Leo-III---1.8.0.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SWW478+1 : TPTP v9.3.1. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 09:10:26 AM UTC 2026

% Result   : Theorem 14.11s 4.82s
% Output   : Refutation 14.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  213
% Syntax   : Number of formulae    :  428 ( 186 unt;   0 typ;   0 def)
%            Number of atoms       :  943 ( 400 equ;   0 cnn)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives : 6774 ( 162   ~;  14   |; 103   &;6097   @)
%                                         (  48 <=>; 350  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   28 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  200 ( 198 usr;  63 con; 0-5 aty)
%            Number of variables   : 1586 (   0   ^;1557   !;  29   ?;1586   :)

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

thf(member773094996on_val_decl,type,
    member773094996on_val: $i > $i > $i ).

thf(hAPP_P1886180715on_val_decl,type,
    hAPP_P1886180715on_val: $i > $i > $i ).

thf(hAPP_P1870962205on_val_decl,type,
    hAPP_P1870962205on_val: $i > $i > $i ).

thf(produc1441475159on_val_decl,type,
    produc1441475159on_val: $i ).

thf(hAPP_P604205461on_val_decl,type,
    hAPP_P604205461on_val: $i > $i > $i ).

thf(hAPP_e1659493427on_val_decl,type,
    hAPP_e1659493427on_val: $i > $i > $i ).

thf(produc1259058957on_val_decl,type,
    produc1259058957on_val: $i ).

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

thf(hAPP_f1727192346on_val_decl,type,
    hAPP_f1727192346on_val: $i > $i > $i ).

thf(hAPP_f1849790461on_val_decl,type,
    hAPP_f1849790461on_val: $i > $i > $i ).

thf(produc899768717on_val_decl,type,
    produc899768717on_val: $i ).

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

thf(fun_up1149430426on_val_decl,type,
    fun_up1149430426on_val: $i > $i > $i > $i ).

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

thf(v_1_decl,type,
    v_1: $i ).

thf(some_val_decl,type,
    some_val: $i > $i ).

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

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

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

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

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

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

thf(hAPP_l512744617ion_ty_decl,type,
    hAPP_l512744617ion_ty: $i > $i > $i ).

thf(cOMBK_1294242658t_char_decl,type,
    cOMBK_1294242658t_char: $i > $i ).

thf(fun_up424764369ion_ty_decl,type,
    fun_up424764369ion_ty: $i > $i > $i > $i ).

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

thf(hAPP_f1175813647l_bool_decl,type,
    hAPP_f1175813647l_bool: $i > $i > $i ).

thf(hAPP_f850751421l_bool_decl,type,
    hAPP_f850751421l_bool: $i > $i > $i ).

thf(hAPP_f399538905l_bool_decl,type,
    hAPP_f399538905l_bool: $i > $i > $i ).

thf(cOMBB_1466889536on_val_decl,type,
    cOMBB_1466889536on_val: $i ).

thf(hAPP_f318082871l_bool_decl,type,
    hAPP_f318082871l_bool: $i > $i > $i ).

thf(hAPP_f1840640125on_val_decl,type,
    hAPP_f1840640125on_val: $i > $i > $i ).

thf(produc1988544340l_bool_decl,type,
    produc1988544340l_bool: $i ).

thf(produc1911463199l_bool_decl,type,
    produc1911463199l_bool: $i ).

thf(hAPP_P159683425l_bool_decl,type,
    hAPP_P159683425l_bool: $i > $i > $i ).

thf(hAPP_f2134824737l_bool_decl,type,
    hAPP_f2134824737l_bool: $i > $i > $i ).

thf(hAPP_f1308714617l_bool_decl,type,
    hAPP_f1308714617l_bool: $i > $i > $i ).

thf(cOMBB_338347573on_val_decl,type,
    cOMBB_338347573on_val: $i ).

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

thf(hAPP_e1833980889l_bool_decl,type,
    hAPP_e1833980889l_bool: $i > $i > $i ).

thf(hAPP_f546724245l_bool_decl,type,
    hAPP_f546724245l_bool: $i > $i > $i ).

thf(hAPP_f917296015l_bool_decl,type,
    hAPP_f917296015l_bool: $i > $i > $i ).

thf(cOMBB_740252943t_char_decl,type,
    cOMBB_740252943t_char: $i ).

thf(hAPP_P1708370145l_bool_decl,type,
    hAPP_P1708370145l_bool: $i > $i > $i ).

thf(hAPP_f926562337l_bool_decl,type,
    hAPP_f926562337l_bool: $i > $i > $i ).

thf(hAPP_f1560238713l_bool_decl,type,
    hAPP_f1560238713l_bool: $i > $i > $i ).

thf(cOMBB_672625589on_val_decl,type,
    cOMBB_672625589on_val: $i ).

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

thf(val_list_char_decl,type,
    val_list_char: $i > $i ).

thf(hAPP_f1033709212l_bool_decl,type,
    hAPP_f1033709212l_bool: $i > $i > $i ).

thf(hAPP_f1233687287l_bool_decl,type,
    hAPP_f1233687287l_bool: $i > $i > $i ).

thf(cOMBB_171276332on_val_decl,type,
    cOMBB_171276332on_val: $i ).

thf(hAPP_f1926378906on_val_decl,type,
    hAPP_f1926378906on_val: $i > $i > $i ).

thf(hAPP_f927043595l_bool_decl,type,
    hAPP_f927043595l_bool: $i > $i > $i ).

thf(hAPP_f1043869573l_bool_decl,type,
    hAPP_f1043869573l_bool: $i > $i > $i ).

thf(cOMBB_1259202826on_val_decl,type,
    cOMBB_1259202826on_val: $i ).

thf(hAPP_f524589473l_bool_decl,type,
    hAPP_f524589473l_bool: $i > $i > $i ).

thf(hAPP_f600512025on_val_decl,type,
    hAPP_f600512025on_val: $i > $i > $i ).

thf(some_ty_decl,type,
    some_ty: $i > $i ).

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

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

thf(hAPP_P1116729363l_bool_decl,type,
    hAPP_P1116729363l_bool: $i > $i > $i ).

thf(hAPP_f1241216909l_bool_decl,type,
    hAPP_f1241216909l_bool: $i > $i > $i ).

thf(hAPP_f1438732387l_bool_decl,type,
    hAPP_f1438732387l_bool: $i > $i > $i ).

thf(cOMBB_635947099on_val_decl,type,
    cOMBB_635947099on_val: $i ).

thf(hAPP_f1712766199l_bool_decl,type,
    hAPP_f1712766199l_bool: $i > $i > $i ).

thf(hAPP_P2083594489on_val_decl,type,
    hAPP_P2083594489on_val: $i > $i > $i ).

thf(hAPP_f603925568l_bool_decl,type,
    hAPP_f603925568l_bool: $i > $i > $i ).

thf(hAPP_f181262431l_bool_decl,type,
    hAPP_f181262431l_bool: $i > $i > $i ).

thf(cOMBC_832625297y_bool_decl,type,
    cOMBC_832625297y_bool: $i ).

thf(hAPP_f1001225811y_bool_decl,type,
    hAPP_f1001225811y_bool: $i > $i > $i ).

thf(hAPP_f2060496320y_bool_decl,type,
    hAPP_f2060496320y_bool: $i > $i > $i ).

thf(produc399384568l_bool_decl,type,
    produc399384568l_bool: $i ).

thf(produc1815960045l_bool_decl,type,
    produc1815960045l_bool: $i ).

thf(hAPP_f641257349l_bool_decl,type,
    hAPP_f641257349l_bool: $i > $i > $i ).

thf(hAPP_f2032347769l_bool_decl,type,
    hAPP_f2032347769l_bool: $i > $i > $i ).

thf(cOMBB_466903633on_val_decl,type,
    cOMBB_466903633on_val: $i ).

thf(hAPP_f2052660463l_bool_decl,type,
    hAPP_f2052660463l_bool: $i > $i > $i ).

thf(cOMBB_1292453606on_val_decl,type,
    cOMBB_1292453606on_val: $i ).

thf(hAPP_P282169671l_bool_decl,type,
    hAPP_P282169671l_bool: $i > $i > $i ).

thf(hAPP_f602593190on_val_decl,type,
    hAPP_f602593190on_val: $i > $i > $i ).

thf(hAPP_l207779698on_val_decl,type,
    hAPP_l207779698on_val: $i > $i > $i ).

thf(cOMBK_1097134891t_char_decl,type,
    cOMBK_1097134891t_char: $i > $i ).

thf(member763590124on_val_decl,type,
    member763590124on_val: $i > $i > $i ).

thf(hAPP_f555424277l_bool_decl,type,
    hAPP_f555424277l_bool: $i > $i > $i ).

thf(hAPP_f1734879897l_bool_decl,type,
    hAPP_f1734879897l_bool: $i > $i > $i ).

thf(cOMBB_1522540928on_val_decl,type,
    cOMBB_1522540928on_val: $i ).

thf(hAPP_f1074020887l_bool_decl,type,
    hAPP_f1074020887l_bool: $i > $i > $i ).

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

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

thf(wf_pro755087577t_char_decl,type,
    wf_pro755087577t_char: $i > $i > $i ).

thf(produc2128769400l_bool_decl,type,
    produc2128769400l_bool: $i ).

thf(produc1958875245l_bool_decl,type,
    produc1958875245l_bool: $i ).

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

thf(hAPP_f550652027l_bool_decl,type,
    hAPP_f550652027l_bool: $i > $i > $i ).

thf(hAPP_f838396643l_bool_decl,type,
    hAPP_f838396643l_bool: $i > $i > $i ).

thf(cOMBC_2027949654l_bool_decl,type,
    cOMBC_2027949654l_bool: $i ).

thf(hAPP_f1617787571l_bool_decl,type,
    hAPP_f1617787571l_bool: $i > $i > $i ).

thf(hAPP_f61040418l_bool_decl,type,
    hAPP_f61040418l_bool: $i > $i > $i ).

thf(cOMBS_570216337l_bool_decl,type,
    cOMBS_570216337l_bool: $i > $i > $i ).

thf(hAPP_f1492320500l_bool_decl,type,
    hAPP_f1492320500l_bool: $i > $i > $i ).

thf(hAPP_f1523875321l_bool_decl,type,
    hAPP_f1523875321l_bool: $i > $i > $i ).

thf(hAPP_f592397849l_bool_decl,type,
    hAPP_f592397849l_bool: $i > $i > $i ).

thf(cOMBB_1718333400on_val_decl,type,
    cOMBB_1718333400on_val: $i ).

thf(hAPP_f1863694447l_bool_decl,type,
    hAPP_f1863694447l_bool: $i > $i > $i ).

thf(hAPP_f1145256474l_bool_decl,type,
    hAPP_f1145256474l_bool: $i > $i > $i ).

thf(cOMBB_383678192on_val_decl,type,
    cOMBB_383678192on_val: $i ).

thf(hAPP_f1301559543l_bool_decl,type,
    hAPP_f1301559543l_bool: $i > $i > $i ).

thf(hAPP_f1825030711l_bool_decl,type,
    hAPP_f1825030711l_bool: $i > $i > $i ).

thf(cOMBB_877741809on_val_decl,type,
    cOMBB_877741809on_val: $i ).

thf(hAPP_P1776198677on_val_decl,type,
    hAPP_P1776198677on_val: $i > $i > $i ).

thf(hAPP_f881985847l_bool_decl,type,
    hAPP_f881985847l_bool: $i > $i > $i ).

thf(cOMBB_1083177073on_val_decl,type,
    cOMBB_1083177073on_val: $i ).

thf(hAPP_P789556885on_val_decl,type,
    hAPP_P789556885on_val: $i > $i > $i ).

thf(hAPP_f1452292669l_bool_decl,type,
    hAPP_f1452292669l_bool: $i > $i > $i ).

thf(hAPP_f1977633121l_bool_decl,type,
    hAPP_f1977633121l_bool: $i > $i > $i ).

thf(cOMBB_1303934920on_val_decl,type,
    cOMBB_1303934920on_val: $i ).

thf(hAPP_b589554111l_bool_decl,type,
    hAPP_b589554111l_bool: $i > $i > $i ).

thf(member840932460on_val_decl,type,
    member840932460on_val: $i > $i > $i ).

thf(hAPP_f857351829l_bool_decl,type,
    hAPP_f857351829l_bool: $i > $i > $i ).

thf(hAPP_f348318673l_bool_decl,type,
    hAPP_f348318673l_bool: $i > $i > $i ).

thf(cOMBB_1518282696on_val_decl,type,
    cOMBB_1518282696on_val: $i ).

thf(hAPP_f1213370163y_bool_decl,type,
    hAPP_f1213370163y_bool: $i > $i > $i ).

thf(widen_2090681816t_char_decl,type,
    widen_2090681816t_char: $i > $i > $i > $i ).

thf(hAPP_f653692369l_bool_decl,type,
    hAPP_f653692369l_bool: $i > $i > $i ).

thf(hAPP_f516738477l_bool_decl,type,
    hAPP_f516738477l_bool: $i > $i > $i ).

thf(cOMBB_819439237t_char_decl,type,
    cOMBB_819439237t_char: $i ).

thf(hAPP_e108155315on_val_decl,type,
    hAPP_e108155315on_val: $i > $i > $i ).

thf(e_decl,type,
    e: $i ).

thf(t_1_decl,type,
    t_1: $i ).

thf(t_decl,type,
    t: $i ).

thf(hAPP_f1363667773l_bool_decl,type,
    hAPP_f1363667773l_bool: $i > $i > $i ).

thf(hAPP_f1050935001l_bool_decl,type,
    hAPP_f1050935001l_bool: $i > $i > $i ).

thf(cOMBB_1153617344on_val_decl,type,
    cOMBB_1153617344on_val: $i ).

thf(hAPP_f1008932791l_bool_decl,type,
    hAPP_f1008932791l_bool: $i > $i > $i ).

thf(hAPP_f635218277l_bool_decl,type,
    hAPP_f635218277l_bool: $i > $i > $i ).

thf(typeSa1234865140_sconf_decl,type,
    typeSa1234865140_sconf: $i > $i > $i ).

thf(hAPP_f1930574389l_bool_decl,type,
    hAPP_f1930574389l_bool: $i > $i > $i ).

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

thf(hAPP_P1988153107l_bool_decl,type,
    hAPP_P1988153107l_bool: $i > $i > $i ).

thf(hAPP_e500528395l_bool_decl,type,
    hAPP_e500528395l_bool: $i > $i > $i ).

thf(hAPP_P595502227l_bool_decl,type,
    hAPP_P595502227l_bool: $i > $i > $i ).

thf(hAPP_f468299289l_bool_decl,type,
    hAPP_f468299289l_bool: $i > $i > $i ).

thf(produc2036005791l_bool_decl,type,
    produc2036005791l_bool: $i ).

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

thf(hAPP_P1953518277l_bool_decl,type,
    hAPP_P1953518277l_bool: $i > $i > $i ).

thf(hAPP_P678729081l_bool_decl,type,
    hAPP_P678729081l_bool: $i > $i > $i ).

thf(hAPP_f1591648613l_bool_decl,type,
    hAPP_f1591648613l_bool: $i > $i > $i ).

thf(produc20018513l_bool_decl,type,
    produc20018513l_bool: $i ).

