LEO-II---2.3.1.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : LEO-II---2.3.1
% Problem  : SWW478+3 : TPTP v9.3.1. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n026.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 : Wed Oct  7 11:01:45 AM UTC 2026

% Result   : Theorem 23.62s 4.19s
% Output   : CNFRefutation 4.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   82
% Syntax   : Number of formulae    : 1143 ( 650 unt;   0 typ;   0 def)
%            Number of atoms       : 6160 (2925 equ;   0 cnn)
%            Maximal formula atoms :    5 (   5 avg)
%            Number of connectives : 23997 (2530   ~;1529   |;  21   &;19668   @)
%                                         (  57 <=>; 192  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     : 1174 (1171 usr; 286 con; 0-6 aty)
%            Number of variables   : 4494 (   0   ^;4464   !;  30   ?;4494   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_add,type,
    add: $i ).

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

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

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

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

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

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

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

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

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

thf(tp_bop,type,
    bop: $i ).

thf(tp_cOMBB_1015721476ol_nat,type,
    cOMBB_1015721476ol_nat: $i ).

thf(tp_cOMBB_1033145403t_char,type,
    cOMBB_1033145403t_char: $i ).

thf(tp_cOMBB_1034324152on_val,type,
    cOMBB_1034324152on_val: $i ).

thf(tp_cOMBB_1035649854t_char,type,
    cOMBB_1035649854t_char: $i ).

thf(tp_cOMBB_1078680455on_val,type,
    cOMBB_1078680455on_val: $i ).

thf(tp_cOMBB_1091123364t_char,type,
    cOMBB_1091123364t_char: $i ).

thf(tp_cOMBB_109816436t_char,type,
    cOMBB_109816436t_char: $i ).

thf(tp_cOMBB_1112666310t_char,type,
    cOMBB_1112666310t_char: $i ).

thf(tp_cOMBB_1153617344on_val,type,
    cOMBB_1153617344on_val: $i ).

thf(tp_cOMBB_1153773871on_val,type,
    cOMBB_1153773871on_val: $i ).

thf(tp_cOMBB_1200577438t_char,type,
    cOMBB_1200577438t_char: $i ).

thf(tp_cOMBB_1223415373on_val,type,
    cOMBB_1223415373on_val: $i ).

thf(tp_cOMBB_123628846t_char,type,
    cOMBB_123628846t_char: $i ).

thf(tp_cOMBB_1270208498t_char,type,
    cOMBB_1270208498t_char: $i ).

thf(tp_cOMBB_1293776864on_val,type,
    cOMBB_1293776864on_val: $i ).

thf(tp_cOMBB_1303934920on_val,type,
    cOMBB_1303934920on_val: $i ).

thf(tp_cOMBB_1458388806ol_bop,type,
    cOMBB_1458388806ol_bop: $i ).

thf(tp_cOMBB_147773915t_char,type,
    cOMBB_147773915t_char: $i ).

thf(tp_cOMBB_1490692730t_char,type,
    cOMBB_1490692730t_char: $i ).

thf(tp_cOMBB_1518282696on_val,type,
    cOMBB_1518282696on_val: $i ).

thf(tp_cOMBB_1520154591t_char,type,
    cOMBB_1520154591t_char: $i ).

thf(tp_cOMBB_1522540928on_val,type,
    cOMBB_1522540928on_val: $i ).

thf(tp_cOMBB_1551681790t_char,type,
    cOMBB_1551681790t_char: $i ).

thf(tp_cOMBB_1558246132t_char,type,
    cOMBB_1558246132t_char: $i ).

thf(tp_cOMBB_1586673472t_char,type,
    cOMBB_1586673472t_char: $i ).

thf(tp_cOMBB_1617503877on_val,type,
    cOMBB_1617503877on_val: $i ).

thf(tp_cOMBB_1643767893t_char,type,
    cOMBB_1643767893t_char: $i ).

thf(tp_cOMBB_1681501894t_char,type,
    cOMBB_1681501894t_char: $i ).

thf(tp_cOMBB_1701031980ol_val,type,
    cOMBB_1701031980ol_val: $i ).

thf(tp_cOMBB_1705938036t_char,type,
    cOMBB_1705938036t_char: $i ).

thf(tp_cOMBB_1718333400on_val,type,
    cOMBB_1718333400on_val: $i ).

thf(tp_cOMBB_1750801836on_val,type,
    cOMBB_1750801836on_val: $i ).

thf(tp_cOMBB_1888336841t_char,type,
    cOMBB_1888336841t_char: $i ).

thf(tp_cOMBB_1977588741on_val,type,
    cOMBB_1977588741on_val: $i ).

thf(tp_cOMBB_2041093409on_val,type,
    cOMBB_2041093409on_val: $i ).

thf(tp_cOMBB_2042763133t_char,type,
    cOMBB_2042763133t_char: $i ).

thf(tp_cOMBB_2078271971st_val,type,
    cOMBB_2078271971st_val: $i ).

thf(tp_cOMBB_2078984970ol_val,type,
    cOMBB_2078984970ol_val: $i ).

thf(tp_cOMBB_2084052674on_val,type,
    cOMBB_2084052674on_val: $i ).

thf(tp_cOMBB_2139740953al_val,type,
    cOMBB_2139740953al_val: $i ).

thf(tp_cOMBB_2143526097t_char,type,
    cOMBB_2143526097t_char: $i ).

thf(tp_cOMBB_308691073st_val,type,
    cOMBB_308691073st_val: $i ).

thf(tp_cOMBB_33167485t_char,type,
    cOMBB_33167485t_char: $i ).

thf(tp_cOMBB_338473166ist_ty,type,
    cOMBB_338473166ist_ty: $i ).

thf(tp_cOMBB_352765746t_char,type,
    cOMBB_352765746t_char: $i ).

thf(tp_cOMBB_383678192on_val,type,
    cOMBB_383678192on_val: $i ).

thf(tp_cOMBB_507006011t_char,type,
    cOMBB_507006011t_char: $i ).

thf(tp_cOMBB_526805108t_char,type,
    cOMBB_526805108t_char: $i ).

thf(tp_cOMBB_550632017t_char,type,
    cOMBB_550632017t_char: $i ).

thf(tp_cOMBB_555068556on_val,type,
    cOMBB_555068556on_val: $i ).

thf(tp_cOMBB_565412073on_val,type,
    cOMBB_565412073on_val: $i ).

thf(tp_cOMBB_565990871t_char,type,
    cOMBB_565990871t_char: $i ).

thf(tp_cOMBB_588525814on_val,type,
    cOMBB_588525814on_val: $i ).

thf(tp_cOMBB_657296617har_ty,type,
    cOMBB_657296617har_ty: $i ).

thf(tp_cOMBB_672864638t_char,type,
    cOMBB_672864638t_char: $i ).

thf(tp_cOMBB_673739729t_char,type,
    cOMBB_673739729t_char: $i ).

thf(tp_cOMBB_68065882ist_ty,type,
    cOMBB_68065882ist_ty: $i ).

thf(tp_cOMBB_705522285on_val,type,
    cOMBB_705522285on_val: $i ).

thf(tp_cOMBB_731867268ol_nat,type,
    cOMBB_731867268ol_nat: $i ).

thf(tp_cOMBB_741416308t_char,type,
    cOMBB_741416308t_char: $i ).

thf(tp_cOMBB_761748254ol_bop,type,
    cOMBB_761748254ol_bop: $i ).

thf(tp_cOMBB_773375802t_char,type,
    cOMBB_773375802t_char: $i ).

thf(tp_cOMBB_773661144t_char,type,
    cOMBB_773661144t_char: $i ).

thf(tp_cOMBB_779086262on_val,type,
    cOMBB_779086262on_val: $i ).

thf(tp_cOMBB_808210516t_char,type,
    cOMBB_808210516t_char: $i ).

thf(tp_cOMBB_815843940ol_val,type,
    cOMBB_815843940ol_val: $i ).

thf(tp_cOMBB_847828016t_char,type,
    cOMBB_847828016t_char: $i ).

thf(tp_cOMBB_859890145har_ty,type,
    cOMBB_859890145har_ty: $i ).

thf(tp_cOMBB_864319000t_char,type,
    cOMBB_864319000t_char: $i ).

thf(tp_cOMBB_961360819t_char,type,
    cOMBB_961360819t_char: $i ).

thf(tp_cOMBB_984708934t_char,type,
    cOMBB_984708934t_char: $i ).

thf(tp_cOMBB_985659173on_val,type,
    cOMBB_985659173on_val: $i ).

thf(tp_cOMBB_bool_bool_nat,type,
    cOMBB_bool_bool_nat: $i ).

thf(tp_cOMBC_1021753250l_bool,type,
    cOMBC_1021753250l_bool: $i ).

thf(tp_cOMBC_1025440566r_bool,type,
    cOMBC_1025440566r_bool: $i ).

thf(tp_cOMBC_1127703214r_bool,type,
    cOMBC_1127703214r_bool: $i ).

thf(tp_cOMBC_1297648632l_bool,type,
    cOMBC_1297648632l_bool: $i ).

thf(tp_cOMBC_1317565126l_bool,type,
    cOMBC_1317565126l_bool: $i ).

thf(tp_cOMBC_1338332465l_bool,type,
    cOMBC_1338332465l_bool: $i ).

thf(tp_cOMBC_1365742487l_bool,type,
    cOMBC_1365742487l_bool: $i ).

thf(tp_cOMBC_1387630958r_bool,type,
    cOMBC_1387630958r_bool: $i ).

thf(tp_cOMBC_1407716098l_bool,type,
    cOMBC_1407716098l_bool: $i ).

thf(tp_cOMBC_148995234l_bool,type,
    cOMBC_148995234l_bool: $i ).

thf(tp_cOMBC_1491642377l_bool,type,
    cOMBC_1491642377l_bool: $i ).

thf(tp_cOMBC_1518234801l_bool,type,
    cOMBC_1518234801l_bool: $i ).

thf(tp_cOMBC_1535683812l_bool,type,
    cOMBC_1535683812l_bool: $i ).

thf(tp_cOMBC_1585774710l_bool,type,
    cOMBC_1585774710l_bool: $i ).

thf(tp_cOMBC_1603044337l_bool,type,
    cOMBC_1603044337l_bool: $i ).

thf(tp_cOMBC_1608987946l_bool,type,
    cOMBC_1608987946l_bool: $i ).

thf(tp_cOMBC_1718404842r_bool,type,
    cOMBC_1718404842r_bool: $i ).

thf(tp_cOMBC_1784597444r_bool,type,
    cOMBC_1784597444r_bool: $i ).

thf(tp_cOMBC_1979963740l_bool,type,
    cOMBC_1979963740l_bool: $i ).

thf(tp_cOMBC_199425070l_bool,type,
    cOMBC_199425070l_bool: $i ).

thf(tp_cOMBC_2027949654l_bool,type,
    cOMBC_2027949654l_bool: $i ).

thf(tp_cOMBC_2141828763l_bool,type,
    cOMBC_2141828763l_bool: $i ).

thf(tp_cOMBC_220519196l_bool,type,
    cOMBC_220519196l_bool: $i ).

thf(tp_cOMBC_226598744l_bool,type,
    cOMBC_226598744l_bool: $i ).

thf(tp_cOMBC_229530231l_bool,type,
    cOMBC_229530231l_bool: $i ).

thf(tp_cOMBC_317789649l_bool,type,
    cOMBC_317789649l_bool: $i ).

thf(tp_cOMBC_331963401l_bool,type,
    cOMBC_331963401l_bool: $i ).

thf(tp_cOMBC_36589090l_bool,type,
    cOMBC_36589090l_bool: $i ).

thf(tp_cOMBC_389248878r_bool,type,
    cOMBC_389248878r_bool: $i ).

thf(tp_cOMBC_390659185l_bool,type,
    cOMBC_390659185l_bool: $i ).

thf(tp_cOMBC_407285762l_bool,type,
    cOMBC_407285762l_bool: $i ).

thf(tp_cOMBC_442485623l_bool,type,
    cOMBC_442485623l_bool: $i ).

thf(tp_cOMBC_475083938l_bool,type,
    cOMBC_475083938l_bool: $i ).

thf(tp_cOMBC_516637475l_bool,type,
    cOMBC_516637475l_bool: $i ).

thf(tp_cOMBC_562612496l_bool,type,
    cOMBC_562612496l_bool: $i ).

thf(tp_cOMBC_622308798l_bool,type,
    cOMBC_622308798l_bool: $i ).

thf(tp_cOMBC_654453230r_bool,type,
    cOMBC_654453230r_bool: $i ).

thf(tp_cOMBC_766524526l_bool,type,
    cOMBC_766524526l_bool: $i ).

thf(tp_cOMBC_790582442r_bool,type,
    cOMBC_790582442r_bool: $i ).

thf(tp_cOMBC_813705475l_bool,type,
    cOMBC_813705475l_bool: $i ).

thf(tp_cOMBC_818212448l_bool,type,
    cOMBC_818212448l_bool: $i ).

thf(tp_cOMBC_832625297y_bool,type,
    cOMBC_832625297y_bool: $i ).

thf(tp_cOMBC_886773442r_bool,type,
    cOMBC_886773442r_bool: $i ).

thf(tp_cOMBC_892477410l_bool,type,
    cOMBC_892477410l_bool: $i ).

thf(tp_cOMBC_967917532l_bool,type,
    cOMBC_967917532l_bool: $i ).

thf(tp_cOMBK_1097134891t_char,type,
    cOMBK_1097134891t_char: $i ).

thf(tp_cOMBK_1294242658t_char,type,
    cOMBK_1294242658t_char: $i ).

thf(tp_cOMBK_184479553on_val,type,
    cOMBK_184479553on_val: $i ).

thf(tp_cOMBK_1867744698t_char,type,
    cOMBK_1867744698t_char: $i ).

thf(tp_cOMBK_1944287343al_nat,type,
    cOMBK_1944287343al_nat: $i ).

thf(tp_cOMBS_1218320756l_bool,type,
    cOMBS_1218320756l_bool: $i > $i > $i ).

thf(tp_cOMBS_1319864284l_bool,type,
    cOMBS_1319864284l_bool: $i > $i > $i ).

thf(tp_cOMBS_1502238389l_bool,type,
    cOMBS_1502238389l_bool: $i > $i > $i ).

thf(tp_cOMBS_1743887558l_bool,type,
    cOMBS_1743887558l_bool: $i > $i > $i ).

thf(tp_cOMBS_350755140l_bool,type,
    cOMBS_350755140l_bool: $i > $i > $i ).

thf(tp_cOMBS_570216337l_bool,type,
    cOMBS_570216337l_bool: $i > $i > $i ).

thf(tp_cOMBS_635570165l_bool,type,
    cOMBS_635570165l_bool: $i > $i > $i ).

thf(tp_cOMBS_nat_bool_bool,type,
    cOMBS_nat_bool_bool: $i > $i > $i ).

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

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

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

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

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

thf(tp_collec1387638140t_char,type,
    collec1387638140t_char: $i > $i ).

thf(tp_collec1583467887t_char,type,
    collec1583467887t_char: $i > $i ).

thf(tp_collec1797130234t_char,type,
    collec1797130234t_char: $i > $i ).

thf(tp_collec2087910442on_val,type,
    collec2087910442on_val: $i > $i ).

thf(tp_collec718040978on_val,type,
    collec718040978on_val: $i > $i ).

thf(tp_collect_list_char,type,
    collect_list_char: $i > $i ).

thf(tp_collect_nat,type,
    collect_nat: $i > $i ).

thf(tp_comp_o1129292306t_char,type,
    comp_o1129292306t_char: $i > $i > $i ).

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

thf(tp_conf_P373316194t_char,type,
    conf_P373316194t_char: $i > $i > $i > $i > $i ).

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

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

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

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

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

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

thf(tp_dom_Pr695701035ar_val,type,
    dom_Pr695701035ar_val: $i > $i ).

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

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

thf(tp_dom_na996029170on_val,type,
    dom_na996029170on_val: $i > $i ).

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

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

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

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

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

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

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

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

thf(tp_fNot,type,
    fNot: $i ).

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

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

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

thf(tp_fequal1937332960on_val,type,
    fequal1937332960on_val: $i ).

thf(tp_fequal_option_val,type,
    fequal_option_val: $i ).

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

thf(tp_fields1147507508t_char,type,
    fields1147507508t_char: $i > $i > $i > $i ).

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

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

thf(tp_fun_up1149430426on_val,type,
    fun_up1149430426on_val: $i > $i > $i > $i ).

thf(tp_fun_up2041264236on_val,type,
    fun_up2041264236on_val: $i > $i > $i > $i ).

thf(tp_fun_up204312361on_val,type,
    fun_up204312361on_val: $i > $i > $i > $i ).

thf(tp_fun_up424764369ion_ty,type,
    fun_up424764369ion_ty: $i > $i > $i > $i ).

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

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

thf(tp_hAPP_P1002912327r_bool,type,
    hAPP_P1002912327r_bool: $i > $i > $i ).

thf(tp_hAPP_P1019319281l_bool,type,
    hAPP_P1019319281l_bool: $i > $i > $i ).

thf(tp_hAPP_P1033205013l_bool,type,
    hAPP_P1033205013l_bool: $i > $i > $i ).

thf(tp_hAPP_P1034346913l_bool,type,
    hAPP_P1034346913l_bool: $i > $i > $i ).

thf(tp_hAPP_P1071727823t_char,type,
    hAPP_P1071727823t_char: $i > $i > $i ).

thf(tp_hAPP_P1085566419p_bool,type,
    hAPP_P1085566419p_bool: $i > $i > $i ).

thf(tp_hAPP_P1116729363l_bool,type,
    hAPP_P1116729363l_bool: $i > $i > $i ).

thf(tp_hAPP_P1180869721l_bool,type,
    hAPP_P1180869721l_bool: $i > $i > $i ).

thf(tp_hAPP_P1183008383l_bool,type,
    hAPP_P1183008383l_bool: $i > $i > $i ).

thf(tp_hAPP_P1183499705r_bool,type,
    hAPP_P1183499705r_bool: $i > $i > $i ).

thf(tp_hAPP_P1187139874r_bool,type,
    hAPP_P1187139874r_bool: $i > $i > $i ).

thf(tp_hAPP_P1198052655l_bool,type,
    hAPP_P1198052655l_bool: $i > $i > $i ).

thf(tp_hAPP_P1217996045l_bool,type,
    hAPP_P1217996045l_bool: $i > $i > $i ).

thf(tp_hAPP_P1220989409t_char,type,
    hAPP_P1220989409t_char: $i > $i > $i ).

thf(tp_hAPP_P1221872711l_bool,type,
    hAPP_P1221872711l_bool: $i > $i > $i ).

thf(tp_hAPP_P1224499548t_char,type,
    hAPP_P1224499548t_char: $i > $i > $i ).

thf(tp_hAPP_P1228500987ion_ty,type,
    hAPP_P1228500987ion_ty: $i > $i > $i ).

thf(tp_hAPP_P1235399154l_bool,type,
    hAPP_P1235399154l_bool: $i > $i > $i ).

thf(tp_hAPP_P1240100515r_bool,type,
    hAPP_P1240100515r_bool: $i > $i > $i ).

thf(tp_hAPP_P124632071l_bool,type,
    hAPP_P124632071l_bool: $i > $i > $i ).

thf(tp_hAPP_P124661l_bool,type,
    hAPP_P124661l_bool: $i > $i > $i ).

thf(tp_hAPP_P1247668062t_char,type,
    hAPP_P1247668062t_char: $i > $i > $i ).

thf(tp_hAPP_P126004409l_bool,type,
    hAPP_P126004409l_bool: $i > $i > $i ).

thf(tp_hAPP_P1293136973l_bool,type,
    hAPP_P1293136973l_bool: $i > $i > $i ).

thf(tp_hAPP_P1303341961l_bool,type,
    hAPP_P1303341961l_bool: $i > $i > $i ).

thf(tp_hAPP_P1313790473l_bool,type,
    hAPP_P1313790473l_bool: $i > $i > $i ).

thf(tp_hAPP_P1327510541l_bool,type,
    hAPP_P1327510541l_bool: $i > $i > $i ).

thf(tp_hAPP_P1333315679l_bool,type,
    hAPP_P1333315679l_bool: $i > $i > $i ).

thf(tp_hAPP_P1333668416t_char,type,
    hAPP_P1333668416t_char: $i > $i > $i ).

thf(tp_hAPP_P1342907945t_char,type,
    hAPP_P1342907945t_char: $i > $i > $i ).

thf(tp_hAPP_P1362631157l_bool,type,
    hAPP_P1362631157l_bool: $i > $i > $i ).

thf(tp_hAPP_P1383068750l_bool,type,
    hAPP_P1383068750l_bool: $i > $i > $i ).

thf(tp_hAPP_P1384137393r_bool,type,
    hAPP_P1384137393r_bool: $i > $i > $i ).

thf(tp_hAPP_P1390376713l_bool,type,
    hAPP_P1390376713l_bool: $i > $i > $i ).

thf(tp_hAPP_P1392904962t_char,type,
    hAPP_P1392904962t_char: $i > $i > $i ).

thf(tp_hAPP_P1402001845l_bool,type,
    hAPP_P1402001845l_bool: $i > $i > $i ).

thf(tp_hAPP_P1418247892l_bool,type,
    hAPP_P1418247892l_bool: $i > $i > $i ).

thf(tp_hAPP_P1423780764t_char,type,
    hAPP_P1423780764t_char: $i > $i > $i ).

thf(tp_hAPP_P1457625805l_bool,type,
    hAPP_P1457625805l_bool: $i > $i > $i ).

thf(tp_hAPP_P1472618637l_bool,type,
    hAPP_P1472618637l_bool: $i > $i > $i ).

thf(tp_hAPP_P1486793863on_val,type,
    hAPP_P1486793863on_val: $i > $i > $i ).

thf(tp_hAPP_P1503283977l_bool,type,
    hAPP_P1503283977l_bool: $i > $i > $i ).

thf(tp_hAPP_P1510515380on_val,type,
    hAPP_P1510515380on_val: $i > $i > $i ).

thf(tp_hAPP_P1517699917l_bool,type,
    hAPP_P1517699917l_bool: $i > $i > $i ).

thf(tp_hAPP_P1526035745on_val,type,
    hAPP_P1526035745on_val: $i > $i > $i ).

thf(tp_hAPP_P153687689l_bool,type,
    hAPP_P153687689l_bool: $i > $i > $i ).

thf(tp_hAPP_P1538518401al_val,type,
    hAPP_P1538518401al_val: $i > $i > $i ).

thf(tp_hAPP_P1539798428t_char,type,
    hAPP_P1539798428t_char: $i > $i > $i ).

thf(tp_hAPP_P1552072218l_bool,type,
    hAPP_P1552072218l_bool: $i > $i > $i ).

thf(tp_hAPP_P1562529797l_bool,type,
    hAPP_P1562529797l_bool: $i > $i > $i ).

thf(tp_hAPP_P1574824955y_bool,type,
    hAPP_P1574824955y_bool: $i > $i > $i ).

thf(tp_hAPP_P159683425l_bool,type,
    hAPP_P159683425l_bool: $i > $i > $i ).

thf(tp_hAPP_P1609485901l_bool,type,
    hAPP_P1609485901l_bool: $i > $i > $i ).

thf(tp_hAPP_P1614880106l_bool,type,
    hAPP_P1614880106l_bool: $i > $i > $i ).

thf(tp_hAPP_P1632759357r_bool,type,
    hAPP_P1632759357r_bool: $i > $i > $i ).

thf(tp_hAPP_P1653675595l_bool,type,
    hAPP_P1653675595l_bool: $i > $i > $i ).

thf(tp_hAPP_P1657265855t_char,type,
    hAPP_P1657265855t_char: $i > $i > $i ).

thf(tp_hAPP_P1661798543t_char,type,
    hAPP_P1661798543t_char: $i > $i > $i ).

thf(tp_hAPP_P1668407995t_char,type,
    hAPP_P1668407995t_char: $i > $i > $i ).

thf(tp_hAPP_P1679186017l_bool,type,
    hAPP_P1679186017l_bool: $i > $i > $i ).

thf(tp_hAPP_P1680401186r_bool,type,
    hAPP_P1680401186r_bool: $i > $i > $i ).

thf(tp_hAPP_P1708370145l_bool,type,
    hAPP_P1708370145l_bool: $i > $i > $i ).

thf(tp_hAPP_P1756548163t_char,type,
    hAPP_P1756548163t_char: $i > $i > $i ).

thf(tp_hAPP_P1758592847on_val,type,
    hAPP_P1758592847on_val: $i > $i > $i ).

thf(tp_hAPP_P1859316965t_char,type,
    hAPP_P1859316965t_char: $i > $i > $i ).

thf(tp_hAPP_P1860450421l_bool,type,
    hAPP_P1860450421l_bool: $i > $i > $i ).

thf(tp_hAPP_P1862681481l_bool,type,
    hAPP_P1862681481l_bool: $i > $i > $i ).

thf(tp_hAPP_P1870962205on_val,type,
    hAPP_P1870962205on_val: $i > $i > $i ).

thf(tp_hAPP_P1874979071al_val,type,
    hAPP_P1874979071al_val: $i > $i > $i ).

thf(tp_hAPP_P1875010047on_val,type,
    hAPP_P1875010047on_val: $i > $i > $i ).

thf(tp_hAPP_P1878549513l_bool,type,
    hAPP_P1878549513l_bool: $i > $i > $i ).

thf(tp_hAPP_P1886180715on_val,type,
    hAPP_P1886180715on_val: $i > $i > $i ).

thf(tp_hAPP_P1907982426r_bool,type,
    hAPP_P1907982426r_bool: $i > $i > $i ).

thf(tp_hAPP_P1926698759r_bool,type,
    hAPP_P1926698759r_bool: $i > $i > $i ).

thf(tp_hAPP_P1953134729l_bool,type,
    hAPP_P1953134729l_bool: $i > $i > $i ).

thf(tp_hAPP_P1958775007t_char,type,
    hAPP_P1958775007t_char: $i > $i > $i ).

thf(tp_hAPP_P1963616220on_val,type,
    hAPP_P1963616220on_val: $i > $i > $i ).

thf(tp_hAPP_P2010574925r_bool,type,
    hAPP_P2010574925r_bool: $i > $i > $i ).

thf(tp_hAPP_P2014166431r_bool,type,
    hAPP_P2014166431r_bool: $i > $i > $i ).

thf(tp_hAPP_P2015431471on_val,type,
    hAPP_P2015431471on_val: $i > $i > $i ).

thf(tp_hAPP_P2015860941l_bool,type,
    hAPP_P2015860941l_bool: $i > $i > $i ).

thf(tp_hAPP_P2028072621l_bool,type,
    hAPP_P2028072621l_bool: $i > $i > $i ).

thf(tp_hAPP_P2028292026l_bool,type,
    hAPP_P2028292026l_bool: $i > $i > $i ).

thf(tp_hAPP_P2053453961y_bool,type,
    hAPP_P2053453961y_bool: $i > $i > $i ).

thf(tp_hAPP_P205570445l_bool,type,
    hAPP_P205570445l_bool: $i > $i > $i ).

thf(tp_hAPP_P2077211775on_val,type,
    hAPP_P2077211775on_val: $i > $i > $i ).

thf(tp_hAPP_P2077557811l_bool,type,
    hAPP_P2077557811l_bool: $i > $i > $i ).

thf(tp_hAPP_P2094403585on_val,type,
    hAPP_P2094403585on_val: $i > $i > $i ).

thf(tp_hAPP_P2115985549l_bool,type,
    hAPP_P2115985549l_bool: $i > $i > $i ).

thf(tp_hAPP_P2118621157r_bool,type,
    hAPP_P2118621157r_bool: $i > $i > $i ).

thf(tp_hAPP_P2123002749l_bool,type,
    hAPP_P2123002749l_bool: $i > $i > $i ).

thf(tp_hAPP_P2123720426al_val,type,
    hAPP_P2123720426al_val: $i > $i > $i ).

thf(tp_hAPP_P2139822957l_bool,type,
    hAPP_P2139822957l_bool: $i > $i > $i ).

thf(tp_hAPP_P240409993l_bool,type,
    hAPP_P240409993l_bool: $i > $i > $i ).

thf(tp_hAPP_P242904598t_char,type,
    hAPP_P242904598t_char: $i > $i > $i ).

thf(tp_hAPP_P265246237on_val,type,
    hAPP_P265246237on_val: $i > $i > $i ).

thf(tp_hAPP_P274544981l_bool,type,
    hAPP_P274544981l_bool: $i > $i > $i ).

thf(tp_hAPP_P27757617y_bool,type,
    hAPP_P27757617y_bool: $i > $i > $i ).

thf(tp_hAPP_P282169671l_bool,type,
    hAPP_P282169671l_bool: $i > $i > $i ).

thf(tp_hAPP_P291613419on_val,type,
    hAPP_P291613419on_val: $i > $i > $i ).

thf(tp_hAPP_P325013257l_bool,type,
    hAPP_P325013257l_bool: $i > $i > $i ).

thf(tp_hAPP_P330218428on_val,type,
    hAPP_P330218428on_val: $i > $i > $i ).

thf(tp_hAPP_P378063101l_bool,type,
    hAPP_P378063101l_bool: $i > $i > $i ).

thf(tp_hAPP_P396425609l_bool,type,
    hAPP_P396425609l_bool: $i > $i > $i ).

thf(tp_hAPP_P409642305l_bool,type,
    hAPP_P409642305l_bool: $i > $i > $i ).

thf(tp_hAPP_P415257547l_bool,type,
    hAPP_P415257547l_bool: $i > $i > $i ).

thf(tp_hAPP_P449474095r_bool,type,
    hAPP_P449474095r_bool: $i > $i > $i ).

thf(tp_hAPP_P468446343l_bool,type,
    hAPP_P468446343l_bool: $i > $i > $i ).

thf(tp_hAPP_P476431815r_bool,type,
    hAPP_P476431815r_bool: $i > $i > $i ).

thf(tp_hAPP_P47773639al_val,type,
    hAPP_P47773639al_val: $i > $i > $i ).

thf(tp_hAPP_P483670507l_bool,type,
    hAPP_P483670507l_bool: $i > $i > $i ).

thf(tp_hAPP_P499022727r_bool,type,
    hAPP_P499022727r_bool: $i > $i > $i ).

thf(tp_hAPP_P502294281l_bool,type,
    hAPP_P502294281l_bool: $i > $i > $i ).

thf(tp_hAPP_P504978887l_bool,type,
    hAPP_P504978887l_bool: $i > $i > $i ).

thf(tp_hAPP_P527298901l_bool,type,
    hAPP_P527298901l_bool: $i > $i > $i ).

thf(tp_hAPP_P530382601l_bool,type,
    hAPP_P530382601l_bool: $i > $i > $i ).

thf(tp_hAPP_P53416969l_bool,type,
    hAPP_P53416969l_bool: $i > $i > $i ).

thf(tp_hAPP_P569585933l_bool,type,
    hAPP_P569585933l_bool: $i > $i > $i ).

thf(tp_hAPP_P579374437t_char,type,
    hAPP_P579374437t_char: $i > $i > $i ).

thf(tp_hAPP_P594889876l_bool,type,
    hAPP_P594889876l_bool: $i > $i > $i ).

thf(tp_hAPP_P604205461on_val,type,
    hAPP_P604205461on_val: $i > $i > $i ).

thf(tp_hAPP_P609938901l_bool,type,
    hAPP_P609938901l_bool: $i > $i > $i ).

thf(tp_hAPP_P638161699l_bool,type,
    hAPP_P638161699l_bool: $i > $i > $i ).

thf(tp_hAPP_P658340954on_val,type,
    hAPP_P658340954on_val: $i > $i > $i ).

thf(tp_hAPP_P659547099r_bool,type,
    hAPP_P659547099r_bool: $i > $i > $i ).

thf(tp_hAPP_P7095645l_bool,type,
    hAPP_P7095645l_bool: $i > $i > $i ).

thf(tp_hAPP_P71593144l_bool,type,
    hAPP_P71593144l_bool: $i > $i > $i ).

thf(tp_hAPP_P719127871t_char,type,
    hAPP_P719127871t_char: $i > $i > $i ).

thf(tp_hAPP_P738987199l_bool,type,
    hAPP_P738987199l_bool: $i > $i > $i ).

thf(tp_hAPP_P748443392y_bool,type,
    hAPP_P748443392y_bool: $i > $i > $i ).

thf(tp_hAPP_P76086873l_bool,type,
    hAPP_P76086873l_bool: $i > $i > $i ).

thf(tp_hAPP_P767818445t_char,type,
    hAPP_P767818445t_char: $i > $i > $i ).

thf(tp_hAPP_P768428603l_bool,type,
    hAPP_P768428603l_bool: $i > $i > $i ).

thf(tp_hAPP_P777914897t_char,type,
    hAPP_P777914897t_char: $i > $i > $i ).

thf(tp_hAPP_P780018708l_bool,type,
    hAPP_P780018708l_bool: $i > $i > $i ).

thf(tp_hAPP_P786771093l_bool,type,
    hAPP_P786771093l_bool: $i > $i > $i ).

thf(tp_hAPP_P801803911r_bool,type,
    hAPP_P801803911r_bool: $i > $i > $i ).

thf(tp_hAPP_P824029447r_bool,type,
    hAPP_P824029447r_bool: $i > $i > $i ).

thf(tp_hAPP_P827589667har_ty,type,
    hAPP_P827589667har_ty: $i > $i > $i ).

thf(tp_hAPP_P828904212r_bool,type,
    hAPP_P828904212r_bool: $i > $i > $i ).

thf(tp_hAPP_P845017029l_bool,type,
    hAPP_P845017029l_bool: $i > $i > $i ).

thf(tp_hAPP_P88824722l_bool,type,
    hAPP_P88824722l_bool: $i > $i > $i ).

thf(tp_hAPP_P895943837l_bool,type,
    hAPP_P895943837l_bool: $i > $i > $i ).

thf(tp_hAPP_P91410073t_char,type,
    hAPP_P91410073t_char: $i > $i > $i ).

thf(tp_hAPP_P92196306r_bool,type,
    hAPP_P92196306r_bool: $i > $i > $i ).

thf(tp_hAPP_P929449287r_bool,type,
    hAPP_P929449287r_bool: $i > $i > $i ).

thf(tp_hAPP_P929466802al_val,type,
    hAPP_P929466802al_val: $i > $i > $i ).

thf(tp_hAPP_P929938951l_bool,type,
    hAPP_P929938951l_bool: $i > $i > $i ).

thf(tp_hAPP_P943837928l_bool,type,
    hAPP_P943837928l_bool: $i > $i > $i ).

thf(tp_hAPP_P975284999r_bool,type,
    hAPP_P975284999r_bool: $i > $i > $i ).

thf(tp_hAPP_P976433298t_char,type,
    hAPP_P976433298t_char: $i > $i > $i ).

thf(tp_hAPP_P982127993l_bool,type,
    hAPP_P982127993l_bool: $i > $i > $i ).

thf(tp_hAPP_P991802092t_char,type,
    hAPP_P991802092t_char: $i > $i > $i ).

thf(tp_hAPP_P998768845l_bool,type,
    hAPP_P998768845l_bool: $i > $i > $i ).

thf(tp_hAPP_b1058859669op_bop,type,
    hAPP_b1058859669op_bop: $i > $i > $i ).

thf(tp_hAPP_b1229254591al_val,type,
    hAPP_b1229254591al_val: $i > $i > $i ).

thf(tp_hAPP_b1257035143l_bool,type,
    hAPP_b1257035143l_bool: $i > $i > $i ).

thf(tp_hAPP_b1909667208op_bop,type,
    hAPP_b1909667208op_bop: $i > $i > $i ).

thf(tp_hAPP_b406740087l_bool,type,
    hAPP_b406740087l_bool: $i > $i > $i ).

thf(tp_hAPP_b589554111l_bool,type,
    hAPP_b589554111l_bool: $i > $i > $i ).

thf(tp_hAPP_b97269396l_bool,type,
    hAPP_b97269396l_bool: $i > $i > $i ).

