COMBC_1_1_COMBC_000tc__Expr__Obop_000tc__fun_Itc__prod_Itc__Expr__Obop_Mtc_, help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc, help_COMBC_1_1_COMBC_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__fun_, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__, fact_544_splitI2, gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool, fact_476_mem__def, fact_582__092_060D_062___092_060D_062s_Osimps_I3_J, fact_493_curryE, fact_595_rev__predicate1D, help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc, fact_263_prod__induct3, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_005, fact_1159_redp__redsp_OCallThrowParams, fact_137_Pair__eq, fact_661_rtrancl_Ortrancl__refl, fact_190_fun__upd__def, fact_354_option_Oinject, fact_473_mem__def, fact_670_subsetD, fact_82_Pair__inject, gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__List__, fact_716_equalityE, fact_1038_red__reds_ORedCastNull, fact_686_the_Osimps, fact_776_rtrancl__induct2, fact_328_PairE, fact_1137_redp__redsp_OCallObj, fact_584_exp_Osimps_I144_J, fact_306_prod_Oexhaust, fact_367_curryI, fact_39_prod__induct4, fact_11_map__upd__triv, fact_901_redp__redsp_ORedFAss, fact_258_prod__induct3, fact_1026_WTrt_H__WTrts_H_Ointros_I17_J, fact_977_WTrt__elim__cases_I4_J, fact_434_split__curry, fact_612_option_Osimps_I3_J, fact_851_extend__eval, fact_560_domD, fact_699_in__mono, fact_236_prod__cases3, fact_687_the_Osimps, fact_650_redp__red__eq, fact_144_split__paired__All, fact_460_map__add__upd__left, fact_723_converse__rtrancl__into__rtrancl, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__List__O, gsy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List, fact_652_redp__redsp_ORedInitBlock, fact_72_Pair__inject, fact_188_fun__upd__def, fact_19_InitBlockRed_I2_J, fact_207_fun__upd__same, fact_1119_typeof__h_Osimps_I2_J, fact_479_split__eta, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olis_007
% 32.87/10.98  % No. of inferences in proof: 2514
% 32.87/10.98  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 10453 ms resp. 9796 ms w/o parsing
% 34.71/11.54  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 34.86/11.56  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------