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

thf(hAPP_P2024243179on_val_decl,type,
    hAPP_P2024243179on_val: $i > $i > $i ).

thf(hAPP_f204556415on_val_decl,type,
    hAPP_f204556415on_val: $i > $i > $i ).

thf(produc1148763895on_val_decl,type,
    produc1148763895on_val: $i ).

thf(hAPP_f2121594859l_bool_decl,type,
    hAPP_f2121594859l_bool: $i > $i > $i ).

thf(hAPP_f1342895119l_bool_decl,type,
    hAPP_f1342895119l_bool: $i > $i > $i ).

thf(hAPP_f639265145l_bool_decl,type,
    hAPP_f639265145l_bool: $i > $i > $i ).

thf(cOMBB_364363975on_val_decl,type,
    cOMBB_364363975on_val: $i ).

thf(hAPP_f365540729l_bool_decl,type,
    hAPP_f365540729l_bool: $i > $i > $i ).

thf(cOMBB_1466662571on_val_decl,type,
    cOMBB_1466662571on_val: $i ).

thf(hAPP_f439412817l_bool_decl,type,
    hAPP_f439412817l_bool: $i > $i > $i ).

thf(hAPP_f1725502637l_bool_decl,type,
    hAPP_f1725502637l_bool: $i > $i > $i ).

thf(cOMBB_1027621637t_char_decl,type,
    cOMBB_1027621637t_char: $i ).

thf(hAPP_f489055607l_bool_decl,type,
    hAPP_f489055607l_bool: $i > $i > $i ).

thf(hconf_97414254t_char_decl,type,
    hconf_97414254t_char: $i > $i ).

thf(hAPP_f2057883639l_bool_decl,type,
    hAPP_f2057883639l_bool: $i > $i > $i ).

thf(cOMBB_1750801836on_val_decl,type,
    cOMBB_1750801836on_val: $i ).

thf(hAPP_f10074679l_bool_decl,type,
    hAPP_f10074679l_bool: $i > $i > $i ).

thf(cOMBB_1759207793on_val_decl,type,
    cOMBB_1759207793on_val: $i ).

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

thf(hAPP_P1134042693l_bool_decl,type,
    hAPP_P1134042693l_bool: $i > $i > $i ).

thf(hAPP_P1826803705l_bool_decl,type,
    hAPP_P1826803705l_bool: $i > $i > $i ).

thf(hAPP_f444383845l_bool_decl,type,
    hAPP_f444383845l_bool: $i > $i > $i ).

thf(produc376702929l_bool_decl,type,
    produc376702929l_bool: $i ).

thf(hAPP_f2011777102l_bool_decl,type,
    hAPP_f2011777102l_bool: $i > $i > $i ).

thf(hAPP_f2144092865l_bool_decl,type,
    hAPP_f2144092865l_bool: $i > $i > $i ).

thf(hAPP_P1638898323l_bool_decl,type,
    hAPP_P1638898323l_bool: $i > $i > $i ).

thf(hAPP_f833559503l_bool_decl,type,
    hAPP_f833559503l_bool: $i > $i > $i ).

thf(produc334393759l_bool_decl,type,
    produc334393759l_bool: $i ).

thf(v_2_decl,type,
    v_2: $i ).

thf(lconf_496643946t_char_decl,type,
    lconf_496643946t_char: $i > $i ).

thf(hAPP_f396019662l_bool_decl,type,
    hAPP_f396019662l_bool: $i > $i > $i ).

thf(hAPP_f2135509569l_bool_decl,type,
    hAPP_f2135509569l_bool: $i > $i > $i ).

thf(hAPP_f1276548047l_bool_decl,type,
    hAPP_f1276548047l_bool: $i > $i > $i ).

thf(produc121041439l_bool_decl,type,
    produc121041439l_bool: $i ).

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

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

thf(hAPP_f204771371l_bool_decl,type,
    hAPP_f204771371l_bool: $i > $i > $i ).

thf(hAPP_f1760682521l_bool_decl,type,
    hAPP_f1760682521l_bool: $i > $i > $i ).

thf(produc1275132703l_bool_decl,type,
    produc1275132703l_bool: $i ).

thf(hAPP_e592495499l_bool_decl,type,
    hAPP_e592495499l_bool: $i > $i > $i ).

thf(hAPP_f1309113673on_val_decl,type,
    hAPP_f1309113673on_val: $i > $i > $i ).

thf(produc901351817on_val_decl,type,
    produc901351817on_val: $i ).

thf(hAPP_P1760219823on_val_decl,type,
    hAPP_P1760219823on_val: $i > $i > $i ).

thf(hAPP_f394183983on_val_decl,type,
    hAPP_f394183983on_val: $i > $i > $i ).

thf(produc1003071703on_val_decl,type,
    produc1003071703on_val: $i ).

thf(hAPP_f1520199827on_val_decl,type,
    hAPP_f1520199827on_val: $i > $i > $i ).

thf(produc1174947465on_val_decl,type,
    produc1174947465on_val: $i ).

thf(39,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ wf_pro755087577t_char ) @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_WellForm_Owf__prog_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Stri) ).

thf(350,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ wf_pro755087577t_char ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(185,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ member773094996on_val ) @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_member_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String_) ).

thf(1036,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ member773094996on_val ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(138,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i,E: $i] :
          ( A
         != ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_prod__cases4) ).

thf(809,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i,E: $i] :
          ( A
         != ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(101,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( I @ red @ ( H @ ( G @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( F @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
     => ( ( B @ ( C @ ( A @ ( D @ ( I @ wTrt ) ) ) ) @ hBOOL )
       => ( ( D @ ( I @ hconf_97414254t_char @ hAPP_f61040418l_bool ) @ hBOOL )
         => ( G @ ( I @ hconf_97414254t_char @ hAPP_f61040418l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_red__preserves__hconf) ).

thf(629,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( I @ red @ ( H @ ( G @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( F @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
     => ( ( B @ ( C @ ( A @ ( D @ ( I @ wTrt ) ) ) ) @ hBOOL )
       => ( ( D @ ( I @ hconf_97414254t_char @ hAPP_f61040418l_bool ) @ hBOOL )
         => ( G @ ( I @ hconf_97414254t_char @ hAPP_f61040418l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(40,axiom,
    produc2128769400l_bool = produc1958875245l_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_internal__split__def) ).

thf(352,plain,
    produc2128769400l_bool = produc1958875245l_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(66,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ seq_list_char ) )
     != ( C @ val_list_char ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_exp_Osimps_I85_J) ).

thf(479,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ seq_list_char ) )
     != ( C @ val_list_char ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(203,axiom,
    ! [A: $i] :
      ( ? [B: $i] : ( B @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL )
    <=> ? [B: $i,C: $i] : ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_split__paired__Ex) ).

thf(1105,plain,
    ! [A: $i] :
      ( ( ? [B: $i,C: $i] : ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL )
       => ? [B: $i] : ( B @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL ) )
      & ( ? [B: $i] : ( B @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL )
       => ? [B: $i,C: $i] : ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(129,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( D != E )
     => ( ( C @ ( E @ ( B @ ( D @ ( A @ fun_up1149430426on_val ) ) @ fun_up1149430426on_val ) ) )
        = ( B @ ( D @ ( C @ ( E @ ( A @ fun_up1149430426on_val ) ) @ fun_up1149430426on_val ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_fun__upd__twist) ).

thf(777,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( D != E )
     => ( ( C @ ( E @ ( B @ ( D @ ( A @ fun_up1149430426on_val ) ) @ fun_up1149430426on_val ) ) )
        = ( B @ ( D @ ( C @ ( E @ ( A @ fun_up1149430426on_val ) ) @ fun_up1149430426on_val ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(84,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
     => ( C @ ( B @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_splitD) ).

thf(555,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
     => ( C @ ( B @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(179,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ hAPP_P1134042693l_bool ) @ hAPP_P595502227l_bool ) @ ( A @ member763590124on_val ) @ hBOOL )
     => ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( B @ ( produc376702929l_bool @ hAPP_f444383845l_bool ) @ hAPP_P1826803705l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_mem__splitI) ).

thf(1005,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ hAPP_P1134042693l_bool ) @ hAPP_P595502227l_bool ) @ ( A @ member763590124on_val ) @ hBOOL )
     => ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( B @ ( produc376702929l_bool @ hAPP_f444383845l_bool ) @ hAPP_P1826803705l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(9,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( none_ty @ ( A @ ( none_ty @ cOMBK_1294242658t_char @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
      = none_ty ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_empty__upd__none) ).

thf(247,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( none_ty @ ( A @ ( none_ty @ cOMBK_1294242658t_char @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
      = none_ty ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(15,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_740252943t_char @ hAPP_f917296015l_bool ) @ hAPP_f546724245l_bool ) @ hAPP_e1833980889l_bool ) )
      = ( C @ ( B @ hAPP_e1833980889l_bool ) @ ( A @ hAPP_f2134824737l_bool ) ) ),
    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(269,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_740252943t_char @ hAPP_f917296015l_bool ) @ hAPP_f546724245l_bool ) @ hAPP_e1833980889l_bool ) )
      = ( C @ ( B @ hAPP_e1833980889l_bool ) @ ( A @ hAPP_f2134824737l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(187,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( C @ some_val @ ( B @ ( A @ fun_up1149430426on_val ) ) )
        = ( E @ some_val @ ( B @ ( D @ fun_up1149430426on_val ) ) ) )
     => ( C = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_map__upd__eqD1) ).

thf(1041,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( C @ some_val @ ( B @ ( A @ fun_up1149430426on_val ) ) )
        = ( E @ some_val @ ( B @ ( D @ fun_up1149430426on_val ) ) ) )
     => ( C = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(148,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ ( A @ fun_up1149430426on_val ) ) )
        = A )
    <=> ( ( B @ ( A @ hAPP_l207779698on_val ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_fun__upd__idem__iff) ).

thf(861,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( B @ ( A @ hAPP_l207779698on_val ) )
          = C )
       => ( ( C @ ( B @ ( A @ fun_up1149430426on_val ) ) )
          = A ) )
      & ( ( ( C @ ( B @ ( A @ fun_up1149430426on_val ) ) )
          = A )
       => ( ( B @ ( A @ hAPP_l207779698on_val ) )
          = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(157,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( B
            = ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
         => ( D @ ( C @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) )
     => ( B @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_splitI2) ).

thf(913,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( B
            = ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
         => ( D @ ( C @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) )
     => ( B @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(193,axiom,
    ! [A: $i] :
      ( ? [B: $i] : ( B @ ( A @ hAPP_P159683425l_bool ) @ hBOOL )
    <=> ? [B: $i,C: $i] : ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ hAPP_P159683425l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_split__paired__Ex) ).

thf(1063,plain,
    ! [A: $i] :
      ( ( ? [B: $i,C: $i] : ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ hAPP_P159683425l_bool ) @ hBOOL )
       => ? [B: $i] : ( B @ ( A @ hAPP_P159683425l_bool ) @ hBOOL ) )
      & ( ? [B: $i] : ( B @ ( A @ hAPP_P159683425l_bool ) @ hBOOL )
       => ? [B: $i,C: $i] : ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ hAPP_P159683425l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(36,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P282169671l_bool ) @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O) ).

thf(340,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P282169671l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(131,axiom,
    ! [A: $i,B: $i] :
      ( ( v @ some_val @ ( v_1 @ ( la @ fun_up1149430426on_val ) ) @ ( ha @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( B @ ( p @ typeSa1234865140_sconf ) @ hAPP_P159683425l_bool ) @ hBOOL )
     => ( ( A @ ( ea @ ( B @ ( ha @ ( p @ wTrt ) ) ) ) @ hBOOL )
       => ? [C: $i] :
            ( ( A @ ( C @ ( p @ widen_2090681816t_char ) ) @ hBOOL )
            & ( C @ ( e_a @ ( B @ ( h_a @ ( p @ wTrt ) ) ) ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_InitBlockRed_I2_J) ).

thf(782,plain,
    ! [A: $i,B: $i] :
      ( ( v @ some_val @ ( v_1 @ ( la @ fun_up1149430426on_val ) ) @ ( ha @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( B @ ( p @ typeSa1234865140_sconf ) @ hAPP_P159683425l_bool ) @ hBOOL )
     => ( ( A @ ( ea @ ( B @ ( ha @ ( p @ wTrt ) ) ) ) @ hBOOL )
       => ? [C: $i] :
            ( ( A @ ( C @ ( p @ widen_2090681816t_char ) ) @ hBOOL )
            & ( C @ ( e_a @ ( B @ ( h_a @ ( p @ wTrt ) ) ) ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(119,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( B @ ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
        <=> ( A @ ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_pred__equals__eq2) ).

thf(709,plain,
    ! [A: $i,B: $i] :
      ( ( ( B = A )
       => ! [C: $i,D: $i] :
            ( ( ( A @ ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
             => ( B @ ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) )
            & ( ( B @ ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
             => ( A @ ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) ) ) )
      & ( ! [C: $i,D: $i] :
            ( ( ( A @ ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
             => ( B @ ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) )
            & ( ( B @ ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
             => ( A @ ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(52,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B @ ( A @ lAss_list_char ) )
     != ( D @ ( C @ seq_list_char ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_exp_Osimps_I144_J) ).

thf(417,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B @ ( A @ lAss_list_char ) )
     != ( D @ ( C @ seq_list_char ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(21,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( B @ ( A @ seq_list_char ) )
     != ( E @ ( D @ ( C @ block_list_char ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_exp_Osimps_I197_J) ).

thf(288,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( B @ ( A @ seq_list_char ) )
     != ( E @ ( D @ ( C @ block_list_char ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(88,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( F @ red @ ( E @ ( D @ val_list_char @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( E @ ( D @ val_list_char @ ( C @ val_list_char @ ( A @ lAss_list_char ) @ seq_list_char ) @ ( B @ ( A @ block_list_char ) ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_red__reds_ORedInitBlock) ).

thf(565,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( F @ red @ ( E @ ( D @ val_list_char @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( E @ ( D @ val_list_char @ ( C @ val_list_char @ ( A @ lAss_list_char ) @ seq_list_char ) @ ( B @ ( A @ block_list_char ) ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(107,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_1750801836on_val @ hAPP_f2057883639l_bool ) @ hAPP_f1008932791l_bool ) @ hAPP_f1033709212l_bool ) )
      = ( C @ ( B @ hAPP_f1727192346on_val ) @ ( A @ hAPP_P159683425l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It) ).

thf(651,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_1750801836on_val @ hAPP_f2057883639l_bool ) @ hAPP_f1008932791l_bool ) @ hAPP_f1033709212l_bool ) )
      = ( C @ ( B @ hAPP_f1727192346on_val ) @ ( A @ hAPP_P159683425l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(146,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( D @ ( C @ some_val @ ( B @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
        = ( E @ some_val ) )
    <=> ( ( ( ( D @ ( A @ hAPP_l207779698on_val ) )
            = ( E @ some_val ) )
          & ( D != B ) )
        | ( ( C = E )
          & ( D = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_map__upd__Some__unfold) ).

thf(838,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( ( ( ( D @ ( A @ hAPP_l207779698on_val ) )
              = ( E @ some_val ) )
            & ( D != B ) )
          | ( ( C = E )
            & ( D = B ) ) )
       => ( ( D @ ( C @ some_val @ ( B @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
          = ( E @ some_val ) ) )
      & ( ( ( D @ ( C @ some_val @ ( B @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
          = ( E @ some_val ) )
       => ( ( ( ( D @ ( A @ hAPP_l207779698on_val ) )
              = ( E @ some_val ) )
            & ( D != B ) )
          | ( ( C = E )
            & ( D = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(166,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
    <=> ( C @ ( B @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_prod_Osimps_I2_J) ).

thf(949,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
       => ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) )
      & ( ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
       => ( C @ ( B @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(199,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
     => ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_prod__caseI) ).

thf(1087,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
     => ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(213,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
     => ~ ! [C: $i,D: $i] :
            ( ( B
              = ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
           => ~ ( D @ ( C @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_splitE) ).