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

thf(tp_hAPP_e1303556805l_bool,type,
    hAPP_e1303556805l_bool: $i > $i > $i ).

thf(tp_hAPP_e1376201919t_char,type,
    hAPP_e1376201919t_char: $i > $i > $i ).

thf(tp_hAPP_e1659493427on_val,type,
    hAPP_e1659493427on_val: $i > $i > $i ).

thf(tp_hAPP_e1705922617l_bool,type,
    hAPP_e1705922617l_bool: $i > $i > $i ).

thf(tp_hAPP_e1752110927t_char,type,
    hAPP_e1752110927t_char: $i > $i > $i ).

thf(tp_hAPP_e1833980889l_bool,type,
    hAPP_e1833980889l_bool: $i > $i > $i ).

thf(tp_hAPP_e286792811l_bool,type,
    hAPP_e286792811l_bool: $i > $i > $i ).

thf(tp_hAPP_e53687815l_bool,type,
    hAPP_e53687815l_bool: $i > $i > $i ).

thf(tp_hAPP_e544220455r_bool,type,
    hAPP_e544220455r_bool: $i > $i > $i ).

thf(tp_hAPP_e817857447t_char,type,
    hAPP_e817857447t_char: $i > $i > $i ).

thf(tp_hAPP_e952791821t_char,type,
    hAPP_e952791821t_char: $i > $i > $i ).

thf(tp_hAPP_f1001225811y_bool,type,
    hAPP_f1001225811y_bool: $i > $i > $i ).

thf(tp_hAPP_f1008932791l_bool,type,
    hAPP_f1008932791l_bool: $i > $i > $i ).

thf(tp_hAPP_f101237475l_bool,type,
    hAPP_f101237475l_bool: $i > $i > $i ).

thf(tp_hAPP_f102021095r_bool,type,
    hAPP_f102021095r_bool: $i > $i > $i ).

thf(tp_hAPP_f1020753317r_bool,type,
    hAPP_f1020753317r_bool: $i > $i > $i ).

thf(tp_hAPP_f1032444159r_bool,type,
    hAPP_f1032444159r_bool: $i > $i > $i ).

thf(tp_hAPP_f1033709212l_bool,type,
    hAPP_f1033709212l_bool: $i > $i > $i ).

thf(tp_hAPP_f1044627221r_bool,type,
    hAPP_f1044627221r_bool: $i > $i > $i ).

thf(tp_hAPP_f1050935001l_bool,type,
    hAPP_f1050935001l_bool: $i > $i > $i ).

thf(tp_hAPP_f1051205629r_bool,type,
    hAPP_f1051205629r_bool: $i > $i > $i ).

thf(tp_hAPP_f1074020887l_bool,type,
    hAPP_f1074020887l_bool: $i > $i > $i ).

thf(tp_hAPP_f1080886329l_bool,type,
    hAPP_f1080886329l_bool: $i > $i > $i ).

thf(tp_hAPP_f108089737r_bool,type,
    hAPP_f108089737r_bool: $i > $i > $i ).

thf(tp_hAPP_f1082373989l_bool,type,
    hAPP_f1082373989l_bool: $i > $i > $i ).

thf(tp_hAPP_f1089788553l_bool,type,
    hAPP_f1089788553l_bool: $i > $i > $i ).

thf(tp_hAPP_f1094343359l_bool,type,
    hAPP_f1094343359l_bool: $i > $i > $i ).

thf(tp_hAPP_f1099622285l_bool,type,
    hAPP_f1099622285l_bool: $i > $i > $i ).

thf(tp_hAPP_f1100052969l_bool,type,
    hAPP_f1100052969l_bool: $i > $i > $i ).

thf(tp_hAPP_f1107475085l_bool,type,
    hAPP_f1107475085l_bool: $i > $i > $i ).

thf(tp_hAPP_f1118567467l_bool,type,
    hAPP_f1118567467l_bool: $i > $i > $i ).

thf(tp_hAPP_f112056853r_bool,type,
    hAPP_f112056853r_bool: $i > $i > $i ).

thf(tp_hAPP_f1134248971r_bool,type,
    hAPP_f1134248971r_bool: $i > $i > $i ).

thf(tp_hAPP_f1134950784l_bool,type,
    hAPP_f1134950784l_bool: $i > $i > $i ).

thf(tp_hAPP_f1135930489l_bool,type,
    hAPP_f1135930489l_bool: $i > $i > $i ).

thf(tp_hAPP_f1136362289l_bool,type,
    hAPP_f1136362289l_bool: $i > $i > $i ).

thf(tp_hAPP_f1145256474l_bool,type,
    hAPP_f1145256474l_bool: $i > $i > $i ).

thf(tp_hAPP_f1145574243l_bool,type,
    hAPP_f1145574243l_bool: $i > $i > $i ).

thf(tp_hAPP_f1146435765on_val,type,
    hAPP_f1146435765on_val: $i > $i > $i ).

thf(tp_hAPP_f1146629647l_bool,type,
    hAPP_f1146629647l_bool: $i > $i > $i ).

thf(tp_hAPP_f1149562121l_bool,type,
    hAPP_f1149562121l_bool: $i > $i > $i ).

thf(tp_hAPP_f1157863905l_bool,type,
    hAPP_f1157863905l_bool: $i > $i > $i ).

thf(tp_hAPP_f1161798306l_bool,type,
    hAPP_f1161798306l_bool: $i > $i > $i ).

thf(tp_hAPP_f1163760061l_bool,type,
    hAPP_f1163760061l_bool: $i > $i > $i ).

thf(tp_hAPP_f1166017719l_bool,type,
    hAPP_f1166017719l_bool: $i > $i > $i ).

thf(tp_hAPP_f1168269397l_bool,type,
    hAPP_f1168269397l_bool: $i > $i > $i ).

thf(tp_hAPP_f1169733153l_bool,type,
    hAPP_f1169733153l_bool: $i > $i > $i ).

thf(tp_hAPP_f1174637065l_bool,type,
    hAPP_f1174637065l_bool: $i > $i > $i ).

thf(tp_hAPP_f1175362209l_bool,type,
    hAPP_f1175362209l_bool: $i > $i > $i ).

thf(tp_hAPP_f1175813647l_bool,type,
    hAPP_f1175813647l_bool: $i > $i > $i ).

thf(tp_hAPP_f1200025813l_bool,type,
    hAPP_f1200025813l_bool: $i > $i > $i ).

thf(tp_hAPP_f1204100177l_bool,type,
    hAPP_f1204100177l_bool: $i > $i > $i ).

thf(tp_hAPP_f1209019955r_bool,type,
    hAPP_f1209019955r_bool: $i > $i > $i ).

thf(tp_hAPP_f1213370163y_bool,type,
    hAPP_f1213370163y_bool: $i > $i > $i ).

thf(tp_hAPP_f1233028029l_bool,type,
    hAPP_f1233028029l_bool: $i > $i > $i ).

thf(tp_hAPP_f1239832973l_bool,type,
    hAPP_f1239832973l_bool: $i > $i > $i ).

thf(tp_hAPP_f1243585741ion_ty,type,
    hAPP_f1243585741ion_ty: $i > $i > $i ).

thf(tp_hAPP_f1250221913l_bool,type,
    hAPP_f1250221913l_bool: $i > $i > $i ).

thf(tp_hAPP_f126136681l_bool,type,
    hAPP_f126136681l_bool: $i > $i > $i ).

thf(tp_hAPP_f1261741735l_bool,type,
    hAPP_f1261741735l_bool: $i > $i > $i ).

thf(tp_hAPP_f126445617l_bool,type,
    hAPP_f126445617l_bool: $i > $i > $i ).

thf(tp_hAPP_f1297673713l_bool,type,
    hAPP_f1297673713l_bool: $i > $i > $i ).

thf(tp_hAPP_f1298720864r_bool,type,
    hAPP_f1298720864r_bool: $i > $i > $i ).

thf(tp_hAPP_f1314764175l_bool,type,
    hAPP_f1314764175l_bool: $i > $i > $i ).

thf(tp_hAPP_f1317381998l_bool,type,
    hAPP_f1317381998l_bool: $i > $i > $i ).

thf(tp_hAPP_f133320957r_bool,type,
    hAPP_f133320957r_bool: $i > $i > $i ).

thf(tp_hAPP_f1335946228l_bool,type,
    hAPP_f1335946228l_bool: $i > $i > $i ).

thf(tp_hAPP_f1363667773l_bool,type,
    hAPP_f1363667773l_bool: $i > $i > $i ).

thf(tp_hAPP_f1365840271l_bool,type,
    hAPP_f1365840271l_bool: $i > $i > $i ).

thf(tp_hAPP_f1367982615r_bool,type,
    hAPP_f1367982615r_bool: $i > $i > $i ).

thf(tp_hAPP_f1370205989l_bool,type,
    hAPP_f1370205989l_bool: $i > $i > $i ).

thf(tp_hAPP_f1371002581r_bool,type,
    hAPP_f1371002581r_bool: $i > $i > $i ).

thf(tp_hAPP_f1374595987l_bool,type,
    hAPP_f1374595987l_bool: $i > $i > $i ).

thf(tp_hAPP_f1394668591l_bool,type,
    hAPP_f1394668591l_bool: $i > $i > $i ).

thf(tp_hAPP_f1406462375l_bool,type,
    hAPP_f1406462375l_bool: $i > $i > $i ).

thf(tp_hAPP_f1407048615l_bool,type,
    hAPP_f1407048615l_bool: $i > $i > $i ).

thf(tp_hAPP_f1409772418l_bool,type,
    hAPP_f1409772418l_bool: $i > $i > $i ).

thf(tp_hAPP_f1410576713r_bool,type,
    hAPP_f1410576713r_bool: $i > $i > $i ).

thf(tp_hAPP_f1419180947r_bool,type,
    hAPP_f1419180947r_bool: $i > $i > $i ).

thf(tp_hAPP_f1427871743l_bool,type,
    hAPP_f1427871743l_bool: $i > $i > $i ).

thf(tp_hAPP_f1443410953l_bool,type,
    hAPP_f1443410953l_bool: $i > $i > $i ).

thf(tp_hAPP_f144783951l_bool,type,
    hAPP_f144783951l_bool: $i > $i > $i ).

thf(tp_hAPP_f1449341487r_bool,type,
    hAPP_f1449341487r_bool: $i > $i > $i ).

thf(tp_hAPP_f1450446905l_bool,type,
    hAPP_f1450446905l_bool: $i > $i > $i ).

thf(tp_hAPP_f1452292669l_bool,type,
    hAPP_f1452292669l_bool: $i > $i > $i ).

thf(tp_hAPP_f1453283057l_bool,type,
    hAPP_f1453283057l_bool: $i > $i > $i ).

thf(tp_hAPP_f1466436665r_bool,type,
    hAPP_f1466436665r_bool: $i > $i > $i ).

thf(tp_hAPP_f1467537159l_bool,type,
    hAPP_f1467537159l_bool: $i > $i > $i ).

thf(tp_hAPP_f1472899487l_bool,type,
    hAPP_f1472899487l_bool: $i > $i > $i ).

thf(tp_hAPP_f1475571983l_bool,type,
    hAPP_f1475571983l_bool: $i > $i > $i ).

thf(tp_hAPP_f1484794973r_bool,type,
    hAPP_f1484794973r_bool: $i > $i > $i ).

thf(tp_hAPP_f1492320500l_bool,type,
    hAPP_f1492320500l_bool: $i > $i > $i ).

thf(tp_hAPP_f1500560577r_bool,type,
    hAPP_f1500560577r_bool: $i > $i > $i ).

thf(tp_hAPP_f1510763001l_bool,type,
    hAPP_f1510763001l_bool: $i > $i > $i ).

thf(tp_hAPP_f1520735791l_bool,type,
    hAPP_f1520735791l_bool: $i > $i > $i ).

thf(tp_hAPP_f1523875321l_bool,type,
    hAPP_f1523875321l_bool: $i > $i > $i ).

thf(tp_hAPP_f1525114763l_bool,type,
    hAPP_f1525114763l_bool: $i > $i > $i ).

thf(tp_hAPP_f1526206996l_bool,type,
    hAPP_f1526206996l_bool: $i > $i > $i ).

thf(tp_hAPP_f1534412387l_bool,type,
    hAPP_f1534412387l_bool: $i > $i > $i ).

thf(tp_hAPP_f1563448447r_bool,type,
    hAPP_f1563448447r_bool: $i > $i > $i ).

thf(tp_hAPP_f1564338425l_bool,type,
    hAPP_f1564338425l_bool: $i > $i > $i ).

thf(tp_hAPP_f156692813l_bool,type,
    hAPP_f156692813l_bool: $i > $i > $i ).

thf(tp_hAPP_f1579743228l_bool,type,
    hAPP_f1579743228l_bool: $i > $i > $i ).

thf(tp_hAPP_f1600936353l_bool,type,
    hAPP_f1600936353l_bool: $i > $i > $i ).

thf(tp_hAPP_f1608277885r_bool,type,
    hAPP_f1608277885r_bool: $i > $i > $i ).

thf(tp_hAPP_f1611569977l_bool,type,
    hAPP_f1611569977l_bool: $i > $i > $i ).

thf(tp_hAPP_f1612138403l_bool,type,
    hAPP_f1612138403l_bool: $i > $i > $i ).

thf(tp_hAPP_f1613448899r_bool,type,
    hAPP_f1613448899r_bool: $i > $i > $i ).

thf(tp_hAPP_f1614195593l_bool,type,
    hAPP_f1614195593l_bool: $i > $i > $i ).

thf(tp_hAPP_f1617787571l_bool,type,
    hAPP_f1617787571l_bool: $i > $i > $i ).

thf(tp_hAPP_f162154931l_bool,type,
    hAPP_f162154931l_bool: $i > $i > $i ).

thf(tp_hAPP_f1634841927l_bool,type,
    hAPP_f1634841927l_bool: $i > $i > $i ).

thf(tp_hAPP_f1639555093l_bool,type,
    hAPP_f1639555093l_bool: $i > $i > $i ).

thf(tp_hAPP_f1646911885l_bool,type,
    hAPP_f1646911885l_bool: $i > $i > $i ).

thf(tp_hAPP_f165071409l_bool,type,
    hAPP_f165071409l_bool: $i > $i > $i ).

thf(tp_hAPP_f1661305905l_bool,type,
    hAPP_f1661305905l_bool: $i > $i > $i ).

thf(tp_hAPP_f1666729379r_bool,type,
    hAPP_f1666729379r_bool: $i > $i > $i ).

thf(tp_hAPP_f1670595613l_bool,type,
    hAPP_f1670595613l_bool: $i > $i > $i ).

thf(tp_hAPP_f1677329295l_bool,type,
    hAPP_f1677329295l_bool: $i > $i > $i ).

thf(tp_hAPP_f1687138147l_bool,type,
    hAPP_f1687138147l_bool: $i > $i > $i ).

thf(tp_hAPP_f1697332217r_bool,type,
    hAPP_f1697332217r_bool: $i > $i > $i ).

thf(tp_hAPP_f1707979241r_bool,type,
    hAPP_f1707979241r_bool: $i > $i > $i ).

thf(tp_hAPP_f1715346603l_bool,type,
    hAPP_f1715346603l_bool: $i > $i > $i ).

thf(tp_hAPP_f1715733055l_bool,type,
    hAPP_f1715733055l_bool: $i > $i > $i ).

thf(tp_hAPP_f1720452391l_bool,type,
    hAPP_f1720452391l_bool: $i > $i > $i ).

thf(tp_hAPP_f1722879237t_bool,type,
    hAPP_f1722879237t_bool: $i > $i > $i ).

thf(tp_hAPP_f1724656343r_bool,type,
    hAPP_f1724656343r_bool: $i > $i > $i ).

thf(tp_hAPP_f1727192346on_val,type,
    hAPP_f1727192346on_val: $i > $i > $i ).

thf(tp_hAPP_f1728541444l_bool,type,
    hAPP_f1728541444l_bool: $i > $i > $i ).

thf(tp_hAPP_f1734260017l_bool,type,
    hAPP_f1734260017l_bool: $i > $i > $i ).

thf(tp_hAPP_f1734879897l_bool,type,
    hAPP_f1734879897l_bool: $i > $i > $i ).

thf(tp_hAPP_f1734997943l_bool,type,
    hAPP_f1734997943l_bool: $i > $i > $i ).

thf(tp_hAPP_f1736484361l_bool,type,
    hAPP_f1736484361l_bool: $i > $i > $i ).

thf(tp_hAPP_f1741070310on_val,type,
    hAPP_f1741070310on_val: $i > $i > $i ).

thf(tp_hAPP_f1744304433on_val,type,
    hAPP_f1744304433on_val: $i > $i > $i ).

thf(tp_hAPP_f1746574980l_bool,type,
    hAPP_f1746574980l_bool: $i > $i > $i ).

thf(tp_hAPP_f1748390065l_bool,type,
    hAPP_f1748390065l_bool: $i > $i > $i ).

thf(tp_hAPP_f1749915625r_bool,type,
    hAPP_f1749915625r_bool: $i > $i > $i ).

thf(tp_hAPP_f1752856401l_bool,type,
    hAPP_f1752856401l_bool: $i > $i > $i ).

thf(tp_hAPP_f1754555101l_bool,type,
    hAPP_f1754555101l_bool: $i > $i > $i ).

thf(tp_hAPP_f1764180741l_bool,type,
    hAPP_f1764180741l_bool: $i > $i > $i ).

thf(tp_hAPP_f1764548711l_bool,type,
    hAPP_f1764548711l_bool: $i > $i > $i ).

thf(tp_hAPP_f1766231913r_bool,type,
    hAPP_f1766231913r_bool: $i > $i > $i ).

thf(tp_hAPP_f1776070952l_bool,type,
    hAPP_f1776070952l_bool: $i > $i > $i ).

thf(tp_hAPP_f1776419603l_bool,type,
    hAPP_f1776419603l_bool: $i > $i > $i ).

thf(tp_hAPP_f1776493709l_bool,type,
    hAPP_f1776493709l_bool: $i > $i > $i ).

thf(tp_hAPP_f1780084320l_bool,type,
    hAPP_f1780084320l_bool: $i > $i > $i ).

thf(tp_hAPP_f179418505r_bool,type,
    hAPP_f179418505r_bool: $i > $i > $i ).

thf(tp_hAPP_f1795246582l_bool,type,
    hAPP_f1795246582l_bool: $i > $i > $i ).

thf(tp_hAPP_f1805337205on_val,type,
    hAPP_f1805337205on_val: $i > $i > $i ).

thf(tp_hAPP_f181262431l_bool,type,
    hAPP_f181262431l_bool: $i > $i > $i ).

thf(tp_hAPP_f1817350437l_bool,type,
    hAPP_f1817350437l_bool: $i > $i > $i ).

thf(tp_hAPP_f1820115955r_bool,type,
    hAPP_f1820115955r_bool: $i > $i > $i ).

thf(tp_hAPP_f1823921107r_bool,type,
    hAPP_f1823921107r_bool: $i > $i > $i ).

thf(tp_hAPP_f183649339l_bool,type,
    hAPP_f183649339l_bool: $i > $i > $i ).

thf(tp_hAPP_f1847120981l_bool,type,
    hAPP_f1847120981l_bool: $i > $i > $i ).

thf(tp_hAPP_f1849790461on_val,type,
    hAPP_f1849790461on_val: $i > $i > $i ).

thf(tp_hAPP_f1850037271l_bool,type,
    hAPP_f1850037271l_bool: $i > $i > $i ).

thf(tp_hAPP_f1853572245r_bool,type,
    hAPP_f1853572245r_bool: $i > $i > $i ).

thf(tp_hAPP_f1854361213l_bool,type,
    hAPP_f1854361213l_bool: $i > $i > $i ).

thf(tp_hAPP_f1856968213l_bool,type,
    hAPP_f1856968213l_bool: $i > $i > $i ).

thf(tp_hAPP_f1859053709l_bool,type,
    hAPP_f1859053709l_bool: $i > $i > $i ).

thf(tp_hAPP_f1860331535l_bool,type,
    hAPP_f1860331535l_bool: $i > $i > $i ).

thf(tp_hAPP_f1861125939r_bool,type,
    hAPP_f1861125939r_bool: $i > $i > $i ).

thf(tp_hAPP_f1863694447l_bool,type,
    hAPP_f1863694447l_bool: $i > $i > $i ).

thf(tp_hAPP_f1868463117l_bool,type,
    hAPP_f1868463117l_bool: $i > $i > $i ).

thf(tp_hAPP_f1874697593r_bool,type,
    hAPP_f1874697593r_bool: $i > $i > $i ).

thf(tp_hAPP_f1876889431r_bool,type,
    hAPP_f1876889431r_bool: $i > $i > $i ).

thf(tp_hAPP_f1880802701l_bool,type,
    hAPP_f1880802701l_bool: $i > $i > $i ).

thf(tp_hAPP_f1889282162l_bool,type,
    hAPP_f1889282162l_bool: $i > $i > $i ).

thf(tp_hAPP_f1930574389l_bool,type,
    hAPP_f1930574389l_bool: $i > $i > $i ).

thf(tp_hAPP_f1931964053l_bool,type,
    hAPP_f1931964053l_bool: $i > $i > $i ).

thf(tp_hAPP_f1933376467r_bool,type,
    hAPP_f1933376467r_bool: $i > $i > $i ).

thf(tp_hAPP_f1937828171l_bool,type,
    hAPP_f1937828171l_bool: $i > $i > $i ).

thf(tp_hAPP_f1946480059l_bool,type,
    hAPP_f1946480059l_bool: $i > $i > $i ).

thf(tp_hAPP_f1957374161r_bool,type,
    hAPP_f1957374161r_bool: $i > $i > $i ).

thf(tp_hAPP_f197435839r_bool,type,
    hAPP_f197435839r_bool: $i > $i > $i ).

thf(tp_hAPP_f1977633121l_bool,type,
    hAPP_f1977633121l_bool: $i > $i > $i ).

thf(tp_hAPP_f1980787287l_bool,type,
    hAPP_f1980787287l_bool: $i > $i > $i ).

thf(tp_hAPP_f1985672189l_bool,type,
    hAPP_f1985672189l_bool: $i > $i > $i ).

thf(tp_hAPP_f198821591l_bool,type,
    hAPP_f198821591l_bool: $i > $i > $i ).

thf(tp_hAPP_f2025561243r_bool,type,
    hAPP_f2025561243r_bool: $i > $i > $i ).

thf(tp_hAPP_f2026692601l_bool,type,
    hAPP_f2026692601l_bool: $i > $i > $i ).

thf(tp_hAPP_f2028441009l_bool,type,
    hAPP_f2028441009l_bool: $i > $i > $i ).

thf(tp_hAPP_f2036784149l_bool,type,
    hAPP_f2036784149l_bool: $i > $i > $i ).

thf(tp_hAPP_f2037329933l_bool,type,
    hAPP_f2037329933l_bool: $i > $i > $i ).

thf(tp_hAPP_f2041029616l_bool,type,
    hAPP_f2041029616l_bool: $i > $i > $i ).

thf(tp_hAPP_f2047757465l_bool,type,
    hAPP_f2047757465l_bool: $i > $i > $i ).

thf(tp_hAPP_f2050077417l_bool,type,
    hAPP_f2050077417l_bool: $i > $i > $i ).

thf(tp_hAPP_f2052909183l_bool,type,
    hAPP_f2052909183l_bool: $i > $i > $i ).

thf(tp_hAPP_f2057883639l_bool,type,
    hAPP_f2057883639l_bool: $i > $i > $i ).

thf(tp_hAPP_f2059406941r_bool,type,
    hAPP_f2059406941r_bool: $i > $i > $i ).

thf(tp_hAPP_f2060496320y_bool,type,
    hAPP_f2060496320y_bool: $i > $i > $i ).

thf(tp_hAPP_f2071159779l_bool,type,
    hAPP_f2071159779l_bool: $i > $i > $i ).

thf(tp_hAPP_f2071340985r_bool,type,
    hAPP_f2071340985r_bool: $i > $i > $i ).

thf(tp_hAPP_f2080627739l_bool,type,
    hAPP_f2080627739l_bool: $i > $i > $i ).

thf(tp_hAPP_f2091926485r_bool,type,
    hAPP_f2091926485r_bool: $i > $i > $i ).

thf(tp_hAPP_f2095325577l_bool,type,
    hAPP_f2095325577l_bool: $i > $i > $i ).

thf(tp_hAPP_f2100207721l_bool,type,
    hAPP_f2100207721l_bool: $i > $i > $i ).

thf(tp_hAPP_f2106398425l_bool,type,
    hAPP_f2106398425l_bool: $i > $i > $i ).

thf(tp_hAPP_f2110071953ion_ty,type,
    hAPP_f2110071953ion_ty: $i > $i > $i ).

thf(tp_hAPP_f2118054305l_bool,type,
    hAPP_f2118054305l_bool: $i > $i > $i ).

thf(tp_hAPP_f2121594859l_bool,type,
    hAPP_f2121594859l_bool: $i > $i > $i ).

thf(tp_hAPP_f2129782055l_bool,type,
    hAPP_f2129782055l_bool: $i > $i > $i ).

thf(tp_hAPP_f2132060507r_bool,type,
    hAPP_f2132060507r_bool: $i > $i > $i ).

thf(tp_hAPP_f2133563379r_bool,type,
    hAPP_f2133563379r_bool: $i > $i > $i ).

thf(tp_hAPP_f225832321r_bool,type,
    hAPP_f225832321r_bool: $i > $i > $i ).

thf(tp_hAPP_f247798919l_bool,type,
    hAPP_f247798919l_bool: $i > $i > $i ).

thf(tp_hAPP_f251669717l_bool,type,
    hAPP_f251669717l_bool: $i > $i > $i ).

thf(tp_hAPP_f252398939r_bool,type,
    hAPP_f252398939r_bool: $i > $i > $i ).

thf(tp_hAPP_f254182519r_bool,type,
    hAPP_f254182519r_bool: $i > $i > $i ).

thf(tp_hAPP_f257113085l_bool,type,
    hAPP_f257113085l_bool: $i > $i > $i ).

thf(tp_hAPP_f258424141l_bool,type,
    hAPP_f258424141l_bool: $i > $i > $i ).

thf(tp_hAPP_f263393637l_bool,type,
    hAPP_f263393637l_bool: $i > $i > $i ).

thf(tp_hAPP_f272179441l_bool,type,
    hAPP_f272179441l_bool: $i > $i > $i ).

thf(tp_hAPP_f279818502r_bool,type,
    hAPP_f279818502r_bool: $i > $i > $i ).

thf(tp_hAPP_f288221747l_bool,type,
    hAPP_f288221747l_bool: $i > $i > $i ).

thf(tp_hAPP_f29105311r_bool,type,
    hAPP_f29105311r_bool: $i > $i > $i ).

thf(tp_hAPP_f292637069l_bool,type,
    hAPP_f292637069l_bool: $i > $i > $i ).

thf(tp_hAPP_f293485653l_bool,type,
    hAPP_f293485653l_bool: $i > $i > $i ).

thf(tp_hAPP_f304993943r_bool,type,
    hAPP_f304993943r_bool: $i > $i > $i ).

thf(tp_hAPP_f306469557r_bool,type,
    hAPP_f306469557r_bool: $i > $i > $i ).

thf(tp_hAPP_f308875635r_bool,type,
    hAPP_f308875635r_bool: $i > $i > $i ).

thf(tp_hAPP_f321462169l_bool,type,
    hAPP_f321462169l_bool: $i > $i > $i ).

thf(tp_hAPP_f32926423l_bool,type,
    hAPP_f32926423l_bool: $i > $i > $i ).

thf(tp_hAPP_f33142364l_bool,type,
    hAPP_f33142364l_bool: $i > $i > $i ).

thf(tp_hAPP_f333583909l_bool,type,
    hAPP_f333583909l_bool: $i > $i > $i ).

thf(tp_hAPP_f335969926r_bool,type,
    hAPP_f335969926r_bool: $i > $i > $i ).

thf(tp_hAPP_f340876351l_bool,type,
    hAPP_f340876351l_bool: $i > $i > $i ).

thf(tp_hAPP_f344506159r_bool,type,
    hAPP_f344506159r_bool: $i > $i > $i ).

thf(tp_hAPP_f348318673l_bool,type,
    hAPP_f348318673l_bool: $i > $i > $i ).

thf(tp_hAPP_f348508809l_bool,type,
    hAPP_f348508809l_bool: $i > $i > $i ).

thf(tp_hAPP_f348753975l_bool,type,
    hAPP_f348753975l_bool: $i > $i > $i ).

thf(tp_hAPP_f350189921l_bool,type,
    hAPP_f350189921l_bool: $i > $i > $i ).

thf(tp_hAPP_f359949478ion_ty,type,
    hAPP_f359949478ion_ty: $i > $i > $i ).

thf(tp_hAPP_f361629773l_bool,type,
    hAPP_f361629773l_bool: $i > $i > $i ).

thf(tp_hAPP_f363827556r_bool,type,
    hAPP_f363827556r_bool: $i > $i > $i ).

thf(tp_hAPP_f368284312on_val,type,
    hAPP_f368284312on_val: $i > $i > $i ).

thf(tp_hAPP_f375531599l_bool,type,
    hAPP_f375531599l_bool: $i > $i > $i ).

thf(tp_hAPP_f379976829l_bool,type,
    hAPP_f379976829l_bool: $i > $i > $i ).

thf(tp_hAPP_f380623487l_bool,type,
    hAPP_f380623487l_bool: $i > $i > $i ).

thf(tp_hAPP_f388097003r_bool,type,
    hAPP_f388097003r_bool: $i > $i > $i ).

thf(tp_hAPP_f388705405r_bool,type,
    hAPP_f388705405r_bool: $i > $i > $i ).

thf(tp_hAPP_f396807521l_bool,type,
    hAPP_f396807521l_bool: $i > $i > $i ).

thf(tp_hAPP_f399018025r_bool,type,
    hAPP_f399018025r_bool: $i > $i > $i ).

thf(tp_hAPP_f400269243l_bool,type,
    hAPP_f400269243l_bool: $i > $i > $i ).

thf(tp_hAPP_f40682957l_bool,type,
    hAPP_f40682957l_bool: $i > $i > $i ).

thf(tp_hAPP_f433445541l_bool,type,
    hAPP_f433445541l_bool: $i > $i > $i ).

thf(tp_hAPP_f434955681l_bool,type,
    hAPP_f434955681l_bool: $i > $i > $i ).

thf(tp_hAPP_f447422815l_bool,type,
    hAPP_f447422815l_bool: $i > $i > $i ).

thf(tp_hAPP_f447563647r_bool,type,
    hAPP_f447563647r_bool: $i > $i > $i ).

thf(tp_hAPP_f451501457ion_ty,type,
    hAPP_f451501457ion_ty: $i > $i > $i ).

thf(tp_hAPP_f454222487r_bool,type,
    hAPP_f454222487r_bool: $i > $i > $i ).

thf(tp_hAPP_f458849545l_bool,type,
    hAPP_f458849545l_bool: $i > $i > $i ).

thf(tp_hAPP_f46308763ion_ty,type,
    hAPP_f46308763ion_ty: $i > $i > $i ).

thf(tp_hAPP_f466945179l_bool,type,
    hAPP_f466945179l_bool: $i > $i > $i ).

thf(tp_hAPP_f47713631l_bool,type,
    hAPP_f47713631l_bool: $i > $i > $i ).

thf(tp_hAPP_f479632753l_bool,type,
    hAPP_f479632753l_bool: $i > $i > $i ).

thf(tp_hAPP_f483496539l_bool,type,
    hAPP_f483496539l_bool: $i > $i > $i ).

thf(tp_hAPP_f489569861t_bool,type,
    hAPP_f489569861t_bool: $i > $i > $i ).

thf(tp_hAPP_f509342689ion_ty,type,
    hAPP_f509342689ion_ty: $i > $i > $i ).

thf(tp_hAPP_f510152537l_bool,type,
    hAPP_f510152537l_bool: $i > $i > $i ).

thf(tp_hAPP_f515912112l_bool,type,
    hAPP_f515912112l_bool: $i > $i > $i ).

thf(tp_hAPP_f521496323r_bool,type,
    hAPP_f521496323r_bool: $i > $i > $i ).

thf(tp_hAPP_f522372661r_bool,type,
    hAPP_f522372661r_bool: $i > $i > $i ).

thf(tp_hAPP_f528956081l_bool,type,
    hAPP_f528956081l_bool: $i > $i > $i ).

thf(tp_hAPP_f531187933r_bool,type,
    hAPP_f531187933r_bool: $i > $i > $i ).

thf(tp_hAPP_f538118321l_bool,type,
    hAPP_f538118321l_bool: $i > $i > $i ).

thf(tp_hAPP_f539072365l_bool,type,
    hAPP_f539072365l_bool: $i > $i > $i ).

thf(tp_hAPP_f54304608l_bool,type,
    hAPP_f54304608l_bool: $i > $i > $i ).

thf(tp_hAPP_f550652027l_bool,type,
    hAPP_f550652027l_bool: $i > $i > $i ).

thf(tp_hAPP_f552300311l_bool,type,
    hAPP_f552300311l_bool: $i > $i > $i ).

thf(tp_hAPP_f555424277l_bool,type,
    hAPP_f555424277l_bool: $i > $i > $i ).

thf(tp_hAPP_f558380429l_bool,type,
    hAPP_f558380429l_bool: $i > $i > $i ).

thf(tp_hAPP_f561246575l_bool,type,
    hAPP_f561246575l_bool: $i > $i > $i ).

thf(tp_hAPP_f565735867l_bool,type,
    hAPP_f565735867l_bool: $i > $i > $i ).

thf(tp_hAPP_f570766339l_bool,type,
    hAPP_f570766339l_bool: $i > $i > $i ).

thf(tp_hAPP_f588675559l_bool,type,
    hAPP_f588675559l_bool: $i > $i > $i ).

thf(tp_hAPP_f592397849l_bool,type,
    hAPP_f592397849l_bool: $i > $i > $i ).

thf(tp_hAPP_f595031537l_bool,type,
    hAPP_f595031537l_bool: $i > $i > $i ).

thf(tp_hAPP_f603925568l_bool,type,
    hAPP_f603925568l_bool: $i > $i > $i ).

thf(tp_hAPP_f605643693r_bool,type,
    hAPP_f605643693r_bool: $i > $i > $i ).

thf(tp_hAPP_f606945057l_bool,type,
    hAPP_f606945057l_bool: $i > $i > $i ).

thf(tp_hAPP_f61040418l_bool,type,
    hAPP_f61040418l_bool: $i > $i > $i ).

thf(tp_hAPP_f613075253l_bool,type,
    hAPP_f613075253l_bool: $i > $i > $i ).

thf(tp_hAPP_f614662951l_bool,type,
    hAPP_f614662951l_bool: $i > $i > $i ).

thf(tp_hAPP_f62511709l_bool,type,
    hAPP_f62511709l_bool: $i > $i > $i ).

thf(tp_hAPP_f635218277l_bool,type,
    hAPP_f635218277l_bool: $i > $i > $i ).

thf(tp_hAPP_f644972157l_bool,type,
    hAPP_f644972157l_bool: $i > $i > $i ).

thf(tp_hAPP_f652398900ion_ty,type,
    hAPP_f652398900ion_ty: $i > $i > $i ).

thf(tp_hAPP_f658521820r_bool,type,
    hAPP_f658521820r_bool: $i > $i > $i ).

thf(tp_hAPP_f665343921l_bool,type,
    hAPP_f665343921l_bool: $i > $i > $i ).

thf(tp_hAPP_f677078775l_bool,type,
    hAPP_f677078775l_bool: $i > $i > $i ).

thf(tp_hAPP_f678833350l_bool,type,
    hAPP_f678833350l_bool: $i > $i > $i ).

thf(tp_hAPP_f693085049l_bool,type,
    hAPP_f693085049l_bool: $i > $i > $i ).

thf(tp_hAPP_f69964139ion_ty,type,
    hAPP_f69964139ion_ty: $i > $i > $i ).

thf(tp_hAPP_f705562443l_bool,type,
    hAPP_f705562443l_bool: $i > $i > $i ).

thf(tp_hAPP_f719350875r_bool,type,
    hAPP_f719350875r_bool: $i > $i > $i ).

thf(tp_hAPP_f720086610l_bool,type,
    hAPP_f720086610l_bool: $i > $i > $i ).

thf(tp_hAPP_f722872225l_bool,type,
    hAPP_f722872225l_bool: $i > $i > $i ).

thf(tp_hAPP_f732843907r_bool,type,
    hAPP_f732843907r_bool: $i > $i > $i ).

thf(tp_hAPP_f742333458l_bool,type,
    hAPP_f742333458l_bool: $i > $i > $i ).

thf(tp_hAPP_f749178132l_bool,type,
    hAPP_f749178132l_bool: $i > $i > $i ).

thf(tp_hAPP_f762728813l_bool,type,
    hAPP_f762728813l_bool: $i > $i > $i ).

thf(tp_hAPP_f7643013ion_ty,type,
    hAPP_f7643013ion_ty: $i > $i > $i ).

thf(tp_hAPP_f764724814r_bool,type,
    hAPP_f764724814r_bool: $i > $i > $i ).

thf(tp_hAPP_f77033475l_bool,type,
    hAPP_f77033475l_bool: $i > $i > $i ).

thf(tp_hAPP_f800510211t_bool,type,
    hAPP_f800510211t_bool: $i > $i > $i ).

thf(tp_hAPP_f802560783ion_ty,type,
    hAPP_f802560783ion_ty: $i > $i > $i ).

thf(tp_hAPP_f810261999l_bool,type,
    hAPP_f810261999l_bool: $i > $i > $i ).

thf(tp_hAPP_f82569901l_bool,type,
    hAPP_f82569901l_bool: $i > $i > $i ).

thf(tp_hAPP_f826324045l_bool,type,
    hAPP_f826324045l_bool: $i > $i > $i ).

thf(tp_hAPP_f837795298l_bool,type,
    hAPP_f837795298l_bool: $i > $i > $i ).

thf(tp_hAPP_f838396643l_bool,type,
    hAPP_f838396643l_bool: $i > $i > $i ).

thf(tp_hAPP_f841257045r_bool,type,
    hAPP_f841257045r_bool: $i > $i > $i ).

thf(tp_hAPP_f842743203r_bool,type,
    hAPP_f842743203r_bool: $i > $i > $i ).

thf(tp_hAPP_f844901525l_bool,type,
    hAPP_f844901525l_bool: $i > $i > $i ).

thf(tp_hAPP_f851858423l_bool,type,
    hAPP_f851858423l_bool: $i > $i > $i ).

thf(tp_hAPP_f857351829l_bool,type,
    hAPP_f857351829l_bool: $i > $i > $i ).

thf(tp_hAPP_f861853459l_bool,type,
    hAPP_f861853459l_bool: $i > $i > $i ).

thf(tp_hAPP_f864891091on_val,type,
    hAPP_f864891091on_val: $i > $i > $i ).

thf(tp_hAPP_f866074145l_bool,type,
    hAPP_f866074145l_bool: $i > $i > $i ).

thf(tp_hAPP_f869803751l_bool,type,
    hAPP_f869803751l_bool: $i > $i > $i ).

thf(tp_hAPP_f876671127l_bool,type,
    hAPP_f876671127l_bool: $i > $i > $i ).

thf(tp_hAPP_f877616419l_bool,type,
    hAPP_f877616419l_bool: $i > $i > $i ).

thf(tp_hAPP_f893576377l_bool,type,
    hAPP_f893576377l_bool: $i > $i > $i ).

thf(tp_hAPP_f894608603t_bool,type,
    hAPP_f894608603t_bool: $i > $i > $i ).

thf(tp_hAPP_f895126887r_bool,type,
    hAPP_f895126887r_bool: $i > $i > $i ).

thf(tp_hAPP_f900686428on_val,type,
    hAPP_f900686428on_val: $i > $i > $i ).

thf(tp_hAPP_f901718717l_bool,type,
    hAPP_f901718717l_bool: $i > $i > $i ).

thf(tp_hAPP_f914702973l_bool,type,
    hAPP_f914702973l_bool: $i > $i > $i ).

thf(tp_hAPP_f91506671l_bool,type,
    hAPP_f91506671l_bool: $i > $i > $i ).

thf(tp_hAPP_f919000597l_bool,type,
    hAPP_f919000597l_bool: $i > $i > $i ).

thf(tp_hAPP_f921434893l_bool,type,
    hAPP_f921434893l_bool: $i > $i > $i ).

thf(tp_hAPP_f926979333l_bool,type,
    hAPP_f926979333l_bool: $i > $i > $i ).

thf(tp_hAPP_f935003377l_bool,type,
    hAPP_f935003377l_bool: $i > $i > $i ).

thf(tp_hAPP_f937861397l_bool,type,
    hAPP_f937861397l_bool: $i > $i > $i ).

thf(tp_hAPP_f952817385r_bool,type,
    hAPP_f952817385r_bool: $i > $i > $i ).

thf(tp_hAPP_f953097879r_bool,type,
    hAPP_f953097879r_bool: $i > $i > $i ).

thf(tp_hAPP_f961387813l_bool,type,
    hAPP_f961387813l_bool: $i > $i > $i ).

thf(tp_hAPP_f966411375l_bool,type,
    hAPP_f966411375l_bool: $i > $i > $i ).

thf(tp_hAPP_f973018659l_bool,type,
    hAPP_f973018659l_bool: $i > $i > $i ).

thf(tp_hAPP_f983152497l_bool,type,
    hAPP_f983152497l_bool: $i > $i > $i ).

thf(tp_hAPP_f986089162l_bool,type,
    hAPP_f986089162l_bool: $i > $i > $i ).

thf(tp_hAPP_f987862447r_bool,type,
    hAPP_f987862447r_bool: $i > $i > $i ).

thf(tp_hAPP_f989077673l_bool,type,
    hAPP_f989077673l_bool: $i > $i > $i ).

thf(tp_hAPP_f998390560l_bool,type,
    hAPP_f998390560l_bool: $i > $i > $i ).

thf(tp_hAPP_l103437071st_val,type,
    hAPP_l103437071st_val: $i > $i > $i ).

thf(tp_hAPP_l1062423959r_bool,type,
    hAPP_l1062423959r_bool: $i > $i > $i ).

thf(tp_hAPP_l1105836155t_char,type,
    hAPP_l1105836155t_char: $i > $i > $i ).

thf(tp_hAPP_l1117138611l_bool,type,
    hAPP_l1117138611l_bool: $i > $i > $i ).

thf(tp_hAPP_l1129005983r_bool,type,
    hAPP_l1129005983r_bool: $i > $i > $i ).

thf(tp_hAPP_l1249476511st_val,type,
    hAPP_l1249476511st_val: $i > $i > $i ).

thf(tp_hAPP_l1275479261on_val,type,
    hAPP_l1275479261on_val: $i > $i > $i ).

thf(tp_hAPP_l1294856089har_ty,type,
    hAPP_l1294856089har_ty: $i > $i > $i ).

thf(tp_hAPP_l1319068228ist_ty,type,
    hAPP_l1319068228ist_ty: $i > $i > $i ).

thf(tp_hAPP_l1334098948t_char,type,
    hAPP_l1334098948t_char: $i > $i > $i ).

thf(tp_hAPP_l1335043179r_bool,type,
    hAPP_l1335043179r_bool: $i > $i > $i ).

thf(tp_hAPP_l1342015621r_bool,type,
    hAPP_l1342015621r_bool: $i > $i > $i ).

thf(tp_hAPP_l1361600383r_bool,type,
    hAPP_l1361600383r_bool: $i > $i > $i ).

thf(tp_hAPP_l1388836853t_char,type,
    hAPP_l1388836853t_char: $i > $i > $i ).

thf(tp_hAPP_l1425867561l_bool,type,
    hAPP_l1425867561l_bool: $i > $i > $i ).

thf(tp_hAPP_l14371579t_char,type,
    hAPP_l14371579t_char: $i > $i > $i ).

thf(tp_hAPP_l1450984463t_char,type,
    hAPP_l1450984463t_char: $i > $i > $i ).

thf(tp_hAPP_l146377954l_bool,type,
    hAPP_l146377954l_bool: $i > $i > $i ).

thf(tp_hAPP_l1536299231l_bool,type,
    hAPP_l1536299231l_bool: $i > $i > $i ).

thf(tp_hAPP_l1571522437l_bool,type,
    hAPP_l1571522437l_bool: $i > $i > $i ).

thf(tp_hAPP_l1591404153l_bool,type,
    hAPP_l1591404153l_bool: $i > $i > $i ).

thf(tp_hAPP_l1646953198l_bool,type,
    hAPP_l1646953198l_bool: $i > $i > $i ).

thf(tp_hAPP_l1648260346t_char,type,
    hAPP_l1648260346t_char: $i > $i > $i ).

thf(tp_hAPP_l165010689r_bool,type,
    hAPP_l165010689r_bool: $i > $i > $i ).

thf(tp_hAPP_l1657578379har_ty,type,
    hAPP_l1657578379har_ty: $i > $i > $i ).

thf(tp_hAPP_l1739862107l_bool,type,
    hAPP_l1739862107l_bool: $i > $i > $i ).

thf(tp_hAPP_l1770520637ist_ty,type,
    hAPP_l1770520637ist_ty: $i > $i > $i ).

thf(tp_hAPP_l177734933l_bool,type,
    hAPP_l177734933l_bool: $i > $i > $i ).

thf(tp_hAPP_l1783480313r_bool,type,
    hAPP_l1783480313r_bool: $i > $i > $i ).

thf(tp_hAPP_l1786340417on_val,type,
    hAPP_l1786340417on_val: $i > $i > $i ).

thf(tp_hAPP_l1842007287l_bool,type,
    hAPP_l1842007287l_bool: $i > $i > $i ).

thf(tp_hAPP_l1845912621l_bool,type,
    hAPP_l1845912621l_bool: $i > $i > $i ).

thf(tp_hAPP_l1859255743t_char,type,
    hAPP_l1859255743t_char: $i > $i > $i ).

thf(tp_hAPP_l1873467853t_char,type,
    hAPP_l1873467853t_char: $i > $i > $i ).

thf(tp_hAPP_l1883348915t_char,type,
    hAPP_l1883348915t_char: $i > $i > $i ).

thf(tp_hAPP_l1903254203l_bool,type,
    hAPP_l1903254203l_bool: $i > $i > $i ).

thf(tp_hAPP_l1948972481har_ty,type,
    hAPP_l1948972481har_ty: $i > $i > $i ).

thf(tp_hAPP_l1987619678r_bool,type,
    hAPP_l1987619678r_bool: $i > $i > $i ).

thf(tp_hAPP_l1988620845r_bool,type,
    hAPP_l1988620845r_bool: $i > $i > $i ).

thf(tp_hAPP_l2000496933ion_ty,type,
    hAPP_l2000496933ion_ty: $i > $i > $i ).

thf(tp_hAPP_l2010421276l_bool,type,
    hAPP_l2010421276l_bool: $i > $i > $i ).

thf(tp_hAPP_l2019537453t_char,type,
    hAPP_l2019537453t_char: $i > $i > $i ).

thf(tp_hAPP_l2048923787t_char,type,
    hAPP_l2048923787t_char: $i > $i > $i ).

thf(tp_hAPP_l2053770731r_bool,type,
    hAPP_l2053770731r_bool: $i > $i > $i ).

thf(tp_hAPP_l2054741776r_bool,type,
    hAPP_l2054741776r_bool: $i > $i > $i ).

thf(tp_hAPP_l207779698on_val,type,
    hAPP_l207779698on_val: $i > $i > $i ).

thf(tp_hAPP_l208357873t_char,type,
    hAPP_l208357873t_char: $i > $i > $i ).

thf(tp_hAPP_l2100324114t_char,type,
    hAPP_l2100324114t_char: $i > $i > $i ).

thf(tp_hAPP_l2111308793l_bool,type,
    hAPP_l2111308793l_bool: $i > $i > $i ).

thf(tp_hAPP_l213519975l_bool,type,
    hAPP_l213519975l_bool: $i > $i > $i ).

thf(tp_hAPP_l2138409430r_bool,type,
    hAPP_l2138409430r_bool: $i > $i > $i ).

thf(tp_hAPP_l2140727500r_bool,type,
    hAPP_l2140727500r_bool: $i > $i > $i ).

thf(tp_hAPP_l214204733r_bool,type,
    hAPP_l214204733r_bool: $i > $i > $i ).

thf(tp_hAPP_l217977712r_bool,type,
    hAPP_l217977712r_bool: $i > $i > $i ).

thf(tp_hAPP_l232580245l_bool,type,
    hAPP_l232580245l_bool: $i > $i > $i ).

thf(tp_hAPP_l24694616r_bool,type,
    hAPP_l24694616r_bool: $i > $i > $i ).

thf(tp_hAPP_l277216047t_char,type,
    hAPP_l277216047t_char: $i > $i > $i ).

thf(tp_hAPP_l296209613r_bool,type,
    hAPP_l296209613r_bool: $i > $i > $i ).

thf(tp_hAPP_l309186817t_char,type,
    hAPP_l309186817t_char: $i > $i > $i ).

thf(tp_hAPP_l352172327t_char,type,
    hAPP_l352172327t_char: $i > $i > $i ).

thf(tp_hAPP_l465799708l_bool,type,
    hAPP_l465799708l_bool: $i > $i > $i ).

thf(tp_hAPP_l512744617ion_ty,type,
    hAPP_l512744617ion_ty: $i > $i > $i ).

thf(tp_hAPP_l551544901l_bool,type,
    hAPP_l551544901l_bool: $i > $i > $i ).

thf(tp_hAPP_l553007690l_bool,type,
    hAPP_l553007690l_bool: $i > $i > $i ).

thf(tp_hAPP_l753659065r_bool,type,
    hAPP_l753659065r_bool: $i > $i > $i ).

thf(tp_hAPP_l796364813t_char,type,
    hAPP_l796364813t_char: $i > $i > $i ).

thf(tp_hAPP_l810309945l_bool,type,
    hAPP_l810309945l_bool: $i > $i > $i ).

thf(tp_hAPP_l902158906r_bool,type,
    hAPP_l902158906r_bool: $i > $i > $i ).

thf(tp_hAPP_l902950593t_char,type,
    hAPP_l902950593t_char: $i > $i > $i ).

thf(tp_hAPP_l923073979r_bool,type,
    hAPP_l923073979r_bool: $i > $i > $i ).

thf(tp_hAPP_l96108383r_bool,type,
    hAPP_l96108383r_bool: $i > $i > $i ).

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

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

thf(tp_hAPP_n1006566506l_bool,type,
    hAPP_n1006566506l_bool: $i > $i > $i ).

thf(tp_hAPP_n215258509l_bool,type,
    hAPP_n215258509l_bool: $i > $i > $i ).

thf(tp_hAPP_n546249108on_val,type,
    hAPP_n546249108on_val: $i > $i > $i ).

thf(tp_hAPP_n95946796l_bool,type,
    hAPP_n95946796l_bool: $i > $i > $i ).

thf(tp_hAPP_nat_bool,type,
    hAPP_nat_bool: $i > $i > $i ).

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

thf(tp_hAPP_o1240645474ion_ty,type,
    hAPP_o1240645474ion_ty: $i > $i > $i ).

thf(tp_hAPP_o1269033393on_val,type,
    hAPP_o1269033393on_val: $i > $i > $i ).

thf(tp_hAPP_o1566711458t_bool,type,
    hAPP_o1566711458t_bool: $i > $i > $i ).

thf(tp_hAPP_o1576581476on_val,type,
    hAPP_o1576581476on_val: $i > $i > $i ).

thf(tp_hAPP_o1968908095l_bool,type,
    hAPP_o1968908095l_bool: $i > $i > $i ).

thf(tp_hAPP_o1977518472on_val,type,
    hAPP_o1977518472on_val: $i > $i > $i ).

thf(tp_hAPP_o2007402111l_bool,type,
    hAPP_o2007402111l_bool: $i > $i > $i ).

thf(tp_hAPP_o285151112r_bool,type,
    hAPP_o285151112r_bool: $i > $i > $i ).

thf(tp_hAPP_o453398608r_bool,type,
    hAPP_o453398608r_bool: $i > $i > $i ).

thf(tp_hAPP_o534509643ion_ty,type,
    hAPP_o534509643ion_ty: $i > $i > $i ).

thf(tp_hAPP_o538043682on_val,type,
    hAPP_o538043682on_val: $i > $i > $i ).

thf(tp_hAPP_o586881855l_bool,type,
    hAPP_o586881855l_bool: $i > $i > $i ).

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

thf(tp_hAPP_option_ty_bool,type,
    hAPP_option_ty_bool: $i > $i > $i ).

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

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

thf(tp_hAPP_option_val_val,type,
    hAPP_option_val_val: $i > $i > $i ).

thf(tp_hAPP_t1369077401t_char,type,
    hAPP_t1369077401t_char: $i > $i > $i ).

thf(tp_hAPP_t1875766236har_ty,type,
    hAPP_t1875766236har_ty: $i > $i > $i ).

thf(tp_hAPP_t708040077har_ty,type,
    hAPP_t708040077har_ty: $i > $i > $i ).

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

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

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

thf(tp_hAPP_v1392248405l_bool,type,
    hAPP_v1392248405l_bool: $i > $i > $i ).

thf(tp_hAPP_v1519391al_val,type,
    hAPP_v1519391al_val: $i > $i > $i ).

thf(tp_hAPP_v1988122071l_bool,type,
    hAPP_v1988122071l_bool: $i > $i > $i ).

thf(tp_hAPP_v3604996l_bool,type,
    hAPP_v3604996l_bool: $i > $i > $i ).

thf(tp_hAPP_v417179479l_bool,type,
    hAPP_v417179479l_bool: $i > $i > $i ).

thf(tp_hAPP_v834067052t_char,type,
    hAPP_v834067052t_char: $i > $i > $i ).

thf(tp_hAPP_v852496844al_val,type,
    hAPP_v852496844al_val: $i > $i > $i ).

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

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

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

thf(tp_hBOOL,type,
    hBOOL: $i > $o ).

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

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

thf(tp_has_fi1183600461t_char,type,
    has_fi1183600461t_char: $i > $i > $i > $i > $i ).

thf(tp_hconf_97414254t_char,type,
    hconf_97414254t_char: $i > $i ).

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

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

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

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

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

thf(tp_is_cla570604648t_char,type,
    is_cla570604648t_char: $i > $i ).

thf(tp_is_fun1083000568p_bool,type,
    is_fun1083000568p_bool: $i > $o ).

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

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

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

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

thf(tp_lconf_496643946t_char,type,
    lconf_496643946t_char: $i > $i ).

thf(tp_lex_pr1038007919on_val,type,
    lex_pr1038007919on_val: $i > $i > $i ).

thf(tp_lex_pr1541028704on_val,type,
    lex_pr1541028704on_val: $i > $i > $i ).

thf(tp_lex_pr1588300168t_char,type,
    lex_pr1588300168t_char: $i > $i > $i ).

thf(tp_lex_pr1668767798t_char,type,
    lex_pr1668767798t_char: $i > $i > $i ).

thf(tp_lex_pr167435119t_char,type,
    lex_pr167435119t_char: $i > $i > $i ).

thf(tp_lex_pr1787105337t_char,type,
    lex_pr1787105337t_char: $i > $i > $i ).

thf(tp_lex_pr1876288492t_char,type,
    lex_pr1876288492t_char: $i > $i > $i ).

thf(tp_lex_pr1932514710al_val,type,
    lex_pr1932514710al_val: $i > $i > $i ).

thf(tp_lex_pr1971266694on_val,type,
    lex_pr1971266694on_val: $i > $i > $i ).

thf(tp_lex_pr2110711565on_val,type,
    lex_pr2110711565on_val: $i > $i > $i ).

thf(tp_lex_pr213428520t_char,type,
    lex_pr213428520t_char: $i > $i > $i ).

thf(tp_lex_pr280535005t_char,type,
    lex_pr280535005t_char: $i > $i > $i ).

thf(tp_lex_pr307591827t_char,type,
    lex_pr307591827t_char: $i > $i > $i ).

thf(tp_lex_pr69619957on_val,type,
    lex_pr69619957on_val: $i > $i > $i ).

thf(tp_lex_pr731210613on_val,type,
    lex_pr731210613on_val: $i > $i > $i ).

thf(tp_lex_prod_val_val,type,
    lex_prod_val_val: $i > $i > $i ).

thf(tp_list_all2_ty_ty,type,
    list_all2_ty_ty: $i > $i > $i > $i ).

thf(tp_map_ad1185064968ar_val,type,
    map_ad1185064968ar_val: $i > $i > $i ).

thf(tp_map_ad325961431ar_val,type,
    map_ad325961431ar_val: $i > $i > $i ).

thf(tp_map_ad61982421on_val,type,
    map_ad61982421on_val: $i > $i > $i ).

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

thf(tp_map_list_char_val,type,
    map_list_char_val: $i > $i > $i ).

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

thf(tp_map_up1085636310ar_val,type,
    map_up1085636310ar_val: $i > $i > $i > $i ).

thf(tp_map_up891053837har_ty,type,
    map_up891053837har_ty: $i > $i > $i > $i ).

thf(tp_map_va1934808527t_char,type,
    map_va1934808527t_char: $i > $i > $i ).

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

thf(tp_member104734088ist_ty,type,
    member104734088ist_ty: $i ).

thf(tp_member1161907014t_char,type,
    member1161907014t_char: $i ).

thf(tp_member1199939018t_char,type,
    member1199939018t_char: $i ).

thf(tp_member125098544t_char,type,
    member125098544t_char: $i ).

thf(tp_member1251428284t_char,type,
    member1251428284t_char: $i ).

thf(tp_member1322055188on_val,type,
    member1322055188on_val: $i ).

thf(tp_member133545693t_char,type,
    member133545693t_char: $i ).

thf(tp_member1337019328on_val,type,
    member1337019328on_val: $i ).

thf(tp_member1379348767t_char,type,
    member1379348767t_char: $i ).

thf(tp_member140606439t_char,type,
    member140606439t_char: $i ).

thf(tp_member1417904245al_val,type,
    member1417904245al_val: $i ).

thf(tp_member1420286996t_char,type,
    member1420286996t_char: $i ).

thf(tp_member1467889965t_char,type,
    member1467889965t_char: $i ).

thf(tp_member1542417277on_val,type,
    member1542417277on_val: $i ).

thf(tp_member1551446420t_char,type,
    member1551446420t_char: $i ).

thf(tp_member1580476948t_char,type,
    member1580476948t_char: $i ).

thf(tp_member1601084734t_char,type,
    member1601084734t_char: $i ).

thf(tp_member1607118676t_char,type,
    member1607118676t_char: $i ).

thf(tp_member162552852t_char,type,
    member162552852t_char: $i ).

thf(tp_member1732271180al_val,type,
    member1732271180al_val: $i ).

thf(tp_member1771544038t_char,type,
    member1771544038t_char: $i ).

thf(tp_member1840112042t_char,type,
    member1840112042t_char: $i ).

thf(tp_member1972431429on_val,type,
    member1972431429on_val: $i ).

thf(tp_member1999287380t_char,type,
    member1999287380t_char: $i ).

thf(tp_member273646106st_val,type,
    member273646106st_val: $i ).

thf(tp_member490182804on_val,type,
    member490182804on_val: $i ).

thf(tp_member520253462har_ty,type,
    member520253462har_ty: $i ).

thf(tp_member563141460on_val,type,
    member563141460on_val: $i ).

thf(tp_member649088532al_val,type,
    member649088532al_val: $i ).

thf(tp_member699351154t_char,type,
    member699351154t_char: $i ).

thf(tp_member763590124on_val,type,
    member763590124on_val: $i ).

thf(tp_member773094996on_val,type,
    member773094996on_val: $i ).

thf(tp_member781783252on_val,type,
    member781783252on_val: $i ).

thf(tp_member794220506t_char,type,
    member794220506t_char: $i ).

thf(tp_member808015754on_val,type,
    member808015754on_val: $i ).

thf(tp_member817832404t_char,type,
    member817832404t_char: $i ).

thf(tp_member837208074al_val,type,
    member837208074al_val: $i ).

thf(tp_member840932460on_val,type,
    member840932460on_val: $i ).

thf(tp_member875476972on_val,type,
    member875476972on_val: $i ).

thf(tp_member88670778on_val,type,
    member88670778on_val: $i ).

thf(tp_member894971540t_char,type,
    member894971540t_char: $i ).

thf(tp_member978285664op_bop,type,
    member978285664op_bop: $i ).

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

thf(tp_member_nat,type,
    member_nat: $i ).

thf(tp_method1809630380t_char,type,
    method1809630380t_char: $i > $i > $i > $i > $i > $i > $i ).

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

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

thf(tp_none_P179726773on_val,type,
    none_P179726773on_val: $i ).

thf(tp_none_f478147469r_bool,type,
    none_f478147469r_bool: $i ).

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

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

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

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

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

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

thf(tp_oconf_1869808039t_char,type,
    oconf_1869808039t_char: $i > $i > $i ).

thf(tp_option1388193227on_val,type,
    option1388193227on_val: $i > $i > $i > $i ).

thf(tp_ord_le1050317687l_bool,type,
    ord_le1050317687l_bool: $i > $i ).

thf(tp_ord_le1080391173l_bool,type,
    ord_le1080391173l_bool: $i > $i ).

thf(tp_ord_le1151384881r_bool,type,
    ord_le1151384881r_bool: $i > $i ).

thf(tp_ord_le117566470r_bool,type,
    ord_le117566470r_bool: $i > $i ).

thf(tp_ord_le1218729222r_bool,type,
    ord_le1218729222r_bool: $i > $i ).

thf(tp_ord_le125655867l_bool,type,
    ord_le125655867l_bool: $i > $i ).

thf(tp_ord_le1270183657l_bool,type,
    ord_le1270183657l_bool: $i > $i ).

thf(tp_ord_le1438917387l_bool,type,
    ord_le1438917387l_bool: $i > $i ).

thf(tp_ord_le1449176264r_bool,type,
    ord_le1449176264r_bool: $i > $i ).

thf(tp_ord_le1461833060l_bool,type,
    ord_le1461833060l_bool: $i > $i ).

thf(tp_ord_le1467847572l_bool,type,
    ord_le1467847572l_bool: $i > $i ).

thf(tp_ord_le1568362934t_bool,type,
    ord_le1568362934t_bool: $i > $i ).

thf(tp_ord_le1579844278r_bool,type,
    ord_le1579844278r_bool: $i > $i ).

thf(tp_ord_le1668954565l_bool,type,
    ord_le1668954565l_bool: $i > $i ).

thf(tp_ord_le1725884030l_bool,type,
    ord_le1725884030l_bool: $i > $i ).

thf(tp_ord_le1734858744r_bool,type,
    ord_le1734858744r_bool: $i > $i ).

thf(tp_ord_le1744419030l_bool,type,
    ord_le1744419030l_bool: $i > $i ).

thf(tp_ord_le176694639r_bool,type,
    ord_le176694639r_bool: $i > $i ).

thf(tp_ord_le1776148979l_bool,type,
    ord_le1776148979l_bool: $i > $i ).

thf(tp_ord_le1852058257r_bool,type,
    ord_le1852058257r_bool: $i > $i ).

thf(tp_ord_le1871967977r_bool,type,
    ord_le1871967977r_bool: $i > $i ).

thf(tp_ord_le188521288l_bool,type,
    ord_le188521288l_bool: $i > $i ).

thf(tp_ord_le1908998213l_bool,type,
    ord_le1908998213l_bool: $i > $i ).

thf(tp_ord_le1987888477r_bool,type,
    ord_le1987888477r_bool: $i > $i ).

thf(tp_ord_le2008677227r_bool,type,
    ord_le2008677227r_bool: $i > $i ).

thf(tp_ord_le2092826700r_bool,type,
    ord_le2092826700r_bool: $i > $i ).

thf(tp_ord_le285175110l_bool,type,
    ord_le285175110l_bool: $i > $i ).

thf(tp_ord_le310098611l_bool,type,
    ord_le310098611l_bool: $i > $i ).

thf(tp_ord_le408082617l_bool,type,
    ord_le408082617l_bool: $i > $i ).

thf(tp_ord_le458107652r_bool,type,
    ord_le458107652r_bool: $i > $i ).

thf(tp_ord_le640323803r_bool,type,
    ord_le640323803r_bool: $i > $i ).

thf(tp_ord_le715555971r_bool,type,
    ord_le715555971r_bool: $i > $i ).

thf(tp_ord_le725666495r_bool,type,
    ord_le725666495r_bool: $i > $i ).

thf(tp_ord_le735260024r_bool,type,
    ord_le735260024r_bool: $i > $i ).

thf(tp_ord_le817953186r_bool,type,
    ord_le817953186r_bool: $i > $i ).

thf(tp_ord_le989574145r_bool,type,
    ord_le989574145r_bool: $i > $i ).

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

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

thf(tp_overri2012515291on_val,type,
    overri2012515291on_val: $i > $i > $i > $i ).

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

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

thf(tp_produc1147572817t_char,type,
    produc1147572817t_char: $i ).

thf(tp_produc1152259904t_char,type,
    produc1152259904t_char: $i ).

thf(tp_produc1159035454l_bool,type,
    produc1159035454l_bool: $i > $i ).

thf(tp_produc1237966615t_char,type,
    produc1237966615t_char: $i ).

thf(tp_produc1244920211al_val,type,
    produc1244920211al_val: $i ).

thf(tp_produc1259058957on_val,type,
    produc1259058957on_val: $i ).

thf(tp_produc1265154397har_ty,type,
    produc1265154397har_ty: $i ).

thf(tp_produc1299387215t_char,type,
    produc1299387215t_char: $i ).

thf(tp_produc1324280167r_bool,type,
    produc1324280167r_bool: $i ).

thf(tp_produc1326056646l_bool,type,
    produc1326056646l_bool: $i ).

thf(tp_produc1331140167t_char,type,
    produc1331140167t_char: $i ).

thf(tp_produc1431439831t_char,type,
    produc1431439831t_char: $i ).

thf(tp_produc1441475159on_val,type,
    produc1441475159on_val: $i ).

thf(tp_produc1483578759t_char,type,
    produc1483578759t_char: $i ).

thf(tp_produc1491230096l_bool,type,
    produc1491230096l_bool: $i ).

thf(tp_produc1545444669t_char,type,
    produc1545444669t_char: $i ).

thf(tp_produc154616760r_bool,type,
    produc154616760r_bool: $i ).

thf(tp_produc1555310053l_bool,type,
    produc1555310053l_bool: $i > $i ).

thf(tp_produc1564932627on_val,type,
    produc1564932627on_val: $i ).

thf(tp_produc156891095r_bool,type,
    produc156891095r_bool: $i > $i ).

thf(tp_produc1574020101r_bool,type,
    produc1574020101r_bool: $i > $i ).

thf(tp_produc1577326610ion_ty,type,
    produc1577326610ion_ty: $i ).

thf(tp_produc1588781647r_bool,type,
    produc1588781647r_bool: $i > $i ).

thf(tp_produc1596557472r_bool,type,
    produc1596557472r_bool: $i ).

thf(tp_produc1611380469on_val,type,
    produc1611380469on_val: $i ).

thf(tp_produc1618304727on_val,type,
    produc1618304727on_val: $i ).

thf(tp_produc1641293463t_char,type,
    produc1641293463t_char: $i ).

thf(tp_produc1675615144ion_ty,type,
    produc1675615144ion_ty: $i > $i ).

thf(tp_produc1704639885r_bool,type,
    produc1704639885r_bool: $i ).

thf(tp_produc1712663241on_val,type,
    produc1712663241on_val: $i ).

thf(tp_produc1732333873r_bool,type,
    produc1732333873r_bool: $i ).

thf(tp_produc1815960045l_bool,type,
    produc1815960045l_bool: $i ).

thf(tp_produc1838470831l_bool,type,
    produc1838470831l_bool: $i > $i ).

thf(tp_produc1860789535har_ty,type,
    produc1860789535har_ty: $i ).

thf(tp_produc1897818327t_char,type,
    produc1897818327t_char: $i ).

thf(tp_produc1909267824t_char,type,
    produc1909267824t_char: $i ).

thf(tp_produc1911463199l_bool,type,
    produc1911463199l_bool: $i ).

thf(tp_produc1911975310l_bool,type,
    produc1911975310l_bool: $i > $i ).

thf(tp_produc1916172923t_char,type,
    produc1916172923t_char: $i ).

thf(tp_produc1924279125al_val,type,
    produc1924279125al_val: $i ).

thf(tp_produc1951691075on_val,type,
    produc1951691075on_val: $i ).

thf(tp_produc1958875245l_bool,type,
    produc1958875245l_bool: $i ).

thf(tp_produc1960514199on_val,type,
    produc1960514199on_val: $i ).

thf(tp_produc2016959032t_char,type,
    produc2016959032t_char: $i ).

thf(tp_produc2027921764r_bool,type,
    produc2027921764r_bool: $i ).

thf(tp_produc2035944023t_char,type,
    produc2035944023t_char: $i ).

thf(tp_produc2053127004l_bool,type,
    produc2053127004l_bool: $i > $i ).

thf(tp_produc2062775566l_bool,type,
    produc2062775566l_bool: $i > $i ).

thf(tp_produc2078839843st_val,type,
    produc2078839843st_val: $i ).

thf(tp_produc2080520419t_char,type,
    produc2080520419t_char: $i ).

thf(tp_produc2116052801r_bool,type,
    produc2116052801r_bool: $i > $i ).

thf(tp_produc2128769400l_bool,type,
    produc2128769400l_bool: $i ).

thf(tp_produc21910851r_bool,type,
    produc21910851r_bool: $i ).

thf(tp_produc24551831t_char,type,
    produc24551831t_char: $i ).

thf(tp_produc251930284har_ty,type,
    produc251930284har_ty: $i ).

thf(tp_produc266042248r_bool,type,
    produc266042248r_bool: $i > $i ).

thf(tp_produc288369490r_bool,type,
    produc288369490r_bool: $i > $i ).

thf(tp_produc379668296on_val,type,
    produc379668296on_val: $i ).

thf(tp_produc392960766l_bool,type,
    produc392960766l_bool: $i ).

thf(tp_produc436875159t_char,type,
    produc436875159t_char: $i ).

thf(tp_produc481748255l_bool,type,
    produc481748255l_bool: $i > $i ).

thf(tp_produc499151895on_val,type,
    produc499151895on_val: $i ).

thf(tp_produc5062597t_char,type,
    produc5062597t_char: $i ).

thf(tp_produc512429457ist_ty,type,
    produc512429457ist_ty: $i ).

thf(tp_produc550034914r_bool,type,
    produc550034914r_bool: $i > $i ).

thf(tp_produc57279289t_char,type,
    produc57279289t_char: $i ).

thf(tp_produc621191550al_val,type,
    produc621191550al_val: $i ).

thf(tp_produc635935767t_char,type,
    produc635935767t_char: $i ).

thf(tp_produc70644925l_bool,type,
    produc70644925l_bool: $i ).

thf(tp_produc723279022r_bool,type,
    produc723279022r_bool: $i ).

thf(tp_produc769963999l_bool,type,
    produc769963999l_bool: $i ).

thf(tp_produc822965838t_char,type,
    produc822965838t_char: $i ).

thf(tp_produc823076510on_val,type,
    produc823076510on_val: $i ).

thf(tp_produc870913623on_val,type,
    produc870913623on_val: $i ).

thf(tp_produc886919678l_bool,type,
    produc886919678l_bool: $i > $i ).

thf(tp_produc899768717on_val,type,
    produc899768717on_val: $i ).

thf(tp_produc907433735ion_ty,type,
    produc907433735ion_ty: $i ).

thf(tp_produc921874948t_char,type,
    produc921874948t_char: $i ).

thf(tp_produc943465171t_char,type,
    produc943465171t_char: $i ).

thf(tp_produc95371820r_bool,type,
    produc95371820r_bool: $i > $i ).