thf(1147,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
     => ~ ! [C: $i,D: $i] :
            ( ( B
              = ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
           => ~ ( D @ ( C @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(53,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_1718333400on_val @ hAPP_f592397849l_bool ) @ hAPP_f1523875321l_bool ) @ hAPP_f1492320500l_bool ) )
      = ( C @ ( B @ hAPP_f1145256474l_bool ) @ ( A @ hAPP_f1863694447l_bool ) ) ),
    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(421,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_1718333400on_val @ hAPP_f592397849l_bool ) @ hAPP_f1523875321l_bool ) @ hAPP_f1492320500l_bool ) )
      = ( C @ ( B @ hAPP_f1145256474l_bool ) @ ( A @ hAPP_f1863694447l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(151,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( B @ hAPP_P282169671l_bool ) @ hBOOL )
     => ( A @ ( B @ hAPP_P282169671l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_prod__induct3) ).

thf(881,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( B @ hAPP_P282169671l_bool ) @ hBOOL )
     => ( A @ ( B @ hAPP_P282169671l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ hAPP_l512744617ion_ty ) @ ( B @ ( A @ fun_up424764369ion_ty ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_fun__upd__triv) ).

thf(228,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ hAPP_l512744617ion_ty ) @ ( B @ ( A @ fun_up424764369ion_ty ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(12,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_1466889536on_val @ hAPP_f399538905l_bool ) @ hAPP_f850751421l_bool ) @ hAPP_f1175813647l_bool ) )
      = ( C @ ( B @ hAPP_f1840640125on_val ) @ ( A @ hAPP_f318082871l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_007) ).

thf(261,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_1466889536on_val @ hAPP_f399538905l_bool ) @ hAPP_f850751421l_bool ) @ hAPP_f1175813647l_bool ) )
      = ( C @ ( B @ hAPP_f1840640125on_val ) @ ( A @ hAPP_f318082871l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(3,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ cOMBK_1294242658t_char @ hAPP_l512744617ion_ty ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__List__Olist_) ).

thf(216,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ cOMBK_1294242658t_char @ hAPP_l512744617ion_ty ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(33,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_1522540928on_val @ hAPP_f1734879897l_bool ) @ hAPP_f555424277l_bool ) @ hAPP_f1175813647l_bool ) )
      = ( C @ ( B @ hAPP_f1175813647l_bool ) @ ( A @ hAPP_f1074020887l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M) ).

thf(321,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_1522540928on_val @ hAPP_f1734879897l_bool ) @ hAPP_f555424277l_bool ) @ hAPP_f1175813647l_bool ) )
      = ( C @ ( B @ hAPP_f1175813647l_bool ) @ ( A @ hAPP_f1074020887l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(49,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ lAss_list_char ) )
     != ( C @ val_list_char ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_exp_Osimps_I75_J) ).

thf(376,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ lAss_list_char ) )
     != ( C @ val_list_char ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(99,axiom,
    ! [A: $i] :
      ( ( produc1441475159on_val @ ( A @ ( cOMBB_1466662571on_val @ hAPP_f365540729l_bool ) @ ( cOMBB_364363975on_val @ hAPP_f639265145l_bool ) @ hAPP_f1342895119l_bool ) @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_split__eta) ).

thf(623,plain,
    ! [A: $i] :
      ( ( produc1441475159on_val @ ( A @ ( cOMBB_1466662571on_val @ hAPP_f365540729l_bool ) @ ( cOMBB_364363975on_val @ hAPP_f639265145l_bool ) @ hAPP_f1342895119l_bool ) @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(162,axiom,
    p @ red @ ( l_a @ ( h_a @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( e_a @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( v @ some_val @ ( v_1 @ ( la @ fun_up1149430426on_val ) ) @ ( ha @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( ea @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_InitBlockRed_I1_J) ).

thf(937,plain,
    p @ red @ ( l_a @ ( h_a @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( e_a @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( v @ some_val @ ( v_1 @ ( la @ fun_up1149430426on_val ) ) @ ( ha @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( ea @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(90,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ member763590124on_val ) @ hBOOL )
    <=> ( A @ ( B @ hAPP_P159683425l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_mem__def) ).

thf(574,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ hAPP_P159683425l_bool ) @ hBOOL )
       => ( B @ ( A @ member763590124on_val ) @ hBOOL ) )
      & ( ( B @ ( A @ member763590124on_val ) @ hBOOL )
       => ( A @ ( B @ hAPP_P159683425l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(105,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
     => ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_splitI) ).

thf(646,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
     => ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(11,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ ( A @ fun_up424764369ion_ty ) ) )
        = A )
    <=> ( ( B @ ( A @ hAPP_l512744617ion_ty ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_fun__upd__idem__iff) ).

thf(253,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( B @ ( A @ hAPP_l512744617ion_ty ) )
          = C )
       => ( ( C @ ( B @ ( A @ fun_up424764369ion_ty ) ) )
          = A ) )
      & ( ( ( C @ ( B @ ( A @ fun_up424764369ion_ty ) ) )
          = A )
       => ( ( B @ ( A @ hAPP_l512744617ion_ty ) )
          = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(191,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
    <=> ( A @ red @ ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_redp__red__eq) ).

thf(1051,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( A @ red @ ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
       => ( E @ ( D @ ( C @ ( B @ ( A @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) )
      & ( ( E @ ( D @ ( C @ ( B @ ( A @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
       => ( A @ red @ ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(142,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
     => ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_splitD) ).

thf(821,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
     => ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(172,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc376702929l_bool @ hAPP_f444383845l_bool ) @ hAPP_P1826803705l_bool ) @ ( A @ member763590124on_val ) @ hBOOL )
     => ~ ! [D: $i,E: $i] :
            ( ( C
              = ( E @ ( D @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
           => ~ ( E @ ( D @ ( B @ hAPP_P1134042693l_bool ) @ hAPP_P595502227l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_mem__splitE) ).

thf(981,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc376702929l_bool @ hAPP_f444383845l_bool ) @ hAPP_P1826803705l_bool ) @ ( A @ member763590124on_val ) @ hBOOL )
     => ~ ! [D: $i,E: $i] :
            ( ( C
              = ( E @ ( D @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
           => ~ ( E @ ( D @ ( B @ hAPP_P1134042693l_bool ) @ hAPP_P595502227l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(118,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( B @ ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ member840932460on_val ) @ hBOOL )
        <=> ( A @ ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ member840932460on_val ) @ hBOOL ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_pred__equals__eq2) ).

thf(692,plain,
    ! [A: $i,B: $i] :
      ( ( ( B = A )
       => ! [C: $i,D: $i] :
            ( ( ( A @ ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ member840932460on_val ) @ hBOOL )
             => ( B @ ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ member840932460on_val ) @ hBOOL ) )
            & ( ( B @ ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ member840932460on_val ) @ hBOOL )
             => ( A @ ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ member840932460on_val ) @ hBOOL ) ) ) )
      & ( ! [C: $i,D: $i] :
            ( ( ( A @ ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ member840932460on_val ) @ hBOOL )
             => ( B @ ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ member840932460on_val ) @ hBOOL ) )
            & ( ( B @ ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ member840932460on_val ) @ hBOOL )
             => ( A @ ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ member840932460on_val ) @ hBOOL ) ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(206,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
    <=> ( C @ ( B @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_prod_Osimps_I2_J) ).

thf(1119,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
       => ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) )
      & ( ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
       => ( C @ ( B @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(177,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ widen_2090681816t_char ) ) @ hBOOL )
     => ( ( A @ ( D @ ( B @ widen_2090681816t_char ) ) @ hBOOL )
       => ( A @ ( C @ ( B @ widen_2090681816t_char ) ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_widen__trans) ).

thf(998,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ widen_2090681816t_char ) ) @ hBOOL )
     => ( ( A @ ( D @ ( B @ widen_2090681816t_char ) ) @ hBOOL )
       => ( A @ ( C @ ( B @ widen_2090681816t_char ) ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(174,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( F @ red @ ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
     => ( F @ red @ ( E @ ( A @ ( D @ seq_list_char ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( A @ ( B @ seq_list_char ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_red__reds_OSeqRed) ).

thf(988,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( F @ red @ ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
     => ( F @ red @ ( E @ ( A @ ( D @ seq_list_char ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( A @ ( B @ seq_list_char ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(55,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B @ ( A @ seq_list_char ) )
     != ( D @ ( C @ lAss_list_char ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_exp_Osimps_I145_J) ).

thf(428,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B @ ( A @ seq_list_char ) )
     != ( D @ ( C @ lAss_list_char ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(29,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_bool )
     => ( B @ ( A @ hAPP_bool_bool ) @ is_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) ).

thf(312,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_bool )
     => ( B @ ( A @ hAPP_bool_bool ) @ is_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(196,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i,E: $i] :
          ( ( C
            = ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
         => ( E @ ( D @ ( B @ hAPP_e592495499l_bool ) @ hAPP_P1638898323l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) )
     => ( C @ ( B @ ( produc1275132703l_bool @ hAPP_f1760682521l_bool ) @ hAPP_P1116729363l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_mem__splitI2) ).

thf(1074,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i,E: $i] :
          ( ( C
            = ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
         => ( E @ ( D @ ( B @ hAPP_e592495499l_bool ) @ hAPP_P1638898323l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) )
     => ( C @ ( B @ ( produc1275132703l_bool @ hAPP_f1760682521l_bool ) @ hAPP_P1116729363l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(22,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P159683425l_bool ) @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It) ).

thf(292,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P159683425l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(50,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( D @ ( C @ some_ty @ ( B @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
        = ( E @ some_ty ) )
    <=> ( ( ( ( D @ ( A @ hAPP_l512744617ion_ty ) )
            = ( E @ some_ty ) )
          & ( D != B ) )
        | ( ( C = E )
          & ( D = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_map__upd__Some__unfold) ).

thf(380,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( ( ( ( D @ ( A @ hAPP_l512744617ion_ty ) )
              = ( E @ some_ty ) )
            & ( D != B ) )
          | ( ( C = E )
            & ( D = B ) ) )
       => ( ( D @ ( C @ some_ty @ ( B @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
          = ( E @ some_ty ) ) )
      & ( ( ( D @ ( C @ some_ty @ ( B @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
          = ( E @ some_ty ) )
       => ( ( ( ( D @ ( A @ hAPP_l512744617ion_ty ) )
              = ( E @ some_ty ) )
            & ( D != B ) )
          | ( ( C = E )
            & ( D = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(135,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) )
        = ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
    <=> ( ( B = D )
        & ( A = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_Pair__eq) ).

thf(793,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( B = D )
          & ( A = C ) )
       => ( ( B @ ( A @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) )
          = ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) ) )
      & ( ( ( B @ ( A @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) )
          = ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
       => ( ( B = D )
          & ( A = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(125,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
     => ( F @ ( A @ ( E @ seq_list_char ) @ ( D @ ( A @ ( C @ seq_list_char ) @ ( B @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_redp__redsp_OSeqRed) ).

thf(761,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
     => ( F @ ( A @ ( E @ seq_list_char ) @ ( D @ ( A @ ( C @ seq_list_char ) @ ( B @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(79,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ ( A @ hAPP_bool_bool ) @ hBOOL )
     => ~ ! [D: $i,E: $i] :
            ( ( C
              = ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
           => ~ ( E @ ( D @ ( B @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ ( A @ hAPP_bool_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_splitE2) ).

thf(534,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ ( A @ hAPP_bool_bool ) @ hBOOL )
     => ~ ! [D: $i,E: $i] :
            ( ( C
              = ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
           => ~ ( E @ ( D @ ( B @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ ( A @ hAPP_bool_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(189,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ hAPP_e592495499l_bool ) @ hAPP_P1638898323l_bool ) @ ( A @ member840932460on_val ) @ hBOOL )
     => ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( B @ ( produc1275132703l_bool @ hAPP_f1760682521l_bool ) @ hAPP_P1116729363l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_mem__splitI) ).

thf(1047,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ hAPP_e592495499l_bool ) @ hAPP_P1638898323l_bool ) @ ( A @ member840932460on_val ) @ hBOOL )
     => ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( B @ ( produc1275132703l_bool @ hAPP_f1760682521l_bool ) @ hAPP_P1116729363l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(192,axiom,
    ! [A: $i] :
      ( ? [B: $i] : ( B @ ( A @ hAPP_P282169671l_bool ) @ hBOOL )
    <=> ? [B: $i,C: $i] : ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ hAPP_P282169671l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_split__paired__Ex) ).

thf(1057,plain,
    ! [A: $i] :
      ( ( ? [B: $i,C: $i] : ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ hAPP_P282169671l_bool ) @ hBOOL )
       => ? [B: $i] : ( B @ ( A @ hAPP_P282169671l_bool ) @ hBOOL ) )
      & ( ? [B: $i] : ( B @ ( A @ hAPP_P282169671l_bool ) @ hBOOL )
       => ? [B: $i,C: $i] : ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ hAPP_P282169671l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(26,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( C @ ( B @ ( A @ block_list_char ) ) )
     != ( E @ ( D @ seq_list_char ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_exp_Osimps_I196_J) ).

thf(302,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( C @ ( B @ ( A @ block_list_char ) ) )
     != ( E @ ( D @ seq_list_char ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(94,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( E @ red @ ( D @ ( C @ val_list_char @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( D @ ( C @ val_list_char @ ( B @ ( A @ block_list_char ) ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_red__reds_ORedBlock) ).

thf(598,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( E @ red @ ( D @ ( C @ val_list_char @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( D @ ( C @ val_list_char @ ( B @ ( A @ block_list_char ) ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(24,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_832625297y_bool @ hAPP_f181262431l_bool ) @ hAPP_f603925568l_bool ) @ hAPP_f1033709212l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f2060496320y_bool ) @ hAPP_f1001225811y_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Optio) ).

thf(297,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_832625297y_bool @ hAPP_f181262431l_bool ) @ hAPP_f603925568l_bool ) @ hAPP_f1033709212l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f2060496320y_bool ) @ hAPP_f1001225811y_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(54,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ! [D: $i] :
          ( ( D @ ( C @ some_ty @ ( B @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
          = none_ty ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_map__upd__nonempty) ).

thf(424,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ! [D: $i] :
          ( ( D @ ( C @ some_ty @ ( B @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
          = none_ty ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(17,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C @ ( B @ ( A @ block_list_char ) ) )
     != ( D @ val_list_char ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_exp_Osimps_I83_J) ).

thf(275,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C @ ( B @ ( A @ block_list_char ) ) )
     != ( D @ val_list_char ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(133,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ hAPP_f2135509569l_bool ) @ hAPP_f396019662l_bool ) @ ( A @ member763590124on_val ) @ hBOOL )
     => ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( B @ ( produc121041439l_bool @ hAPP_f1276548047l_bool ) @ hAPP_P1988153107l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_mem__splitI) ).

thf(788,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ hAPP_f2135509569l_bool ) @ hAPP_f396019662l_bool ) @ ( A @ member763590124on_val ) @ hBOOL )
     => ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( B @ ( produc121041439l_bool @ hAPP_f1276548047l_bool ) @ hAPP_P1988153107l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(57,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_877741809on_val @ hAPP_f1825030711l_bool ) @ hAPP_f1301559543l_bool ) @ hAPP_P159683425l_bool ) )
      = ( C @ ( B @ hAPP_P1776198677on_val ) @ ( A @ hAPP_P159683425l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_003) ).

thf(435,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_877741809on_val @ hAPP_f1825030711l_bool ) @ hAPP_f1301559543l_bool ) @ hAPP_P159683425l_bool ) )
      = ( C @ ( B @ hAPP_P1776198677on_val ) @ ( A @ hAPP_P159683425l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(63,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1033709212l_bool ) @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption_001) ).

thf(461,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1033709212l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(197,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc1003071703on_val @ hAPP_f394183983on_val ) @ hAPP_P1760219823on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
    <=> ( C @ ( B @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ ( cOMBB_1083177073on_val @ hAPP_f881985847l_bool ) @ ( cOMBB_635947099on_val @ hAPP_f1438732387l_bool ) @ hAPP_f1241216909l_bool ) @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_split__twice) ).