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

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

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

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

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

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

thf(tp_restri761823004ar_val,type,
    restri761823004ar_val: $i > $i > $i ).

thf(tp_sK10_SY700,type,
    sK10_SY700: $i > $i ).

thf(tp_sK11_SY701,type,
    sK11_SY701: $i > $i ).

thf(tp_sK12_SY737,type,
    sK12_SY737: $i > $i ).

thf(tp_sK13_SY755,type,
    sK13_SY755: $i > $i ).

thf(tp_sK14_SY758,type,
    sK14_SY758: $i > $i ).

thf(tp_sK15_SY763,type,
    sK15_SY763: $i > $i ).

thf(tp_sK16_SY772,type,
    sK16_SY772: $i > $i ).

thf(tp_sK17_SY774,type,
    sK17_SY774: $i > $i ).

thf(tp_sK18_SY782,type,
    sK18_SY782: $i > $i ).

thf(tp_sK19_SY785,type,
    sK19_SY785: $i > $i ).

thf(tp_sK1_SY323,type,
    sK1_SY323: $i > $i ).

thf(tp_sK20_SY576,type,
    sK20_SY576: $i > $i > $i ).

thf(tp_sK21_SY613,type,
    sK21_SY613: $i > $i > $i ).

thf(tp_sK22_SY636,type,
    sK22_SY636: $i > $i > $i ).

thf(tp_sK23_SY814,type,
    sK23_SY814: $i > $i ).

thf(tp_sK24_SY664,type,
    sK24_SY664: $i > $i > $i ).

thf(tp_sK25_SY824,type,
    sK25_SY824: $i > $i ).

thf(tp_sK26_SY832,type,
    sK26_SY832: $i > $i > $i ).

thf(tp_sK27_SY393,type,
    sK27_SY393: $i > $i ).

thf(tp_sK28_SY839,type,
    sK28_SY839: $i > $i > $i ).

thf(tp_sK29_SY846,type,
    sK29_SY846: $i > $i > $i ).

thf(tp_sK2_SY327,type,
    sK2_SY327: $i > $i ).

thf(tp_sK30_SY853,type,
    sK30_SY853: $i > $i ).

thf(tp_sK31_SY331,type,
    sK31_SY331: $i > $i ).

thf(tp_sK32_SY334,type,
    sK32_SY334: $i > $i ).

thf(tp_sK33_SY863,type,
    sK33_SY863: $i > $i > $i ).

thf(tp_sK34_SY398,type,
    sK34_SY398: $i > $i ).

thf(tp_sK35_SY865,type,
    sK35_SY865: $i > $i > $i ).

thf(tp_sK36_SY868,type,
    sK36_SY868: $i > $i > $i ).

thf(tp_sK37_SY527,type,
    sK37_SY527: $i > $i ).

thf(tp_sK38_SY530,type,
    sK38_SY530: $i > $i ).

thf(tp_sK39_SY535,type,
    sK39_SY535: $i > $i ).

thf(tp_sK3_SY429,type,
    sK3_SY429: $i > $i ).

thf(tp_sK40_SY538,type,
    sK40_SY538: $i > $i ).

thf(tp_sK41_SY877,type,
    sK41_SY877: $i > $i ).

thf(tp_sK42_SY593,type,
    sK42_SY593: $i > $i > $i ).

thf(tp_sK43_SY879,type,
    sK43_SY879: $i > $i > $i ).

thf(tp_sK44_SY881,type,
    sK44_SY881: $i > $i ).

thf(tp_sK45_SY882,type,
    sK45_SY882: $i > $i ).

thf(tp_sK46_SY886,type,
    sK46_SY886: $i > $i > $i ).

thf(tp_sK47_SY408,type,
    sK47_SY408: $i > $i ).

thf(tp_sK48_SY729,type,
    sK48_SY729: $i > $i > $i > $i ).

thf(tp_sK49_SY764,type,
    sK49_SY764: $i > $i > $i > $i ).

thf(tp_sK4_SY484,type,
    sK4_SY484: $i > $i ).

thf(tp_sK50_SY368,type,
    sK50_SY368: $i > $i > $i ).

thf(tp_sK51_SY459,type,
    sK51_SY459: $i > $i > $i ).

thf(tp_sK52_SY499,type,
    sK52_SY499: $i > $i > $i ).

thf(tp_sK53_SY837,type,
    sK53_SY837: $i > $i > $i > $i > $i > $i ).

thf(tp_sK54_SY895,type,
    sK54_SY895: $i > $i > $i > $i > $i > $i ).

thf(tp_sK55_SY892,type,
    sK55_SY892: $i > $i > $i ).

thf(tp_sK56_SY372,type,
    sK56_SY372: $i > $i > $i > $i ).

thf(tp_sK57_SY893,type,
    sK57_SY893: $i > $i > $i ).

thf(tp_sK58_SY463,type,
    sK58_SY463: $i > $i > $i > $i ).

thf(tp_sK59_SY894,type,
    sK59_SY894: $i > $i > $i ).

thf(tp_sK5_SY488,type,
    sK5_SY488: $i > $i ).

thf(tp_sK60_SY503,type,
    sK60_SY503: $i > $i > $i > $i ).

thf(tp_sK6_SY508,type,
    sK6_SY508: $i > $i ).

thf(tp_sK7_SY524,type,
    sK7_SY524: $i > $i ).

thf(tp_sK8_SY541,type,
    sK8_SY541: $i > $i ).

thf(tp_sK9_SY556,type,
    sK9_SY556: $i > $i ).

thf(tp_semila1168318597r_bool,type,
    semila1168318597r_bool: $i > $i > $i ).

thf(tp_semila1346223580r_bool,type,
    semila1346223580r_bool: $i > $i > $i ).

thf(tp_semila1731249415r_bool,type,
    semila1731249415r_bool: $i > $i > $i ).

thf(tp_semila449273525l_bool,type,
    semila449273525l_bool: $i > $i > $i ).

thf(tp_semila465093516t_bool,type,
    semila465093516t_bool: $i > $i > $i ).

thf(tp_semila751111325l_bool,type,
    semila751111325l_bool: $i > $i > $i ).

thf(tp_semila919158006r_bool,type,
    semila919158006r_bool: $i > $i > $i ).

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

thf(tp_set_Pr1494163115t_char,type,
    set_Pr1494163115t_char: $i > $i ).

thf(tp_set_Pr2033386304t_char,type,
    set_Pr2033386304t_char: $i > $i ).

thf(tp_set_list_char,type,
    set_list_char: $i > $i ).

thf(tp_size_s1143674878t_char,type,
    size_s1143674878t_char: $i > $i ).

thf(tp_size_s2113983095t_char,type,
    size_s2113983095t_char: $i > $i ).

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

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

thf(tp_some_P948696889on_val,type,
    some_P948696889on_val: $i ).

thf(tp_some_f80346385r_bool,type,
    some_f80346385r_bool: $i ).

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

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

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

thf(tp_subcls744239332t_char,type,
    subcls744239332t_char: $i > $i ).

thf(tp_subcls851966956t_char,type,
    subcls851966956t_char: $i > $i ).

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

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

thf(tp_t_1,type,
    t_1: $i ).

thf(tp_the_Pr431167171on_val,type,
    the_Pr431167171on_val: $i ).

thf(tp_the_fu297177755r_bool,type,
    the_fu297177755r_bool: $i ).

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

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

thf(tp_the_val,type,
    the_val: $i ).

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

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

thf(tp_transi1065307915t_char,type,
    transi1065307915t_char: $i > $i ).

thf(tp_transi1095029602t_char,type,
    transi1095029602t_char: $i > $i ).

thf(tp_transi1123801095t_char,type,
    transi1123801095t_char: $i > $i ).

thf(tp_transi122195895t_char,type,
    transi122195895t_char: $i > $i ).

thf(tp_transi1257872013t_char,type,
    transi1257872013t_char: $i > $i ).

thf(tp_transi1395422419t_char,type,
    transi1395422419t_char: $i > $i ).

thf(tp_transi1423755450al_val,type,
    transi1423755450al_val: $i > $i ).

thf(tp_transi1789604888t_char,type,
    transi1789604888t_char: $i > $i ).

thf(tp_transi1906258203al_val,type,
    transi1906258203al_val: $i > $i ).

thf(tp_transi198989188t_char,type,
    transi198989188t_char: $i > $i ).

thf(tp_transi2005320128t_char,type,
    transi2005320128t_char: $i > $i ).

thf(tp_transi2024712006on_val,type,
    transi2024712006on_val: $i > $i ).

thf(tp_transi208336786on_val,type,
    transi208336786on_val: $i > $i ).

thf(tp_transi374442731on_val,type,
    transi374442731on_val: $i > $i ).

thf(tp_transi61620055on_val,type,
    transi61620055on_val: $i > $i ).

thf(tp_transi772168185t_char,type,
    transi772168185t_char: $i > $i ).

thf(tp_transi910771962on_val,type,
    transi910771962on_val: $i > $i ).

thf(tp_transi921647814on_val,type,
    transi921647814on_val: $i > $i ).

thf(tp_transi935034983cl_val,type,
    transi935034983cl_val: $i > $i ).

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

thf(tp_typeSa1700205512_sconf,type,
    typeSa1700205512_sconf: $i > $i > $i ).

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

thf(tp_undefined_bop,type,
    undefined_bop: $i > $i ).

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

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

thf(tp_v_1,type,
    v_1: $i ).

thf(tp_v_2,type,
    v_2: $i ).

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

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

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

thf(tp_wTrt_1,type,
    wTrt_1: $i > $i > $i > $i > $i > $i ).

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

thf(tp_wTrts_1,type,
    wTrts_1: $i > $i > $i > $i > $i > $i ).

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

thf(tp_wf_pro755087577t_char,type,
    wf_pro755087577t_char: $i > $i > $i ).

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

thf(tp_widen_2090681816t_char,type,
    widen_2090681816t_char: $i > $i ).

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

thf(139,axiom,
    ~ ( hBOOL @ fFalse ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).

thf(147,axiom,
    hBOOL @ fTrue,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).

thf(210,axiom,
    ! [M: $i,Esa: $i,Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ Eb @ M @ Esa ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ E_b @ M @ Esa ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1139_red__reds_OCallObj) ).

thf(253,axiom,
    ! [E_1_1: $i,E_2: $i,Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ Eb @ E_1_1 @ E_2 ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ E_b @ E_1_1 @ E_2 ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1096_red__reds_OCondRed) ).

thf(282,axiom,
    ! [Bool_1: $i,Bool: $i] :
      ( ( ( bool @ Bool_1 )
        = ( bool @ Bool ) )
    <=> ( ( hBOOL @ Bool_1 )
      <=> ( hBOOL @ Bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1067_val_Osimps_I1_J) ).

thf(361,axiom,
    ! [C: $i,Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ C @ Eb ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ C @ E_b ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_988_red__reds_OCastRed) ).

thf(385,axiom,
    ! [C: $i,Va_1: $i,E_2: $i,Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ Eb @ C @ Va_1 @ E_2 ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ E_b @ C @ Va_1 @ E_2 ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_964_red__reds_OTryRed) ).

thf(388,axiom,
    ! [Bop: $i,E_2: $i,Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ Eb @ Bop @ E_2 ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ E_b @ Bop @ E_2 ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_961_red__reds_OBinOpRed1) ).

thf(421,axiom,
    ! [F: $i,D: $i,Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ Eb @ F @ D ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ E_b @ F @ D ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_928_red__reds_OFAccRed) ).

thf(424,axiom,
    ! [Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ Eb ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E_b ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_925_red__reds_OThrowRed) ).

thf(425,axiom,
    ! [Eb: $i,S: $i,Pa: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( throw_list_char @ Eb ) ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ Eb ) ) @ S ) ) ) @ ( red @ Pa ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_924_red__reds_OThrowThrow) ).

thf(453,axiom,
    ! [F: $i,D: $i,E_2: $i,Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ Eb @ F @ D @ E_2 ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ E_b @ F @ D @ E_2 ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_896_red__reds_OFAssRed1) ).

thf(477,axiom,
    ! [A_2: $i,C_2: $i,B_1: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C_2 ) @ B_1 ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C_2 ) @ A_2 ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C_2 ) @ ( semila751111325l_bool @ A_2 @ B_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_872_UnCI) ).

thf(484,axiom,
    ! [C_2: $i,A_2: $i,B_1: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C_2 ) @ ( semila751111325l_bool @ A_2 @ B_1 ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C_2 ) @ A_2 ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C_2 ) @ B_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_865_UnE) ).

thf(509,axiom,
    ! [X_2: $i,Z_1: $i,R_1: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ X_2 ) @ Z_1 ) ) @ ( transi2024712006on_val @ R_1 ) ) )
     => ( ( X_2 != Z_1 )
       => ~ ! [Y_1: $i] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ X_2 ) @ Y_1 ) ) @ R_1 ) )
             => ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ Y_1 ) @ Z_1 ) ) @ ( transi2024712006on_val @ R_1 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_840_converse__rtranclE) ).

thf(513,axiom,
    ! [A: $i,B: $i,R_1: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( transi2024712006on_val @ R_1 ) ) )
     => ( ( A != B )
       => ~ ! [Y_1: $i] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ Y_1 ) ) @ ( transi2024712006on_val @ R_1 ) ) )
             => ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ Y_1 ) @ B ) ) @ R_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_836_rtranclE) ).

thf(556,axiom,
    ! [Y_3: $i] :
      ( ( Y_3 != none_val )
     => ~ ! [A_1: $i] :
            ( Y_3
           != ( hAPP_val_option_val @ some_val @ A_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_793_option_Oexhaust) ).

thf(607,axiom,
    ! [Xa_1: $i,Xb_1: $i,Za: $i,Zb: $i,R_1: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Xa_1 ) @ Xb_1 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Za ) @ Zb ) ) ) @ ( transi2024712006on_val @ R_1 ) ) )
     => ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Xa_1 ) @ Xb_1 )
         != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Za ) @ Zb ) )
       => ~ ! [A_1: $i,B_2: $i] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Xa_1 ) @ Xb_1 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A_1 ) @ B_2 ) ) ) @ R_1 ) )
             => ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A_1 ) @ B_2 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Za ) @ Zb ) ) ) @ ( transi2024712006on_val @ R_1 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_742_converse__rtranclE2) ).

thf(609,axiom,
    ! [B_1: $i,A_2: $i] :
      ( ! [X_1: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ X_1 ) @ A_2 ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ X_1 ) @ B_1 ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A_2 ) @ B_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_740_subsetI) ).

thf(617,axiom,
    ! [C_2: $i,A: $i,B: $i,R_1: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( transi2024712006on_val @ R_1 ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C_2 ) ) @ ( transi2024712006on_val @ R_1 ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ C_2 ) ) @ ( transi2024712006on_val @ R_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_732_rtrancl__trans) ).

thf(621,axiom,
    ! [C_2: $i,A: $i,B: $i,R_1: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( transi2024712006on_val @ R_1 ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C_2 ) ) @ R_1 ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ C_2 ) ) @ ( transi2024712006on_val @ R_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_728_rtrancl_Ortrancl__into__rtrancl) ).

thf(625,axiom,
    ! [C_2: $i,A: $i,B: $i,R_1: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ R_1 ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C_2 ) ) @ ( transi2024712006on_val @ R_1 ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ C_2 ) ) @ ( transi2024712006on_val @ R_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_724_converse__rtrancl__into__rtrancl) ).

thf(635,axiom,
    ! [X_2: $i,A_2: $i,B_1: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A_2 ) @ B_1 ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ X_2 ) @ A_2 ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ X_2 ) @ B_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_714_set__mp) ).

thf(642,axiom,
    ! [B_1: $i,X_2: $i,A_2: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ X_2 ) @ A_2 ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A_2 ) @ B_1 ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ X_2 ) @ B_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_707_set__rev__mp) ).

thf(649,axiom,
    ! [X_2: $i,A_2: $i,B_1: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A_2 ) @ B_1 ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ X_2 ) @ A_2 ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ X_2 ) @ B_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_700_in__mono) ).

thf(674,axiom,
    ! [C_2: $i,A_2: $i,B_1: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A_2 ) @ B_1 ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C_2 ) @ A_2 ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C_2 ) @ B_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_675_subsetD) ).

thf(682,axiom,
    ! [P_1: $i,R_1: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ P_1 ) @ R_1 ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ P_1 ) @ ( transi2024712006on_val @ R_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_667_r__into__rtrancl) ).

thf(688,axiom,
    ! [A: $i,R_1: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ A ) ) @ ( transi2024712006on_val @ R_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_661_rtrancl_Ortrancl__refl) ).

thf(727,axiom,
    ! [X_2: $i] :
      ( ( X_2 != none_val )
    <=> ? [Y_1: $i] :
          ( X_2
          = ( hAPP_val_option_val @ some_val @ Y_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_622_not__None__eq) ).

thf(732,axiom,
    ! [X_2: $i] :
      ( ! [Y_1: $i] :
          ( X_2
         != ( hAPP_val_option_val @ some_val @ Y_1 ) )
    <=> ( X_2 = none_val ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_617_not__Some__eq) ).

thf(737,axiom,
    ! [A_4: $i] :
      ( ( hAPP_val_option_val @ some_val @ A_4 )
     != none_val ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_612_option_Osimps_I3_J) ).

thf(742,axiom,
    ! [A_5: $i] :
      ( none_val
     != ( hAPP_val_option_val @ some_val @ A_5 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_607_option_Osimps_I2_J) ).

thf(784,axiom,
    ! [H_4: $i,Hb: $i,H_b: $i] :
      ( ( hBOOL @ ( hext @ Hb @ H_b ) )
     => ( ( hBOOL @ ( hext @ H_b @ H_4 ) )
       => ( hBOOL @ ( hext @ Hb @ H_4 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_565_hext__trans) ).

thf(793,axiom,
    ! [Hb: $i] : ( hBOOL @ ( hext @ Hb @ Hb ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_556_hext__refl) ).

thf(832,axiom,
    ! [F_1: $i,G: $i,X_2: $i,Y_2: $i] :
      ( ( map_ad325961431ar_val @ F_1 @ ( fun_up1149430426on_val @ G @ X_2 @ ( hAPP_val_option_val @ some_val @ Y_2 ) ) )
      = ( fun_up1149430426on_val @ ( map_ad325961431ar_val @ F_1 @ G ) @ X_2 @ ( hAPP_val_option_val @ some_val @ Y_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_517_map__add__upd) ).

thf(868,axiom,
    ! [E_2: $i,Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ Eb @ E_2 ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ E_b @ E_2 ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_481_red__reds_OSeqRed) ).

thf(869,axiom,
    ! [Va_1: $i,Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ Va_1 @ Eb ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ Va_1 @ E_b ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_480_red__reds_OLAssRed) ).

thf(872,axiom,
    ! [X_2: $i,A_2: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ X_2 ) @ A_2 ) )
    <=> ( hBOOL @ ( hAPP_P282169671l_bool @ A_2 @ X_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_477_mem__def) ).

thf(976,axiom,
    ! [L_0: $i,Eb: $i,Hb: $i,Lb: $i,E_b: $i,H_b: $i,L_b: $i,Pa: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ Hb ) @ Lb ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H_b ) @ L_b ) ) ) ) @ ( red @ Pa ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ Hb ) @ ( map_ad325961431ar_val @ L_0 @ Lb ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H_b ) @ ( map_ad325961431ar_val @ L_0 @ L_b ) ) ) ) ) @ ( red @ Pa ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_373_red__lcl__add) ).

thf(993,axiom,
    ! [A: $i,A_3: $i] :
      ( ( ( hAPP_val_option_val @ some_val @ A )
        = ( hAPP_val_option_val @ some_val @ A_3 ) )
    <=> ( A = A_3 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_356_option_Oinject) ).

thf(999,axiom,
    ! [Eb: $i,Hb: $i,Lb: $i,E_b: $i,H_b: $i,L_b: $i,Pa: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ Hb ) @ Lb ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H_b ) @ L_b ) ) ) ) @ ( red @ Pa ) ) )
     => ( hBOOL @ ( hext @ Hb @ H_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_red__hext__incr) ).

thf(1003,axiom,
    ! [Pa: $i] :
      ( ? [X1: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ Pa @ X1 ) )
    <=> ? [A_1: $i,B_2: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ Pa @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A_1 ) @ B_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_split__paired__Ex) ).

thf(1004,axiom,
    ! [Pa: $i] :
      ( ? [X1: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ Pa @ X1 ) )
    <=> ? [A_1: $i,B_2: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ Pa @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A_1 ) @ B_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_split__paired__Ex) ).

thf(1005,axiom,
    ! [Pa: $i] :
      ( ? [X1: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ Pa @ X1 ) )
    <=> ? [A_1: $i,B_2: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ Pa @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A_1 ) @ B_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_split__paired__Ex) ).

thf(1019,axiom,
    ! [P_1: $i] :
      ~ ! [X_1: $i,Y_1: $i] :
          ( P_1
         != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ X_1 ) @ Y_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_PairE) ).

thf(1020,axiom,
    ! [P_1: $i] :
      ~ ! [X_1: $i,Y_1: $i] :
          ( P_1
         != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ X_1 ) @ Y_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_PairE) ).

thf(1021,axiom,
    ! [P_1: $i] :
      ~ ! [X_1: $i,Y_1: $i] :
          ( P_1
         != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ X_1 ) @ Y_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_PairE) ).

thf(1035,axiom,
    ! [Y_2: $i] :
      ~ ! [A_1: $i,B_2: $i] :
          ( Y_2
         != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A_1 ) @ B_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_prod_Oexhaust) ).

thf(1036,axiom,
    ! [Y_2: $i] :
      ~ ! [A_1: $i,B_2: $i] :
          ( Y_2
         != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A_1 ) @ B_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_prod_Oexhaust) ).

thf(1037,axiom,
    ! [Y_2: $i] :
      ~ ! [A_1: $i,B_2: $i] :
          ( Y_2
         != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A_1 ) @ B_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_prod_Oexhaust) ).

thf(1055,axiom,
    ! [S_4: $i,R_2: $i] :
      ( ! [X_1: $i,Xa: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ X_1 ) @ Xa ) ) @ R_2 ) )
        <=> ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ X_1 ) @ Xa ) ) @ S_4 ) ) )
    <=> ( R_2 = S_4 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_pred__equals__eq2) ).

thf(1101,axiom,
    ! [X_2: $i,Pa: $i] :
      ( ! [A_1: $i,B_2: $i,C_4: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ Pa @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A_1 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B_2 ) @ C_4 ) ) ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ Pa @ X_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_prod__induct3) ).

thf(1102,axiom,
    ! [X_2: $i,Pa: $i] :
      ( ! [A_1: $i,B_2: $i,C_4: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ Pa @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A_1 ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B_2 ) @ C_4 ) ) ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ Pa @ X_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_prod__induct3) ).

thf(1125,axiom,
    ! [Y_2: $i] :
      ~ ! [A_1: $i,B_2: $i,C_4: $i] :
          ( Y_2
         != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A_1 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B_2 ) @ C_4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_prod__cases3) ).

thf(1126,axiom,
    ! [Y_2: $i] :
      ~ ! [A_1: $i,B_2: $i,C_4: $i] :
          ( Y_2
         != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A_1 ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B_2 ) @ C_4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_prod__cases3) ).

thf(1134,axiom,
    ! [F_1: $i,X_2: $i,Y_2: $i] :
      ( ( ( fun_up1149430426on_val @ F_1 @ X_2 @ Y_2 )
        = F_1 )
    <=> ( ( hAPP_l207779698on_val @ F_1 @ X_2 )
        = Y_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_fun__upd__idem__iff) ).

thf(1138,axiom,
    ! [F_1: $i,X_2: $i,Y_2: $i,Z_1: $i] :
      ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ F_1 @ X_2 @ Y_2 ) @ X_2 @ Z_1 )
      = ( fun_up1149430426on_val @ F_1 @ X_2 @ Z_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_fun__upd__upd) ).

thf(1142,axiom,
    ! [F_1: $i,X_2: $i,Y_2: $i] :
      ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ F_1 @ X_2 @ Y_2 ) @ X_2 )
      = Y_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_fun__upd__same) ).

thf(1146,axiom,
    ! [F_1: $i,Y_2: $i,Z_1: $i,X_2: $i] :
      ( ( ( Z_1 = X_2 )
       => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ F_1 @ X_2 @ Y_2 ) @ Z_1 )
          = Y_2 ) )
      & ( ( Z_1 != X_2 )
       => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ F_1 @ X_2 @ Y_2 ) @ Z_1 )
          = ( hAPP_l207779698on_val @ F_1 @ Z_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_fun__upd__apply) ).

thf(1150,axiom,
    ! [M_1: $i,B: $i,D_1: $i,A: $i,C_2: $i] :
      ( ( A != C_2 )
     => ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ M_1 @ A @ B ) @ C_2 @ D_1 )
        = ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ M_1 @ C_2 @ D_1 ) @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_fun__upd__twist) ).

thf(1154,axiom,
    ! [F_1: $i,Y_2: $i,Z_1: $i,X_2: $i] :
      ( ( Z_1 != X_2 )
     => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ F_1 @ X_2 @ Y_2 ) @ Z_1 )
        = ( hAPP_l207779698on_val @ F_1 @ Z_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_fun__upd__other) ).

thf(1158,axiom,
    ! [F_1: $i,X_2: $i,Y_2: $i] :
      ( ( ( hAPP_l207779698on_val @ F_1 @ X_2 )
        = Y_2 )
     => ( ( fun_up1149430426on_val @ F_1 @ X_2 @ Y_2 )
        = F_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_fun__upd__idem) ).

thf(1162,axiom,
    ! [F_1: $i,B: $i,A: $i,X_1: $i] :
      ( ( ( X_1 = A )
       => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ F_1 @ A @ B ) @ X_1 )
          = B ) )
      & ( ( X_1 != A )
       => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ F_1 @ A @ B ) @ X_1 )
          = ( hAPP_l207779698on_val @ F_1 @ X_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_fun__upd__def) ).

thf(1176,axiom,
    ! [Pa: $i] :
      ( ! [X1: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ Pa @ X1 ) )
    <=> ! [A_1: $i,B_2: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ Pa @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A_1 ) @ B_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_split__paired__All) ).

thf(1177,axiom,
    ! [Pa: $i] :
      ( ! [X1: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ Pa @ X1 ) )
    <=> ! [A_1: $i,B_2: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ Pa @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A_1 ) @ B_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_split__paired__All) ).

thf(1178,axiom,
    ! [Pa: $i] :
      ( ! [X1: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ Pa @ X1 ) )
    <=> ! [A_1: $i,B_2: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ Pa @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A_1 ) @ B_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_split__paired__All) ).

thf(1220,axiom,
    ! [A: $i,B: $i,A_3: $i,B_3: $i] :
      ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B )
        = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A_3 ) @ B_3 ) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_Pair__eq) ).

thf(1221,axiom,
    ! [A: $i,B: $i,A_3: $i,B_3: $i] :
      ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B )
        = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A_3 ) @ B_3 ) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_Pair__eq) ).

thf(1222,axiom,
    ! [A: $i,B: $i,A_3: $i,B_3: $i] :
      ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B )
        = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A_3 ) @ B_3 ) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_Pair__eq) ).

thf(1264,axiom,
    ! [A: $i,B: $i,A_3: $i,B_3: $i] :
      ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B )
        = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A_3 ) @ B_3 ) )
     => ~ ( ( A = A_3 )
         => ( B != B_3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_Pair__inject) ).

thf(1265,axiom,
    ! [A: $i,B: $i,A_3: $i,B_3: $i] :
      ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B )
        = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A_3 ) @ B_3 ) )
     => ~ ( ( A = A_3 )
         => ( B != B_3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_Pair__inject) ).

thf(1266,axiom,
    ! [A: $i,B: $i,A_3: $i,B_3: $i] :
      ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B )
        = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A_3 ) @ B_3 ) )
     => ~ ( ( A = A_3 )
         => ( B != B_3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Pair__inject) ).

thf(1306,axiom,
    ! [Y_2: $i] :
      ~ ! [A_1: $i,B_2: $i,C_4: $i,D_2: $i] :
          ( Y_2
         != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A_1 ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B_2 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C_4 ) @ D_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_prod__cases4) ).

thf(1318,axiom,
    ! [X_2: $i,Pa: $i] :
      ( ! [A_1: $i,B_2: $i,C_4: $i,D_2: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ Pa @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A_1 ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B_2 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C_4 ) @ D_2 ) ) ) ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ Pa @ X_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_prod__induct4) ).

thf(1331,axiom,
    ! [M_1: $i,A: $i,X_2: $i,N: $i,Y_2: $i] :
      ( ( ( fun_up204312361on_val @ M_1 @ A @ ( hAPP_val_option_val @ some_val @ X_2 ) )
        = ( fun_up204312361on_val @ N @ A @ ( hAPP_val_option_val @ some_val @ Y_2 ) ) )
     => ( X_2 = Y_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_map__upd__eqD1) ).

thf(1334,axiom,
    ! [M_1: $i,A: $i,X_2: $i,N: $i,Y_2: $i] :
      ( ( ( fun_up1149430426on_val @ M_1 @ A @ ( hAPP_val_option_val @ some_val @ X_2 ) )
        = ( fun_up1149430426on_val @ N @ A @ ( hAPP_val_option_val @ some_val @ Y_2 ) ) )
     => ( X_2 = Y_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_map__upd__eqD1) ).

thf(1338,axiom,
    ! [T_2: $i,K: $i,X_2: $i] :
      ( ( ( hAPP_l207779698on_val @ T_2 @ K )
        = ( hAPP_val_option_val @ some_val @ X_2 ) )
     => ( ( fun_up1149430426on_val @ T_2 @ K @ ( hAPP_val_option_val @ some_val @ X_2 ) )
        = T_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_map__upd__triv) ).

thf(1342,axiom,
    ! [M_1: $i,A: $i,B: $i,X_2: $i,Y_2: $i] :
      ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ M_1 @ A @ ( hAPP_val_option_val @ some_val @ B ) ) @ X_2 )
        = ( hAPP_val_option_val @ some_val @ Y_2 ) )
    <=> ( ( ( X_2 = A )
          & ( B = Y_2 ) )
        | ( ( X_2 != A )
          & ( ( hAPP_l207779698on_val @ M_1 @ X_2 )
            = ( hAPP_val_option_val @ some_val @ Y_2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_map__upd__Some__unfold) ).

thf(1347,axiom,
    ! [F_1: $i,X_2: $i] :
      ( ( fun_up1149430426on_val @ F_1 @ X_2 @ ( hAPP_l207779698on_val @ F_1 @ X_2 ) )
      = F_1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_fun__upd__triv) ).

thf(1348,axiom,
    hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ea ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( hAPP_val_option_val @ some_val @ v ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ e_a ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ h_a ) @ l_a ) ) ) ) @ ( red @ p ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_InitBlockRed_I1_J) ).

thf(1490,axiom,
    ! [B_1_1: $i,B_2_1: $i] : ( is_bool @ ( hAPP_f1453283057l_bool @ B_1_1 @ B_2_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__) ).

thf(1491,conjecture,
    hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ea ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( hAPP_val_option_val @ some_val @ v ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ e_a ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ h_a ) @ l_a ) ) ) ) @ ( red @ p ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(1492,negated_conjecture,
    ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ea ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( hAPP_val_option_val @ some_val @ v ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ e_a ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ h_a ) @ l_a ) ) ) ) @ ( red @ p ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1491]) ).

thf(1493,plain,
    ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ea ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( hAPP_val_option_val @ some_val @ v ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ e_a ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ h_a ) @ l_a ) ) ) ) @ ( red @ p ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[1492]) ).

thf(1494,plain,
    ( ( ~ ( hBOOL @ fFalse ) )
    = $true ),
    inference(unfold_def,[status(thm)],[139]) ).

thf(1495,plain,
    ( ( hBOOL @ fTrue )
    = $true ),
    inference(unfold_def,[status(thm)],[147]) ).

thf(1496,plain,
    ( ( ! [M: $i,Esa: $i,Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ Eb @ M @ Esa ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ E_b @ M @ Esa ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[210]) ).

thf(1497,plain,
    ( ( ! [E_1_1: $i,E_2: $i,Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ Eb @ E_1_1 @ E_2 ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ E_b @ E_1_1 @ E_2 ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[253]) ).

thf(1498,plain,
    ( ( ! [Bool_1: $i,Bool: $i] :
          ( ( ( bool @ Bool_1 )
            = ( bool @ Bool ) )
        <=> ( ( hBOOL @ Bool_1 )
          <=> ( hBOOL @ Bool ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[282]) ).

thf(1499,plain,
    ( ( ! [C: $i,Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ C @ Eb ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ C @ E_b ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[361]) ).

thf(1500,plain,
    ( ( ! [C: $i,Va_1: $i,E_2: $i,Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ Eb @ C @ Va_1 @ E_2 ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ E_b @ C @ Va_1 @ E_2 ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[385]) ).

thf(1501,plain,
    ( ( ! [Bop: $i,E_2: $i,Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ Eb @ Bop @ E_2 ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ E_b @ Bop @ E_2 ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[388]) ).

thf(1502,plain,
    ( ( ! [F: $i,D: $i,Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ Eb @ F @ D ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ E_b @ F @ D ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[421]) ).

thf(1503,plain,
    ( ( ! [Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ Eb ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E_b ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[424]) ).

thf(1504,plain,
    ( ( ! [Eb: $i,S: $i,Pa: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( throw_list_char @ Eb ) ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ Eb ) ) @ S ) ) ) @ ( red @ Pa ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[425]) ).

thf(1505,plain,
    ( ( ! [F: $i,D: $i,E_2: $i,Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ Eb @ F @ D @ E_2 ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ E_b @ F @ D @ E_2 ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[453]) ).

thf(1506,plain,
    ( ( ! [A_2: $i,C_2: $i,B_1: $i] :
          ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C_2 ) @ B_1 ) )
           => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C_2 ) @ A_2 ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C_2 ) @ ( semila751111325l_bool @ A_2 @ B_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[477]) ).

thf(1507,plain,
    ( ( ! [C_2: $i,A_2: $i,B_1: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C_2 ) @ ( semila751111325l_bool @ A_2 @ B_1 ) ) )
         => ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C_2 ) @ A_2 ) )
           => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C_2 ) @ B_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[484]) ).

thf(1508,plain,
    ( ( ! [X_2: $i,Z_1: $i,R_1: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ X_2 ) @ Z_1 ) ) @ ( transi2024712006on_val @ R_1 ) ) )
         => ( ( X_2 != Z_1 )
           => ~ ! [Y_1: $i] :
                  ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ X_2 ) @ Y_1 ) ) @ R_1 ) )
                 => ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ Y_1 ) @ Z_1 ) ) @ ( transi2024712006on_val @ R_1 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[509]) ).

thf(1509,plain,
    ( ( ! [A: $i,B: $i,R_1: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( transi2024712006on_val @ R_1 ) ) )
         => ( ( A != B )
           => ~ ! [Y_1: $i] :
                  ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ Y_1 ) ) @ ( transi2024712006on_val @ R_1 ) ) )
                 => ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ Y_1 ) @ B ) ) @ R_1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[513]) ).

thf(1510,plain,
    ( ( ! [Y_3: $i] :
          ( ( Y_3 != none_val )
         => ~ ! [A_1: $i] :
                ( Y_3
               != ( hAPP_val_option_val @ some_val @ A_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[556]) ).

thf(1511,plain,
    ( ( ! [Xa_1: $i,Xb_1: $i,Za: $i,Zb: $i,R_1: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Xa_1 ) @ Xb_1 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Za ) @ Zb ) ) ) @ ( transi2024712006on_val @ R_1 ) ) )
         => ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Xa_1 ) @ Xb_1 )
             != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Za ) @ Zb ) )
           => ~ ! [A_1: $i,B_2: $i] :
                  ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Xa_1 ) @ Xb_1 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A_1 ) @ B_2 ) ) ) @ R_1 ) )
                 => ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A_1 ) @ B_2 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Za ) @ Zb ) ) ) @ ( transi2024712006on_val @ R_1 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[607]) ).

thf(1512,plain,
    ( ( ! [B_1: $i,A_2: $i] :
          ( ! [X_1: $i] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ X_1 ) @ A_2 ) )
             => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ X_1 ) @ B_1 ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A_2 ) @ B_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[609]) ).

thf(1513,plain,
    ( ( ! [C_2: $i,A: $i,B: $i,R_1: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( transi2024712006on_val @ R_1 ) ) )
         => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C_2 ) ) @ ( transi2024712006on_val @ R_1 ) ) )
           => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ C_2 ) ) @ ( transi2024712006on_val @ R_1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[617]) ).

thf(1514,plain,
    ( ( ! [C_2: $i,A: $i,B: $i,R_1: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( transi2024712006on_val @ R_1 ) ) )
         => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C_2 ) ) @ R_1 ) )
           => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ C_2 ) ) @ ( transi2024712006on_val @ R_1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[621]) ).

thf(1515,plain,
    ( ( ! [C_2: $i,A: $i,B: $i,R_1: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ R_1 ) )
         => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C_2 ) ) @ ( transi2024712006on_val @ R_1 ) ) )
           => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ C_2 ) ) @ ( transi2024712006on_val @ R_1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[625]) ).

thf(1516,plain,
    ( ( ! [X_2: $i,A_2: $i,B_1: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A_2 ) @ B_1 ) )
         => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ X_2 ) @ A_2 ) )
           => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ X_2 ) @ B_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[635]) ).

thf(1517,plain,
    ( ( ! [B_1: $i,X_2: $i,A_2: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ X_2 ) @ A_2 ) )
         => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A_2 ) @ B_1 ) )
           => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ X_2 ) @ B_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[642]) ).

thf(1518,plain,
    ( ( ! [X_2: $i,A_2: $i,B_1: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A_2 ) @ B_1 ) )
         => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ X_2 ) @ A_2 ) )
           => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ X_2 ) @ B_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[649]) ).

thf(1519,plain,
    ( ( ! [C_2: $i,A_2: $i,B_1: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A_2 ) @ B_1 ) )
         => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C_2 ) @ A_2 ) )
           => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C_2 ) @ B_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[674]) ).

thf(1520,plain,
    ( ( ! [P_1: $i,R_1: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ P_1 ) @ R_1 ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ P_1 ) @ ( transi2024712006on_val @ R_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[682]) ).

thf(1521,plain,
    ( ( ! [A: $i,R_1: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ A ) ) @ ( transi2024712006on_val @ R_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[688]) ).

thf(1522,plain,
    ( ( ! [X_2: $i] :
          ( ( X_2 != none_val )
        <=> ? [Y_1: $i] :
              ( X_2
              = ( hAPP_val_option_val @ some_val @ Y_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[727]) ).

thf(1523,plain,
    ( ( ! [X_2: $i] :
          ( ! [Y_1: $i] :
              ( X_2
             != ( hAPP_val_option_val @ some_val @ Y_1 ) )
        <=> ( X_2 = none_val ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[732]) ).

thf(1524,plain,
    ( ( ! [A_4: $i] :
          ( ( hAPP_val_option_val @ some_val @ A_4 )
         != none_val ) )
    = $true ),
    inference(unfold_def,[status(thm)],[737]) ).