thf(1079,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ ( cOMBB_1083177073on_val @ hAPP_f881985847l_bool ) @ ( cOMBB_635947099on_val @ hAPP_f1438732387l_bool ) @ hAPP_f1241216909l_bool ) @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
       => ( C @ ( B @ ( produc1003071703on_val @ hAPP_f394183983on_val ) @ hAPP_P1760219823on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) )
      & ( ( C @ ( B @ ( produc1003071703on_val @ hAPP_f394183983on_val ) @ hAPP_P1760219823on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
       => ( C @ ( B @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ ( cOMBB_1083177073on_val @ hAPP_f881985847l_bool ) @ ( cOMBB_635947099on_val @ hAPP_f1438732387l_bool ) @ hAPP_f1241216909l_bool ) @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(20,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ hAPP_l512744617ion_ty ) )
        = ( C @ some_ty ) )
     => ( ( C @ some_ty @ ( B @ ( A @ fun_up424764369ion_ty ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_map__upd__triv) ).

thf(285,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ hAPP_l512744617ion_ty ) )
        = ( C @ some_ty ) )
     => ( ( C @ some_ty @ ( B @ ( A @ fun_up424764369ion_ty ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(34,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( E @ ( D @ ( C @ ( B @ ( A @ wTrt ) ) ) ) @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_WellTypeRT_OWTrt) ).

thf(324,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( E @ ( D @ ( C @ ( B @ ( A @ wTrt ) ) ) ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(170,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i,E: $i] :
          ( ( C
            = ( E @ ( D @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
         => ( E @ ( D @ ( B @ hAPP_P1953518277l_bool ) @ hAPP_P1116729363l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) )
     => ( C @ ( B @ ( produc20018513l_bool @ hAPP_f1591648613l_bool ) @ hAPP_P678729081l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_mem__splitI2) ).

thf(974,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i,E: $i] :
          ( ( C
            = ( E @ ( D @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
         => ( E @ ( D @ ( B @ hAPP_P1953518277l_bool ) @ hAPP_P1116729363l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) )
     => ( C @ ( B @ ( produc20018513l_bool @ hAPP_f1591648613l_bool ) @ hAPP_P678729081l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(200,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i,E: $i] :
          ( ( C
            = ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
         => ( E @ ( D @ ( B @ hAPP_f2144092865l_bool ) @ hAPP_f2011777102l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) )
     => ( C @ ( B @ ( produc334393759l_bool @ hAPP_f833559503l_bool ) @ hAPP_P1638898323l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_mem__splitI2) ).

thf(1089,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i,E: $i] :
          ( ( C
            = ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
         => ( E @ ( D @ ( B @ hAPP_f2144092865l_bool ) @ hAPP_f2011777102l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) )
     => ( C @ ( B @ ( produc334393759l_bool @ hAPP_f833559503l_bool ) @ hAPP_P1638898323l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(31,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P1708370145l_bool ) @ is_bool ),
    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(317,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P1708370145l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(204,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( B @ ( A @ hAPP_P159683425l_bool ) @ hBOOL )
    <=> ! [B: $i,C: $i] : ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ hAPP_P159683425l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_split__paired__All) ).

thf(1111,plain,
    ! [A: $i] :
      ( ( ! [B: $i,C: $i] : ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ hAPP_P159683425l_bool ) @ hBOOL )
       => ! [B: $i] : ( B @ ( A @ hAPP_P159683425l_bool ) @ hBOOL ) )
      & ( ! [B: $i] : ( B @ ( A @ hAPP_P159683425l_bool ) @ hBOOL )
       => ! [B: $i,C: $i] : ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ hAPP_P159683425l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(149,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
    <=> ( C @ ( B @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_split__conv) ).

thf(869,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
       => ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) )
      & ( ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
       => ( C @ ( B @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(73,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) )
        = ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
    <=> ( ( B = D )
        & ( A = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_Pair__eq) ).

thf(499,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( B = D )
          & ( A = C ) )
       => ( ( B @ ( A @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) )
          = ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) ) )
      & ( ( ( B @ ( A @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) )
          = ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
       => ( ( B = D )
          & ( A = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(147,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_prod__cases3) ).

thf(857,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(211,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_364363975on_val @ hAPP_f639265145l_bool ) @ hAPP_f1342895119l_bool ) @ hAPP_P1116729363l_bool ) )
      = ( C @ ( B @ hAPP_P1870962205on_val ) @ ( A @ hAPP_f204771371l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc___013) ).

thf(1138,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_364363975on_val @ hAPP_f639265145l_bool ) @ hAPP_f1342895119l_bool ) @ hAPP_P1116729363l_bool ) )
      = ( C @ ( B @ hAPP_P1870962205on_val ) @ ( A @ hAPP_f204771371l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(42,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( B @ ( C @ ( B @ ( A @ fun_up424764369ion_ty ) ) @ fun_up424764369ion_ty ) ) )
      = ( D @ ( B @ ( A @ fun_up424764369ion_ty ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_fun__upd__upd) ).

thf(356,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( B @ ( C @ ( B @ ( A @ fun_up424764369ion_ty ) ) @ fun_up424764369ion_ty ) ) )
      = ( D @ ( B @ ( A @ fun_up424764369ion_ty ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(69,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_819439237t_char @ hAPP_f516738477l_bool ) @ hAPP_f653692369l_bool ) @ hAPP_e1833980889l_bool ) )
      = ( C @ ( B @ hAPP_e108155315on_val ) @ ( A @ hAPP_f1301559543l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_008) ).

thf(488,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_819439237t_char @ hAPP_f516738477l_bool ) @ hAPP_f653692369l_bool ) @ hAPP_e1833980889l_bool ) )
      = ( C @ ( B @ hAPP_e108155315on_val ) @ ( A @ hAPP_f1301559543l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(112,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( B
            = ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
         => ( D @ ( C @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL ) )
     => ( B @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_splitI2) ).

thf(669,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( B
            = ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
         => ( D @ ( C @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL ) )
     => ( B @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(155,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( B @ ( A @ hAPP_P282169671l_bool ) @ hBOOL )
    <=> ! [B: $i,C: $i] : ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ hAPP_P282169671l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_split__paired__All) ).

thf(901,plain,
    ! [A: $i] :
      ( ( ! [B: $i,C: $i] : ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ hAPP_P282169671l_bool ) @ hBOOL )
       => ! [B: $i] : ( B @ ( A @ hAPP_P282169671l_bool ) @ hBOOL ) )
      & ( ! [B: $i] : ( B @ ( A @ hAPP_P282169671l_bool ) @ hBOOL )
       => ! [B: $i,C: $i] : ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ hAPP_P282169671l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(77,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) )
        = ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_Pair__inject) ).

thf(526,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) )
        = ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(104,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D != C )
       => ( ( D @ ( B @ ( C @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
          = ( D @ ( A @ hAPP_l207779698on_val ) ) ) )
      & ( ( D = C )
       => ( ( D @ ( B @ ( C @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_fun__upd__def) ).

thf(637,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D != C )
       => ( ( D @ ( B @ ( C @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
          = ( D @ ( A @ hAPP_l207779698on_val ) ) ) )
      & ( ( D = C )
       => ( ( D @ ( B @ ( C @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(114,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( G @ ( F @ ( E @ some_ty @ ( D @ ( C @ fun_up424764369ion_ty ) ) @ ( B @ ( A @ wTrt ) ) ) ) @ hBOOL )
     => ( G @ ( F @ ( E @ ( D @ block_list_char ) ) @ ( C @ ( B @ ( A @ wTrt ) ) ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_WTrtBlock) ).

thf(679,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( G @ ( F @ ( E @ some_ty @ ( D @ ( C @ fun_up424764369ion_ty ) ) @ ( B @ ( A @ wTrt ) ) ) ) @ hBOOL )
     => ( G @ ( F @ ( E @ ( D @ block_list_char ) ) @ ( C @ ( B @ ( A @ wTrt ) ) ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(82,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
     => ~ ! [C: $i,D: $i] :
            ( ( B
              = ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
           => ~ ( D @ ( C @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_splitE) ).

thf(547,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
     => ~ ! [C: $i,D: $i] :
            ( ( B
              = ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
           => ~ ( D @ ( C @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(181,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
      | ~ ( A @ hBOOL )
      | ~ ( B @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).

thf(1016,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
      | ~ ( A @ hBOOL )
      | ~ ( B @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(92,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc1148763895on_val @ hAPP_f204556415on_val ) @ hAPP_P2024243179on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
    <=> ( C @ ( B @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ ( cOMBB_1292453606on_val @ hAPP_f2052660463l_bool ) @ ( cOMBB_1259202826on_val @ hAPP_f1043869573l_bool ) @ hAPP_f927043595l_bool ) @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_split__twice) ).

thf(590,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ ( cOMBB_1292453606on_val @ hAPP_f2052660463l_bool ) @ ( cOMBB_1259202826on_val @ hAPP_f1043869573l_bool ) @ hAPP_f927043595l_bool ) @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
       => ( C @ ( B @ ( produc1148763895on_val @ hAPP_f204556415on_val ) @ hAPP_P2024243179on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) )
      & ( ( C @ ( B @ ( produc1148763895on_val @ hAPP_f204556415on_val ) @ hAPP_P2024243179on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
       => ( C @ ( B @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ ( cOMBB_1292453606on_val @ hAPP_f2052660463l_bool ) @ ( cOMBB_1259202826on_val @ hAPP_f1043869573l_bool ) @ hAPP_f927043595l_bool ) @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(202,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ member840932460on_val ) @ hBOOL )
    <=> ( A @ ( B @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_mem__def) ).

thf(1099,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ hAPP_P1708370145l_bool ) @ hBOOL )
       => ( B @ ( A @ member840932460on_val ) @ hBOOL ) )
      & ( ( B @ ( A @ member840932460on_val ) @ hBOOL )
       => ( A @ ( B @ hAPP_P1708370145l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(62,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( B @ ( A @ lAss_list_char ) )
     != ( E @ ( D @ ( C @ block_list_char ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_exp_Osimps_I142_J) ).

thf(457,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( B @ ( A @ lAss_list_char ) )
     != ( E @ ( D @ ( C @ block_list_char ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(96,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( D @ ( C @ ( B @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
        <=> ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL ) )
     => ( ( B @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_cond__split__eta) ).

thf(605,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL )
           => ( D @ ( C @ ( B @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) )
          & ( ( D @ ( C @ ( B @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
           => ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL ) ) )
     => ( ( B @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(209,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
     => ( C @ ( B @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_splitD) ).

thf(1131,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
     => ( C @ ( B @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(108,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ hAPP_l207779698on_val ) @ ( B @ ( A @ fun_up1149430426on_val ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_fun__upd__triv) ).

thf(654,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ hAPP_l207779698on_val ) @ ( B @ ( A @ fun_up1149430426on_val ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(8,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( B @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_fun__upd__same) ).

thf(244,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( B @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(163,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc334393759l_bool @ hAPP_f833559503l_bool ) @ hAPP_P1638898323l_bool ) @ ( A @ member840932460on_val ) @ hBOOL )
     => ~ ! [D: $i,E: $i] :
            ( ( C
              = ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
           => ~ ( E @ ( D @ ( B @ hAPP_f2144092865l_bool ) @ hAPP_f2011777102l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_mem__splitE) ).

thf(938,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc334393759l_bool @ hAPP_f833559503l_bool ) @ hAPP_P1638898323l_bool ) @ ( A @ member840932460on_val ) @ hBOOL )
     => ~ ! [D: $i,E: $i] :
            ( ( C
              = ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
           => ~ ( E @ ( D @ ( B @ hAPP_f2144092865l_bool ) @ hAPP_f2011777102l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(14,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_338347573on_val @ hAPP_f1308714617l_bool ) @ hAPP_f2134824737l_bool ) @ hAPP_P159683425l_bool ) )
      = ( C @ ( B @ hAPP_P159683425l_bool ) @ ( A @ hAPP_bool_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__prod_Itc__fun_It) ).

thf(266,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_338347573on_val @ hAPP_f1308714617l_bool ) @ hAPP_f2134824737l_bool ) @ hAPP_P159683425l_bool ) )
      = ( C @ ( B @ hAPP_P159683425l_bool ) @ ( A @ hAPP_bool_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(103,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_prod_Oexhaust) ).

thf(633,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(109,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i,F: $i] : ( F @ ( E @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( B @ hAPP_P282169671l_bool ) @ hBOOL )
     => ( A @ ( B @ hAPP_P282169671l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_prod__induct4) ).

thf(657,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i,F: $i] : ( F @ ( E @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( B @ hAPP_P282169671l_bool ) @ hBOOL )
     => ( A @ ( B @ hAPP_P282169671l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(195,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( J @ red @ ( I @ ( H @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( G @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( none_val @ ( F @ ( E @ fun_up1149430426on_val ) ) @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
     => ( ( ( F @ ( I @ hAPP_l207779698on_val ) )
          = ( B @ some_val ) )
       => ( ~ ( C @ ( F @ assigned ) @ hBOOL )
         => ( J @ red @ ( F @ ( E @ hAPP_l207779698on_val ) @ ( F @ ( I @ fun_up1149430426on_val ) ) @ ( H @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( G @ ( B @ val_list_char @ ( F @ lAss_list_char ) @ seq_list_char ) @ ( A @ ( F @ block_list_char ) ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( A @ ( F @ block_list_char ) ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_red__reds_OBlockRedSome) ).

thf(1071,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( J @ red @ ( I @ ( H @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( G @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( none_val @ ( F @ ( E @ fun_up1149430426on_val ) ) @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
     => ( ( ( F @ ( I @ hAPP_l207779698on_val ) )
          = ( B @ some_val ) )
       => ( ~ ( C @ ( F @ assigned ) @ hBOOL )
         => ( J @ red @ ( F @ ( E @ hAPP_l207779698on_val ) @ ( F @ ( I @ fun_up1149430426on_val ) ) @ ( H @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( G @ ( B @ val_list_char @ ( F @ lAss_list_char ) @ seq_list_char ) @ ( A @ ( F @ block_list_char ) ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( A @ ( F @ block_list_char ) ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(113,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc20018513l_bool @ hAPP_f1591648613l_bool ) @ hAPP_P678729081l_bool ) @ ( A @ member840932460on_val ) @ hBOOL )
     => ~ ! [D: $i,E: $i] :
            ( ( C
              = ( E @ ( D @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
           => ~ ( E @ ( D @ ( B @ hAPP_P1953518277l_bool ) @ hAPP_P1116729363l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_mem__splitE) ).

thf(674,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc20018513l_bool @ hAPP_f1591648613l_bool ) @ hAPP_P678729081l_bool ) @ ( A @ member840932460on_val ) @ hBOOL )
     => ~ ! [D: $i,E: $i] :
            ( ( C
              = ( E @ ( D @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
           => ~ ( E @ ( D @ ( B @ hAPP_P1953518277l_bool ) @ hAPP_P1116729363l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(111,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ ( cOMBB_383678192on_val @ hAPP_f1863694447l_bool ) @ ( cOMBB_1522540928on_val @ hAPP_f1734879897l_bool ) @ hAPP_f555424277l_bool ) @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
    <=> ( ( C @ ( B @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
        & ( A @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_split__part) ).

thf(662,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( C @ ( B @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
          & ( A @ hBOOL ) )
       => ( C @ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ ( cOMBB_383678192on_val @ hAPP_f1863694447l_bool ) @ ( cOMBB_1522540928on_val @ hAPP_f1734879897l_bool ) @ hAPP_f555424277l_bool ) @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) )
      & ( ( C @ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ ( cOMBB_383678192on_val @ hAPP_f1863694447l_bool ) @ ( cOMBB_1522540928on_val @ hAPP_f1734879897l_bool ) @ hAPP_f555424277l_bool ) @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
       => ( ( C @ ( B @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
          & ( A @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(13,axiom,
    produc1988544340l_bool = produc1911463199l_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_internal__split__def) ).

thf(264,plain,
    produc1988544340l_bool = produc1911463199l_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(18,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_171276332on_val @ hAPP_f1233687287l_bool ) @ hAPP_f318082871l_bool ) @ hAPP_f1033709212l_bool ) )
      = ( C @ ( B @ hAPP_f1926378906on_val ) @ ( A @ hAPP_P1708370145l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O) ).

thf(279,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_171276332on_val @ hAPP_f1233687287l_bool ) @ hAPP_f318082871l_bool ) @ hAPP_f1033709212l_bool ) )
      = ( C @ ( B @ hAPP_f1926378906on_val ) @ ( A @ hAPP_P1708370145l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(141,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( G @ red @ ( F @ ( E @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
     => ( ( B @ ( C @ ( A @ ( D @ hp @ ( G @ wTrt ) ) ) ) @ hBOOL )
       => ( ( D @ ( A @ ( G @ typeSa1234865140_sconf ) @ hAPP_P159683425l_bool ) @ hBOOL )
         => ( F @ ( A @ ( G @ typeSa1234865140_sconf ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_red__preserves__sconf) ).

thf(819,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( G @ red @ ( F @ ( E @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
     => ( ( B @ ( C @ ( A @ ( D @ hp @ ( G @ wTrt ) ) ) ) @ hBOOL )
       => ( ( D @ ( A @ ( G @ typeSa1234865140_sconf ) @ hAPP_P159683425l_bool ) @ hBOOL )
         => ( F @ ( A @ ( G @ typeSa1234865140_sconf ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(86,axiom,
    p @ ( wf_J_mdecl @ wf_pro755087577t_char ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_assms) ).

thf(562,plain,
    p @ ( wf_J_mdecl @ wf_pro755087577t_char ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(180,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( C != D )
       => ( ( C @ ( B @ ( D @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
          = ( C @ ( A @ hAPP_l207779698on_val ) ) ) )
      & ( ( C = D )
       => ( ( C @ ( B @ ( D @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_fun__upd__apply) ).

thf(1007,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( C != D )
       => ( ( C @ ( B @ ( D @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
          = ( C @ ( A @ hAPP_l207779698on_val ) ) ) )
      & ( ( C = D )
       => ( ( C @ ( B @ ( D @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(207,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_prod_Oexhaust) ).

thf(1125,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(121,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i,E: $i] :
          ( ( C
            = ( E @ ( D @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
         => ( E @ ( D @ ( B @ hAPP_P1134042693l_bool ) @ hAPP_P595502227l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) )
     => ( C @ ( B @ ( produc376702929l_bool @ hAPP_f444383845l_bool ) @ hAPP_P1826803705l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_mem__splitI2) ).

thf(743,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i,E: $i] :
          ( ( C
            = ( E @ ( D @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
         => ( E @ ( D @ ( B @ hAPP_P1134042693l_bool ) @ hAPP_P595502227l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) )
     => ( C @ ( B @ ( produc376702929l_bool @ hAPP_f444383845l_bool ) @ hAPP_P1826803705l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(150,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
    <=> ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_prod_Osimps_I2_J) ).

thf(875,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL )
       => ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) )
      & ( ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
       => ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(81,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( F @ ( E @ val_list_char @ ( F @ ( E @ val_list_char @ ( D @ val_list_char @ ( B @ lAss_list_char ) @ seq_list_char ) @ ( C @ ( B @ block_list_char ) ) @ ( A @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_redp__redsp_ORedInitBlock) ).

thf(545,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( F @ ( E @ val_list_char @ ( F @ ( E @ val_list_char @ ( D @ val_list_char @ ( B @ lAss_list_char ) @ seq_list_char ) @ ( C @ ( B @ block_list_char ) ) @ ( A @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(171,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL )
     => ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_prod__caseI) ).

thf(979,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL )
     => ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(144,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_PairE) ).

thf(831,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(115,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_1759207793on_val @ hAPP_f10074679l_bool ) @ hAPP_f489055607l_bool ) @ hAPP_P159683425l_bool ) )
      = ( C @ ( B @ hAPP_P604205461on_val ) @ ( A @ hAPP_P1708370145l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O_004) ).

thf(681,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_1759207793on_val @ hAPP_f10074679l_bool ) @ hAPP_f489055607l_bool ) @ hAPP_P159683425l_bool ) )
      = ( C @ ( B @ hAPP_P604205461on_val ) @ ( A @ hAPP_P1708370145l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(4,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( C != D )
       => ( ( C @ ( B @ ( D @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
          = ( C @ ( A @ hAPP_l512744617ion_ty ) ) ) )
      & ( ( C = D )
       => ( ( C @ ( B @ ( D @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_fun__upd__apply) ).

thf(219,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( C != D )
       => ( ( C @ ( B @ ( D @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
          = ( C @ ( A @ hAPP_l512744617ion_ty ) ) ) )
      & ( ( C = D )
       => ( ( C @ ( B @ ( D @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(205,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ hBOOL )
      | ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).

thf(1117,plain,
    ! [A: $i,B: $i] :
      ( ( B @ hBOOL )
      | ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(74,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( D @ ( C @ ( B @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
        <=> ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ hAPP_P282169671l_bool ) @ hBOOL ) )
     => ( ( B @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_cond__split__eta) ).

thf(509,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ hAPP_P282169671l_bool ) @ hBOOL )
           => ( D @ ( C @ ( B @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) )
          & ( ( D @ ( C @ ( B @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
           => ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ hAPP_P282169671l_bool ) @ hBOOL ) ) )
     => ( ( B @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(97,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ ( A @ hAPP_bool_bool ) @ hBOOL )
     => ~ ! [D: $i,E: $i] :
            ( ( C
              = ( E @ ( D @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
           => ~ ( E @ ( D @ ( B @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ ( A @ hAPP_bool_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_splitE2) ).

thf(616,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ ( A @ hAPP_bool_bool ) @ hBOOL )
     => ~ ! [D: $i,E: $i] :
            ( ( C
              = ( E @ ( D @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
           => ~ ( E @ ( D @ ( B @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ ( A @ hAPP_bool_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(175,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ member773094996on_val ) @ hBOOL )
    <=> ( A @ ( B @ hAPP_P282169671l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_mem__def) ).

thf(990,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ hAPP_P282169671l_bool ) @ hBOOL )
       => ( B @ ( A @ member773094996on_val ) @ hBOOL ) )
      & ( ( B @ ( A @ member773094996on_val ) @ hBOOL )
       => ( A @ ( B @ hAPP_P282169671l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(176,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] : ( D @ ( C @ ( D @ ( C @ ( B @ val_list_char @ seq_list_char ) @ ( A @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_redp__redsp_ORedSeq) ).

thf(996,plain,
    ! [A: $i,B: $i,C: $i,D: $i] : ( D @ ( C @ ( D @ ( C @ ( B @ val_list_char @ seq_list_char ) @ ( A @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(44,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f61040418l_bool ) @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__O) ).

thf(362,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f61040418l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(60,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( D != E )
     => ( ( C @ ( E @ ( B @ ( D @ ( A @ fun_up424764369ion_ty ) ) @ fun_up424764369ion_ty ) ) )
        = ( B @ ( D @ ( C @ ( E @ ( A @ fun_up424764369ion_ty ) ) @ fun_up424764369ion_ty ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_fun__upd__twist) ).

thf(451,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( D != E )
     => ( ( C @ ( E @ ( B @ ( D @ ( A @ fun_up424764369ion_ty ) ) @ fun_up424764369ion_ty ) ) )
        = ( B @ ( D @ ( C @ ( E @ ( A @ fun_up424764369ion_ty ) ) @ fun_up424764369ion_ty ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(89,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ ( cOMBB_338347573on_val @ hAPP_f1308714617l_bool ) @ ( cOMBB_740252943t_char @ hAPP_f917296015l_bool ) @ hAPP_f546724245l_bool ) @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
    <=> ( ( C @ ( B @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
        & ( A @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_split__part) ).

thf(567,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( C @ ( B @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
          & ( A @ hBOOL ) )
       => ( C @ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ ( cOMBB_338347573on_val @ hAPP_f1308714617l_bool ) @ ( cOMBB_740252943t_char @ hAPP_f917296015l_bool ) @ hAPP_f546724245l_bool ) @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) )
      & ( ( C @ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ ( cOMBB_338347573on_val @ hAPP_f1308714617l_bool ) @ ( cOMBB_740252943t_char @ hAPP_f917296015l_bool ) @ hAPP_f546724245l_bool ) @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
       => ( ( C @ ( B @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
          & ( A @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(65,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ member840932460on_val ) @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_member_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J) ).

thf(477,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ member840932460on_val ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(102,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( F @ red @ ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
     => ( F @ red @ ( E @ ( D @ ( A @ lAss_list_char ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( B @ ( A @ lAss_list_char ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_red__reds_OLAssRed) ).

thf(631,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( F @ red @ ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
     => ( F @ red @ ( E @ ( D @ ( A @ lAss_list_char ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( B @ ( A @ lAss_list_char ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(124,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ hBOOL )
      | ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).

thf(758,plain,
    ! [A: $i,B: $i] :
      ( ( A @ hBOOL )
      | ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(140,axiom,
    ! [A: $i] :
      ( ( produc899768717on_val @ ( A @ ( cOMBB_1750801836on_val @ hAPP_f2057883639l_bool ) @ ( cOMBB_1153617344on_val @ hAPP_f1050935001l_bool ) @ hAPP_f1363667773l_bool ) @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_split__eta) ).

thf(816,plain,
    ! [A: $i] :
      ( ( produc899768717on_val @ ( A @ ( cOMBB_1750801836on_val @ hAPP_f2057883639l_bool ) @ ( cOMBB_1153617344on_val @ hAPP_f1050935001l_bool ) @ hAPP_f1363667773l_bool ) @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(120,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( B @ ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ member763590124on_val ) @ hBOOL )
        <=> ( A @ ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ member763590124on_val ) @ hBOOL ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_pred__equals__eq2) ).

thf(726,plain,
    ! [A: $i,B: $i] :
      ( ( ( B = A )
       => ! [C: $i,D: $i] :
            ( ( ( A @ ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ member763590124on_val ) @ hBOOL )
             => ( B @ ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ member763590124on_val ) @ hBOOL ) )
            & ( ( B @ ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ member763590124on_val ) @ hBOOL )
             => ( A @ ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ member763590124on_val ) @ hBOOL ) ) ) )
      & ( ! [C: $i,D: $i] :
            ( ( ( A @ ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ member763590124on_val ) @ hBOOL )
             => ( B @ ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ member763590124on_val ) @ hBOOL ) )
            & ( ( B @ ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ member763590124on_val ) @ hBOOL )
             => ( A @ ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ member763590124on_val ) @ hBOOL ) ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(98,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
     => ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_splitI) ).

thf(621,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
     => ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(67,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_1518282696on_val @ hAPP_f348318673l_bool ) @ hAPP_f857351829l_bool ) @ hAPP_f1617787571l_bool ) )
      = ( C @ ( B @ hAPP_f1213370163y_bool ) @ ( A @ hAPP_f181262431l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_002) ).

thf(483,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_1518282696on_val @ hAPP_f348318673l_bool ) @ hAPP_f857351829l_bool ) @ hAPP_f1617787571l_bool ) )
      = ( C @ ( B @ hAPP_f1213370163y_bool ) @ ( A @ hAPP_f181262431l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(75,axiom,
    la @ ( ha @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( e @ ( p @ typeSa1234865140_sconf ) @ hAPP_P159683425l_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_InitBlockRed_I4_J) ).

thf(520,plain,
    la @ ( ha @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( e @ ( p @ typeSa1234865140_sconf ) @ hAPP_P159683425l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(7,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ hAPP_l512744617ion_ty ) )
        = C )
     => ( ( C @ ( B @ ( A @ fun_up424764369ion_ty ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_fun__upd__idem) ).

thf(240,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ hAPP_l512744617ion_ty ) )
        = C )
     => ( ( C @ ( B @ ( A @ fun_up424764369ion_ty ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(100,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_1027621637t_char @ hAPP_f1725502637l_bool ) @ hAPP_f439412817l_bool ) @ hAPP_e1833980889l_bool ) )
      = ( C @ ( B @ hAPP_e1659493427on_val ) @ ( A @ hAPP_f489055607l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_009) ).

thf(626,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_1027621637t_char @ hAPP_f1725502637l_bool ) @ hAPP_f439412817l_bool ) @ hAPP_e1833980889l_bool ) )
      = ( C @ ( B @ hAPP_e1659493427on_val ) @ ( A @ hAPP_f489055607l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(128,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( B @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
      <=> ( C @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_split__weak__cong) ).

thf(769,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( ( C @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
         => ( B @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) )
        & ( ( B @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
         => ( C @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(164,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_1466662571on_val @ hAPP_f365540729l_bool ) @ hAPP_f204771371l_bool ) @ hAPP_P1708370145l_bool ) )
      = ( C @ ( B @ hAPP_P1886180715on_val ) @ ( A @ hAPP_P282169671l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__010) ).

thf(943,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_1466662571on_val @ hAPP_f365540729l_bool ) @ hAPP_f204771371l_bool ) @ hAPP_P1708370145l_bool ) )
      = ( C @ ( B @ hAPP_P1886180715on_val ) @ ( A @ hAPP_P282169671l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(46,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( C @ some_ty @ ( B @ ( A @ fun_up424764369ion_ty ) ) )
        = ( E @ some_ty @ ( B @ ( D @ fun_up424764369ion_ty ) ) ) )
     => ( C = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_map__upd__eqD1) ).

thf(367,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( C @ some_ty @ ( B @ ( A @ fun_up424764369ion_ty ) ) )
        = ( E @ some_ty @ ( B @ ( D @ fun_up424764369ion_ty ) ) ) )
     => ( C = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(83,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C != D )
     => ( ( C @ ( B @ ( D @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
        = ( C @ ( A @ hAPP_l207779698on_val ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_fun__upd__other) ).

thf(552,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C != D )
     => ( ( C @ ( B @ ( D @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
        = ( C @ ( A @ hAPP_l207779698on_val ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(76,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( B
            = ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
         => ( D @ ( C @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) )
     => ( B @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_splitI2) ).

thf(521,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( B
            = ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
         => ( D @ ( C @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) )
     => ( B @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(51,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( C @ ( B @ ( A @ block_list_char ) ) )
        = ( F @ ( E @ ( D @ block_list_char ) ) ) )
    <=> ( ( C = F )
        & ( B = E )
        & ( A = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_exp_Osimps_I10_J) ).

thf(399,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( ( C = F )
          & ( B = E )
          & ( A = D ) )
       => ( ( C @ ( B @ ( A @ block_list_char ) ) )
          = ( F @ ( E @ ( D @ block_list_char ) ) ) ) )
      & ( ( ( C @ ( B @ ( A @ block_list_char ) ) )
          = ( F @ ( E @ ( D @ block_list_char ) ) ) )
       => ( ( C = F )
          & ( B = E )
          & ( A = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(188,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( none_val @ ( A @ ( none_val @ cOMBK_1097134891t_char @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
      = none_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_empty__upd__none) ).

thf(1044,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( none_val @ ( A @ ( none_val @ cOMBK_1097134891t_char @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
      = none_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(130,axiom,
    ( ( v_1 @ ( l_a @ hAPP_l207779698on_val ) )
    = ( v_2 @ some_val ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_InitBlockRed_I3_J) ).

thf(780,plain,
    ( ( v_1 @ ( l_a @ hAPP_l207779698on_val ) )
    = ( v_2 @ some_val ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(152,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( B @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
      <=> ( C @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_split__weak__cong) ).