thf(1525,plain,
    ( ( ! [A_5: $i] :
          ( none_val
         != ( hAPP_val_option_val @ some_val @ A_5 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[742]) ).

thf(1526,plain,
    ( ( ! [H_4: $i,Hb: $i,H_b: $i] :
          ( ( hBOOL @ ( hext @ Hb @ H_b ) )
         => ( ( hBOOL @ ( hext @ H_b @ H_4 ) )
           => ( hBOOL @ ( hext @ Hb @ H_4 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[784]) ).

thf(1527,plain,
    ( ( ! [Hb: $i] : ( hBOOL @ ( hext @ Hb @ Hb ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[793]) ).

thf(1528,plain,
    ( ( ! [F_1: $i,G: $i,X_2: $i,Y_2: $i] :
          ( ( map_ad325961431ar_val @ F_1 @ ( fun_up1149430426on_val @ G @ X_2 @ ( hAPP_val_option_val @ some_val @ Y_2 ) ) )
          = ( fun_up1149430426on_val @ ( map_ad325961431ar_val @ F_1 @ G ) @ X_2 @ ( hAPP_val_option_val @ some_val @ Y_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[832]) ).

thf(1529,plain,
    ( ( ! [E_2: $i,Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ Eb @ E_2 ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ E_b @ E_2 ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[868]) ).

thf(1530,plain,
    ( ( ! [Va_1: $i,Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ Va_1 @ Eb ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ Va_1 @ E_b ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[869]) ).

thf(1531,plain,
    ( ( ! [X_2: $i,A_2: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ X_2 ) @ A_2 ) )
        <=> ( hBOOL @ ( hAPP_P282169671l_bool @ A_2 @ X_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[872]) ).

thf(1532,plain,
    ( ( ! [L_0: $i,Eb: $i,Hb: $i,Lb: $i,E_b: $i,H_b: $i,L_b: $i,Pa: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ Hb ) @ Lb ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H_b ) @ L_b ) ) ) ) @ ( red @ Pa ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ Hb ) @ ( map_ad325961431ar_val @ L_0 @ Lb ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H_b ) @ ( map_ad325961431ar_val @ L_0 @ L_b ) ) ) ) ) @ ( red @ Pa ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[976]) ).

thf(1533,plain,
    ( ( ! [A: $i,A_3: $i] :
          ( ( ( hAPP_val_option_val @ some_val @ A )
            = ( hAPP_val_option_val @ some_val @ A_3 ) )
        <=> ( A = A_3 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[993]) ).

thf(1534,plain,
    ( ( ! [Eb: $i,Hb: $i,Lb: $i,E_b: $i,H_b: $i,L_b: $i,Pa: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ Hb ) @ Lb ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H_b ) @ L_b ) ) ) ) @ ( red @ Pa ) ) )
         => ( hBOOL @ ( hext @ Hb @ H_b ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[999]) ).

thf(1535,plain,
    ( ( ! [Pa: $i] :
          ( ? [X1: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ Pa @ X1 ) )
        <=> ? [A_1: $i,B_2: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ Pa @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A_1 ) @ B_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1003]) ).

thf(1536,plain,
    ( ( ! [Pa: $i] :
          ( ? [X1: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ Pa @ X1 ) )
        <=> ? [A_1: $i,B_2: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ Pa @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A_1 ) @ B_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1004]) ).

thf(1537,plain,
    ( ( ! [Pa: $i] :
          ( ? [X1: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ Pa @ X1 ) )
        <=> ? [A_1: $i,B_2: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ Pa @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A_1 ) @ B_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1005]) ).

thf(1538,plain,
    ( ( ! [P_1: $i] :
          ~ ! [X_1: $i,Y_1: $i] :
              ( P_1
             != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ X_1 ) @ Y_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1019]) ).

thf(1539,plain,
    ( ( ! [P_1: $i] :
          ~ ! [X_1: $i,Y_1: $i] :
              ( P_1
             != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ X_1 ) @ Y_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1020]) ).

thf(1540,plain,
    ( ( ! [P_1: $i] :
          ~ ! [X_1: $i,Y_1: $i] :
              ( P_1
             != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ X_1 ) @ Y_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1021]) ).

thf(1541,plain,
    ( ( ! [Y_2: $i] :
          ~ ! [A_1: $i,B_2: $i] :
              ( Y_2
             != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A_1 ) @ B_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1035]) ).

thf(1542,plain,
    ( ( ! [Y_2: $i] :
          ~ ! [A_1: $i,B_2: $i] :
              ( Y_2
             != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A_1 ) @ B_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1036]) ).

thf(1543,plain,
    ( ( ! [Y_2: $i] :
          ~ ! [A_1: $i,B_2: $i] :
              ( Y_2
             != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A_1 ) @ B_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1037]) ).

thf(1544,plain,
    ( ( ! [S_4: $i,R_2: $i] :
          ( ! [X_1: $i,Xa: $i] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ X_1 ) @ Xa ) ) @ R_2 ) )
            <=> ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ X_1 ) @ Xa ) ) @ S_4 ) ) )
        <=> ( R_2 = S_4 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1055]) ).

thf(1545,plain,
    ( ( ! [X_2: $i,Pa: $i] :
          ( ! [A_1: $i,B_2: $i,C_4: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ Pa @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A_1 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B_2 ) @ C_4 ) ) ) )
         => ( hBOOL @ ( hAPP_P1708370145l_bool @ Pa @ X_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1101]) ).

thf(1546,plain,
    ( ( ! [X_2: $i,Pa: $i] :
          ( ! [A_1: $i,B_2: $i,C_4: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ Pa @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A_1 ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B_2 ) @ C_4 ) ) ) )
         => ( hBOOL @ ( hAPP_P282169671l_bool @ Pa @ X_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1102]) ).

thf(1547,plain,
    ( ( ! [Y_2: $i] :
          ~ ! [A_1: $i,B_2: $i,C_4: $i] :
              ( Y_2
             != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A_1 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B_2 ) @ C_4 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1125]) ).

thf(1548,plain,
    ( ( ! [Y_2: $i] :
          ~ ! [A_1: $i,B_2: $i,C_4: $i] :
              ( Y_2
             != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A_1 ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B_2 ) @ C_4 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1126]) ).

thf(1549,plain,
    ( ( ! [F_1: $i,X_2: $i,Y_2: $i] :
          ( ( ( fun_up1149430426on_val @ F_1 @ X_2 @ Y_2 )
            = F_1 )
        <=> ( ( hAPP_l207779698on_val @ F_1 @ X_2 )
            = Y_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1134]) ).

thf(1550,plain,
    ( ( ! [F_1: $i,X_2: $i,Y_2: $i,Z_1: $i] :
          ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ F_1 @ X_2 @ Y_2 ) @ X_2 @ Z_1 )
          = ( fun_up1149430426on_val @ F_1 @ X_2 @ Z_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1138]) ).

thf(1551,plain,
    ( ( ! [F_1: $i,X_2: $i,Y_2: $i] :
          ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ F_1 @ X_2 @ Y_2 ) @ X_2 )
          = Y_2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1142]) ).

thf(1552,plain,
    ( ( ! [F_1: $i,Y_2: $i,Z_1: $i,X_2: $i] :
          ( ( ( Z_1 = X_2 )
           => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ F_1 @ X_2 @ Y_2 ) @ Z_1 )
              = Y_2 ) )
          & ( ( Z_1 != X_2 )
           => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ F_1 @ X_2 @ Y_2 ) @ Z_1 )
              = ( hAPP_l207779698on_val @ F_1 @ Z_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1146]) ).

thf(1553,plain,
    ( ( ! [M_1: $i,B: $i,D_1: $i,A: $i,C_2: $i] :
          ( ( A != C_2 )
         => ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ M_1 @ A @ B ) @ C_2 @ D_1 )
            = ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ M_1 @ C_2 @ D_1 ) @ A @ B ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1150]) ).

thf(1554,plain,
    ( ( ! [F_1: $i,Y_2: $i,Z_1: $i,X_2: $i] :
          ( ( Z_1 != X_2 )
         => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ F_1 @ X_2 @ Y_2 ) @ Z_1 )
            = ( hAPP_l207779698on_val @ F_1 @ Z_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1154]) ).

thf(1555,plain,
    ( ( ! [F_1: $i,X_2: $i,Y_2: $i] :
          ( ( ( hAPP_l207779698on_val @ F_1 @ X_2 )
            = Y_2 )
         => ( ( fun_up1149430426on_val @ F_1 @ X_2 @ Y_2 )
            = F_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1158]) ).

thf(1556,plain,
    ( ( ! [F_1: $i,B: $i,A: $i,X_1: $i] :
          ( ( ( X_1 = A )
           => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ F_1 @ A @ B ) @ X_1 )
              = B ) )
          & ( ( X_1 != A )
           => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ F_1 @ A @ B ) @ X_1 )
              = ( hAPP_l207779698on_val @ F_1 @ X_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1162]) ).

thf(1557,plain,
    ( ( ! [Pa: $i] :
          ( ! [X1: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ Pa @ X1 ) )
        <=> ! [A_1: $i,B_2: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ Pa @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A_1 ) @ B_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1176]) ).

thf(1558,plain,
    ( ( ! [Pa: $i] :
          ( ! [X1: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ Pa @ X1 ) )
        <=> ! [A_1: $i,B_2: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ Pa @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A_1 ) @ B_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1177]) ).

thf(1559,plain,
    ( ( ! [Pa: $i] :
          ( ! [X1: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ Pa @ X1 ) )
        <=> ! [A_1: $i,B_2: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ Pa @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A_1 ) @ B_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1178]) ).

thf(1560,plain,
    ( ( ! [A: $i,B: $i,A_3: $i,B_3: $i] :
          ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B )
            = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A_3 ) @ B_3 ) )
        <=> ( ( A = A_3 )
            & ( B = B_3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1220]) ).

thf(1561,plain,
    ( ( ! [A: $i,B: $i,A_3: $i,B_3: $i] :
          ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B )
            = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A_3 ) @ B_3 ) )
        <=> ( ( A = A_3 )
            & ( B = B_3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1221]) ).

thf(1562,plain,
    ( ( ! [A: $i,B: $i,A_3: $i,B_3: $i] :
          ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B )
            = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A_3 ) @ B_3 ) )
        <=> ( ( A = A_3 )
            & ( B = B_3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1222]) ).

thf(1563,plain,
    ( ( ! [A: $i,B: $i,A_3: $i,B_3: $i] :
          ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B )
            = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A_3 ) @ B_3 ) )
         => ~ ( ( A = A_3 )
             => ( B != B_3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1264]) ).

thf(1564,plain,
    ( ( ! [A: $i,B: $i,A_3: $i,B_3: $i] :
          ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B )
            = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A_3 ) @ B_3 ) )
         => ~ ( ( A = A_3 )
             => ( B != B_3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1265]) ).

thf(1565,plain,
    ( ( ! [A: $i,B: $i,A_3: $i,B_3: $i] :
          ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B )
            = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A_3 ) @ B_3 ) )
         => ~ ( ( A = A_3 )
             => ( B != B_3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1266]) ).

thf(1566,plain,
    ( ( ! [Y_2: $i] :
          ~ ! [A_1: $i,B_2: $i,C_4: $i,D_2: $i] :
              ( Y_2
             != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A_1 ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B_2 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C_4 ) @ D_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1306]) ).

thf(1567,plain,
    ( ( ! [X_2: $i,Pa: $i] :
          ( ! [A_1: $i,B_2: $i,C_4: $i,D_2: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ Pa @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A_1 ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B_2 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C_4 ) @ D_2 ) ) ) ) )
         => ( hBOOL @ ( hAPP_P282169671l_bool @ Pa @ X_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1318]) ).

thf(1568,plain,
    ( ( ! [M_1: $i,A: $i,X_2: $i,N: $i,Y_2: $i] :
          ( ( ( fun_up204312361on_val @ M_1 @ A @ ( hAPP_val_option_val @ some_val @ X_2 ) )
            = ( fun_up204312361on_val @ N @ A @ ( hAPP_val_option_val @ some_val @ Y_2 ) ) )
         => ( X_2 = Y_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1331]) ).

thf(1569,plain,
    ( ( ! [M_1: $i,A: $i,X_2: $i,N: $i,Y_2: $i] :
          ( ( ( fun_up1149430426on_val @ M_1 @ A @ ( hAPP_val_option_val @ some_val @ X_2 ) )
            = ( fun_up1149430426on_val @ N @ A @ ( hAPP_val_option_val @ some_val @ Y_2 ) ) )
         => ( X_2 = Y_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1334]) ).

thf(1570,plain,
    ( ( ! [T_2: $i,K: $i,X_2: $i] :
          ( ( ( hAPP_l207779698on_val @ T_2 @ K )
            = ( hAPP_val_option_val @ some_val @ X_2 ) )
         => ( ( fun_up1149430426on_val @ T_2 @ K @ ( hAPP_val_option_val @ some_val @ X_2 ) )
            = T_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1338]) ).

thf(1571,plain,
    ( ( ! [M_1: $i,A: $i,B: $i,X_2: $i,Y_2: $i] :
          ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ M_1 @ A @ ( hAPP_val_option_val @ some_val @ B ) ) @ X_2 )
            = ( hAPP_val_option_val @ some_val @ Y_2 ) )
        <=> ( ( ( X_2 = A )
              & ( B = Y_2 ) )
            | ( ( X_2 != A )
              & ( ( hAPP_l207779698on_val @ M_1 @ X_2 )
                = ( hAPP_val_option_val @ some_val @ Y_2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1342]) ).

thf(1572,plain,
    ( ( ! [F_1: $i,X_2: $i] :
          ( ( fun_up1149430426on_val @ F_1 @ X_2 @ ( hAPP_l207779698on_val @ F_1 @ X_2 ) )
          = F_1 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1347]) ).

thf(1573,plain,
    ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ea ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( hAPP_val_option_val @ some_val @ v ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ e_a ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ h_a ) @ l_a ) ) ) ) @ ( red @ p ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1348]) ).

thf(1574,plain,
    ( ( ! [B_1_1: $i,B_2_1: $i] : ( is_bool @ ( hAPP_f1453283057l_bool @ B_1_1 @ B_2_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1490]) ).

thf(1575,plain,
    ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ea ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( hAPP_val_option_val @ some_val @ v ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ e_a ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ h_a ) @ l_a ) ) ) ) @ ( red @ p ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[1493]) ).

thf(1576,plain,
    ( ( ! [B_1_1: $i,B_2_1: $i] : ( is_bool @ ( hAPP_f1453283057l_bool @ B_1_1 @ B_2_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1574]) ).

thf(1577,plain,
    ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ea ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( hAPP_val_option_val @ some_val @ v ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ e_a ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ h_a ) @ l_a ) ) ) ) @ ( red @ p ) ) )
    = $true ),
    inference(copy,[status(thm)],[1573]) ).

thf(1578,plain,
    ( ( ! [F_1: $i,X_2: $i] :
          ( ( fun_up1149430426on_val @ F_1 @ X_2 @ ( hAPP_l207779698on_val @ F_1 @ X_2 ) )
          = F_1 ) )
    = $true ),
    inference(copy,[status(thm)],[1572]) ).

thf(1579,plain,
    ( ( ! [M_1: $i,A: $i,B: $i,X_2: $i,Y_2: $i] :
          ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ M_1 @ A @ ( hAPP_val_option_val @ some_val @ B ) ) @ X_2 )
            = ( hAPP_val_option_val @ some_val @ Y_2 ) )
        <=> ( ( ( X_2 = A )
              & ( B = Y_2 ) )
            | ( ( X_2 != A )
              & ( ( hAPP_l207779698on_val @ M_1 @ X_2 )
                = ( hAPP_val_option_val @ some_val @ Y_2 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1571]) ).

thf(1580,plain,
    ( ( ! [T_2: $i,K: $i,X_2: $i] :
          ( ( ( hAPP_l207779698on_val @ T_2 @ K )
            = ( hAPP_val_option_val @ some_val @ X_2 ) )
         => ( ( fun_up1149430426on_val @ T_2 @ K @ ( hAPP_val_option_val @ some_val @ X_2 ) )
            = T_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1570]) ).

thf(1581,plain,
    ( ( ! [M_1: $i,A: $i,X_2: $i,N: $i,Y_2: $i] :
          ( ( ( fun_up1149430426on_val @ M_1 @ A @ ( hAPP_val_option_val @ some_val @ X_2 ) )
            = ( fun_up1149430426on_val @ N @ A @ ( hAPP_val_option_val @ some_val @ Y_2 ) ) )
         => ( X_2 = Y_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1569]) ).

thf(1582,plain,
    ( ( ! [M_1: $i,A: $i,X_2: $i,N: $i,Y_2: $i] :
          ( ( ( fun_up204312361on_val @ M_1 @ A @ ( hAPP_val_option_val @ some_val @ X_2 ) )
            = ( fun_up204312361on_val @ N @ A @ ( hAPP_val_option_val @ some_val @ Y_2 ) ) )
         => ( X_2 = Y_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1568]) ).

thf(1583,plain,
    ( ( ! [X_2: $i,Pa: $i] :
          ( ! [A_1: $i,B_2: $i,C_4: $i,D_2: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ Pa @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A_1 ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B_2 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C_4 ) @ D_2 ) ) ) ) )
         => ( hBOOL @ ( hAPP_P282169671l_bool @ Pa @ X_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1567]) ).

thf(1584,plain,
    ( ( ! [Y_2: $i] :
          ~ ! [A_1: $i,B_2: $i,C_4: $i,D_2: $i] :
              ( Y_2
             != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A_1 ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B_2 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C_4 ) @ D_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1566]) ).

thf(1585,plain,
    ( ( ! [A: $i,B: $i,A_3: $i,B_3: $i] :
          ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B )
            = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A_3 ) @ B_3 ) )
         => ~ ( ( A = A_3 )
             => ( B != B_3 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1565]) ).

thf(1586,plain,
    ( ( ! [A: $i,B: $i,A_3: $i,B_3: $i] :
          ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B )
            = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A_3 ) @ B_3 ) )
         => ~ ( ( A = A_3 )
             => ( B != B_3 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1564]) ).

thf(1587,plain,
    ( ( ! [A: $i,B: $i,A_3: $i,B_3: $i] :
          ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B )
            = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A_3 ) @ B_3 ) )
         => ~ ( ( A = A_3 )
             => ( B != B_3 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1563]) ).

thf(1588,plain,
    ( ( ! [A: $i,B: $i,A_3: $i,B_3: $i] :
          ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B )
            = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A_3 ) @ B_3 ) )
        <=> ( ( A = A_3 )
            & ( B = B_3 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1562]) ).

thf(1589,plain,
    ( ( ! [A: $i,B: $i,A_3: $i,B_3: $i] :
          ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B )
            = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A_3 ) @ B_3 ) )
        <=> ( ( A = A_3 )
            & ( B = B_3 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1561]) ).

thf(1590,plain,
    ( ( ! [A: $i,B: $i,A_3: $i,B_3: $i] :
          ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B )
            = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A_3 ) @ B_3 ) )
        <=> ( ( A = A_3 )
            & ( B = B_3 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1560]) ).

thf(1591,plain,
    ( ( ! [Pa: $i] :
          ( ! [X1: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ Pa @ X1 ) )
        <=> ! [A_1: $i,B_2: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ Pa @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A_1 ) @ B_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1559]) ).

thf(1592,plain,
    ( ( ! [Pa: $i] :
          ( ! [X1: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ Pa @ X1 ) )
        <=> ! [A_1: $i,B_2: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ Pa @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A_1 ) @ B_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1558]) ).

thf(1593,plain,
    ( ( ! [Pa: $i] :
          ( ! [X1: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ Pa @ X1 ) )
        <=> ! [A_1: $i,B_2: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ Pa @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A_1 ) @ B_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1557]) ).

thf(1594,plain,
    ( ( ! [F_1: $i,B: $i,A: $i,X_1: $i] :
          ( ( ( X_1 = A )
           => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ F_1 @ A @ B ) @ X_1 )
              = B ) )
          & ( ( X_1 != A )
           => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ F_1 @ A @ B ) @ X_1 )
              = ( hAPP_l207779698on_val @ F_1 @ X_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1556]) ).

thf(1595,plain,
    ( ( ! [F_1: $i,X_2: $i,Y_2: $i] :
          ( ( ( hAPP_l207779698on_val @ F_1 @ X_2 )
            = Y_2 )
         => ( ( fun_up1149430426on_val @ F_1 @ X_2 @ Y_2 )
            = F_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1555]) ).

thf(1596,plain,
    ( ( ! [F_1: $i,Y_2: $i,Z_1: $i,X_2: $i] :
          ( ( Z_1 != X_2 )
         => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ F_1 @ X_2 @ Y_2 ) @ Z_1 )
            = ( hAPP_l207779698on_val @ F_1 @ Z_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1554]) ).

thf(1597,plain,
    ( ( ! [M_1: $i,B: $i,D_1: $i,A: $i,C_2: $i] :
          ( ( A != C_2 )
         => ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ M_1 @ A @ B ) @ C_2 @ D_1 )
            = ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ M_1 @ C_2 @ D_1 ) @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1553]) ).

thf(1598,plain,
    ( ( ! [F_1: $i,Y_2: $i,Z_1: $i,X_2: $i] :
          ( ( ( Z_1 = X_2 )
           => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ F_1 @ X_2 @ Y_2 ) @ Z_1 )
              = Y_2 ) )
          & ( ( Z_1 != X_2 )
           => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ F_1 @ X_2 @ Y_2 ) @ Z_1 )
              = ( hAPP_l207779698on_val @ F_1 @ Z_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1552]) ).

thf(1599,plain,
    ( ( ! [F_1: $i,X_2: $i,Y_2: $i] :
          ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ F_1 @ X_2 @ Y_2 ) @ X_2 )
          = Y_2 ) )
    = $true ),
    inference(copy,[status(thm)],[1551]) ).

thf(1600,plain,
    ( ( ! [F_1: $i,X_2: $i,Y_2: $i,Z_1: $i] :
          ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ F_1 @ X_2 @ Y_2 ) @ X_2 @ Z_1 )
          = ( fun_up1149430426on_val @ F_1 @ X_2 @ Z_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1550]) ).

thf(1601,plain,
    ( ( ! [F_1: $i,X_2: $i,Y_2: $i] :
          ( ( ( fun_up1149430426on_val @ F_1 @ X_2 @ Y_2 )
            = F_1 )
        <=> ( ( hAPP_l207779698on_val @ F_1 @ X_2 )
            = Y_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1549]) ).

thf(1602,plain,
    ( ( ! [Y_2: $i] :
          ~ ! [A_1: $i,B_2: $i,C_4: $i] :
              ( Y_2
             != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A_1 ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B_2 ) @ C_4 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1548]) ).

thf(1603,plain,
    ( ( ! [Y_2: $i] :
          ~ ! [A_1: $i,B_2: $i,C_4: $i] :
              ( Y_2
             != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A_1 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B_2 ) @ C_4 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1547]) ).

thf(1604,plain,
    ( ( ! [X_2: $i,Pa: $i] :
          ( ! [A_1: $i,B_2: $i,C_4: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ Pa @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A_1 ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B_2 ) @ C_4 ) ) ) )
         => ( hBOOL @ ( hAPP_P282169671l_bool @ Pa @ X_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1546]) ).

thf(1605,plain,
    ( ( ! [X_2: $i,Pa: $i] :
          ( ! [A_1: $i,B_2: $i,C_4: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ Pa @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A_1 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B_2 ) @ C_4 ) ) ) )
         => ( hBOOL @ ( hAPP_P1708370145l_bool @ Pa @ X_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1545]) ).

thf(1606,plain,
    ( ( ! [S_4: $i,R_2: $i] :
          ( ! [X_1: $i,Xa: $i] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ X_1 ) @ Xa ) ) @ R_2 ) )
            <=> ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ X_1 ) @ Xa ) ) @ S_4 ) ) )
        <=> ( R_2 = S_4 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1544]) ).

thf(1607,plain,
    ( ( ! [Y_2: $i] :
          ~ ! [A_1: $i,B_2: $i] :
              ( Y_2
             != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A_1 ) @ B_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1543]) ).

thf(1608,plain,
    ( ( ! [Y_2: $i] :
          ~ ! [A_1: $i,B_2: $i] :
              ( Y_2
             != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A_1 ) @ B_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1542]) ).

thf(1609,plain,
    ( ( ! [Y_2: $i] :
          ~ ! [A_1: $i,B_2: $i] :
              ( Y_2
             != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A_1 ) @ B_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1541]) ).

thf(1610,plain,
    ( ( ! [P_1: $i] :
          ~ ! [X_1: $i,Y_1: $i] :
              ( P_1
             != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ X_1 ) @ Y_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1540]) ).

thf(1611,plain,
    ( ( ! [P_1: $i] :
          ~ ! [X_1: $i,Y_1: $i] :
              ( P_1
             != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ X_1 ) @ Y_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1539]) ).

thf(1612,plain,
    ( ( ! [P_1: $i] :
          ~ ! [X_1: $i,Y_1: $i] :
              ( P_1
             != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ X_1 ) @ Y_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1538]) ).

thf(1613,plain,
    ( ( ! [Pa: $i] :
          ( ? [X1: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ Pa @ X1 ) )
        <=> ? [A_1: $i,B_2: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ Pa @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A_1 ) @ B_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1537]) ).

thf(1614,plain,
    ( ( ! [Pa: $i] :
          ( ? [X1: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ Pa @ X1 ) )
        <=> ? [A_1: $i,B_2: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ Pa @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A_1 ) @ B_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1536]) ).

thf(1615,plain,
    ( ( ! [Pa: $i] :
          ( ? [X1: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ Pa @ X1 ) )
        <=> ? [A_1: $i,B_2: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ Pa @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A_1 ) @ B_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1535]) ).

thf(1616,plain,
    ( ( ! [Eb: $i,Hb: $i,Lb: $i,E_b: $i,H_b: $i,L_b: $i,Pa: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ Hb ) @ Lb ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H_b ) @ L_b ) ) ) ) @ ( red @ Pa ) ) )
         => ( hBOOL @ ( hext @ Hb @ H_b ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1534]) ).

thf(1617,plain,
    ( ( ! [A: $i,A_3: $i] :
          ( ( ( hAPP_val_option_val @ some_val @ A )
            = ( hAPP_val_option_val @ some_val @ A_3 ) )
        <=> ( A = A_3 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1533]) ).

thf(1618,plain,
    ( ( ! [L_0: $i,Eb: $i,Hb: $i,Lb: $i,E_b: $i,H_b: $i,L_b: $i,Pa: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ Hb ) @ Lb ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H_b ) @ L_b ) ) ) ) @ ( red @ Pa ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ Hb ) @ ( map_ad325961431ar_val @ L_0 @ Lb ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H_b ) @ ( map_ad325961431ar_val @ L_0 @ L_b ) ) ) ) ) @ ( red @ Pa ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1532]) ).

thf(1619,plain,
    ( ( ! [X_2: $i,A_2: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ X_2 ) @ A_2 ) )
        <=> ( hBOOL @ ( hAPP_P282169671l_bool @ A_2 @ X_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1531]) ).

thf(1620,plain,
    ( ( ! [Va_1: $i,Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ Va_1 @ Eb ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ Va_1 @ E_b ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1530]) ).

thf(1621,plain,
    ( ( ! [E_2: $i,Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ Eb @ E_2 ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ E_b @ E_2 ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1529]) ).

thf(1622,plain,
    ( ( ! [F_1: $i,G: $i,X_2: $i,Y_2: $i] :
          ( ( map_ad325961431ar_val @ F_1 @ ( fun_up1149430426on_val @ G @ X_2 @ ( hAPP_val_option_val @ some_val @ Y_2 ) ) )
          = ( fun_up1149430426on_val @ ( map_ad325961431ar_val @ F_1 @ G ) @ X_2 @ ( hAPP_val_option_val @ some_val @ Y_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1528]) ).

thf(1623,plain,
    ( ( ! [Hb: $i] : ( hBOOL @ ( hext @ Hb @ Hb ) ) )
    = $true ),
    inference(copy,[status(thm)],[1527]) ).

thf(1624,plain,
    ( ( ! [H_4: $i,Hb: $i,H_b: $i] :
          ( ( hBOOL @ ( hext @ Hb @ H_b ) )
         => ( ( hBOOL @ ( hext @ H_b @ H_4 ) )
           => ( hBOOL @ ( hext @ Hb @ H_4 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1526]) ).

thf(1625,plain,
    ( ( ! [A_5: $i] :
          ( none_val
         != ( hAPP_val_option_val @ some_val @ A_5 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1525]) ).

thf(1626,plain,
    ( ( ! [A_4: $i] :
          ( ( hAPP_val_option_val @ some_val @ A_4 )
         != none_val ) )
    = $true ),
    inference(copy,[status(thm)],[1524]) ).

thf(1627,plain,
    ( ( ! [X_2: $i] :
          ( ! [Y_1: $i] :
              ( X_2
             != ( hAPP_val_option_val @ some_val @ Y_1 ) )
        <=> ( X_2 = none_val ) ) )
    = $true ),
    inference(copy,[status(thm)],[1523]) ).

thf(1628,plain,
    ( ( ! [X_2: $i] :
          ( ( X_2 != none_val )
        <=> ? [Y_1: $i] :
              ( X_2
              = ( hAPP_val_option_val @ some_val @ Y_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1522]) ).

thf(1629,plain,
    ( ( ! [A: $i,R_1: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ A ) ) @ ( transi2024712006on_val @ R_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1521]) ).

thf(1630,plain,
    ( ( ! [P_1: $i,R_1: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ P_1 ) @ R_1 ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ P_1 ) @ ( transi2024712006on_val @ R_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1520]) ).

thf(1631,plain,
    ( ( ! [C_2: $i,A_2: $i,B_1: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A_2 ) @ B_1 ) )
         => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C_2 ) @ A_2 ) )
           => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C_2 ) @ B_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1519]) ).

thf(1632,plain,
    ( ( ! [X_2: $i,A_2: $i,B_1: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A_2 ) @ B_1 ) )
         => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ X_2 ) @ A_2 ) )
           => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ X_2 ) @ B_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1518]) ).

thf(1633,plain,
    ( ( ! [B_1: $i,X_2: $i,A_2: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ X_2 ) @ A_2 ) )
         => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A_2 ) @ B_1 ) )
           => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ X_2 ) @ B_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1517]) ).

thf(1634,plain,
    ( ( ! [X_2: $i,A_2: $i,B_1: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A_2 ) @ B_1 ) )
         => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ X_2 ) @ A_2 ) )
           => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ X_2 ) @ B_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1516]) ).

thf(1635,plain,
    ( ( ! [C_2: $i,A: $i,B: $i,R_1: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ R_1 ) )
         => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C_2 ) ) @ ( transi2024712006on_val @ R_1 ) ) )
           => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ C_2 ) ) @ ( transi2024712006on_val @ R_1 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1515]) ).

thf(1636,plain,
    ( ( ! [C_2: $i,A: $i,B: $i,R_1: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( transi2024712006on_val @ R_1 ) ) )
         => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C_2 ) ) @ R_1 ) )
           => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ C_2 ) ) @ ( transi2024712006on_val @ R_1 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1514]) ).

thf(1637,plain,
    ( ( ! [C_2: $i,A: $i,B: $i,R_1: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( transi2024712006on_val @ R_1 ) ) )
         => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C_2 ) ) @ ( transi2024712006on_val @ R_1 ) ) )
           => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ C_2 ) ) @ ( transi2024712006on_val @ R_1 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1513]) ).

thf(1638,plain,
    ( ( ! [B_1: $i,A_2: $i] :
          ( ! [X_1: $i] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ X_1 ) @ A_2 ) )
             => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ X_1 ) @ B_1 ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A_2 ) @ B_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1512]) ).

thf(1639,plain,
    ( ( ! [Xa_1: $i,Xb_1: $i,Za: $i,Zb: $i,R_1: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Xa_1 ) @ Xb_1 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Za ) @ Zb ) ) ) @ ( transi2024712006on_val @ R_1 ) ) )
         => ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Xa_1 ) @ Xb_1 )
             != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Za ) @ Zb ) )
           => ~ ! [A_1: $i,B_2: $i] :
                  ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Xa_1 ) @ Xb_1 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A_1 ) @ B_2 ) ) ) @ R_1 ) )
                 => ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A_1 ) @ B_2 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Za ) @ Zb ) ) ) @ ( transi2024712006on_val @ R_1 ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1511]) ).

thf(1640,plain,
    ( ( ! [Y_3: $i] :
          ( ( Y_3 != none_val )
         => ~ ! [A_1: $i] :
                ( Y_3
               != ( hAPP_val_option_val @ some_val @ A_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1510]) ).

thf(1641,plain,
    ( ( ! [A: $i,B: $i,R_1: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( transi2024712006on_val @ R_1 ) ) )
         => ( ( A != B )
           => ~ ! [Y_1: $i] :
                  ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ Y_1 ) ) @ ( transi2024712006on_val @ R_1 ) ) )
                 => ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ Y_1 ) @ B ) ) @ R_1 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1509]) ).

thf(1642,plain,
    ( ( ! [X_2: $i,Z_1: $i,R_1: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ X_2 ) @ Z_1 ) ) @ ( transi2024712006on_val @ R_1 ) ) )
         => ( ( X_2 != Z_1 )
           => ~ ! [Y_1: $i] :
                  ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ X_2 ) @ Y_1 ) ) @ R_1 ) )
                 => ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ Y_1 ) @ Z_1 ) ) @ ( transi2024712006on_val @ R_1 ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1508]) ).

thf(1643,plain,
    ( ( ! [C_2: $i,A_2: $i,B_1: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C_2 ) @ ( semila751111325l_bool @ A_2 @ B_1 ) ) )
         => ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C_2 ) @ A_2 ) )
           => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C_2 ) @ B_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1507]) ).

thf(1644,plain,
    ( ( ! [A_2: $i,C_2: $i,B_1: $i] :
          ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C_2 ) @ B_1 ) )
           => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C_2 ) @ A_2 ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C_2 ) @ ( semila751111325l_bool @ A_2 @ B_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1506]) ).

thf(1645,plain,
    ( ( ! [F: $i,D: $i,E_2: $i,Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ Eb @ F @ D @ E_2 ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ E_b @ F @ D @ E_2 ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1505]) ).

thf(1646,plain,
    ( ( ! [Eb: $i,S: $i,Pa: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( throw_list_char @ Eb ) ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ Eb ) ) @ S ) ) ) @ ( red @ Pa ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1504]) ).

thf(1647,plain,
    ( ( ! [Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ Eb ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E_b ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1503]) ).

thf(1648,plain,
    ( ( ! [F: $i,D: $i,Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ Eb @ F @ D ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ E_b @ F @ D ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1502]) ).

thf(1649,plain,
    ( ( ! [Bop: $i,E_2: $i,Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ Eb @ Bop @ E_2 ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ E_b @ Bop @ E_2 ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1501]) ).

thf(1650,plain,
    ( ( ! [C: $i,Va_1: $i,E_2: $i,Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ Eb @ C @ Va_1 @ E_2 ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ E_b @ C @ Va_1 @ E_2 ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1500]) ).

thf(1651,plain,
    ( ( ! [C: $i,Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ C @ Eb ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ C @ E_b ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1499]) ).

thf(1652,plain,
    ( ( ! [Bool_1: $i,Bool: $i] :
          ( ( ( bool @ Bool_1 )
            = ( bool @ Bool ) )
        <=> ( ( hBOOL @ Bool_1 )
          <=> ( hBOOL @ Bool ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1498]) ).

thf(1653,plain,
    ( ( ! [E_1_1: $i,E_2: $i,Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ Eb @ E_1_1 @ E_2 ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ E_b @ E_1_1 @ E_2 ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1497]) ).

thf(1654,plain,
    ( ( ! [M: $i,Esa: $i,Eb: $i,S: $i,E_b: $i,S_2: $i,Pa: $i] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Eb ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E_b ) @ S_2 ) ) ) @ ( red @ Pa ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ Eb @ M @ Esa ) ) @ S ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ E_b @ M @ Esa ) ) @ S_2 ) ) ) @ ( red @ Pa ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1496]) ).

thf(1655,plain,
    ( ( hBOOL @ fTrue )
    = $true ),
    inference(copy,[status(thm)],[1495]) ).

thf(1656,plain,
    ( ( ~ ( hBOOL @ fFalse ) )
    = $true ),
    inference(copy,[status(thm)],[1494]) ).

thf(1657,plain,
    ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ea ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( hAPP_val_option_val @ some_val @ v ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ e_a ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ h_a ) @ l_a ) ) ) ) @ ( red @ p ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1575]) ).

thf(1658,plain,
    ( ( ! [SX0: $i] :
          ~ ! [SX1: $i,SX2: $i] :
              ( SX0
             != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX1 ) @ SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1611]) ).