thf(883,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( ( C @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
         => ( B @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) )
        & ( ( B @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
         => ( C @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(87,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ hAPP_P1953518277l_bool ) @ hAPP_P1116729363l_bool ) @ ( A @ member840932460on_val ) @ hBOOL )
     => ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( B @ ( produc20018513l_bool @ hAPP_f1591648613l_bool ) @ hAPP_P678729081l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_mem__splitI) ).

thf(563,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ hAPP_P1953518277l_bool ) @ hAPP_P1116729363l_bool ) @ ( A @ member840932460on_val ) @ hBOOL )
     => ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( B @ ( produc20018513l_bool @ hAPP_f1591648613l_bool ) @ hAPP_P678729081l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(178,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc2036005791l_bool @ hAPP_f468299289l_bool ) @ hAPP_P595502227l_bool ) @ ( A @ member763590124on_val ) @ hBOOL )
     => ~ ! [D: $i,E: $i] :
            ( ( C
              = ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
           => ~ ( E @ ( D @ ( B @ hAPP_e500528395l_bool ) @ hAPP_P1988153107l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_mem__splitE) ).

thf(1000,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc2036005791l_bool @ hAPP_f468299289l_bool ) @ hAPP_P595502227l_bool ) @ ( A @ member763590124on_val ) @ hBOOL )
     => ~ ! [D: $i,E: $i] :
            ( ( C
              = ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
           => ~ ( E @ ( D @ ( B @ hAPP_e500528395l_bool ) @ hAPP_P1988153107l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(58,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_1083177073on_val @ hAPP_f881985847l_bool ) @ hAPP_f1712766199l_bool ) @ hAPP_P1708370145l_bool ) )
      = ( C @ ( B @ hAPP_P789556885on_val ) @ ( A @ hAPP_P159683425l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_005) ).

thf(438,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_1083177073on_val @ hAPP_f881985847l_bool ) @ hAPP_f1712766199l_bool ) @ hAPP_P1708370145l_bool ) )
      = ( C @ ( B @ hAPP_P789556885on_val ) @ ( A @ hAPP_P159683425l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(159,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ typeSa1234865140_sconf ) @ hAPP_P159683425l_bool ) @ hBOOL )
    <=> ( C @ ( B @ ( A @ lconf_496643946t_char @ ( cOMBC_832625297y_bool @ ( cOMBB_1518282696on_val @ hAPP_f348318673l_bool ) @ hAPP_f857351829l_bool ) @ ( cOMBC_2027949654l_bool @ hAPP_f838396643l_bool ) @ hAPP_f550652027l_bool ) @ ( A @ hconf_97414254t_char @ ( fconj @ ( cOMBB_1303934920on_val @ hAPP_f1977633121l_bool ) @ hAPP_f1452292669l_bool ) @ ( cOMBB_383678192on_val @ ( cOMBB_1718333400on_val @ hAPP_f592397849l_bool ) @ hAPP_f1523875321l_bool ) @ cOMBS_570216337l_bool ) @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_sconf__def) ).

thf(922,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ ( A @ lconf_496643946t_char @ ( cOMBC_832625297y_bool @ ( cOMBB_1518282696on_val @ hAPP_f348318673l_bool ) @ hAPP_f857351829l_bool ) @ ( cOMBC_2027949654l_bool @ hAPP_f838396643l_bool ) @ hAPP_f550652027l_bool ) @ ( A @ hconf_97414254t_char @ ( fconj @ ( cOMBB_1303934920on_val @ hAPP_f1977633121l_bool ) @ hAPP_f1452292669l_bool ) @ ( cOMBB_383678192on_val @ ( cOMBB_1718333400on_val @ hAPP_f592397849l_bool ) @ hAPP_f1523875321l_bool ) @ cOMBS_570216337l_bool ) @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
       => ( C @ ( B @ ( A @ typeSa1234865140_sconf ) @ hAPP_P159683425l_bool ) @ hBOOL ) )
      & ( ( C @ ( B @ ( A @ typeSa1234865140_sconf ) @ hAPP_P159683425l_bool ) @ hBOOL )
       => ( C @ ( B @ ( A @ lconf_496643946t_char @ ( cOMBC_832625297y_bool @ ( cOMBB_1518282696on_val @ hAPP_f348318673l_bool ) @ hAPP_f857351829l_bool ) @ ( cOMBC_2027949654l_bool @ hAPP_f838396643l_bool ) @ hAPP_f550652027l_bool ) @ ( A @ hconf_97414254t_char @ ( fconj @ ( cOMBB_1303934920on_val @ hAPP_f1977633121l_bool ) @ hAPP_f1452292669l_bool ) @ ( cOMBB_383678192on_val @ ( cOMBB_1718333400on_val @ hAPP_f592397849l_bool ) @ hAPP_f1523875321l_bool ) @ cOMBS_570216337l_bool ) @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(173,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( B @ hAPP_P1708370145l_bool ) @ hBOOL )
     => ( A @ ( B @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_prod__induct3) ).

thf(986,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i,E: $i] : ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( B @ hAPP_P1708370145l_bool ) @ hBOOL )
     => ( A @ ( B @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(27,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_466903633on_val @ hAPP_f2032347769l_bool ) @ hAPP_f641257349l_bool ) @ hAPP_P1116729363l_bool ) )
      = ( C @ ( B @ hAPP_P1116729363l_bool ) @ ( A @ hAPP_f926562337l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__) ).

thf(306,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_466903633on_val @ hAPP_f2032347769l_bool ) @ hAPP_f641257349l_bool ) @ hAPP_P1116729363l_bool ) )
      = ( C @ ( B @ hAPP_P1116729363l_bool ) @ ( A @ hAPP_f926562337l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(48,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1001225811y_bool ) @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption) ).

thf(374,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1001225811y_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(106,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( B @ ( C @ ( B @ ( A @ fun_up1149430426on_val ) ) @ fun_up1149430426on_val ) ) )
      = ( D @ ( B @ ( A @ fun_up1149430426on_val ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_fun__upd__upd) ).

thf(648,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( B @ ( C @ ( B @ ( A @ fun_up1149430426on_val ) ) @ fun_up1149430426on_val ) ) )
      = ( D @ ( B @ ( A @ fun_up1149430426on_val ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(37,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ val_list_char )
     != ( C @ ( B @ lAss_list_char ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_exp_Osimps_I74_J) ).

thf(342,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ val_list_char )
     != ( C @ ( B @ lAss_list_char ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(182,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ ( cOMBB_672625589on_val @ hAPP_f1560238713l_bool ) @ ( cOMBB_466903633on_val @ hAPP_f2032347769l_bool ) @ hAPP_f641257349l_bool ) @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
    <=> ( ( C @ ( B @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
        & ( A @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_split__part) ).

thf(1018,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( C @ ( B @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
          & ( A @ hBOOL ) )
       => ( C @ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ ( cOMBB_672625589on_val @ hAPP_f1560238713l_bool ) @ ( cOMBB_466903633on_val @ hAPP_f2032347769l_bool ) @ hAPP_f641257349l_bool ) @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) )
      & ( ( C @ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ ( cOMBB_672625589on_val @ hAPP_f1560238713l_bool ) @ ( cOMBB_466903633on_val @ hAPP_f2032347769l_bool ) @ hAPP_f641257349l_bool ) @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
       => ( ( C @ ( B @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
          & ( A @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(143,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( B @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
      <=> ( C @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_split__weak__cong) ).

thf(823,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( ( C @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
         => ( B @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) )
        & ( ( B @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
         => ( C @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(190,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
     => ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_prod__caseI) ).

thf(1049,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
     => ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(85,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i,E: $i] :
          ( ( C
            = ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
         => ( E @ ( D @ ( B @ hAPP_e500528395l_bool ) @ hAPP_P1988153107l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) )
     => ( C @ ( B @ ( produc2036005791l_bool @ hAPP_f468299289l_bool ) @ hAPP_P595502227l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_mem__splitI2) ).

thf(557,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i,E: $i] :
          ( ( C
            = ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
         => ( E @ ( D @ ( B @ hAPP_e500528395l_bool ) @ hAPP_P1988153107l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) )
     => ( C @ ( B @ ( produc2036005791l_bool @ hAPP_f468299289l_bool ) @ hAPP_P595502227l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(91,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) )
        = ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
    <=> ( ( B = D )
        & ( A = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_Pair__eq) ).

thf(580,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( B = D )
          & ( A = C ) )
       => ( ( B @ ( A @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) )
          = ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) ) )
      & ( ( ( B @ ( A @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) )
          = ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
       => ( ( B = D )
          & ( A = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(117,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( E @ red @ ( B @ some_val @ ( A @ ( D @ fun_up1149430426on_val ) ) @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( unit @ val_list_char @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( B @ val_list_char @ ( A @ lAss_list_char ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_red__reds_ORedLAss) ).

thf(690,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( E @ red @ ( B @ some_val @ ( A @ ( D @ fun_up1149430426on_val ) ) @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( unit @ val_list_char @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( B @ val_list_char @ ( A @ lAss_list_char ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(183,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc1275132703l_bool @ hAPP_f1760682521l_bool ) @ hAPP_P1116729363l_bool ) @ ( A @ member840932460on_val ) @ hBOOL )
     => ~ ! [D: $i,E: $i] :
            ( ( C
              = ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
           => ~ ( E @ ( D @ ( B @ hAPP_e592495499l_bool ) @ hAPP_P1638898323l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_mem__splitE) ).

thf(1025,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc1275132703l_bool @ hAPP_f1760682521l_bool ) @ hAPP_P1116729363l_bool ) @ ( A @ member840932460on_val ) @ hBOOL )
     => ~ ! [D: $i,E: $i] :
            ( ( C
              = ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
           => ~ ( E @ ( D @ ( B @ hAPP_e592495499l_bool ) @ hAPP_P1638898323l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(19,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_1259202826on_val @ hAPP_f1043869573l_bool ) @ hAPP_f927043595l_bool ) @ hAPP_f1175813647l_bool ) )
      = ( C @ ( B @ hAPP_f600512025on_val ) @ ( A @ hAPP_f524589473l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_011) ).

thf(282,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_1259202826on_val @ hAPP_f1043869573l_bool ) @ hAPP_f927043595l_bool ) @ hAPP_f1175813647l_bool ) )
      = ( C @ ( B @ hAPP_f600512025on_val ) @ ( A @ hAPP_f524589473l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(59,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ val_list_char )
        = ( B @ val_list_char ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_exp_Osimps_I3_J) ).

thf(441,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
       => ( ( A @ val_list_char )
          = ( B @ val_list_char ) ) )
      & ( ( ( A @ val_list_char )
          = ( B @ val_list_char ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(64,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ seq_list_char ) )
        = ( D @ ( C @ seq_list_char ) ) )
    <=> ( ( B = D )
        & ( A = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_exp_Osimps_I11_J) ).

thf(463,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( B = D )
          & ( A = C ) )
       => ( ( B @ ( A @ seq_list_char ) )
          = ( D @ ( C @ seq_list_char ) ) ) )
      & ( ( ( B @ ( A @ seq_list_char ) )
          = ( D @ ( C @ seq_list_char ) ) )
       => ( ( B = D )
          & ( A = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(198,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL )
     => ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_splitI) ).

thf(1085,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL )
     => ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(43,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_2027949654l_bool @ hAPP_f838396643l_bool ) @ hAPP_f550652027l_bool ) @ hAPP_f1175813647l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f1617787571l_bool ) @ hAPP_f603925568l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It) ).

thf(359,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_2027949654l_bool @ hAPP_f838396643l_bool ) @ hAPP_f550652027l_bool ) @ hAPP_f1175813647l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f1617787571l_bool ) @ hAPP_f603925568l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(156,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) )
        = ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_Pair__inject) ).

thf(907,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) )
        = ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(186,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
      ( ( K @ red @ ( J @ ( I @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( H @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( G @ some_val @ ( F @ ( E @ fun_up1149430426on_val ) ) @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
     => ( ( ( F @ ( J @ hAPP_l207779698on_val ) )
          = ( B @ some_val ) )
       => ( K @ red @ ( F @ ( E @ hAPP_l207779698on_val ) @ ( F @ ( J @ fun_up1149430426on_val ) ) @ ( I @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( H @ ( B @ val_list_char @ ( F @ lAss_list_char ) @ seq_list_char ) @ ( A @ ( F @ block_list_char ) ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( G @ val_list_char @ ( F @ lAss_list_char ) @ seq_list_char ) @ ( A @ ( F @ block_list_char ) ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_red__reds_OInitBlockRed) ).

thf(1038,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
      ( ( K @ red @ ( J @ ( I @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( H @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( G @ some_val @ ( F @ ( E @ fun_up1149430426on_val ) ) @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
     => ( ( ( F @ ( J @ hAPP_l207779698on_val ) )
          = ( B @ some_val ) )
       => ( K @ red @ ( F @ ( E @ hAPP_l207779698on_val ) @ ( F @ ( J @ fun_up1149430426on_val ) ) @ ( I @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( H @ ( B @ val_list_char @ ( F @ lAss_list_char ) @ seq_list_char ) @ ( A @ ( F @ block_list_char ) ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( G @ val_list_char @ ( F @ lAss_list_char ) @ seq_list_char ) @ ( A @ ( F @ block_list_char ) ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(47,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ val_list_char )
     != ( C @ ( B @ seq_list_char ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_exp_Osimps_I84_J) ).

thf(370,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ val_list_char )
     != ( C @ ( B @ seq_list_char ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(212,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc1174947465on_val @ hAPP_f1520199827on_val ) @ hAPP_P789556885on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
    <=> ( C @ ( B @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ ( cOMBB_877741809on_val @ hAPP_f1825030711l_bool ) @ ( cOMBB_819439237t_char @ hAPP_f516738477l_bool ) @ hAPP_f653692369l_bool ) @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_split__twice) ).

thf(1141,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ ( cOMBB_877741809on_val @ hAPP_f1825030711l_bool ) @ ( cOMBB_819439237t_char @ hAPP_f516738477l_bool ) @ hAPP_f653692369l_bool ) @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
       => ( C @ ( B @ ( produc1174947465on_val @ hAPP_f1520199827on_val ) @ hAPP_P789556885on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) )
      & ( ( C @ ( B @ ( produc1174947465on_val @ hAPP_f1520199827on_val ) @ hAPP_P789556885on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
       => ( C @ ( B @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ ( cOMBB_877741809on_val @ hAPP_f1825030711l_bool ) @ ( cOMBB_819439237t_char @ hAPP_f516738477l_bool ) @ hAPP_f653692369l_bool ) @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(95,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ ( A @ hAPP_bool_bool ) @ hBOOL )
     => ~ ! [D: $i,E: $i] :
            ( ( C
              = ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
           => ~ ( E @ ( D @ ( B @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ ( A @ hAPP_bool_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_splitE2) ).

thf(600,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ ( A @ hAPP_bool_bool ) @ hBOOL )
     => ~ ! [D: $i,E: $i] :
            ( ( C
              = ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
           => ~ ( E @ ( D @ ( B @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ ( A @ hAPP_bool_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(201,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
     => ~ ! [C: $i,D: $i] :
            ( ( B
              = ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
           => ~ ( D @ ( C @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_splitE) ).

thf(1094,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
     => ~ ! [C: $i,D: $i] :
            ( ( B
              = ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
           => ~ ( D @ ( C @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(30,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ cOMBK_1097134891t_char @ hAPP_l207779698on_val ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__List__Olis) ).

thf(314,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ cOMBK_1097134891t_char @ hAPP_l207779698on_val ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(71,axiom,
    t @ ( ea @ ( v @ val_list_char @ ( v_1 @ lAss_list_char ) @ seq_list_char ) @ ( t_1 @ ( v_1 @ block_list_char ) ) @ ( e @ ( ha @ ( p @ wTrt ) ) ) ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_InitBlockRed_I5_J) ).