thf(1659,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SX1 ) @ SX2 ) )
          | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SX0 ) @ SX1 ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SX0 ) @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1634]) ).

thf(1660,plain,
    ( ( ! [SX0: $i] :
          ~ ! [SX1: $i,SX2: $i,SX3: $i] :
              ( SX0
             != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX1 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SX2 ) @ SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1603]) ).

thf(1661,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SX0 ) @ SX1 ) )
                | ( hBOOL @ ( hAPP_P282169671l_bool @ SX1 @ SX0 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SX1 @ SX0 ) )
                | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SX0 ) @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1619]) ).

thf(1662,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ( ~ ! [SX1: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SX0 @ SX1 ) )
                | ! [SX1: $i,SX2: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SX0 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX1 ) @ SX2 ) ) ) )
            | ~ ( ~ ! [SX1: $i,SX2: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SX0 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX1 ) @ SX2 ) ) )
                | ! [SX1: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1592]) ).

thf(1663,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX0 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SX1 ) @ SX2 ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX3 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SX4 ) @ SX5 ) ) ) ) @ ( red @ SX6 ) ) )
          | ( hBOOL @ ( hext @ SX1 @ SX4 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1616]) ).

thf(1664,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ! [SX2: $i,SX3: $i,SX4: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SX1 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX2 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SX3 ) @ SX4 ) ) ) )
          | ( hBOOL @ ( hAPP_P1708370145l_bool @ SX1 @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1605]) ).

thf(1665,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX1 ) @ SX2 ) ) @ SX3 ) )
          | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX2 ) @ SX0 ) ) @ ( transi2024712006on_val @ SX3 ) ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX1 ) @ SX0 ) ) @ ( transi2024712006on_val @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1635]) ).

thf(1666,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX1 ) @ SX2 ) ) @ ( transi2024712006on_val @ SX3 ) ) )
          | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX2 ) @ SX0 ) ) @ SX3 ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX1 ) @ SX0 ) ) @ ( transi2024712006on_val @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1636]) ).

thf(1667,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX1 ) @ SX2 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX3 ) @ SX4 ) ) ) @ ( red @ SX5 ) ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ SX0 @ SX1 ) ) @ SX2 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ SX0 @ SX3 ) ) @ SX4 ) ) ) @ ( red @ SX5 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1651]) ).

thf(1668,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SX1 ) @ SX2 ) )
          | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SX0 ) @ SX1 ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SX0 ) @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1632]) ).

thf(1669,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
          ( ( ( fun_up204312361on_val @ SX0 @ SX1 @ ( hAPP_val_option_val @ some_val @ SX2 ) )
           != ( fun_up204312361on_val @ SX3 @ SX1 @ ( hAPP_val_option_val @ some_val @ SX4 ) ) )
          | ( SX2 = SX4 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1582]) ).

thf(1670,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ~ ( ~ ( ( SX3 != SX2 )
                | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SX0 @ SX2 @ SX1 ) @ SX3 )
                  = SX1 ) )
            | ~ ( ~ ( ( SX3 != SX2 ) )
                | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SX0 @ SX2 @ SX1 ) @ SX3 )
                  = ( hAPP_l207779698on_val @ SX0 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1594]) ).

thf(1671,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ( ~ ~ ! [SX1: $i] :
                        ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SX0 @ SX1 ) )
                | ~ ! [SX1: $i] :
                      ~ ~ ! [SX2: $i] :
                            ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SX0 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SX1 ) @ SX2 ) ) ) )
            | ~ ( ~ ~ ! [SX1: $i] :
                        ~ ~ ! [SX2: $i] :
                              ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SX0 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SX1 ) @ SX2 ) ) )
                | ~ ! [SX1: $i] :
                      ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1613]) ).

thf(1672,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ( ~ ! [SX2: $i,SX3: $i] :
                      ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX2 ) @ SX3 ) ) @ SX1 ) )
                            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX2 ) @ SX3 ) ) @ SX0 ) ) )
                        | ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX2 ) @ SX3 ) ) @ SX0 ) )
                            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX2 ) @ SX3 ) ) @ SX1 ) ) ) )
                | ( SX1 = SX0 ) )
            | ~ ( ( SX1 != SX0 )
                | ! [SX2: $i,SX3: $i] :
                    ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX2 ) @ SX3 ) ) @ SX1 ) )
                          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX2 ) @ SX3 ) ) @ SX0 ) ) )
                      | ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX2 ) @ SX3 ) ) @ SX0 ) )
                          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX2 ) @ SX3 ) ) @ SX1 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1606]) ).

thf(1673,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX2 ) @ SX3 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX4 ) @ SX5 ) ) ) @ ( red @ SX6 ) ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ SX2 @ SX0 @ SX1 ) ) @ SX3 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ SX4 @ SX0 @ SX1 ) ) @ SX5 ) ) ) @ ( red @ SX6 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1648]) ).

thf(1674,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX0 ) @ SX1 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX2 ) @ SX3 ) ) ) @ ( transi2024712006on_val @ SX4 ) ) )
          | ~ ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX0 ) @ SX1 )
               != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX2 ) @ SX3 ) ) )
          | ~ ! [SX5: $i,SX6: $i] :
                ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX0 ) @ SX1 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX5 ) @ SX6 ) ) ) @ SX4 ) )
                | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX5 ) @ SX6 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX2 ) @ SX3 ) ) ) @ ( transi2024712006on_val @ SX4 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1639]) ).

thf(1675,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SX0 ) @ SX1 ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SX0 ) @ ( transi2024712006on_val @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1630]) ).

thf(1676,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ( ( hAPP_l207779698on_val @ SX0 @ SX1 )
           != ( hAPP_val_option_val @ some_val @ SX2 ) )
          | ( ( fun_up1149430426on_val @ SX0 @ SX1 @ ( hAPP_val_option_val @ some_val @ SX2 ) )
            = SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1580]) ).

thf(1677,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( ( SX0 != none_val ) )
          | ~ ! [SX1: $i] :
                ( SX0
               != ( hAPP_val_option_val @ some_val @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1640]) ).

thf(1678,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ~ ( ~ ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX0 ) @ SX1 )
                 != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX2 ) @ SX3 ) )
                | ~ ( ( SX0 != SX2 )
                    | ( SX1 != SX3 ) ) )
            | ~ ( ~ ~ ( ( SX0 != SX2 )
                      | ( SX1 != SX3 ) )
                | ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX0 ) @ SX1 )
                  = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX2 ) @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1589]) ).

thf(1679,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ( ( ( hAPP_val_option_val @ some_val @ SX0 )
                 != ( hAPP_val_option_val @ some_val @ SX1 ) )
                | ( SX0 = SX1 ) )
            | ~ ( ( SX0 != SX1 )
                | ( ( hAPP_val_option_val @ some_val @ SX0 )
                  = ( hAPP_val_option_val @ some_val @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1617]) ).

thf(1680,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ( ~ ! [SX1: $i] :
                      ( SX0
                     != ( hAPP_val_option_val @ some_val @ SX1 ) )
                | ( SX0 = none_val ) )
            | ~ ( ( SX0 != none_val )
                | ! [SX1: $i] :
                    ( SX0
                   != ( hAPP_val_option_val @ some_val @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1627]) ).

thf(1681,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
          ( ( ( fun_up1149430426on_val @ SX0 @ SX1 @ ( hAPP_val_option_val @ some_val @ SX2 ) )
           != ( fun_up1149430426on_val @ SX3 @ SX1 @ ( hAPP_val_option_val @ some_val @ SX4 ) ) )
          | ( SX2 = SX4 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1581]) ).

thf(1682,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ! [SX2: $i,SX3: $i,SX4: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SX1 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX2 ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX3 ) @ SX4 ) ) ) )
          | ( hBOOL @ ( hAPP_P282169671l_bool @ SX1 @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1604]) ).

thf(1683,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ( ~ ( ( SX0 != none_val ) )
                | ~ ! [SX1: $i] :
                      ( SX0
                     != ( hAPP_val_option_val @ some_val @ SX1 ) ) )
            | ~ ( ~ ~ ! [SX1: $i] :
                        ( SX0
                       != ( hAPP_val_option_val @ some_val @ SX1 ) )
                | ( SX0 != none_val ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1628]) ).

thf(1684,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX1 ) @ SX2 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX3 ) @ SX4 ) ) ) @ ( red @ SX5 ) ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ SX1 @ SX0 ) ) @ SX2 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ SX3 @ SX0 ) ) @ SX4 ) ) ) @ ( red @ SX5 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1621]) ).

thf(1685,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX0 ) @ SX1 ) ) @ ( transi2024712006on_val @ SX2 ) ) )
          | ~ ( ( SX0 != SX1 ) )
          | ~ ! [SX3: $i] :
                ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX0 ) @ SX3 ) ) @ ( transi2024712006on_val @ SX2 ) ) )
                | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX3 ) @ SX1 ) ) @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1641]) ).

thf(1686,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX3 ) @ SX4 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX5 ) @ SX6 ) ) ) @ ( red @ SX7 ) ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ SX3 @ SX0 @ SX1 @ SX2 ) ) @ SX4 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ SX5 @ SX0 @ SX1 @ SX2 ) ) @ SX6 ) ) ) @ ( red @ SX7 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1645]) ).

thf(1687,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
          ~ ( ~ ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SX0 @ SX1 @ ( hAPP_val_option_val @ some_val @ SX2 ) ) @ SX3 )
                 != ( hAPP_val_option_val @ some_val @ SX4 ) )
                | ~ ( ( SX3 != SX1 )
                    | ( SX2 != SX4 ) )
                | ~ ( ~ ( ( SX3 != SX1 ) )
                    | ( ( hAPP_l207779698on_val @ SX0 @ SX3 )
                     != ( hAPP_val_option_val @ some_val @ SX4 ) ) ) )
            | ~ ( ~ ( ~ ( ( SX3 != SX1 )
                        | ( SX2 != SX4 ) )
                    | ~ ( ~ ( ( SX3 != SX1 ) )
                        | ( ( hAPP_l207779698on_val @ SX0 @ SX3 )
                         != ( hAPP_val_option_val @ some_val @ SX4 ) ) ) )
                | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SX0 @ SX1 @ ( hAPP_val_option_val @ some_val @ SX2 ) ) @ SX3 )
                  = ( hAPP_val_option_val @ some_val @ SX4 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1579]) ).

thf(1688,plain,
    ( ( ! [SX0: $i] :
          ~ ! [SX1: $i,SX2: $i] :
              ( SX0
             != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SX1 ) @ SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1610]) ).

thf(1689,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX1 ) @ SX2 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX3 ) @ SX4 ) ) ) @ ( red @ SX5 ) ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ SX0 @ SX1 ) ) @ SX2 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ SX0 @ SX3 ) ) @ SX4 ) ) ) @ ( red @ SX5 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1620]) ).

thf(1690,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ( ( hAPP_l207779698on_val @ SX0 @ SX1 )
           != SX2 )
          | ( ( fun_up1149430426on_val @ SX0 @ SX1 @ SX2 )
            = SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1595]) ).

thf(1691,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ! [SX2: $i,SX3: $i,SX4: $i,SX5: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SX1 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX2 ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX3 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SX4 ) @ SX5 ) ) ) ) )
          | ( hBOOL @ ( hAPP_P282169671l_bool @ SX1 @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1583]) ).

thf(1692,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX1 ) @ SX2 ) ) @ ( transi2024712006on_val @ SX3 ) ) )
          | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX2 ) @ SX0 ) ) @ ( transi2024712006on_val @ SX3 ) ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX1 ) @ SX0 ) ) @ ( transi2024712006on_val @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1637]) ).

thf(1693,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SX0 ) @ SX1 )
           != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SX2 ) @ SX3 ) )
          | ~ ( ( SX0 != SX2 )
              | ( SX1 != SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1587]) ).

thf(1694,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ~ ( ~ ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX0 ) @ SX1 )
                 != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX2 ) @ SX3 ) )
                | ~ ( ( SX0 != SX2 )
                    | ( SX1 != SX3 ) ) )
            | ~ ( ~ ~ ( ( SX0 != SX2 )
                      | ( SX1 != SX3 ) )
                | ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX0 ) @ SX1 )
                  = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX2 ) @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1588]) ).

thf(1695,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ~ ( ~ ( ( SX2 != SX3 )
                | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SX0 @ SX3 @ SX1 ) @ SX2 )
                  = SX1 ) )
            | ~ ( ~ ( ( SX2 != SX3 ) )
                | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SX0 @ SX3 @ SX1 ) @ SX2 )
                  = ( hAPP_l207779698on_val @ SX0 @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1598]) ).

thf(1696,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SX1 ) @ SX2 ) )
          | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SX2 ) @ SX0 ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1633]) ).

thf(1697,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ( ( ( bool @ SX0 )
                 != ( bool @ SX1 ) )
                | ~ ( ~ ( ~ ( hBOOL @ SX0 )
                        | ( hBOOL @ SX1 ) )
                    | ~ ( ~ ( hBOOL @ SX1 )
                        | ( hBOOL @ SX0 ) ) ) )
            | ~ ( ~ ~ ( ~ ( ~ ( hBOOL @ SX0 )
                          | ( hBOOL @ SX1 ) )
                      | ~ ( ~ ( hBOOL @ SX1 )
                          | ( hBOOL @ SX0 ) ) )
                | ( ( bool @ SX0 )
                  = ( bool @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1652]) ).

thf(1698,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ( ~ ~ ! [SX1: $i] :
                        ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SX0 @ SX1 ) )
                | ~ ! [SX1: $i] :
                      ~ ~ ! [SX2: $i] :
                            ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SX0 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX1 ) @ SX2 ) ) ) )
            | ~ ( ~ ~ ! [SX1: $i] :
                        ~ ~ ! [SX2: $i] :
                              ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SX0 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX1 ) @ SX2 ) ) )
                | ~ ! [SX1: $i] :
                      ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1615]) ).

thf(1699,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX2 ) @ SX3 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX4 ) @ SX5 ) ) ) @ ( red @ SX6 ) ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ SX2 @ SX0 @ SX1 ) ) @ SX3 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ SX4 @ SX0 @ SX1 ) ) @ SX5 ) ) ) @ ( red @ SX6 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1649]) ).

thf(1700,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ~ ( ~ ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SX0 ) @ SX1 )
                 != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SX2 ) @ SX3 ) )
                | ~ ( ( SX0 != SX2 )
                    | ( SX1 != SX3 ) ) )
            | ~ ( ~ ~ ( ( SX0 != SX2 )
                      | ( SX1 != SX3 ) )
                | ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SX0 ) @ SX1 )
                  = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SX2 ) @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1590]) ).

thf(1701,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ~ ( ( SX2 != SX3 ) )
          | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SX0 @ SX3 @ SX1 ) @ SX2 )
            = ( hAPP_l207779698on_val @ SX0 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1596]) ).

thf(1702,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SX0 ) @ ( semila751111325l_bool @ SX1 @ SX2 ) ) )
          | ~ ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SX0 ) @ SX1 ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SX0 ) @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1643]) ).

thf(1703,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX2 ) @ SX3 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX4 ) @ SX5 ) ) ) @ ( red @ SX6 ) ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ SX2 @ SX0 @ SX1 ) ) @ SX3 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ SX4 @ SX0 @ SX1 ) ) @ SX5 ) ) ) @ ( red @ SX6 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1653]) ).

thf(1704,plain,
    ( ( ! [SX0: $i] :
          ~ ! [SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
              ( SX0
             != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX1 ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX2 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SX3 ) @ SX4 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1584]) ).

thf(1705,plain,
    ( ( ! [SX0: $i] :
          ~ ! [SX1: $i,SX2: $i] :
              ( SX0
             != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SX1 ) @ SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1607]) ).

thf(1706,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ! [SX2: $i] :
                ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SX2 ) @ SX1 ) )
                | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SX2 ) @ SX0 ) ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1638]) ).

thf(1707,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX2 ) @ SX3 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX4 ) @ SX5 ) ) ) @ ( red @ SX6 ) ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ SX2 @ SX0 @ SX1 ) ) @ SX3 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ SX4 @ SX0 @ SX1 ) ) @ SX5 ) ) ) @ ( red @ SX6 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1654]) ).

thf(1708,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ( ~ ~ ! [SX1: $i] :
                        ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SX0 @ SX1 ) )
                | ~ ! [SX1: $i] :
                      ~ ~ ! [SX2: $i] :
                            ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SX0 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX1 ) @ SX2 ) ) ) )
            | ~ ( ~ ~ ! [SX1: $i] :
                        ~ ~ ! [SX2: $i] :
                              ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SX0 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX1 ) @ SX2 ) ) )
                | ~ ! [SX1: $i] :
                      ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1614]) ).

thf(1709,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SX1 ) @ SX2 ) )
          | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SX0 ) @ SX1 ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SX0 ) @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1631]) ).

thf(1710,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ( ( ( fun_up1149430426on_val @ SX0 @ SX1 @ SX2 )
                 != SX0 )
                | ( ( hAPP_l207779698on_val @ SX0 @ SX1 )
                  = SX2 ) )
            | ~ ( ( ( hAPP_l207779698on_val @ SX0 @ SX1 )
                 != SX2 )
                | ( ( fun_up1149430426on_val @ SX0 @ SX1 @ SX2 )
                  = SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1601]) ).

thf(1711,plain,
    ( ( ! [SX0: $i] :
          ~ ! [SX1: $i,SX2: $i] :
              ( SX0
             != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX1 ) @ SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1608]) ).

thf(1712,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX0 ) @ SX1 ) ) @ ( transi2024712006on_val @ SX2 ) ) )
          | ~ ( ( SX0 != SX1 ) )
          | ~ ! [SX3: $i] :
                ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX0 ) @ SX3 ) ) @ SX2 ) )
                | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX3 ) @ SX1 ) ) @ ( transi2024712006on_val @ SX2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1642]) ).

thf(1713,plain,
    ( ( ! [SX0: $i] :
          ( none_val
         != ( hAPP_val_option_val @ some_val @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1625]) ).

thf(1714,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
          ( ~ ( ( SX3 != SX4 ) )
          | ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ SX0 @ SX3 @ SX1 ) @ SX4 @ SX2 )
            = ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ SX0 @ SX4 @ SX2 ) @ SX3 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1597]) ).

thf(1715,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX1 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SX2 ) @ SX3 ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX4 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SX5 ) @ SX6 ) ) ) ) @ ( red @ SX7 ) ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX1 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SX2 ) @ ( map_ad325961431ar_val @ SX0 @ SX3 ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX4 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SX5 ) @ ( map_ad325961431ar_val @ SX0 @ SX6 ) ) ) ) ) @ ( red @ SX7 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1618]) ).

thf(1716,plain,
    ( ( ! [SX0: $i] :
          ~ ! [SX1: $i,SX2: $i,SX3: $i] :
              ( SX0
             != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX1 ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX2 ) @ SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1602]) ).

thf(1717,plain,
    ( ( ! [SX0: $i] :
          ( ( hAPP_val_option_val @ some_val @ SX0 )
         != none_val ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1626]) ).

thf(1718,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ( ~ ! [SX1: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SX0 @ SX1 ) )
                | ! [SX1: $i,SX2: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SX0 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX1 ) @ SX2 ) ) ) )
            | ~ ( ~ ! [SX1: $i,SX2: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SX0 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX1 ) @ SX2 ) ) )
                | ! [SX1: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1591]) ).

thf(1719,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( ~ ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SX1 ) @ SX2 ) )
              | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SX1 ) @ SX0 ) ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SX1 ) @ ( semila751111325l_bool @ SX0 @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1644]) ).

thf(1720,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ( ~ ! [SX1: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SX0 @ SX1 ) )
                | ! [SX1: $i,SX2: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SX0 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SX1 ) @ SX2 ) ) ) )
            | ~ ( ~ ! [SX1: $i,SX2: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SX0 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SX1 ) @ SX2 ) ) )
                | ! [SX1: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1593]) ).

thf(1721,plain,
    ( ( ! [SX0: $i] :
          ~ ! [SX1: $i,SX2: $i] :
              ( SX0
             != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX1 ) @ SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1609]) ).

thf(1722,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX0 ) @ SX1 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX2 ) @ SX3 ) ) ) @ ( red @ SX4 ) ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ SX0 ) ) @ SX1 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ SX2 ) ) @ SX3 ) ) ) @ ( red @ SX4 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1647]) ).

thf(1723,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX3 ) @ SX4 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX5 ) @ SX6 ) ) ) @ ( red @ SX7 ) ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ SX3 @ SX0 @ SX1 @ SX2 ) ) @ SX4 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ SX5 @ SX0 @ SX1 @ SX2 ) ) @ SX6 ) ) ) @ ( red @ SX7 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1650]) ).

thf(1724,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hext @ SX1 @ SX2 ) )
          | ~ ( hBOOL @ ( hext @ SX2 @ SX0 ) )
          | ( hBOOL @ ( hext @ SX1 @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1624]) ).

thf(1725,plain,
    ( ( ! [SX0: $i] :
          ~ ! [SX1: $i,SX2: $i] :
              ( SX0
             != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX1 ) @ SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1612]) ).

thf(1726,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX0 ) @ SX1 )
           != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX2 ) @ SX3 ) )
          | ~ ( ( SX0 != SX2 )
              | ( SX1 != SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1586]) ).

thf(1727,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX0 ) @ SX1 )
           != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX2 ) @ SX3 ) )
          | ~ ( ( SX0 != SX2 )
              | ( SX1 != SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1585]) ).

thf(1728,plain,
    ! [SV1: $i] :
      ( ( ! [SY310: $i] : ( is_bool @ ( hAPP_f1453283057l_bool @ SV1 @ SY310 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1576]) ).

thf(1729,plain,
    ! [SV2: $i] :
      ( ( ! [SY311: $i] :
            ( ( fun_up1149430426on_val @ SV2 @ SY311 @ ( hAPP_l207779698on_val @ SV2 @ SY311 ) )
            = SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1578]) ).

thf(1730,plain,
    ! [SV3: $i] :
      ( ( ! [SY312: $i,SY313: $i] :
            ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV3 @ SY312 @ SY313 ) @ SY312 )
            = SY313 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1599]) ).

thf(1731,plain,
    ! [SV4: $i] :
      ( ( ! [SY314: $i,SY315: $i,SY316: $i] :
            ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ SV4 @ SY314 @ SY315 ) @ SY314 @ SY316 )
            = ( fun_up1149430426on_val @ SV4 @ SY314 @ SY316 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1600]) ).

thf(1732,plain,
    ! [SV5: $i] :
      ( ( ! [SY317: $i,SY318: $i,SY319: $i] :
            ( ( map_ad325961431ar_val @ SV5 @ ( fun_up1149430426on_val @ SY317 @ SY318 @ ( hAPP_val_option_val @ some_val @ SY319 ) ) )
            = ( fun_up1149430426on_val @ ( map_ad325961431ar_val @ SV5 @ SY317 ) @ SY318 @ ( hAPP_val_option_val @ some_val @ SY319 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1622]) ).

thf(1733,plain,
    ! [SV6: $i] :
      ( ( hBOOL @ ( hext @ SV6 @ SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1623]) ).

thf(1734,plain,
    ! [SV7: $i] :
      ( ( ! [SY320: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV7 ) @ SV7 ) ) @ ( transi2024712006on_val @ SY320 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1629]) ).

thf(1735,plain,
    ! [SV8: $i] :
      ( ( ! [SY321: $i,SY322: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( throw_list_char @ SV8 ) ) ) @ SY321 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ SV8 ) ) @ SY321 ) ) ) @ ( red @ SY322 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1646]) ).

thf(1736,plain,
    ( ( hBOOL @ fFalse )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1656]) ).

thf(1737,plain,
    ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ea ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( hAPP_val_option_val @ some_val @ v ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ e_a ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ h_a ) @ l_a ) ) ) ) @ ( red @ p ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1657]) ).

thf(1738,plain,
    ! [SV9: $i] :
      ( ( ~ ! [SY323: $i,SY324: $i] :
              ( SV9
             != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY323 ) @ SY324 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1658]) ).

thf(1739,plain,
    ! [SV10: $i] :
      ( ( ! [SY325: $i,SY326: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SY325 ) @ SY326 ) )
            | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV10 ) @ SY325 ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV10 ) @ SY326 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1659]) ).

thf(1740,plain,
    ! [SV11: $i] :
      ( ( ~ ! [SY327: $i,SY328: $i,SY329: $i] :
              ( SV11
             != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY327 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY328 ) @ SY329 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1660]) ).

thf(1741,plain,
    ! [SV12: $i] :
      ( ( ! [SY330: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV12 ) @ SY330 ) )
                  | ( hBOOL @ ( hAPP_P282169671l_bool @ SY330 @ SV12 ) ) )
              | ~ ( ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SY330 @ SV12 ) )
                  | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV12 ) @ SY330 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1661]) ).

thf(1742,plain,
    ! [SV13: $i] :
      ( ( ~ ( ~ ( ~ ! [SY331: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ SY331 ) )
                | ! [SY332: $i,SY333: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY332 ) @ SY333 ) ) ) )
            | ~ ( ~ ! [SY334: $i,SY335: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY334 ) @ SY335 ) ) )
                | ! [SY336: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ SY336 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1662]) ).

thf(1743,plain,
    ! [SV14: $i] :
      ( ( ! [SY337: $i,SY338: $i,SY339: $i,SY340: $i,SY341: $i,SY342: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV14 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY337 ) @ SY338 ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY339 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY340 ) @ SY341 ) ) ) ) @ ( red @ SY342 ) ) )
            | ( hBOOL @ ( hext @ SY337 @ SY340 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1663]) ).

thf(1744,plain,
    ! [SV15: $i] :
      ( ( ! [SY343: $i] :
            ( ~ ! [SX2: $i,SX3: $i,SX4: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SY343 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX2 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SX3 ) @ SX4 ) ) ) )
            | ( hBOOL @ ( hAPP_P1708370145l_bool @ SY343 @ SV15 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1664]) ).

thf(1745,plain,
    ! [SV16: $i] :
      ( ( ! [SY347: $i,SY348: $i,SY349: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY347 ) @ SY348 ) ) @ SY349 ) )
            | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY348 ) @ SV16 ) ) @ ( transi2024712006on_val @ SY349 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY347 ) @ SV16 ) ) @ ( transi2024712006on_val @ SY349 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1665]) ).

thf(1746,plain,
    ! [SV17: $i] :
      ( ( ! [SY350: $i,SY351: $i,SY352: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY350 ) @ SY351 ) ) @ ( transi2024712006on_val @ SY352 ) ) )
            | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY351 ) @ SV17 ) ) @ SY352 ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY350 ) @ SV17 ) ) @ ( transi2024712006on_val @ SY352 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1666]) ).

thf(1747,plain,
    ! [SV18: $i] :
      ( ( ! [SY353: $i,SY354: $i,SY355: $i,SY356: $i,SY357: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY353 ) @ SY354 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY355 ) @ SY356 ) ) ) @ ( red @ SY357 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ SV18 @ SY353 ) ) @ SY354 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ SV18 @ SY355 ) ) @ SY356 ) ) ) @ ( red @ SY357 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1667]) ).

thf(1748,plain,
    ! [SV19: $i] :
      ( ( ! [SY358: $i,SY359: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SY358 ) @ SY359 ) )
            | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV19 ) @ SY358 ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV19 ) @ SY359 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1668]) ).

thf(1749,plain,
    ! [SV20: $i] :
      ( ( ! [SY360: $i,SY361: $i,SY362: $i,SY363: $i] :
            ( ( ( fun_up204312361on_val @ SV20 @ SY360 @ ( hAPP_val_option_val @ some_val @ SY361 ) )
             != ( fun_up204312361on_val @ SY362 @ SY360 @ ( hAPP_val_option_val @ some_val @ SY363 ) ) )
            | ( SY361 = SY363 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1669]) ).

thf(1750,plain,
    ! [SV21: $i] :
      ( ( ! [SY364: $i,SY365: $i,SY366: $i] :
            ~ ( ~ ( ( SY366 != SY365 )
                  | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV21 @ SY365 @ SY364 ) @ SY366 )
                    = SY364 ) )
              | ~ ( ~ ( ( SY366 != SY365 ) )
                  | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV21 @ SY365 @ SY364 ) @ SY366 )
                    = ( hAPP_l207779698on_val @ SV21 @ SY366 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1670]) ).

thf(1751,plain,
    ! [SV22: $i] :
      ( ( ~ ( ~ ( ~ ~ ! [SY367: $i] :
                        ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ SY367 ) )
                | ~ ! [SY368: $i] :
                      ~ ~ ! [SY369: $i] :
                            ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY368 ) @ SY369 ) ) ) )
            | ~ ( ~ ~ ! [SY370: $i] :
                        ~ ~ ! [SY371: $i] :
                              ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY370 ) @ SY371 ) ) )
                | ~ ! [SY372: $i] :
                      ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ SY372 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1671]) ).

thf(1752,plain,
    ! [SV23: $i] :
      ( ( ! [SY373: $i] :
            ~ ( ~ ( ~ ! [SY374: $i,SY375: $i] :
                        ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY374 ) @ SY375 ) ) @ SY373 ) )
                              | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY374 ) @ SY375 ) ) @ SV23 ) ) )
                          | ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY374 ) @ SY375 ) ) @ SV23 ) )
                              | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY374 ) @ SY375 ) ) @ SY373 ) ) ) )
                  | ( SY373 = SV23 ) )
              | ~ ( ( SY373 != SV23 )
                  | ! [SY376: $i,SY377: $i] :
                      ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY376 ) @ SY377 ) ) @ SY373 ) )
                            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY376 ) @ SY377 ) ) @ SV23 ) ) )
                        | ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY376 ) @ SY377 ) ) @ SV23 ) )
                            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY376 ) @ SY377 ) ) @ SY373 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1672]) ).

thf(1753,plain,
    ! [SV24: $i] :
      ( ( ! [SY378: $i,SY379: $i,SY380: $i,SY381: $i,SY382: $i,SY383: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY379 ) @ SY380 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY381 ) @ SY382 ) ) ) @ ( red @ SY383 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ SY379 @ SV24 @ SY378 ) ) @ SY380 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ SY381 @ SV24 @ SY378 ) ) @ SY382 ) ) ) @ ( red @ SY383 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1673]) ).

thf(1754,plain,
    ! [SV25: $i] :
      ( ( ! [SY384: $i,SY385: $i,SY386: $i,SY387: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SY384 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY385 ) @ SY386 ) ) ) @ ( transi2024712006on_val @ SY387 ) ) )
            | ~ ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SY384 )
                 != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY385 ) @ SY386 ) ) )
            | ~ ! [SY388: $i,SY389: $i] :
                  ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SY384 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY388 ) @ SY389 ) ) ) @ SY387 ) )
                  | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY388 ) @ SY389 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY385 ) @ SY386 ) ) ) @ ( transi2024712006on_val @ SY387 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1674]) ).

thf(1755,plain,
    ! [SV26: $i] :
      ( ( ! [SY390: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV26 ) @ SY390 ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV26 ) @ ( transi2024712006on_val @ SY390 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1675]) ).

thf(1756,plain,
    ! [SV27: $i] :
      ( ( ! [SY391: $i,SY392: $i] :
            ( ( ( hAPP_l207779698on_val @ SV27 @ SY391 )
             != ( hAPP_val_option_val @ some_val @ SY392 ) )
            | ( ( fun_up1149430426on_val @ SV27 @ SY391 @ ( hAPP_val_option_val @ some_val @ SY392 ) )
              = SV27 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1676]) ).

thf(1757,plain,
    ! [SV28: $i] :
      ( ( ~ ( ( SV28 != none_val ) )
        | ~ ! [SY393: $i] :
              ( SV28
             != ( hAPP_val_option_val @ some_val @ SY393 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1677]) ).

thf(1758,plain,
    ! [SV29: $i] :
      ( ( ! [SY394: $i,SY395: $i,SY396: $i] :
            ~ ( ~ ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV29 ) @ SY394 )
                   != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY395 ) @ SY396 ) )
                  | ~ ( ( SV29 != SY395 )
                      | ( SY394 != SY396 ) ) )
              | ~ ( ~ ~ ( ( SV29 != SY395 )
                        | ( SY394 != SY396 ) )
                  | ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV29 ) @ SY394 )
                    = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY395 ) @ SY396 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1678]) ).

thf(1759,plain,
    ! [SV30: $i] :
      ( ( ! [SY397: $i] :
            ~ ( ~ ( ( ( hAPP_val_option_val @ some_val @ SV30 )
                   != ( hAPP_val_option_val @ some_val @ SY397 ) )
                  | ( SV30 = SY397 ) )
              | ~ ( ( SV30 != SY397 )
                  | ( ( hAPP_val_option_val @ some_val @ SV30 )
                    = ( hAPP_val_option_val @ some_val @ SY397 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1679]) ).

thf(1760,plain,
    ! [SV31: $i] :
      ( ( ~ ( ~ ( ~ ! [SY398: $i] :
                      ( SV31
                     != ( hAPP_val_option_val @ some_val @ SY398 ) )
                | ( SV31 = none_val ) )
            | ~ ( ( SV31 != none_val )
                | ! [SY399: $i] :
                    ( SV31
                   != ( hAPP_val_option_val @ some_val @ SY399 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1680]) ).

thf(1761,plain,
    ! [SV32: $i] :
      ( ( ! [SY400: $i,SY401: $i,SY402: $i,SY403: $i] :
            ( ( ( fun_up1149430426on_val @ SV32 @ SY400 @ ( hAPP_val_option_val @ some_val @ SY401 ) )
             != ( fun_up1149430426on_val @ SY402 @ SY400 @ ( hAPP_val_option_val @ some_val @ SY403 ) ) )
            | ( SY401 = SY403 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1681]) ).

thf(1762,plain,
    ! [SV33: $i] :
      ( ( ! [SY404: $i] :
            ( ~ ! [SX2: $i,SX3: $i,SX4: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SY404 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX2 ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX3 ) @ SX4 ) ) ) )
            | ( hBOOL @ ( hAPP_P282169671l_bool @ SY404 @ SV33 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1682]) ).

thf(1763,plain,
    ! [SV34: $i] :
      ( ( ~ ( ~ ( ~ ( ( SV34 != none_val ) )
                | ~ ! [SY408: $i] :
                      ( SV34
                     != ( hAPP_val_option_val @ some_val @ SY408 ) ) )
            | ~ ( ~ ~ ! [SY409: $i] :
                        ( SV34
                       != ( hAPP_val_option_val @ some_val @ SY409 ) )
                | ( SV34 != none_val ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1683]) ).

thf(1764,plain,
    ! [SV35: $i] :
      ( ( ! [SY410: $i,SY411: $i,SY412: $i,SY413: $i,SY414: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY410 ) @ SY411 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY412 ) @ SY413 ) ) ) @ ( red @ SY414 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ SY410 @ SV35 ) ) @ SY411 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ SY412 @ SV35 ) ) @ SY413 ) ) ) @ ( red @ SY414 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1684]) ).

thf(1765,plain,
    ! [SV36: $i] :
      ( ( ! [SY415: $i,SY416: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV36 ) @ SY415 ) ) @ ( transi2024712006on_val @ SY416 ) ) )
            | ~ ( ( SV36 != SY415 ) )
            | ~ ! [SY417: $i] :
                  ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV36 ) @ SY417 ) ) @ ( transi2024712006on_val @ SY416 ) ) )
                  | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY417 ) @ SY415 ) ) @ SY416 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1685]) ).

thf(1766,plain,
    ! [SV37: $i] :
      ( ( ! [SY418: $i,SY419: $i,SY420: $i,SY421: $i,SY422: $i,SY423: $i,SY424: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY420 ) @ SY421 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY422 ) @ SY423 ) ) ) @ ( red @ SY424 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ SY420 @ SV37 @ SY418 @ SY419 ) ) @ SY421 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ SY422 @ SV37 @ SY418 @ SY419 ) ) @ SY423 ) ) ) @ ( red @ SY424 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1686]) ).

thf(1767,plain,
    ! [SV38: $i] :
      ( ( ! [SY425: $i,SY426: $i,SY427: $i,SY428: $i] :
            ~ ( ~ ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SY425 @ ( hAPP_val_option_val @ some_val @ SY426 ) ) @ SY427 )
                   != ( hAPP_val_option_val @ some_val @ SY428 ) )
                  | ~ ( ( SY427 != SY425 )
                      | ( SY426 != SY428 ) )
                  | ~ ( ~ ( ( SY427 != SY425 ) )
                      | ( ( hAPP_l207779698on_val @ SV38 @ SY427 )
                       != ( hAPP_val_option_val @ some_val @ SY428 ) ) ) )
              | ~ ( ~ ( ~ ( ( SY427 != SY425 )
                          | ( SY426 != SY428 ) )
                      | ~ ( ~ ( ( SY427 != SY425 ) )
                          | ( ( hAPP_l207779698on_val @ SV38 @ SY427 )
                           != ( hAPP_val_option_val @ some_val @ SY428 ) ) ) )
                  | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SY425 @ ( hAPP_val_option_val @ some_val @ SY426 ) ) @ SY427 )
                    = ( hAPP_val_option_val @ some_val @ SY428 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1687]) ).

thf(1768,plain,
    ! [SV39: $i] :
      ( ( ~ ! [SY429: $i,SY430: $i] :
              ( SV39
             != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY429 ) @ SY430 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1688]) ).

thf(1769,plain,
    ! [SV40: $i] :
      ( ( ! [SY431: $i,SY432: $i,SY433: $i,SY434: $i,SY435: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY431 ) @ SY432 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY433 ) @ SY434 ) ) ) @ ( red @ SY435 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ SV40 @ SY431 ) ) @ SY432 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ SV40 @ SY433 ) ) @ SY434 ) ) ) @ ( red @ SY435 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1689]) ).

thf(1770,plain,
    ! [SV41: $i] :
      ( ( ! [SY436: $i,SY437: $i] :
            ( ( ( hAPP_l207779698on_val @ SV41 @ SY436 )
             != SY437 )
            | ( ( fun_up1149430426on_val @ SV41 @ SY436 @ SY437 )
              = SV41 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1690]) ).

thf(1771,plain,
    ! [SV42: $i] :
      ( ( ! [SY438: $i] :
            ( ~ ! [SX2: $i,SX3: $i,SX4: $i,SX5: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SY438 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SX2 ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SX3 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SX4 ) @ SX5 ) ) ) ) )
            | ( hBOOL @ ( hAPP_P282169671l_bool @ SY438 @ SV42 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1691]) ).

thf(1772,plain,
    ! [SV43: $i] :
      ( ( ! [SY443: $i,SY444: $i,SY445: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY443 ) @ SY444 ) ) @ ( transi2024712006on_val @ SY445 ) ) )
            | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY444 ) @ SV43 ) ) @ ( transi2024712006on_val @ SY445 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY443 ) @ SV43 ) ) @ ( transi2024712006on_val @ SY445 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1692]) ).

thf(1773,plain,
    ! [SV44: $i] :
      ( ( ! [SY446: $i,SY447: $i,SY448: $i] :
            ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV44 ) @ SY446 )
             != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY447 ) @ SY448 ) )
            | ~ ( ( SV44 != SY447 )
                | ( SY446 != SY448 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1693]) ).

thf(1774,plain,
    ! [SV45: $i] :
      ( ( ! [SY449: $i,SY450: $i,SY451: $i] :
            ~ ( ~ ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV45 ) @ SY449 )
                   != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY450 ) @ SY451 ) )
                  | ~ ( ( SV45 != SY450 )
                      | ( SY449 != SY451 ) ) )
              | ~ ( ~ ~ ( ( SV45 != SY450 )
                        | ( SY449 != SY451 ) )
                  | ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV45 ) @ SY449 )
                    = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY450 ) @ SY451 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1694]) ).

thf(1775,plain,
    ! [SV46: $i] :
      ( ( ! [SY452: $i,SY453: $i,SY454: $i] :
            ~ ( ~ ( ( SY453 != SY454 )
                  | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV46 @ SY454 @ SY452 ) @ SY453 )
                    = SY452 ) )
              | ~ ( ~ ( ( SY453 != SY454 ) )
                  | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV46 @ SY454 @ SY452 ) @ SY453 )
                    = ( hAPP_l207779698on_val @ SV46 @ SY453 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1695]) ).

thf(1776,plain,
    ! [SV47: $i] :
      ( ( ! [SY455: $i,SY456: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SY455 ) @ SY456 ) )
            | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SY456 ) @ SV47 ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SY455 ) @ SV47 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1696]) ).

thf(1777,plain,
    ! [SV48: $i] :
      ( ( ! [SY457: $i] :
            ~ ( ~ ( ( ( bool @ SV48 )
                   != ( bool @ SY457 ) )
                  | ~ ( ~ ( ~ ( hBOOL @ SV48 )
                          | ( hBOOL @ SY457 ) )
                      | ~ ( ~ ( hBOOL @ SY457 )
                          | ( hBOOL @ SV48 ) ) ) )
              | ~ ( ~ ~ ( ~ ( ~ ( hBOOL @ SV48 )
                            | ( hBOOL @ SY457 ) )
                        | ~ ( ~ ( hBOOL @ SY457 )
                            | ( hBOOL @ SV48 ) ) )
                  | ( ( bool @ SV48 )
                    = ( bool @ SY457 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1697]) ).

thf(1778,plain,
    ! [SV49: $i] :
      ( ( ~ ( ~ ( ~ ~ ! [SY458: $i] :
                        ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ SY458 ) )
                | ~ ! [SY459: $i] :
                      ~ ~ ! [SY460: $i] :
                            ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY459 ) @ SY460 ) ) ) )
            | ~ ( ~ ~ ! [SY461: $i] :
                        ~ ~ ! [SY462: $i] :
                              ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY461 ) @ SY462 ) ) )
                | ~ ! [SY463: $i] :
                      ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ SY463 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1698]) ).

thf(1779,plain,
    ! [SV50: $i] :
      ( ( ! [SY464: $i,SY465: $i,SY466: $i,SY467: $i,SY468: $i,SY469: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY465 ) @ SY466 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY467 ) @ SY468 ) ) ) @ ( red @ SY469 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ SY465 @ SV50 @ SY464 ) ) @ SY466 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ SY467 @ SV50 @ SY464 ) ) @ SY468 ) ) ) @ ( red @ SY469 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1699]) ).

thf(1780,plain,
    ! [SV51: $i] :
      ( ( ! [SY470: $i,SY471: $i,SY472: $i] :
            ~ ( ~ ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV51 ) @ SY470 )
                   != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY471 ) @ SY472 ) )
                  | ~ ( ( SV51 != SY471 )
                      | ( SY470 != SY472 ) ) )
              | ~ ( ~ ~ ( ( SV51 != SY471 )
                        | ( SY470 != SY472 ) )
                  | ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV51 ) @ SY470 )
                    = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY471 ) @ SY472 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1700]) ).

thf(1781,plain,
    ! [SV52: $i] :
      ( ( ! [SY473: $i,SY474: $i,SY475: $i] :
            ( ~ ( ( SY474 != SY475 ) )
            | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV52 @ SY475 @ SY473 ) @ SY474 )
              = ( hAPP_l207779698on_val @ SV52 @ SY474 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1701]) ).

thf(1782,plain,
    ! [SV53: $i] :
      ( ( ! [SY476: $i,SY477: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV53 ) @ ( semila751111325l_bool @ SY476 @ SY477 ) ) )
            | ~ ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV53 ) @ SY476 ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV53 ) @ SY477 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1702]) ).

thf(1783,plain,
    ! [SV54: $i] :
      ( ( ! [SY478: $i,SY479: $i,SY480: $i,SY481: $i,SY482: $i,SY483: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY479 ) @ SY480 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY481 ) @ SY482 ) ) ) @ ( red @ SY483 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ SY479 @ SV54 @ SY478 ) ) @ SY480 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ SY481 @ SV54 @ SY478 ) ) @ SY482 ) ) ) @ ( red @ SY483 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1703]) ).

thf(1784,plain,
    ! [SV55: $i] :
      ( ( ~ ! [SY484: $i,SY485: $i,SY486: $i,SY487: $i] :
              ( SV55
             != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY484 ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY485 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY486 ) @ SY487 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1704]) ).

thf(1785,plain,
    ! [SV56: $i] :
      ( ( ~ ! [SY488: $i,SY489: $i] :
              ( SV56
             != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY488 ) @ SY489 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1705]) ).

thf(1786,plain,
    ! [SV57: $i] :
      ( ( ! [SY490: $i] :
            ( ~ ! [SY491: $i] :
                  ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SY491 ) @ SY490 ) )
                  | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SY491 ) @ SV57 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SY490 ) @ SV57 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1706]) ).

thf(1787,plain,
    ! [SV58: $i] :
      ( ( ! [SY492: $i,SY493: $i,SY494: $i,SY495: $i,SY496: $i,SY497: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY493 ) @ SY494 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY495 ) @ SY496 ) ) ) @ ( red @ SY497 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ SY493 @ SV58 @ SY492 ) ) @ SY494 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ SY495 @ SV58 @ SY492 ) ) @ SY496 ) ) ) @ ( red @ SY497 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1707]) ).

thf(1788,plain,
    ! [SV59: $i] :
      ( ( ~ ( ~ ( ~ ~ ! [SY498: $i] :
                        ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ SY498 ) )
                | ~ ! [SY499: $i] :
                      ~ ~ ! [SY500: $i] :
                            ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY499 ) @ SY500 ) ) ) )
            | ~ ( ~ ~ ! [SY501: $i] :
                        ~ ~ ! [SY502: $i] :
                              ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY501 ) @ SY502 ) ) )
                | ~ ! [SY503: $i] :
                      ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ SY503 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1708]) ).

thf(1789,plain,
    ! [SV60: $i] :
      ( ( ! [SY504: $i,SY505: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SY504 ) @ SY505 ) )
            | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV60 ) @ SY504 ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV60 ) @ SY505 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1709]) ).

thf(1790,plain,
    ! [SV61: $i] :
      ( ( ! [SY506: $i,SY507: $i] :
            ~ ( ~ ( ( ( fun_up1149430426on_val @ SV61 @ SY506 @ SY507 )
                   != SV61 )
                  | ( ( hAPP_l207779698on_val @ SV61 @ SY506 )
                    = SY507 ) )
              | ~ ( ( ( hAPP_l207779698on_val @ SV61 @ SY506 )
                   != SY507 )
                  | ( ( fun_up1149430426on_val @ SV61 @ SY506 @ SY507 )
                    = SV61 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1710]) ).

thf(1791,plain,
    ! [SV62: $i] :
      ( ( ~ ! [SY508: $i,SY509: $i] :
              ( SV62
             != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY508 ) @ SY509 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1711]) ).

thf(1792,plain,
    ! [SV63: $i] :
      ( ( ! [SY510: $i,SY511: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV63 ) @ SY510 ) ) @ ( transi2024712006on_val @ SY511 ) ) )
            | ~ ( ( SV63 != SY510 ) )
            | ~ ! [SY512: $i] :
                  ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV63 ) @ SY512 ) ) @ SY511 ) )
                  | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY512 ) @ SY510 ) ) @ ( transi2024712006on_val @ SY511 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1712]) ).

thf(1793,plain,
    ! [SV64: $i] :
      ( ( none_val
       != ( hAPP_val_option_val @ some_val @ SV64 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1713]) ).

thf(1794,plain,
    ! [SV65: $i] :
      ( ( ! [SY513: $i,SY514: $i,SY515: $i,SY516: $i] :
            ( ~ ( ( SY515 != SY516 ) )
            | ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ SV65 @ SY515 @ SY513 ) @ SY516 @ SY514 )
              = ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ SV65 @ SY516 @ SY514 ) @ SY515 @ SY513 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1714]) ).

thf(1795,plain,
    ! [SV66: $i] :
      ( ( ! [SY517: $i,SY518: $i,SY519: $i,SY520: $i,SY521: $i,SY522: $i,SY523: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY517 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY518 ) @ SY519 ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY520 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY521 ) @ SY522 ) ) ) ) @ ( red @ SY523 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY517 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY518 ) @ ( map_ad325961431ar_val @ SV66 @ SY519 ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY520 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY521 ) @ ( map_ad325961431ar_val @ SV66 @ SY522 ) ) ) ) ) @ ( red @ SY523 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1715]) ).

thf(1796,plain,
    ! [SV67: $i] :
      ( ( ~ ! [SY524: $i,SY525: $i,SY526: $i] :
              ( SV67
             != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY524 ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY525 ) @ SY526 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1716]) ).

thf(1797,plain,
    ! [SV68: $i] :
      ( ( ( hAPP_val_option_val @ some_val @ SV68 )
       != none_val )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1717]) ).

thf(1798,plain,
    ! [SV69: $i] :
      ( ( ~ ( ~ ( ~ ! [SY527: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ SY527 ) )
                | ! [SY528: $i,SY529: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY528 ) @ SY529 ) ) ) )
            | ~ ( ~ ! [SY530: $i,SY531: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY530 ) @ SY531 ) ) )
                | ! [SY532: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ SY532 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1718]) ).

thf(1799,plain,
    ! [SV70: $i] :
      ( ( ! [SY533: $i,SY534: $i] :
            ( ~ ( ~ ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SY533 ) @ SY534 ) )
                | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SY533 ) @ SV70 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SY533 ) @ ( semila751111325l_bool @ SV70 @ SY534 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1719]) ).

thf(1800,plain,
    ! [SV71: $i] :
      ( ( ~ ( ~ ( ~ ! [SY535: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ SY535 ) )
                | ! [SY536: $i,SY537: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY536 ) @ SY537 ) ) ) )
            | ~ ( ~ ! [SY538: $i,SY539: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY538 ) @ SY539 ) ) )
                | ! [SY540: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ SY540 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1720]) ).

thf(1801,plain,
    ! [SV72: $i] :
      ( ( ~ ! [SY541: $i,SY542: $i] :
              ( SV72
             != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY541 ) @ SY542 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1721]) ).

thf(1802,plain,
    ! [SV73: $i] :
      ( ( ! [SY543: $i,SY544: $i,SY545: $i,SY546: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV73 ) @ SY543 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY544 ) @ SY545 ) ) ) @ ( red @ SY546 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ SV73 ) ) @ SY543 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ SY544 ) ) @ SY545 ) ) ) @ ( red @ SY546 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1722]) ).

thf(1803,plain,
    ! [SV74: $i] :
      ( ( ! [SY547: $i,SY548: $i,SY549: $i,SY550: $i,SY551: $i,SY552: $i,SY553: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY549 ) @ SY550 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY551 ) @ SY552 ) ) ) @ ( red @ SY553 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ SY549 @ SV74 @ SY547 @ SY548 ) ) @ SY550 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ SY551 @ SV74 @ SY547 @ SY548 ) ) @ SY552 ) ) ) @ ( red @ SY553 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1723]) ).

thf(1804,plain,
    ! [SV75: $i] :
      ( ( ! [SY554: $i,SY555: $i] :
            ( ~ ( hBOOL @ ( hext @ SY554 @ SY555 ) )
            | ~ ( hBOOL @ ( hext @ SY555 @ SV75 ) )
            | ( hBOOL @ ( hext @ SY554 @ SV75 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1724]) ).

thf(1805,plain,
    ! [SV76: $i] :
      ( ( ~ ! [SY556: $i,SY557: $i] :
              ( SV76
             != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY556 ) @ SY557 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1725]) ).

thf(1806,plain,
    ! [SV77: $i] :
      ( ( ! [SY558: $i,SY559: $i,SY560: $i] :
            ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV77 ) @ SY558 )
             != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY559 ) @ SY560 ) )
            | ~ ( ( SV77 != SY559 )
                | ( SY558 != SY560 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1726]) ).

thf(1807,plain,
    ! [SV78: $i] :
      ( ( ! [SY561: $i,SY562: $i,SY563: $i] :
            ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV78 ) @ SY561 )
             != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY562 ) @ SY563 ) )
            | ~ ( ( SV78 != SY562 )
                | ( SY561 != SY563 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1727]) ).

thf(1808,plain,
    ! [SV79: $i,SV1: $i] :
      ( ( is_bool @ ( hAPP_f1453283057l_bool @ SV1 @ SV79 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1728]) ).

thf(1809,plain,
    ! [SV80: $i,SV2: $i] :
      ( ( ( fun_up1149430426on_val @ SV2 @ SV80 @ ( hAPP_l207779698on_val @ SV2 @ SV80 ) )
        = SV2 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1729]) ).

thf(1810,plain,
    ! [SV81: $i,SV3: $i] :
      ( ( ! [SY564: $i] :
            ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV3 @ SV81 @ SY564 ) @ SV81 )
            = SY564 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1730]) ).

thf(1811,plain,
    ! [SV82: $i,SV4: $i] :
      ( ( ! [SY565: $i,SY566: $i] :
            ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ SV4 @ SV82 @ SY565 ) @ SV82 @ SY566 )
            = ( fun_up1149430426on_val @ SV4 @ SV82 @ SY566 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1731]) ).

thf(1812,plain,
    ! [SV83: $i,SV5: $i] :
      ( ( ! [SY567: $i,SY568: $i] :
            ( ( map_ad325961431ar_val @ SV5 @ ( fun_up1149430426on_val @ SV83 @ SY567 @ ( hAPP_val_option_val @ some_val @ SY568 ) ) )
            = ( fun_up1149430426on_val @ ( map_ad325961431ar_val @ SV5 @ SV83 ) @ SY567 @ ( hAPP_val_option_val @ some_val @ SY568 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1732]) ).

thf(1813,plain,
    ! [SV84: $i,SV7: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV7 ) @ SV7 ) ) @ ( transi2024712006on_val @ SV84 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1734]) ).

thf(1814,plain,
    ! [SV85: $i,SV8: $i] :
      ( ( ! [SY569: $i] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( throw_list_char @ SV8 ) ) ) @ SV85 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ SV8 ) ) @ SV85 ) ) ) @ ( red @ SY569 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1735]) ).

thf(1815,plain,
    ! [SV9: $i] :
      ( ( ! [SY323: $i,SY324: $i] :
            ( SV9
           != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY323 ) @ SY324 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1738]) ).

thf(1816,plain,
    ! [SV10: $i,SV86: $i] :
      ( ( ! [SY570: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV86 ) @ SY570 ) )
            | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV10 ) @ SV86 ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV10 ) @ SY570 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1739]) ).

thf(1817,plain,
    ! [SV11: $i] :
      ( ( ! [SY327: $i,SY328: $i,SY329: $i] :
            ( SV11
           != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY327 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY328 ) @ SY329 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1740]) ).

thf(1818,plain,
    ! [SV87: $i,SV12: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV12 ) @ SV87 ) )
                | ( hBOOL @ ( hAPP_P282169671l_bool @ SV87 @ SV12 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV87 @ SV12 ) )
                | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV12 ) @ SV87 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1741]) ).

thf(1819,plain,
    ! [SV13: $i] :
      ( ( ~ ( ~ ! [SY331: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ SY331 ) )
            | ! [SY332: $i,SY333: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY332 ) @ SY333 ) ) ) )
        | ~ ( ~ ! [SY334: $i,SY335: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY334 ) @ SY335 ) ) )
            | ! [SY336: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ SY336 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1742]) ).

thf(1820,plain,
    ! [SV88: $i,SV14: $i] :
      ( ( ! [SY571: $i,SY572: $i,SY573: $i,SY574: $i,SY575: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV14 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV88 ) @ SY571 ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY572 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY573 ) @ SY574 ) ) ) ) @ ( red @ SY575 ) ) )
            | ( hBOOL @ ( hext @ SV88 @ SY573 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1743]) ).

thf(1821,plain,
    ! [SV15: $i,SV89: $i] :
      ( ( ~ ! [SY576: $i,SY577: $i,SY578: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV89 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY576 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY577 ) @ SY578 ) ) ) )
        | ( hBOOL @ ( hAPP_P1708370145l_bool @ SV89 @ SV15 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1744]) ).

thf(1822,plain,
    ! [SV16: $i,SV90: $i] :
      ( ( ! [SY579: $i,SY580: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV90 ) @ SY579 ) ) @ SY580 ) )
            | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY579 ) @ SV16 ) ) @ ( transi2024712006on_val @ SY580 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV90 ) @ SV16 ) ) @ ( transi2024712006on_val @ SY580 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1745]) ).

thf(1823,plain,
    ! [SV17: $i,SV91: $i] :
      ( ( ! [SY581: $i,SY582: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV91 ) @ SY581 ) ) @ ( transi2024712006on_val @ SY582 ) ) )
            | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY581 ) @ SV17 ) ) @ SY582 ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV91 ) @ SV17 ) ) @ ( transi2024712006on_val @ SY582 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1746]) ).

thf(1824,plain,
    ! [SV18: $i,SV92: $i] :
      ( ( ! [SY583: $i,SY584: $i,SY585: $i,SY586: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV92 ) @ SY583 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY584 ) @ SY585 ) ) ) @ ( red @ SY586 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ SV18 @ SV92 ) ) @ SY583 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ SV18 @ SY584 ) ) @ SY585 ) ) ) @ ( red @ SY586 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1747]) ).

thf(1825,plain,
    ! [SV19: $i,SV93: $i] :
      ( ( ! [SY587: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV93 ) @ SY587 ) )
            | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV19 ) @ SV93 ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV19 ) @ SY587 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1748]) ).

thf(1826,plain,
    ! [SV94: $i,SV20: $i] :
      ( ( ! [SY588: $i,SY589: $i,SY590: $i] :
            ( ( ( fun_up204312361on_val @ SV20 @ SV94 @ ( hAPP_val_option_val @ some_val @ SY588 ) )
             != ( fun_up204312361on_val @ SY589 @ SV94 @ ( hAPP_val_option_val @ some_val @ SY590 ) ) )
            | ( SY588 = SY590 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1749]) ).

thf(1827,plain,
    ! [SV95: $i,SV21: $i] :
      ( ( ! [SY591: $i,SY592: $i] :
            ~ ( ~ ( ( SY592 != SY591 )
                  | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV21 @ SY591 @ SV95 ) @ SY592 )
                    = SV95 ) )
              | ~ ( ~ ( ( SY592 != SY591 ) )
                  | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV21 @ SY591 @ SV95 ) @ SY592 )
                    = ( hAPP_l207779698on_val @ SV21 @ SY592 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1750]) ).

thf(1828,plain,
    ! [SV22: $i] :
      ( ( ~ ( ~ ~ ! [SY367: $i] :
                    ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ SY367 ) )
            | ~ ! [SY368: $i] :
                  ~ ~ ! [SY369: $i] :
                        ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY368 ) @ SY369 ) ) ) )
        | ~ ( ~ ~ ! [SY370: $i] :
                    ~ ~ ! [SY371: $i] :
                          ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY370 ) @ SY371 ) ) )
            | ~ ! [SY372: $i] :
                  ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ SY372 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1751]) ).

thf(1829,plain,
    ! [SV23: $i,SV96: $i] :
      ( ( ~ ( ~ ( ~ ! [SY593: $i,SY594: $i] :
                      ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY593 ) @ SY594 ) ) @ SV96 ) )
                            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY593 ) @ SY594 ) ) @ SV23 ) ) )
                        | ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY593 ) @ SY594 ) ) @ SV23 ) )
                            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY593 ) @ SY594 ) ) @ SV96 ) ) ) )
                | ( SV96 = SV23 ) )
            | ~ ( ( SV96 != SV23 )
                | ! [SY595: $i,SY596: $i] :
                    ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY595 ) @ SY596 ) ) @ SV96 ) )
                          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY595 ) @ SY596 ) ) @ SV23 ) ) )
                      | ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY595 ) @ SY596 ) ) @ SV23 ) )
                          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY595 ) @ SY596 ) ) @ SV96 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1752]) ).

thf(1830,plain,
    ! [SV97: $i,SV24: $i] :
      ( ( ! [SY597: $i,SY598: $i,SY599: $i,SY600: $i,SY601: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY597 ) @ SY598 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY599 ) @ SY600 ) ) ) @ ( red @ SY601 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ SY597 @ SV24 @ SV97 ) ) @ SY598 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ SY599 @ SV24 @ SV97 ) ) @ SY600 ) ) ) @ ( red @ SY601 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1753]) ).

thf(1831,plain,
    ! [SV98: $i,SV25: $i] :
      ( ( ! [SY602: $i,SY603: $i,SY604: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY602 ) @ SY603 ) ) ) @ ( transi2024712006on_val @ SY604 ) ) )
            | ~ ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 )
                 != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY602 ) @ SY603 ) ) )
            | ~ ! [SY605: $i,SY606: $i] :
                  ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY605 ) @ SY606 ) ) ) @ SY604 ) )
                  | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY605 ) @ SY606 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY602 ) @ SY603 ) ) ) @ ( transi2024712006on_val @ SY604 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1754]) ).

thf(1832,plain,
    ! [SV99: $i,SV26: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV26 ) @ SV99 ) )
        | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV26 ) @ ( transi2024712006on_val @ SV99 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1755]) ).

thf(1833,plain,
    ! [SV100: $i,SV27: $i] :
      ( ( ! [SY607: $i] :
            ( ( ( hAPP_l207779698on_val @ SV27 @ SV100 )
             != ( hAPP_val_option_val @ some_val @ SY607 ) )
            | ( ( fun_up1149430426on_val @ SV27 @ SV100 @ ( hAPP_val_option_val @ some_val @ SY607 ) )
              = SV27 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1756]) ).

thf(1834,plain,
    ! [SV28: $i] :
      ( ( ( ~ ( ( SV28 != none_val ) ) )
        = $true )
      | ( ( ~ ! [SY393: $i] :
                ( SV28
               != ( hAPP_val_option_val @ some_val @ SY393 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1757]) ).

thf(1835,plain,
    ! [SV101: $i,SV29: $i] :
      ( ( ! [SY608: $i,SY609: $i] :
            ~ ( ~ ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV29 ) @ SV101 )
                   != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY608 ) @ SY609 ) )
                  | ~ ( ( SV29 != SY608 )
                      | ( SV101 != SY609 ) ) )
              | ~ ( ~ ~ ( ( SV29 != SY608 )
                        | ( SV101 != SY609 ) )
                  | ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV29 ) @ SV101 )
                    = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY608 ) @ SY609 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1758]) ).

thf(1836,plain,
    ! [SV102: $i,SV30: $i] :
      ( ( ~ ( ~ ( ( ( hAPP_val_option_val @ some_val @ SV30 )
                 != ( hAPP_val_option_val @ some_val @ SV102 ) )
                | ( SV30 = SV102 ) )
            | ~ ( ( SV30 != SV102 )
                | ( ( hAPP_val_option_val @ some_val @ SV30 )
                  = ( hAPP_val_option_val @ some_val @ SV102 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1759]) ).

thf(1837,plain,
    ! [SV31: $i] :
      ( ( ~ ( ~ ! [SY398: $i] :
                  ( SV31
                 != ( hAPP_val_option_val @ some_val @ SY398 ) )
            | ( SV31 = none_val ) )
        | ~ ( ( SV31 != none_val )
            | ! [SY399: $i] :
                ( SV31
               != ( hAPP_val_option_val @ some_val @ SY399 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1760]) ).

thf(1838,plain,
    ! [SV103: $i,SV32: $i] :
      ( ( ! [SY610: $i,SY611: $i,SY612: $i] :
            ( ( ( fun_up1149430426on_val @ SV32 @ SV103 @ ( hAPP_val_option_val @ some_val @ SY610 ) )
             != ( fun_up1149430426on_val @ SY611 @ SV103 @ ( hAPP_val_option_val @ some_val @ SY612 ) ) )
            | ( SY610 = SY612 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1761]) ).

thf(1839,plain,
    ! [SV33: $i,SV104: $i] :
      ( ( ~ ! [SY613: $i,SY614: $i,SY615: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV104 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY613 ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY614 ) @ SY615 ) ) ) )
        | ( hBOOL @ ( hAPP_P282169671l_bool @ SV104 @ SV33 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1762]) ).

thf(1840,plain,
    ! [SV34: $i] :
      ( ( ~ ( ~ ( ( SV34 != none_val ) )
            | ~ ! [SY408: $i] :
                  ( SV34
                 != ( hAPP_val_option_val @ some_val @ SY408 ) ) )
        | ~ ( ~ ~ ! [SY409: $i] :
                    ( SV34
                   != ( hAPP_val_option_val @ some_val @ SY409 ) )
            | ( SV34 != none_val ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1763]) ).

thf(1841,plain,
    ! [SV35: $i,SV105: $i] :
      ( ( ! [SY616: $i,SY617: $i,SY618: $i,SY619: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV105 ) @ SY616 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY617 ) @ SY618 ) ) ) @ ( red @ SY619 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ SV105 @ SV35 ) ) @ SY616 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ SY617 @ SV35 ) ) @ SY618 ) ) ) @ ( red @ SY619 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1764]) ).

thf(1842,plain,
    ! [SV106: $i,SV36: $i] :
      ( ( ! [SY620: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV36 ) @ SV106 ) ) @ ( transi2024712006on_val @ SY620 ) ) )
            | ~ ( ( SV36 != SV106 ) )
            | ~ ! [SY621: $i] :
                  ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV36 ) @ SY621 ) ) @ ( transi2024712006on_val @ SY620 ) ) )
                  | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY621 ) @ SV106 ) ) @ SY620 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1765]) ).

thf(1843,plain,
    ! [SV107: $i,SV37: $i] :
      ( ( ! [SY622: $i,SY623: $i,SY624: $i,SY625: $i,SY626: $i,SY627: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY623 ) @ SY624 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY625 ) @ SY626 ) ) ) @ ( red @ SY627 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ SY623 @ SV37 @ SV107 @ SY622 ) ) @ SY624 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ SY625 @ SV37 @ SV107 @ SY622 ) ) @ SY626 ) ) ) @ ( red @ SY627 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1766]) ).

thf(1844,plain,
    ! [SV108: $i,SV38: $i] :
      ( ( ! [SY628: $i,SY629: $i,SY630: $i] :
            ~ ( ~ ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SY628 ) ) @ SY629 )
                   != ( hAPP_val_option_val @ some_val @ SY630 ) )
                  | ~ ( ( SY629 != SV108 )
                      | ( SY628 != SY630 ) )
                  | ~ ( ~ ( ( SY629 != SV108 ) )
                      | ( ( hAPP_l207779698on_val @ SV38 @ SY629 )
                       != ( hAPP_val_option_val @ some_val @ SY630 ) ) ) )
              | ~ ( ~ ( ~ ( ( SY629 != SV108 )
                          | ( SY628 != SY630 ) )
                      | ~ ( ~ ( ( SY629 != SV108 ) )
                          | ( ( hAPP_l207779698on_val @ SV38 @ SY629 )
                           != ( hAPP_val_option_val @ some_val @ SY630 ) ) ) )
                  | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SY628 ) ) @ SY629 )
                    = ( hAPP_val_option_val @ some_val @ SY630 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1767]) ).

thf(1845,plain,
    ! [SV39: $i] :
      ( ( ! [SY429: $i,SY430: $i] :
            ( SV39
           != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY429 ) @ SY430 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1768]) ).

thf(1846,plain,
    ! [SV40: $i,SV109: $i] :
      ( ( ! [SY631: $i,SY632: $i,SY633: $i,SY634: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV109 ) @ SY631 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY632 ) @ SY633 ) ) ) @ ( red @ SY634 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ SV40 @ SV109 ) ) @ SY631 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ SV40 @ SY632 ) ) @ SY633 ) ) ) @ ( red @ SY634 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1769]) ).

thf(1847,plain,
    ! [SV110: $i,SV41: $i] :
      ( ( ! [SY635: $i] :
            ( ( ( hAPP_l207779698on_val @ SV41 @ SV110 )
             != SY635 )
            | ( ( fun_up1149430426on_val @ SV41 @ SV110 @ SY635 )
              = SV41 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1770]) ).

thf(1848,plain,
    ! [SV42: $i,SV111: $i] :
      ( ( ~ ! [SY636: $i,SY637: $i,SY638: $i,SY639: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV111 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY636 ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY637 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY638 ) @ SY639 ) ) ) ) )
        | ( hBOOL @ ( hAPP_P282169671l_bool @ SV111 @ SV42 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1771]) ).

thf(1849,plain,
    ! [SV43: $i,SV112: $i] :
      ( ( ! [SY640: $i,SY641: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV112 ) @ SY640 ) ) @ ( transi2024712006on_val @ SY641 ) ) )
            | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY640 ) @ SV43 ) ) @ ( transi2024712006on_val @ SY641 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV112 ) @ SV43 ) ) @ ( transi2024712006on_val @ SY641 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1772]) ).

thf(1850,plain,
    ! [SV113: $i,SV44: $i] :
      ( ( ! [SY642: $i,SY643: $i] :
            ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV44 ) @ SV113 )
             != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY642 ) @ SY643 ) )
            | ~ ( ( SV44 != SY642 )
                | ( SV113 != SY643 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1773]) ).

thf(1851,plain,
    ! [SV114: $i,SV45: $i] :
      ( ( ! [SY644: $i,SY645: $i] :
            ~ ( ~ ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV45 ) @ SV114 )
                   != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY644 ) @ SY645 ) )
                  | ~ ( ( SV45 != SY644 )
                      | ( SV114 != SY645 ) ) )
              | ~ ( ~ ~ ( ( SV45 != SY644 )
                        | ( SV114 != SY645 ) )
                  | ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV45 ) @ SV114 )
                    = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY644 ) @ SY645 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1774]) ).

thf(1852,plain,
    ! [SV115: $i,SV46: $i] :
      ( ( ! [SY646: $i,SY647: $i] :
            ~ ( ~ ( ( SY646 != SY647 )
                  | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV46 @ SY647 @ SV115 ) @ SY646 )
                    = SV115 ) )
              | ~ ( ~ ( ( SY646 != SY647 ) )
                  | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV46 @ SY647 @ SV115 ) @ SY646 )
                    = ( hAPP_l207779698on_val @ SV46 @ SY646 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1775]) ).

thf(1853,plain,
    ! [SV47: $i,SV116: $i] :
      ( ( ! [SY648: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV116 ) @ SY648 ) )
            | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SY648 ) @ SV47 ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV116 ) @ SV47 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1776]) ).

thf(1854,plain,
    ! [SV117: $i,SV48: $i] :
      ( ( ~ ( ~ ( ( ( bool @ SV48 )
                 != ( bool @ SV117 ) )
                | ~ ( ~ ( ~ ( hBOOL @ SV48 )
                        | ( hBOOL @ SV117 ) )
                    | ~ ( ~ ( hBOOL @ SV117 )
                        | ( hBOOL @ SV48 ) ) ) )
            | ~ ( ~ ~ ( ~ ( ~ ( hBOOL @ SV48 )
                          | ( hBOOL @ SV117 ) )
                      | ~ ( ~ ( hBOOL @ SV117 )
                          | ( hBOOL @ SV48 ) ) )
                | ( ( bool @ SV48 )
                  = ( bool @ SV117 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1777]) ).

thf(1855,plain,
    ! [SV49: $i] :
      ( ( ~ ( ~ ~ ! [SY458: $i] :
                    ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ SY458 ) )
            | ~ ! [SY459: $i] :
                  ~ ~ ! [SY460: $i] :
                        ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY459 ) @ SY460 ) ) ) )
        | ~ ( ~ ~ ! [SY461: $i] :
                    ~ ~ ! [SY462: $i] :
                          ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY461 ) @ SY462 ) ) )
            | ~ ! [SY463: $i] :
                  ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ SY463 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1778]) ).

thf(1856,plain,
    ! [SV118: $i,SV50: $i] :
      ( ( ! [SY649: $i,SY650: $i,SY651: $i,SY652: $i,SY653: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY649 ) @ SY650 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY651 ) @ SY652 ) ) ) @ ( red @ SY653 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ SY649 @ SV50 @ SV118 ) ) @ SY650 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ SY651 @ SV50 @ SV118 ) ) @ SY652 ) ) ) @ ( red @ SY653 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1779]) ).

thf(1857,plain,
    ! [SV119: $i,SV51: $i] :
      ( ( ! [SY654: $i,SY655: $i] :
            ~ ( ~ ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV51 ) @ SV119 )
                   != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY654 ) @ SY655 ) )
                  | ~ ( ( SV51 != SY654 )
                      | ( SV119 != SY655 ) ) )
              | ~ ( ~ ~ ( ( SV51 != SY654 )
                        | ( SV119 != SY655 ) )
                  | ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV51 ) @ SV119 )
                    = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY654 ) @ SY655 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1780]) ).

thf(1858,plain,
    ! [SV120: $i,SV52: $i] :
      ( ( ! [SY656: $i,SY657: $i] :
            ( ~ ( ( SY656 != SY657 ) )
            | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV52 @ SY657 @ SV120 ) @ SY656 )
              = ( hAPP_l207779698on_val @ SV52 @ SY656 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1781]) ).

thf(1859,plain,
    ! [SV121: $i,SV53: $i] :
      ( ( ! [SY658: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV53 ) @ ( semila751111325l_bool @ SV121 @ SY658 ) ) )
            | ~ ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV53 ) @ SV121 ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV53 ) @ SY658 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1782]) ).

thf(1860,plain,
    ! [SV122: $i,SV54: $i] :
      ( ( ! [SY659: $i,SY660: $i,SY661: $i,SY662: $i,SY663: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY659 ) @ SY660 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY661 ) @ SY662 ) ) ) @ ( red @ SY663 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ SY659 @ SV54 @ SV122 ) ) @ SY660 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ SY661 @ SV54 @ SV122 ) ) @ SY662 ) ) ) @ ( red @ SY663 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1783]) ).