thf(495,plain,
    t @ ( ea @ ( v @ val_list_char @ ( v_1 @ lAss_list_char ) @ seq_list_char ) @ ( t_1 @ ( v_1 @ block_list_char ) ) @ ( e @ ( ha @ ( p @ wTrt ) ) ) ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(153,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
    <=> ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_split__conv) ).

thf(891,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL )
       => ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) )
      & ( ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
       => ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(10,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C != D )
     => ( ( C @ ( B @ ( D @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
        = ( C @ ( A @ hAPP_l512744617ion_ty ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_fun__upd__other) ).

thf(250,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C != D )
     => ( ( C @ ( B @ ( D @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
        = ( C @ ( A @ hAPP_l512744617ion_ty ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(6,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D != C )
       => ( ( D @ ( B @ ( C @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
          = ( D @ ( A @ hAPP_l512744617ion_ty ) ) ) )
      & ( ( D = C )
       => ( ( D @ ( B @ ( C @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_fun__upd__def) ).

thf(231,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D != C )
       => ( ( D @ ( B @ ( C @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
          = ( D @ ( A @ hAPP_l512744617ion_ty ) ) ) )
      & ( ( D = C )
       => ( ( D @ ( B @ ( C @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(161,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) )
        = ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_Pair__inject) ).

thf(931,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) )
        = ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(80,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
    <=> ( C @ ( B @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_split__conv) ).

thf(539,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
       => ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) )
      & ( ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
       => ( C @ ( B @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(139,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
      ( ( K @ ( J @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( I @ ( H @ some_val @ ( G @ ( F @ fun_up1149430426on_val ) ) @ ( E @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( D @ ( C @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
     => ( ( ( G @ ( K @ hAPP_l207779698on_val ) )
          = ( B @ some_val ) )
       => ( G @ ( F @ hAPP_l207779698on_val ) @ ( G @ ( K @ fun_up1149430426on_val ) ) @ ( J @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( I @ ( B @ val_list_char @ ( G @ lAss_list_char ) @ seq_list_char ) @ ( A @ ( G @ block_list_char ) ) @ ( F @ ( E @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( D @ ( H @ val_list_char @ ( G @ lAss_list_char ) @ seq_list_char ) @ ( A @ ( G @ block_list_char ) ) @ ( C @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_redp__redsp_OInitBlockRed) ).

thf(813,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
      ( ( K @ ( J @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( I @ ( H @ some_val @ ( G @ ( F @ fun_up1149430426on_val ) ) @ ( E @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( D @ ( C @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
     => ( ( ( G @ ( K @ hAPP_l207779698on_val ) )
          = ( B @ some_val ) )
       => ( G @ ( F @ hAPP_l207779698on_val ) @ ( G @ ( K @ fun_up1149430426on_val ) ) @ ( J @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( I @ ( B @ val_list_char @ ( G @ lAss_list_char ) @ seq_list_char ) @ ( A @ ( G @ block_list_char ) ) @ ( F @ ( E @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( D @ ( H @ val_list_char @ ( G @ lAss_list_char ) @ seq_list_char ) @ ( A @ ( G @ block_list_char ) ) @ ( C @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(169,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( D @ ( C @ ( B @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL )
        <=> ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ hAPP_P159683425l_bool ) @ hBOOL ) )
     => ( ( B @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_cond__split__eta) ).

thf(963,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ hAPP_P159683425l_bool ) @ hBOOL )
           => ( D @ ( C @ ( B @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL ) )
          & ( ( D @ ( C @ ( B @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL )
           => ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ hAPP_P159683425l_bool ) @ hBOOL ) ) )
     => ( ( B @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(32,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ member763590124on_val ) @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_member_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_) ).

thf(319,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ member763590124on_val ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(122,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_PairE) ).

thf(748,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(165,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( B @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_fun__upd__same) ).

thf(946,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( B @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(132,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( I @ red @ ( H @ ( G @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( F @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
     => ( ( B @ ( C @ ( A @ ( D @ ( I @ wTrt ) ) ) ) @ hBOOL )
       => ( ( A @ ( E @ ( D @ ( I @ lconf_496643946t_char @ hAPP_f1213370163y_bool ) @ hAPP_f2060496320y_bool ) @ hAPP_f1001225811y_bool ) @ hBOOL )
         => ( A @ ( H @ ( G @ ( I @ lconf_496643946t_char @ hAPP_f1213370163y_bool ) @ hAPP_f2060496320y_bool ) @ hAPP_f1001225811y_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_red__preserves__lconf) ).

thf(786,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( I @ red @ ( H @ ( G @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( F @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
     => ( ( B @ ( C @ ( A @ ( D @ ( I @ wTrt ) ) ) ) @ hBOOL )
       => ( ( A @ ( E @ ( D @ ( I @ lconf_496643946t_char @ hAPP_f1213370163y_bool ) @ hAPP_f2060496320y_bool ) @ hAPP_f1001225811y_bool ) @ hBOOL )
         => ( A @ ( H @ ( G @ ( I @ lconf_496643946t_char @ hAPP_f1213370163y_bool ) @ hAPP_f2060496320y_bool ) @ hAPP_f1001225811y_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(184,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc901351817on_val @ hAPP_f1309113673on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
    <=> ( C @ ( B @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ ( cOMBB_171276332on_val @ hAPP_f1233687287l_bool ) @ ( cOMBB_1466889536on_val @ hAPP_f399538905l_bool ) @ hAPP_f850751421l_bool ) @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_split__twice) ).

thf(1030,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ ( cOMBB_171276332on_val @ hAPP_f1233687287l_bool ) @ ( cOMBB_1466889536on_val @ hAPP_f399538905l_bool ) @ hAPP_f850751421l_bool ) @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
       => ( C @ ( B @ ( produc901351817on_val @ hAPP_f1309113673on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) )
      & ( ( C @ ( B @ ( produc901351817on_val @ hAPP_f1309113673on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
       => ( C @ ( B @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ ( cOMBB_171276332on_val @ hAPP_f1233687287l_bool ) @ ( cOMBB_1466889536on_val @ hAPP_f399538905l_bool ) @ hAPP_f850751421l_bool ) @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(116,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( B @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL )
    <=> ! [B: $i,C: $i] : ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_split__paired__All) ).

thf(684,plain,
    ! [A: $i] :
      ( ( ! [B: $i,C: $i] : ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL )
       => ! [B: $i] : ( B @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL ) )
      & ( ! [B: $i] : ( B @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL )
       => ! [B: $i,C: $i] : ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(38,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( C @ ( B @ ( A @ block_list_char ) ) )
     != ( E @ ( D @ lAss_list_char ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_exp_Osimps_I143_J) ).

thf(346,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( C @ ( B @ ( A @ block_list_char ) ) )
     != ( E @ ( D @ lAss_list_char ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(126,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_prod__cases3) ).

thf(763,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i,D: $i] :
          ( A
         != ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(16,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_672625589on_val @ hAPP_f1560238713l_bool ) @ hAPP_f926562337l_bool ) @ hAPP_P1708370145l_bool ) )
      = ( C @ ( B @ hAPP_P1708370145l_bool ) @ ( A @ hAPP_bool_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__prod_Itc__Expr__) ).

thf(272,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_672625589on_val @ hAPP_f1560238713l_bool ) @ hAPP_f926562337l_bool ) @ hAPP_P1708370145l_bool ) )
      = ( C @ ( B @ hAPP_P1708370145l_bool ) @ ( A @ hAPP_bool_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(210,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i,E: $i] :
          ( ( C
            = ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
         => ( E @ ( D @ ( B @ hAPP_f2135509569l_bool ) @ hAPP_f396019662l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) )
     => ( C @ ( B @ ( produc121041439l_bool @ hAPP_f1276548047l_bool ) @ hAPP_P1988153107l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_mem__splitI2) ).

thf(1133,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i,E: $i] :
          ( ( C
            = ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
         => ( E @ ( D @ ( B @ hAPP_f2135509569l_bool ) @ hAPP_f396019662l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) )
     => ( C @ ( B @ ( produc121041439l_bool @ hAPP_f1276548047l_bool ) @ hAPP_P1988153107l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(25,axiom,
    produc399384568l_bool = produc1815960045l_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_internal__split__def) ).

thf(300,plain,
    produc399384568l_bool = produc1815960045l_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(123,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc2128769400l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
    <=> ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_internal__split__conv) ).

thf(752,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL )
       => ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc2128769400l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) )
      & ( ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc2128769400l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
       => ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(56,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_383678192on_val @ hAPP_f1863694447l_bool ) @ hAPP_f1074020887l_bool ) @ hAPP_f1033709212l_bool ) )
      = ( C @ ( B @ hAPP_f1033709212l_bool ) @ ( A @ hAPP_bool_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__List__O) ).

thf(432,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_383678192on_val @ hAPP_f1863694447l_bool ) @ hAPP_f1074020887l_bool ) @ hAPP_f1033709212l_bool ) )
      = ( C @ ( B @ hAPP_f1033709212l_bool ) @ ( A @ hAPP_bool_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(145,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( I @ ( H @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( G @ ( none_val @ ( F @ ( E @ fun_up1149430426on_val ) ) @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( B @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
     => ( ( ( F @ ( I @ hAPP_l207779698on_val ) )
          = none_val )
       => ( ~ ( C @ ( F @ assigned ) @ hBOOL )
         => ( F @ ( E @ hAPP_l207779698on_val ) @ ( F @ ( I @ fun_up1149430426on_val ) ) @ ( H @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( G @ ( A @ ( F @ block_list_char ) ) @ ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( A @ ( F @ block_list_char ) ) @ ( B @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_redp__redsp_OBlockRedNone) ).

thf(835,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( I @ ( H @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( G @ ( none_val @ ( F @ ( E @ fun_up1149430426on_val ) ) @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( B @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
     => ( ( ( F @ ( I @ hAPP_l207779698on_val ) )
          = none_val )
       => ( ~ ( C @ ( F @ assigned ) @ hBOOL )
         => ( F @ ( E @ hAPP_l207779698on_val ) @ ( F @ ( I @ fun_up1149430426on_val ) ) @ ( H @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( G @ ( A @ ( F @ block_list_char ) ) @ ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( A @ ( F @ block_list_char ) ) @ ( B @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(134,axiom,
    ! [A: $i] :
      ( ( produc1259058957on_val @ ( A @ ( cOMBB_1759207793on_val @ hAPP_f10074679l_bool ) @ ( cOMBB_1027621637t_char @ hAPP_f1725502637l_bool ) @ hAPP_f439412817l_bool ) @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_split__eta) ).

thf(790,plain,
    ! [A: $i] :
      ( ( produc1259058957on_val @ ( A @ ( cOMBB_1759207793on_val @ hAPP_f10074679l_bool ) @ ( cOMBB_1027621637t_char @ hAPP_f1725502637l_bool ) @ hAPP_f439412817l_bool ) @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(35,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ lAss_list_char ) )
        = ( D @ ( C @ lAss_list_char ) ) )
    <=> ( ( B = D )
        & ( A = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_exp_Osimps_I6_J) ).

thf(326,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( B = D )
          & ( A = C ) )
       => ( ( B @ ( A @ lAss_list_char ) )
          = ( D @ ( C @ lAss_list_char ) ) ) )
      & ( ( ( B @ ( A @ lAss_list_char ) )
          = ( D @ ( C @ lAss_list_char ) ) )
       => ( ( B = D )
          & ( A = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(137,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( E @ ( D @ val_list_char @ ( E @ ( D @ val_list_char @ ( C @ ( B @ block_list_char ) ) @ ( A @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_redp__redsp_ORedBlock) ).

thf(807,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( E @ ( D @ val_list_char @ ( E @ ( D @ val_list_char @ ( C @ ( B @ block_list_char ) ) @ ( A @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(168,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ hAPP_l207779698on_val ) )
        = ( C @ some_val ) )
     => ( ( C @ some_val @ ( B @ ( A @ fun_up1149430426on_val ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_map__upd__triv) ).

thf(960,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ hAPP_l207779698on_val ) )
        = ( C @ some_val ) )
     => ( ( C @ some_val @ ( B @ ( A @ fun_up1149430426on_val ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(78,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] : ( D @ red @ ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( B @ ( A @ val_list_char @ seq_list_char ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_red__reds_ORedSeq) ).

thf(532,plain,
    ! [A: $i,B: $i,C: $i,D: $i] : ( D @ red @ ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( B @ ( A @ val_list_char @ seq_list_char ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(167,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc121041439l_bool @ hAPP_f1276548047l_bool ) @ hAPP_P1988153107l_bool ) @ ( A @ member763590124on_val ) @ hBOOL )
     => ~ ! [D: $i,E: $i] :
            ( ( C
              = ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
           => ~ ( E @ ( D @ ( B @ hAPP_f2135509569l_bool ) @ hAPP_f396019662l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_mem__splitE) ).

thf(955,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( produc121041439l_bool @ hAPP_f1276548047l_bool ) @ hAPP_P1988153107l_bool ) @ ( A @ member763590124on_val ) @ hBOOL )
     => ~ ! [D: $i,E: $i] :
            ( ( C
              = ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
           => ~ ( E @ ( D @ ( B @ hAPP_f2135509569l_bool ) @ hAPP_f396019662l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(160,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( J @ ( I @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( H @ ( none_val @ ( G @ ( F @ fun_up1149430426on_val ) ) @ ( E @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( D @ ( C @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
     => ( ( ( G @ ( J @ hAPP_l207779698on_val ) )
          = ( B @ some_val ) )
       => ( ~ ( D @ ( G @ assigned ) @ hBOOL )
         => ( G @ ( F @ hAPP_l207779698on_val ) @ ( G @ ( J @ fun_up1149430426on_val ) ) @ ( I @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( H @ ( B @ val_list_char @ ( G @ lAss_list_char ) @ seq_list_char ) @ ( A @ ( G @ block_list_char ) ) @ ( F @ ( E @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( D @ ( A @ ( G @ block_list_char ) ) @ ( C @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_redp__redsp_OBlockRedSome) ).

thf(928,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( J @ ( I @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( H @ ( none_val @ ( G @ ( F @ fun_up1149430426on_val ) ) @ ( E @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( D @ ( C @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
     => ( ( ( G @ ( J @ hAPP_l207779698on_val ) )
          = ( B @ some_val ) )
       => ( ~ ( D @ ( G @ assigned ) @ hBOOL )
         => ( G @ ( F @ hAPP_l207779698on_val ) @ ( G @ ( J @ fun_up1149430426on_val ) ) @ ( I @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( H @ ( B @ val_list_char @ ( G @ lAss_list_char ) @ seq_list_char ) @ ( A @ ( G @ block_list_char ) ) @ ( F @ ( E @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( D @ ( A @ ( G @ block_list_char ) ) @ ( C @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(23,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_635947099on_val @ hAPP_f1438732387l_bool ) @ hAPP_f1241216909l_bool ) @ hAPP_P1116729363l_bool ) )
      = ( C @ ( B @ hAPP_P2083594489on_val ) @ ( A @ hAPP_f1712766199l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc___012) ).

thf(294,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_635947099on_val @ hAPP_f1438732387l_bool ) @ hAPP_f1241216909l_bool ) @ hAPP_P1116729363l_bool ) )
      = ( C @ ( B @ hAPP_P2083594489on_val ) @ ( A @ hAPP_f1712766199l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(158,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_PairE) ).

thf(918,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(154,axiom,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_prod_Oexhaust) ).

thf(897,plain,
    ! [A: $i] :
      ~ ! [B: $i,C: $i] :
          ( A
         != ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(127,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ hAPP_f2144092865l_bool ) @ hAPP_f2011777102l_bool ) @ ( A @ member840932460on_val ) @ hBOOL )
     => ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( B @ ( produc334393759l_bool @ hAPP_f833559503l_bool ) @ hAPP_P1638898323l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_mem__splitI) ).

thf(767,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ hAPP_f2144092865l_bool ) @ hAPP_f2011777102l_bool ) @ ( A @ member840932460on_val ) @ hBOOL )
     => ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( B @ ( produc334393759l_bool @ hAPP_f833559503l_bool ) @ hAPP_P1638898323l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(208,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
     => ( F @ ( E @ ( A @ lAss_list_char ) @ ( D @ ( C @ ( A @ lAss_list_char ) @ ( B @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_redp__redsp_OLAssRed) ).

thf(1129,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
     => ( F @ ( E @ ( A @ lAss_list_char ) @ ( D @ ( C @ ( A @ lAss_list_char ) @ ( B @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(214,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ! [D: $i] :
          ( ( D @ ( C @ some_val @ ( B @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
          = none_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_map__upd__nonempty) ).

thf(1152,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ! [D: $i] :
          ( ( D @ ( C @ some_val @ ( B @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
          = none_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(93,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ hAPP_e500528395l_bool ) @ hAPP_P1988153107l_bool ) @ ( A @ member763590124on_val ) @ hBOOL )
     => ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( B @ ( produc2036005791l_bool @ hAPP_f468299289l_bool ) @ hAPP_P595502227l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_mem__splitI) ).

thf(596,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ hAPP_e500528395l_bool ) @ hAPP_P1988153107l_bool ) @ ( A @ member763590124on_val ) @ hBOOL )
     => ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( B @ ( produc2036005791l_bool @ hAPP_f468299289l_bool ) @ hAPP_P595502227l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(68,axiom,
    ! [A: $i,B: $i,C: $i] : ( C @ ( B @ ( A @ widen_2090681816t_char ) ) @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_TypeRel_Owiden_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__) ).

thf(486,plain,
    ! [A: $i,B: $i,C: $i] : ( C @ ( B @ ( A @ widen_2090681816t_char ) ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(136,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ hAPP_l207779698on_val ) )
        = C )
     => ( ( C @ ( B @ ( A @ fun_up1149430426on_val ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_fun__upd__idem) ).

thf(803,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ hAPP_l207779698on_val ) )
        = C )
     => ( ( C @ ( B @ ( A @ fun_up1149430426on_val ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(41,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ assigned ) @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_SmallStep_Oassigned) ).

thf(354,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ assigned ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(1,conjecture,
    p @ red @ ( l_a @ ( h_a @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( e_a @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( v @ some_val @ ( v_1 @ ( la @ fun_up1149430426on_val ) ) @ ( ha @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( ea @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ( p @ red @ ( l_a @ ( h_a @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( e_a @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( v @ some_val @ ( v_1 @ ( la @ fun_up1149430426on_val ) ) @ ( ha @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( ea @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(215,plain,
    ~ ( p @ red @ ( l_a @ ( h_a @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( e_a @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( v @ some_val @ ( v_1 @ ( la @ fun_up1149430426on_val ) ) @ ( ha @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( ea @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(70,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( A @ val_list_char )
     != ( D @ ( C @ ( B @ block_list_char ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_exp_Osimps_I82_J) ).

thf(491,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( A @ val_list_char )
     != ( D @ ( C @ ( B @ block_list_char ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(45,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBS_570216337l_bool ) @ hAPP_f1175813647l_bool ) )
      = ( C @ ( B @ hAPP_f1175813647l_bool ) @ ( C @ ( A @ hAPP_f1492320500l_bool ) @ hAPP_f1074020887l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It) ).

thf(364,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBS_570216337l_bool ) @ hAPP_f1175813647l_bool ) )
      = ( C @ ( B @ hAPP_f1175813647l_bool ) @ ( C @ ( A @ hAPP_f1492320500l_bool ) @ hAPP_f1074020887l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(28,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_1292453606on_val @ hAPP_f2052660463l_bool ) @ hAPP_f524589473l_bool ) @ hAPP_f1033709212l_bool ) )
      = ( C @ ( B @ hAPP_f602593190on_val ) @ ( A @ hAPP_P282169671l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_) ).

thf(309,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_1292453606on_val @ hAPP_f2052660463l_bool ) @ hAPP_f524589473l_bool ) @ hAPP_f1033709212l_bool ) )
      = ( C @ ( B @ hAPP_f602593190on_val ) @ ( A @ hAPP_P282169671l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(110,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( G @ ( F @ ( E @ ( D @ ( C @ wTrt ) ) ) ) @ hBOOL )
     => ( ( B @ ( A @ ( E @ ( D @ ( C @ wTrt ) ) ) ) @ hBOOL )
       => ( B @ ( A @ ( F @ seq_list_char ) @ ( E @ ( D @ ( C @ wTrt ) ) ) ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_WTrtSeq) ).

thf(659,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( G @ ( F @ ( E @ ( D @ ( C @ wTrt ) ) ) ) @ hBOOL )
     => ( ( B @ ( A @ ( E @ ( D @ ( C @ wTrt ) ) ) ) @ hBOOL )
       => ( B @ ( A @ ( F @ seq_list_char ) @ ( E @ ( D @ ( C @ wTrt ) ) ) ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(72,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_1153617344on_val @ hAPP_f1050935001l_bool ) @ hAPP_f1363667773l_bool ) @ hAPP_f1175813647l_bool ) )
      = ( C @ ( B @ hAPP_f1849790461on_val ) @ ( A @ hAPP_f1008932791l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_006) ).

thf(496,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_1153617344on_val @ hAPP_f1050935001l_bool ) @ hAPP_f1363667773l_bool ) @ hAPP_f1175813647l_bool ) )
      = ( C @ ( B @ hAPP_f1849790461on_val ) @ ( A @ hAPP_f1008932791l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(61,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_1303934920on_val @ hAPP_f1977633121l_bool ) @ hAPP_f1452292669l_bool ) @ hAPP_f1145256474l_bool ) )
      = ( C @ ( B @ hAPP_f61040418l_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).

thf(454,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBB_1303934920on_val @ hAPP_f1977633121l_bool ) @ hAPP_f1452292669l_bool ) @ hAPP_f1145256474l_bool ) )
      = ( C @ ( B @ hAPP_f61040418l_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(194,axiom,
    ! [A: $i,B: $i] : ( B @ ( B @ ( A @ widen_2090681816t_char ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_widen__refl) ).

thf(1069,plain,
    ! [A: $i,B: $i] : ( B @ ( B @ ( A @ widen_2090681816t_char ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(1159,plain,
    $false,
    inference(e,[status(thm)],[350,1036,809,629,352,479,1105,777,555,1005,247,269,1041,861,913,1063,340,782,709,417,288,565,651,838,949,1087,1147,421,881,228,261,216,321,376,623,937,574,646,253,1051,821,981,692,1119,998,988,428,312,1074,292,380,793,761,534,1047,1057,302,598,297,424,275,788,435,461,1079,285,324,974,1089,317,1111,869,499,857,1138,356,488,669,901,526,637,679,547,1016,590,1099,457,605,1131,654,244,938,266,633,657,1071,674,662,264,279,819,562,1007,1125,743,875,545,979,831,681,219,1117,509,616,990,996,362,451,567,477,631,758,816,726,621,483,520,240,626,769,943,367,552,521,399,1044,780,883,563,1000,438,922,986,306,374,648,342,1018,823,1049,557,580,690,1025,282,441,463,1085,359,907,1038,370,1141,600,1094,314,495,891,250,231,931,539,813,963,319,748,946,786,1030,684,346,763,272,1133,300,752,432,835,790,326,807,960,532,955,928,294,918,897,767,1129,1152,596,486,803,354,215,491,364,309,659,496,454,1069]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWW478+1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.07  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.39  % Computer : n015.cluster.edu
% 0.12/0.39  % Model    : x86_64 x86_64
% 0.12/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39  % Memory   : 8046.5625MB
% 0.12/0.39  % OS       : Linux 6.8.0-71-generic
% 0.12/0.39  % CPULimit : 300
% 0.12/0.39  % WCLimit  : 300
% 0.12/0.39  % DateTime : Sat Sep 26 16:10:43 UTC 2026
% 0.12/0.39  % CPUTime  : 
% 0.12/0.39  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.87/0.98  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.00/1.30  % [INFO] 	 Parsing done (317ms). 
% 2.00/1.31  % [INFO] 	 Running in sequential loop mode. 
% 3.06/1.70  % [INFO] 	 eprover registered as external prover. 
% 3.06/1.71  % [INFO] 	 Scanning for conjecture ... 
% 3.36/1.89  % [INFO] 	 Found a conjecture (or negated_conjecture) and 212 axioms. Running axiom selection ... 
% 4.09/2.08  % [INFO] 	 Axiom selection finished. Selected 212 axioms (removed 0 axioms). 
% 5.08/2.35  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 5.08/2.37  % [INFO] 	 Type checking passed. 
% 5.08/2.38  % [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 ... 
% 14.11/4.81  % External prover 'e' found a proof!
% 14.11/4.81  % [INFO] 	 Killing All external provers ... 
% 14.11/4.81  % Time passed: 4277ms (effective reasoning time: 3492ms)
% 14.11/4.81  % 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)>
% 14.11/4.82  % Axioms used in derivation (212): fact_129_cond__split__eta, fact_100_splitE, fact_111_red__reds_OSeqRed, fact_4_assms, gsy_c_hAPP_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O, fact_69_splitI, help_COMBB_1_1_COMBB_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc, fact_24_fun__upd__def, fact_17_Pair__inject, gsy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It, fact_145_exp_Osimps_I85_J, fact_63_sconf__def, fact_65_prod__caseI, fact_116_mem__splitE, fact_19_Pair__eq, fact_134_exp_Osimps_I143_J, fact_98_splitI2, help_fconj_3_1_U, fact_25_fun__upd__def, gsy_c_WellTypeRT_OWTrt, fact_5_map__upd__Some__unfold, fact_166_redp__redsp_ORedInitBlock, fact_60_PairE, fact_109_mem__splitI, fact_136_exp_Osimps_I3_J, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc___012, fact_105_mem__splitI, fact_6_map__upd__Some__unfold, fact_67_splitI, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__prod_Itc__Expr__, fact_78_internal__split__def, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_009, fact_104_mem__splitI, fact_86_prod_Osimps_I2_J, fact_57_split__paired__Ex, fact_7_map__upd__triv, fact_11_InitBlockRed_I2_J, fact_32_fun__upd__apply, fact_139_mem__def, fact_27_fun__upd__idem, fact_54_widen__trans, fact_0_InitBlockRed_I3_J, help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It, fact_23_split__paired__All, fact_2_fun__upd__triv, fact_148_exp_Osimps_I83_J, fact_91_split__conv, fact_42_red__preserves__lconf, fact_117_mem__splitE, fact_158_redp__redsp_ORedSeq, fact_33_fun__upd__apply, help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_006, fact_76_internal__split__def, help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__010, fact_114_red__reds_ORedBlock, fact_26_fun__upd__idem, fact_130_cond__split__eta, fact_140_mem__def, fact_125_mem__splitI2, fact_137_exp_Osimps_I11_J, fact_102_splitE, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O, fact_39_fun__upd__idem__iff, fact_93_split__eta, fact_66_prod__caseI, fact_46_prod__induct3, fact_28_fun__upd__other, fact_12_prod__induct4, fact_132_splitE2, fact_30_fun__upd__twist, fact_94_split__eta, fact_123_mem__splitI2, help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_, gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption, gsy_c_member_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_, help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__List__Olist_, fact_53_prod_Oexhaust, fact_152_exp_Osimps_I142_J, fact_151_exp_Osimps_I197_J, gsy_c_member_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J, fact_126_mem__splitI2, fact_52_prod_Oexhaust, fact_71_splitD, fact_64_prod__caseI, fact_59_PairE, fact_164_redp__redsp_OBlockRedSome, fact_22_split__paired__All, fact_106_mem__splitI, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc___013, fact_34_fun__upd__same, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_008, fact_144_exp_Osimps_I74_J, fact_61_PairE, fact_89_split__conv, fact_142_exp_Osimps_I10_J, help_fconj_2_1_U, fact_9_map__upd__eqD1, fact_103_WTrtBlock, help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_007, fact_83_split__part, fact_95_red__reds_OInitBlockRed, fact_45_prod__induct3, fact_41_red__preserves__hconf, fact_38_fun__upd__idem__iff, fact_20_Pair__eq, fact_113_red__reds_ORedSeq, fact_118_mem__splitE, fact_13_prod__cases4, fact_121_mem__splitI2, fact_50_pred__equals__eq2, help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O_004, fact_37_fun__upd__upd, fact_138_exp_Osimps_I6_J, fact_56_split__paired__Ex, fact_157_redp__redsp_OBlockRedNone, help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O, gsy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_M, fact_84_split__part, fact_131_splitE2, help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__List__Olis, fact_29_fun__upd__other, fact_141_mem__def, fact_10_map__upd__eqD1, fact_68_splitI, fact_101_splitE, fact_15_Pair__inject, fact_143_exp_Osimps_I84_J, fact_35_fun__upd__same, fact_55_InitBlockRed_I5_J, fact_127_red__reds_ORedLAss, fact_110_WTrtSeq, fact_36_fun__upd__upd, fact_154_red__reds_OBlockRedSome, fact_156_redp__redsp_OLAssRed, help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_005, fact_124_mem__splitI2, fact_107_mem__splitI, gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__O, fact_48_pred__equals__eq2, help_COMBC_1_1_COMBC_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Optio, fact_161_redp__redsp_ORedBlock, help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__, help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_002, fact_88_prod_Osimps_I2_J, fact_155_redp__redsp_OSeqRed, fact_40_widen__refl, fact_92_split__eta, fact_162_empty__upd__none, fact_51_prod_Oexhaust, gsy_c_TypeRel_Owiden_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__, fact_82_split__twice, fact_43_prod__cases3, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo, fact_16_Pair__inject, fact_165_redp__red__eq, fact_62_internal__split__conv, help_fconj_1_1_U, fact_85_split__part, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__prod_Itc__fun_It, help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_011, fact_149_exp_Osimps_I145_J, fact_159_map__upd__nonempty, fact_122_mem__splitI2, fact_163_empty__upd__none, fact_8_map__upd__triv, fact_72_splitD, fact_74_split__weak__cong, fact_18_Pair__eq, fact_99_splitI2, fact_160_map__upd__nonempty, fact_3_fun__upd__triv, fact_1_InitBlockRed_I1_J, gsy_c_WellForm_Owf__prog_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Stri, fact_58_split__paired__Ex, fact_147_exp_Osimps_I82_J, fact_70_splitD, fact_75_split__weak__cong, help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It, fact_120_mem__splitE, help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M, fact_49_pred__equals__eq2, fact_119_mem__splitE, fact_21_split__paired__All, fact_44_prod__cases3, fact_150_exp_Osimps_I144_J, fact_81_split__twice, fact_47_red__preserves__sconf, fact_146_exp_Osimps_I75_J, fact_96_red__reds_ORedInitBlock, fact_87_prod_Osimps_I2_J, fact_128_cond__split__eta, gsy_c_member_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String_, fact_97_splitI2, fact_79_split__twice, fact_90_split__conv, gsy_c_SmallStep_Oassigned, help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_003, fact_133_splitE2, fact_77_internal__split__def, fact_115_mem__splitE, gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool, fact_112_red__reds_OLAssRed, gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption_001, fact_73_split__weak__cong, fact_80_split__twice, fact_135_exp_Osimps_I196_J, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__List__O, fact_153_redp__redsp_OInitBlockRed, fact_14_InitBlockRed_I4_J, fact_108_mem__splitI, fact_31_fun__upd__twist
% 14.11/4.82  % No. of inferences in proof: 428
% 14.11/4.82  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4277 ms resp. 3492 ms w/o parsing
% 14.86/5.05  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.86/5.06  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------