thf(1861,plain,
    ! [SV55: $i] :
      ( ( ! [SY484: $i,SY485: $i,SY486: $i,SY487: $i] :
            ( SV55
           != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY484 ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY485 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY486 ) @ SY487 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1784]) ).

thf(1862,plain,
    ! [SV56: $i] :
      ( ( ! [SY488: $i,SY489: $i] :
            ( SV56
           != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY488 ) @ SY489 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1785]) ).

thf(1863,plain,
    ! [SV57: $i,SV123: $i] :
      ( ( ~ ! [SY664: $i] :
              ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SY664 ) @ SV123 ) )
              | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SY664 ) @ SV57 ) ) )
        | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV123 ) @ SV57 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1786]) ).

thf(1864,plain,
    ! [SV124: $i,SV58: $i] :
      ( ( ! [SY665: $i,SY666: $i,SY667: $i,SY668: $i,SY669: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY665 ) @ SY666 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY667 ) @ SY668 ) ) ) @ ( red @ SY669 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ SY665 @ SV58 @ SV124 ) ) @ SY666 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ SY667 @ SV58 @ SV124 ) ) @ SY668 ) ) ) @ ( red @ SY669 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1787]) ).

thf(1865,plain,
    ! [SV59: $i] :
      ( ( ~ ( ~ ~ ! [SY498: $i] :
                    ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ SY498 ) )
            | ~ ! [SY499: $i] :
                  ~ ~ ! [SY500: $i] :
                        ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY499 ) @ SY500 ) ) ) )
        | ~ ( ~ ~ ! [SY501: $i] :
                    ~ ~ ! [SY502: $i] :
                          ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY501 ) @ SY502 ) ) )
            | ~ ! [SY503: $i] :
                  ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ SY503 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1788]) ).

thf(1866,plain,
    ! [SV60: $i,SV125: $i] :
      ( ( ! [SY670: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV125 ) @ SY670 ) )
            | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV60 ) @ SV125 ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV60 ) @ SY670 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1789]) ).

thf(1867,plain,
    ! [SV126: $i,SV61: $i] :
      ( ( ! [SY671: $i] :
            ~ ( ~ ( ( ( fun_up1149430426on_val @ SV61 @ SV126 @ SY671 )
                   != SV61 )
                  | ( ( hAPP_l207779698on_val @ SV61 @ SV126 )
                    = SY671 ) )
              | ~ ( ( ( hAPP_l207779698on_val @ SV61 @ SV126 )
                   != SY671 )
                  | ( ( fun_up1149430426on_val @ SV61 @ SV126 @ SY671 )
                    = SV61 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1790]) ).

thf(1868,plain,
    ! [SV62: $i] :
      ( ( ! [SY508: $i,SY509: $i] :
            ( SV62
           != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY508 ) @ SY509 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1791]) ).

thf(1869,plain,
    ! [SV127: $i,SV63: $i] :
      ( ( ! [SY672: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV63 ) @ SV127 ) ) @ ( transi2024712006on_val @ SY672 ) ) )
            | ~ ( ( SV63 != SV127 ) )
            | ~ ! [SY673: $i] :
                  ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV63 ) @ SY673 ) ) @ SY672 ) )
                  | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY673 ) @ SV127 ) ) @ ( transi2024712006on_val @ SY672 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1792]) ).

thf(1870,plain,
    ! [SV64: $i] :
      ( ( none_val
        = ( hAPP_val_option_val @ some_val @ SV64 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1793]) ).

thf(1871,plain,
    ! [SV128: $i,SV65: $i] :
      ( ( ! [SY674: $i,SY675: $i,SY676: $i] :
            ( ~ ( ( SY675 != SY676 ) )
            | ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ SV65 @ SY675 @ SV128 ) @ SY676 @ SY674 )
              = ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ SV65 @ SY676 @ SY674 ) @ SY675 @ SV128 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1794]) ).

thf(1872,plain,
    ! [SV66: $i,SV129: $i] :
      ( ( ! [SY677: $i,SY678: $i,SY679: $i,SY680: $i,SY681: $i,SY682: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV129 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY677 ) @ SY678 ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY679 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY680 ) @ SY681 ) ) ) ) @ ( red @ SY682 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV129 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY677 ) @ ( map_ad325961431ar_val @ SV66 @ SY678 ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY679 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY680 ) @ ( map_ad325961431ar_val @ SV66 @ SY681 ) ) ) ) ) @ ( red @ SY682 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1795]) ).

thf(1873,plain,
    ! [SV67: $i] :
      ( ( ! [SY524: $i,SY525: $i,SY526: $i] :
            ( SV67
           != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY524 ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY525 ) @ SY526 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1796]) ).

thf(1874,plain,
    ! [SV68: $i] :
      ( ( ( hAPP_val_option_val @ some_val @ SV68 )
        = none_val )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1797]) ).

thf(1875,plain,
    ! [SV69: $i] :
      ( ( ~ ( ~ ! [SY527: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ SY527 ) )
            | ! [SY528: $i,SY529: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY528 ) @ SY529 ) ) ) )
        | ~ ( ~ ! [SY530: $i,SY531: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY530 ) @ SY531 ) ) )
            | ! [SY532: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ SY532 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1798]) ).

thf(1876,plain,
    ! [SV70: $i,SV130: $i] :
      ( ( ! [SY683: $i] :
            ( ~ ( ~ ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV130 ) @ SY683 ) )
                | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV130 ) @ SV70 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV130 ) @ ( semila751111325l_bool @ SV70 @ SY683 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1799]) ).

thf(1877,plain,
    ! [SV71: $i] :
      ( ( ~ ( ~ ! [SY535: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ SY535 ) )
            | ! [SY536: $i,SY537: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY536 ) @ SY537 ) ) ) )
        | ~ ( ~ ! [SY538: $i,SY539: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY538 ) @ SY539 ) ) )
            | ! [SY540: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ SY540 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1800]) ).

thf(1878,plain,
    ! [SV72: $i] :
      ( ( ! [SY541: $i,SY542: $i] :
            ( SV72
           != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY541 ) @ SY542 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1801]) ).

thf(1879,plain,
    ! [SV131: $i,SV73: $i] :
      ( ( ! [SY684: $i,SY685: $i,SY686: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV73 ) @ SV131 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY684 ) @ SY685 ) ) ) @ ( red @ SY686 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ SV73 ) ) @ SV131 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ SY684 ) ) @ SY685 ) ) ) @ ( red @ SY686 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1802]) ).

thf(1880,plain,
    ! [SV132: $i,SV74: $i] :
      ( ( ! [SY687: $i,SY688: $i,SY689: $i,SY690: $i,SY691: $i,SY692: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY688 ) @ SY689 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY690 ) @ SY691 ) ) ) @ ( red @ SY692 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ SY688 @ SV74 @ SV132 @ SY687 ) ) @ SY689 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ SY690 @ SV74 @ SV132 @ SY687 ) ) @ SY691 ) ) ) @ ( red @ SY692 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1803]) ).

thf(1881,plain,
    ! [SV75: $i,SV133: $i] :
      ( ( ! [SY693: $i] :
            ( ~ ( hBOOL @ ( hext @ SV133 @ SY693 ) )
            | ~ ( hBOOL @ ( hext @ SY693 @ SV75 ) )
            | ( hBOOL @ ( hext @ SV133 @ SV75 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1804]) ).

thf(1882,plain,
    ! [SV76: $i] :
      ( ( ! [SY556: $i,SY557: $i] :
            ( SV76
           != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY556 ) @ SY557 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1805]) ).

thf(1883,plain,
    ! [SV134: $i,SV77: $i] :
      ( ( ! [SY694: $i,SY695: $i] :
            ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV77 ) @ SV134 )
             != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY694 ) @ SY695 ) )
            | ~ ( ( SV77 != SY694 )
                | ( SV134 != SY695 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1806]) ).

thf(1884,plain,
    ! [SV135: $i,SV78: $i] :
      ( ( ! [SY696: $i,SY697: $i] :
            ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV78 ) @ SV135 )
             != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY696 ) @ SY697 ) )
            | ~ ( ( SV78 != SY696 )
                | ( SV135 != SY697 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1807]) ).

thf(1885,plain,
    ! [SV136: $i,SV81: $i,SV3: $i] :
      ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV3 @ SV81 @ SV136 ) @ SV81 )
        = SV136 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1810]) ).

thf(1886,plain,
    ! [SV137: $i,SV82: $i,SV4: $i] :
      ( ( ! [SY698: $i] :
            ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ SV4 @ SV82 @ SV137 ) @ SV82 @ SY698 )
            = ( fun_up1149430426on_val @ SV4 @ SV82 @ SY698 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1811]) ).

thf(1887,plain,
    ! [SV138: $i,SV83: $i,SV5: $i] :
      ( ( ! [SY699: $i] :
            ( ( map_ad325961431ar_val @ SV5 @ ( fun_up1149430426on_val @ SV83 @ SV138 @ ( hAPP_val_option_val @ some_val @ SY699 ) ) )
            = ( fun_up1149430426on_val @ ( map_ad325961431ar_val @ SV5 @ SV83 ) @ SV138 @ ( hAPP_val_option_val @ some_val @ SY699 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1812]) ).

thf(1888,plain,
    ! [SV139: $i,SV85: $i,SV8: $i] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( throw_list_char @ SV8 ) ) ) @ SV85 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ SV8 ) ) @ SV85 ) ) ) @ ( red @ SV139 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1814]) ).

thf(1889,plain,
    ! [SV9: $i] :
      ( ( ! [SY700: $i] :
            ( SV9
           != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK1_SY323 @ SV9 ) ) @ SY700 ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[1815]) ).

thf(1890,plain,
    ! [SV10: $i,SV140: $i,SV86: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV86 ) @ SV140 ) )
        | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV10 ) @ SV86 ) )
        | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV10 ) @ SV140 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1816]) ).

thf(1891,plain,
    ! [SV11: $i] :
      ( ( ! [SY701: $i,SY702: $i] :
            ( SV11
           != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK2_SY327 @ SV11 ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY701 ) @ SY702 ) ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[1817]) ).

thf(1892,plain,
    ! [SV87: $i,SV12: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV12 ) @ SV87 ) )
            | ( hBOOL @ ( hAPP_P282169671l_bool @ SV87 @ SV12 ) ) )
        | ~ ( ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV87 @ SV12 ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV12 ) @ SV87 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1818]) ).

thf(1893,plain,
    ! [SV13: $i] :
      ( ( ~ ( ~ ! [SY331: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ SY331 ) )
            | ! [SY332: $i,SY333: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY332 ) @ SY333 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1819]) ).

thf(1894,plain,
    ! [SV13: $i] :
      ( ( ~ ( ~ ! [SY334: $i,SY335: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY334 ) @ SY335 ) ) )
            | ! [SY336: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ SY336 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1819]) ).

thf(1895,plain,
    ! [SV141: $i,SV88: $i,SV14: $i] :
      ( ( ! [SY703: $i,SY704: $i,SY705: $i,SY706: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV14 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV88 ) @ SV141 ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY703 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY704 ) @ SY705 ) ) ) ) @ ( red @ SY706 ) ) )
            | ( hBOOL @ ( hext @ SV88 @ SY704 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1820]) ).

thf(1896,plain,
    ! [SV15: $i,SV89: $i] :
      ( ( ( ~ ! [SY576: $i,SY577: $i,SY578: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV89 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY576 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY577 ) @ SY578 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_P1708370145l_bool @ SV89 @ SV15 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1821]) ).

thf(1897,plain,
    ! [SV16: $i,SV142: $i,SV90: $i] :
      ( ( ! [SY707: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV90 ) @ SV142 ) ) @ SY707 ) )
            | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV142 ) @ SV16 ) ) @ ( transi2024712006on_val @ SY707 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV90 ) @ SV16 ) ) @ ( transi2024712006on_val @ SY707 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1822]) ).

thf(1898,plain,
    ! [SV17: $i,SV143: $i,SV91: $i] :
      ( ( ! [SY708: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV91 ) @ SV143 ) ) @ ( transi2024712006on_val @ SY708 ) ) )
            | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV143 ) @ SV17 ) ) @ SY708 ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV91 ) @ SV17 ) ) @ ( transi2024712006on_val @ SY708 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1823]) ).

thf(1899,plain,
    ! [SV18: $i,SV144: $i,SV92: $i] :
      ( ( ! [SY709: $i,SY710: $i,SY711: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV92 ) @ SV144 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY709 ) @ SY710 ) ) ) @ ( red @ SY711 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ SV18 @ SV92 ) ) @ SV144 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ SV18 @ SY709 ) ) @ SY710 ) ) ) @ ( red @ SY711 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1824]) ).

thf(1900,plain,
    ! [SV19: $i,SV145: $i,SV93: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV93 ) @ SV145 ) )
        | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV19 ) @ SV93 ) )
        | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV19 ) @ SV145 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1825]) ).

thf(1901,plain,
    ! [SV146: $i,SV94: $i,SV20: $i] :
      ( ( ! [SY712: $i,SY713: $i] :
            ( ( ( fun_up204312361on_val @ SV20 @ SV94 @ ( hAPP_val_option_val @ some_val @ SV146 ) )
             != ( fun_up204312361on_val @ SY712 @ SV94 @ ( hAPP_val_option_val @ some_val @ SY713 ) ) )
            | ( SV146 = SY713 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1826]) ).

thf(1902,plain,
    ! [SV95: $i,SV21: $i,SV147: $i] :
      ( ( ! [SY714: $i] :
            ~ ( ~ ( ( SY714 != SV147 )
                  | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV21 @ SV147 @ SV95 ) @ SY714 )
                    = SV95 ) )
              | ~ ( ~ ( ( SY714 != SV147 ) )
                  | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV21 @ SV147 @ SV95 ) @ SY714 )
                    = ( hAPP_l207779698on_val @ SV21 @ SY714 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1827]) ).

thf(1903,plain,
    ! [SV22: $i] :
      ( ( ~ ( ~ ~ ! [SY367: $i] :
                    ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ SY367 ) )
            | ~ ! [SY368: $i] :
                  ~ ~ ! [SY369: $i] :
                        ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY368 ) @ SY369 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1828]) ).

thf(1904,plain,
    ! [SV22: $i] :
      ( ( ~ ( ~ ~ ! [SY370: $i] :
                    ~ ~ ! [SY371: $i] :
                          ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY370 ) @ SY371 ) ) )
            | ~ ! [SY372: $i] :
                  ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ SY372 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1828]) ).

thf(1905,plain,
    ! [SV23: $i,SV96: $i] :
      ( ( ~ ( ~ ! [SY593: $i,SY594: $i] :
                  ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY593 ) @ SY594 ) ) @ SV96 ) )
                        | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY593 ) @ SY594 ) ) @ SV23 ) ) )
                    | ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY593 ) @ SY594 ) ) @ SV23 ) )
                        | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY593 ) @ SY594 ) ) @ SV96 ) ) ) )
            | ( SV96 = SV23 ) )
        | ~ ( ( SV96 != SV23 )
            | ! [SY595: $i,SY596: $i] :
                ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY595 ) @ SY596 ) ) @ SV96 ) )
                      | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY595 ) @ SY596 ) ) @ SV23 ) ) )
                  | ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY595 ) @ SY596 ) ) @ SV23 ) )
                      | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY595 ) @ SY596 ) ) @ SV96 ) ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1829]) ).

thf(1906,plain,
    ! [SV97: $i,SV24: $i,SV148: $i] :
      ( ( ! [SY715: $i,SY716: $i,SY717: $i,SY718: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV148 ) @ SY715 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY716 ) @ SY717 ) ) ) @ ( red @ SY718 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ SV148 @ SV24 @ SV97 ) ) @ SY715 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ SY716 @ SV24 @ SV97 ) ) @ SY717 ) ) ) @ ( red @ SY718 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1830]) ).

thf(1907,plain,
    ! [SV149: $i,SV98: $i,SV25: $i] :
      ( ( ! [SY719: $i,SY720: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SY719 ) ) ) @ ( transi2024712006on_val @ SY720 ) ) )
            | ~ ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 )
                 != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SY719 ) ) )
            | ~ ! [SY721: $i,SY722: $i] :
                  ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY721 ) @ SY722 ) ) ) @ SY720 ) )
                  | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY721 ) @ SY722 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SY719 ) ) ) @ ( transi2024712006on_val @ SY720 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1831]) ).

thf(1908,plain,
    ! [SV99: $i,SV26: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV26 ) @ SV99 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV26 ) @ ( transi2024712006on_val @ SV99 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1832]) ).

thf(1909,plain,
    ! [SV150: $i,SV100: $i,SV27: $i] :
      ( ( ( ( hAPP_l207779698on_val @ SV27 @ SV100 )
         != ( hAPP_val_option_val @ some_val @ SV150 ) )
        | ( ( fun_up1149430426on_val @ SV27 @ SV100 @ ( hAPP_val_option_val @ some_val @ SV150 ) )
          = SV27 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1833]) ).

thf(1910,plain,
    ! [SV28: $i] :
      ( ( ( SV28 != none_val )
        = $false )
      | ( ( ~ ! [SY393: $i] :
                ( SV28
               != ( hAPP_val_option_val @ some_val @ SY393 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1834]) ).

thf(1911,plain,
    ! [SV151: $i,SV101: $i,SV29: $i] :
      ( ( ! [SY723: $i] :
            ~ ( ~ ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV29 ) @ SV101 )
                   != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV151 ) @ SY723 ) )
                  | ~ ( ( SV29 != SV151 )
                      | ( SV101 != SY723 ) ) )
              | ~ ( ~ ~ ( ( SV29 != SV151 )
                        | ( SV101 != SY723 ) )
                  | ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV29 ) @ SV101 )
                    = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV151 ) @ SY723 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1835]) ).

thf(1912,plain,
    ! [SV102: $i,SV30: $i] :
      ( ( ~ ( ( ( hAPP_val_option_val @ some_val @ SV30 )
             != ( hAPP_val_option_val @ some_val @ SV102 ) )
            | ( SV30 = SV102 ) )
        | ~ ( ( SV30 != SV102 )
            | ( ( hAPP_val_option_val @ some_val @ SV30 )
              = ( hAPP_val_option_val @ some_val @ SV102 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1836]) ).

thf(1913,plain,
    ! [SV31: $i] :
      ( ( ~ ( ~ ! [SY398: $i] :
                  ( SV31
                 != ( hAPP_val_option_val @ some_val @ SY398 ) )
            | ( SV31 = none_val ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1837]) ).

thf(1914,plain,
    ! [SV31: $i] :
      ( ( ~ ( ( SV31 != none_val )
            | ! [SY399: $i] :
                ( SV31
               != ( hAPP_val_option_val @ some_val @ SY399 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1837]) ).

thf(1915,plain,
    ! [SV152: $i,SV103: $i,SV32: $i] :
      ( ( ! [SY724: $i,SY725: $i] :
            ( ( ( fun_up1149430426on_val @ SV32 @ SV103 @ ( hAPP_val_option_val @ some_val @ SV152 ) )
             != ( fun_up1149430426on_val @ SY724 @ SV103 @ ( hAPP_val_option_val @ some_val @ SY725 ) ) )
            | ( SV152 = SY725 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1838]) ).

thf(1916,plain,
    ! [SV33: $i,SV104: $i] :
      ( ( ( ~ ! [SY613: $i,SY614: $i,SY615: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV104 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY613 ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY614 ) @ SY615 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV104 @ SV33 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1839]) ).

thf(1917,plain,
    ! [SV34: $i] :
      ( ( ~ ( ~ ( ( SV34 != none_val ) )
            | ~ ! [SY408: $i] :
                  ( SV34
                 != ( hAPP_val_option_val @ some_val @ SY408 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1840]) ).

thf(1918,plain,
    ! [SV34: $i] :
      ( ( ~ ( ~ ~ ! [SY409: $i] :
                    ( SV34
                   != ( hAPP_val_option_val @ some_val @ SY409 ) )
            | ( SV34 != none_val ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1840]) ).

thf(1919,plain,
    ! [SV35: $i,SV153: $i,SV105: $i] :
      ( ( ! [SY726: $i,SY727: $i,SY728: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV105 ) @ SV153 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY726 ) @ SY727 ) ) ) @ ( red @ SY728 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ SV105 @ SV35 ) ) @ SV153 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ SY726 @ SV35 ) ) @ SY727 ) ) ) @ ( red @ SY728 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1841]) ).

thf(1920,plain,
    ! [SV154: $i,SV106: $i,SV36: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV36 ) @ SV106 ) ) @ ( transi2024712006on_val @ SV154 ) ) )
        | ~ ( ( SV36 != SV106 ) )
        | ~ ! [SY729: $i] :
              ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV36 ) @ SY729 ) ) @ ( transi2024712006on_val @ SV154 ) ) )
              | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY729 ) @ SV106 ) ) @ SV154 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1842]) ).

thf(1921,plain,
    ! [SV155: $i,SV107: $i,SV37: $i] :
      ( ( ! [SY730: $i,SY731: $i,SY732: $i,SY733: $i,SY734: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY730 ) @ SY731 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY732 ) @ SY733 ) ) ) @ ( red @ SY734 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ SY730 @ SV37 @ SV107 @ SV155 ) ) @ SY731 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ SY732 @ SV37 @ SV107 @ SV155 ) ) @ SY733 ) ) ) @ ( red @ SY734 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1843]) ).

thf(1922,plain,
    ! [SV156: $i,SV108: $i,SV38: $i] :
      ( ( ! [SY735: $i,SY736: $i] :
            ~ ( ~ ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SY735 )
                   != ( hAPP_val_option_val @ some_val @ SY736 ) )
                  | ~ ( ( SY735 != SV108 )
                      | ( SV156 != SY736 ) )
                  | ~ ( ~ ( ( SY735 != SV108 ) )
                      | ( ( hAPP_l207779698on_val @ SV38 @ SY735 )
                       != ( hAPP_val_option_val @ some_val @ SY736 ) ) ) )
              | ~ ( ~ ( ~ ( ( SY735 != SV108 )
                          | ( SV156 != SY736 ) )
                      | ~ ( ~ ( ( SY735 != SV108 ) )
                          | ( ( hAPP_l207779698on_val @ SV38 @ SY735 )
                           != ( hAPP_val_option_val @ some_val @ SY736 ) ) ) )
                  | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SY735 )
                    = ( hAPP_val_option_val @ some_val @ SY736 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1844]) ).

thf(1923,plain,
    ! [SV39: $i] :
      ( ( ! [SY737: $i] :
            ( SV39
           != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( sK3_SY429 @ SV39 ) ) @ SY737 ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[1845]) ).

thf(1924,plain,
    ! [SV40: $i,SV157: $i,SV109: $i] :
      ( ( ! [SY738: $i,SY739: $i,SY740: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV109 ) @ SV157 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY738 ) @ SY739 ) ) ) @ ( red @ SY740 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ SV40 @ SV109 ) ) @ SV157 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ SV40 @ SY738 ) ) @ SY739 ) ) ) @ ( red @ SY740 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1846]) ).

thf(1925,plain,
    ! [SV158: $i,SV110: $i,SV41: $i] :
      ( ( ( ( hAPP_l207779698on_val @ SV41 @ SV110 )
         != SV158 )
        | ( ( fun_up1149430426on_val @ SV41 @ SV110 @ SV158 )
          = SV41 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1847]) ).

thf(1926,plain,
    ! [SV42: $i,SV111: $i] :
      ( ( ( ~ ! [SY636: $i,SY637: $i,SY638: $i,SY639: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV111 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY636 ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY637 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY638 ) @ SY639 ) ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV111 @ SV42 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1848]) ).

thf(1927,plain,
    ! [SV43: $i,SV159: $i,SV112: $i] :
      ( ( ! [SY741: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV112 ) @ SV159 ) ) @ ( transi2024712006on_val @ SY741 ) ) )
            | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV159 ) @ SV43 ) ) @ ( transi2024712006on_val @ SY741 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV112 ) @ SV43 ) ) @ ( transi2024712006on_val @ SY741 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1849]) ).

thf(1928,plain,
    ! [SV160: $i,SV113: $i,SV44: $i] :
      ( ( ! [SY742: $i] :
            ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV44 ) @ SV113 )
             != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV160 ) @ SY742 ) )
            | ~ ( ( SV44 != SV160 )
                | ( SV113 != SY742 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1850]) ).

thf(1929,plain,
    ! [SV161: $i,SV114: $i,SV45: $i] :
      ( ( ! [SY743: $i] :
            ~ ( ~ ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV45 ) @ SV114 )
                   != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV161 ) @ SY743 ) )
                  | ~ ( ( SV45 != SV161 )
                      | ( SV114 != SY743 ) ) )
              | ~ ( ~ ~ ( ( SV45 != SV161 )
                        | ( SV114 != SY743 ) )
                  | ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV45 ) @ SV114 )
                    = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV161 ) @ SY743 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1851]) ).

thf(1930,plain,
    ! [SV115: $i,SV46: $i,SV162: $i] :
      ( ( ! [SY744: $i] :
            ~ ( ~ ( ( SV162 != SY744 )
                  | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV46 @ SY744 @ SV115 ) @ SV162 )
                    = SV115 ) )
              | ~ ( ~ ( ( SV162 != SY744 ) )
                  | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV46 @ SY744 @ SV115 ) @ SV162 )
                    = ( hAPP_l207779698on_val @ SV46 @ SV162 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1852]) ).

thf(1931,plain,
    ! [SV47: $i,SV163: $i,SV116: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV116 ) @ SV163 ) )
        | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV163 ) @ SV47 ) )
        | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV116 ) @ SV47 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1853]) ).

thf(1932,plain,
    ! [SV117: $i,SV48: $i] :
      ( ( ~ ( ( ( bool @ SV48 )
             != ( bool @ SV117 ) )
            | ~ ( ~ ( ~ ( hBOOL @ SV48 )
                    | ( hBOOL @ SV117 ) )
                | ~ ( ~ ( hBOOL @ SV117 )
                    | ( hBOOL @ SV48 ) ) ) )
        | ~ ( ~ ~ ( ~ ( ~ ( hBOOL @ SV48 )
                      | ( hBOOL @ SV117 ) )
                  | ~ ( ~ ( hBOOL @ SV117 )
                      | ( hBOOL @ SV48 ) ) )
            | ( ( bool @ SV48 )
              = ( bool @ SV117 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1854]) ).

thf(1933,plain,
    ! [SV49: $i] :
      ( ( ~ ( ~ ~ ! [SY458: $i] :
                    ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ SY458 ) )
            | ~ ! [SY459: $i] :
                  ~ ~ ! [SY460: $i] :
                        ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY459 ) @ SY460 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1855]) ).

thf(1934,plain,
    ! [SV49: $i] :
      ( ( ~ ( ~ ~ ! [SY461: $i] :
                    ~ ~ ! [SY462: $i] :
                          ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY461 ) @ SY462 ) ) )
            | ~ ! [SY463: $i] :
                  ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ SY463 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1855]) ).

thf(1935,plain,
    ! [SV118: $i,SV50: $i,SV164: $i] :
      ( ( ! [SY745: $i,SY746: $i,SY747: $i,SY748: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV164 ) @ SY745 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY746 ) @ SY747 ) ) ) @ ( red @ SY748 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ SV164 @ SV50 @ SV118 ) ) @ SY745 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ SY746 @ SV50 @ SV118 ) ) @ SY747 ) ) ) @ ( red @ SY748 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1856]) ).

thf(1936,plain,
    ! [SV165: $i,SV119: $i,SV51: $i] :
      ( ( ! [SY749: $i] :
            ~ ( ~ ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV51 ) @ SV119 )
                   != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV165 ) @ SY749 ) )
                  | ~ ( ( SV51 != SV165 )
                      | ( SV119 != SY749 ) ) )
              | ~ ( ~ ~ ( ( SV51 != SV165 )
                        | ( SV119 != SY749 ) )
                  | ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV51 ) @ SV119 )
                    = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV165 ) @ SY749 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1857]) ).

thf(1937,plain,
    ! [SV120: $i,SV52: $i,SV166: $i] :
      ( ( ! [SY750: $i] :
            ( ~ ( ( SV166 != SY750 ) )
            | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV52 @ SY750 @ SV120 ) @ SV166 )
              = ( hAPP_l207779698on_val @ SV52 @ SV166 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1858]) ).

thf(1938,plain,
    ! [SV167: $i,SV121: $i,SV53: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV53 ) @ ( semila751111325l_bool @ SV121 @ SV167 ) ) )
        | ~ ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV53 ) @ SV121 ) )
        | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV53 ) @ SV167 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1859]) ).

thf(1939,plain,
    ! [SV122: $i,SV54: $i,SV168: $i] :
      ( ( ! [SY751: $i,SY752: $i,SY753: $i,SY754: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV168 ) @ SY751 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY752 ) @ SY753 ) ) ) @ ( red @ SY754 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ SV168 @ SV54 @ SV122 ) ) @ SY751 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ SY752 @ SV54 @ SV122 ) ) @ SY753 ) ) ) @ ( red @ SY754 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1860]) ).

thf(1940,plain,
    ! [SV55: $i] :
      ( ( ! [SY755: $i,SY756: $i,SY757: $i] :
            ( SV55
           != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK4_SY484 @ SV55 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY755 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY756 ) @ SY757 ) ) ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[1861]) ).

thf(1941,plain,
    ! [SV56: $i] :
      ( ( ! [SY758: $i] :
            ( SV56
           != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( sK5_SY488 @ SV56 ) ) @ SY758 ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[1862]) ).

thf(1942,plain,
    ! [SV57: $i,SV123: $i] :
      ( ( ( ~ ! [SY664: $i] :
                ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SY664 ) @ SV123 ) )
                | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SY664 ) @ SV57 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV123 ) @ SV57 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1863]) ).

thf(1943,plain,
    ! [SV124: $i,SV58: $i,SV169: $i] :
      ( ( ! [SY759: $i,SY760: $i,SY761: $i,SY762: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV169 ) @ SY759 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY760 ) @ SY761 ) ) ) @ ( red @ SY762 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ SV169 @ SV58 @ SV124 ) ) @ SY759 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ SY760 @ SV58 @ SV124 ) ) @ SY761 ) ) ) @ ( red @ SY762 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1864]) ).

thf(1944,plain,
    ! [SV59: $i] :
      ( ( ~ ( ~ ~ ! [SY498: $i] :
                    ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ SY498 ) )
            | ~ ! [SY499: $i] :
                  ~ ~ ! [SY500: $i] :
                        ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY499 ) @ SY500 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1865]) ).

thf(1945,plain,
    ! [SV59: $i] :
      ( ( ~ ( ~ ~ ! [SY501: $i] :
                    ~ ~ ! [SY502: $i] :
                          ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY501 ) @ SY502 ) ) )
            | ~ ! [SY503: $i] :
                  ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ SY503 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1865]) ).

thf(1946,plain,
    ! [SV60: $i,SV170: $i,SV125: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV125 ) @ SV170 ) )
        | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV60 ) @ SV125 ) )
        | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV60 ) @ SV170 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1866]) ).

thf(1947,plain,
    ! [SV171: $i,SV126: $i,SV61: $i] :
      ( ( ~ ( ~ ( ( ( fun_up1149430426on_val @ SV61 @ SV126 @ SV171 )
                 != SV61 )
                | ( ( hAPP_l207779698on_val @ SV61 @ SV126 )
                  = SV171 ) )
            | ~ ( ( ( hAPP_l207779698on_val @ SV61 @ SV126 )
                 != SV171 )
                | ( ( fun_up1149430426on_val @ SV61 @ SV126 @ SV171 )
                  = SV61 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1867]) ).

thf(1948,plain,
    ! [SV62: $i] :
      ( ( ! [SY763: $i] :
            ( SV62
           != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK6_SY508 @ SV62 ) ) @ SY763 ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[1868]) ).

thf(1949,plain,
    ! [SV172: $i,SV127: $i,SV63: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV63 ) @ SV127 ) ) @ ( transi2024712006on_val @ SV172 ) ) )
        | ~ ( ( SV63 != SV127 ) )
        | ~ ! [SY764: $i] :
              ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV63 ) @ SY764 ) ) @ SV172 ) )
              | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY764 ) @ SV127 ) ) @ ( transi2024712006on_val @ SV172 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1869]) ).

thf(1950,plain,
    ! [SV173: $i,SV128: $i,SV65: $i] :
      ( ( ! [SY765: $i,SY766: $i] :
            ( ~ ( ( SY765 != SY766 ) )
            | ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ SV65 @ SY765 @ SV128 ) @ SY766 @ SV173 )
              = ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ SV65 @ SY766 @ SV173 ) @ SY765 @ SV128 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1871]) ).

thf(1951,plain,
    ! [SV66: $i,SV174: $i,SV129: $i] :
      ( ( ! [SY767: $i,SY768: $i,SY769: $i,SY770: $i,SY771: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV129 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV174 ) @ SY767 ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY768 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY769 ) @ SY770 ) ) ) ) @ ( red @ SY771 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV129 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV174 ) @ ( map_ad325961431ar_val @ SV66 @ SY767 ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY768 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY769 ) @ ( map_ad325961431ar_val @ SV66 @ SY770 ) ) ) ) ) @ ( red @ SY771 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1872]) ).

thf(1952,plain,
    ! [SV67: $i] :
      ( ( ! [SY772: $i,SY773: $i] :
            ( SV67
           != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK7_SY524 @ SV67 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY772 ) @ SY773 ) ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[1873]) ).

thf(1953,plain,
    ! [SV69: $i] :
      ( ( ~ ( ~ ! [SY527: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ SY527 ) )
            | ! [SY528: $i,SY529: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY528 ) @ SY529 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1875]) ).

thf(1954,plain,
    ! [SV69: $i] :
      ( ( ~ ( ~ ! [SY530: $i,SY531: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY530 ) @ SY531 ) ) )
            | ! [SY532: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ SY532 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1875]) ).

thf(1955,plain,
    ! [SV70: $i,SV175: $i,SV130: $i] :
      ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV130 ) @ SV175 ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV130 ) @ SV70 ) ) )
        | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV130 ) @ ( semila751111325l_bool @ SV70 @ SV175 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1876]) ).

thf(1956,plain,
    ! [SV71: $i] :
      ( ( ~ ( ~ ! [SY535: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ SY535 ) )
            | ! [SY536: $i,SY537: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY536 ) @ SY537 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1877]) ).

thf(1957,plain,
    ! [SV71: $i] :
      ( ( ~ ( ~ ! [SY538: $i,SY539: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY538 ) @ SY539 ) ) )
            | ! [SY540: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ SY540 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1877]) ).

thf(1958,plain,
    ! [SV72: $i] :
      ( ( ! [SY774: $i] :
            ( SV72
           != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK8_SY541 @ SV72 ) ) @ SY774 ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[1878]) ).

thf(1959,plain,
    ! [SV176: $i,SV131: $i,SV73: $i] :
      ( ( ! [SY775: $i,SY776: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV73 ) @ SV131 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV176 ) @ SY775 ) ) ) @ ( red @ SY776 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ SV73 ) ) @ SV131 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ SV176 ) ) @ SY775 ) ) ) @ ( red @ SY776 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1879]) ).

thf(1960,plain,
    ! [SV177: $i,SV132: $i,SV74: $i] :
      ( ( ! [SY777: $i,SY778: $i,SY779: $i,SY780: $i,SY781: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY777 ) @ SY778 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY779 ) @ SY780 ) ) ) @ ( red @ SY781 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ SY777 @ SV74 @ SV132 @ SV177 ) ) @ SY778 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ SY779 @ SV74 @ SV132 @ SV177 ) ) @ SY780 ) ) ) @ ( red @ SY781 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1880]) ).

thf(1961,plain,
    ! [SV75: $i,SV178: $i,SV133: $i] :
      ( ( ~ ( hBOOL @ ( hext @ SV133 @ SV178 ) )
        | ~ ( hBOOL @ ( hext @ SV178 @ SV75 ) )
        | ( hBOOL @ ( hext @ SV133 @ SV75 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1881]) ).

thf(1962,plain,
    ! [SV76: $i] :
      ( ( ! [SY782: $i] :
            ( SV76
           != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK9_SY556 @ SV76 ) ) @ SY782 ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[1882]) ).

thf(1963,plain,
    ! [SV179: $i,SV134: $i,SV77: $i] :
      ( ( ! [SY783: $i] :
            ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV77 ) @ SV134 )
             != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV179 ) @ SY783 ) )
            | ~ ( ( SV77 != SV179 )
                | ( SV134 != SY783 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1883]) ).

thf(1964,plain,
    ! [SV180: $i,SV135: $i,SV78: $i] :
      ( ( ! [SY784: $i] :
            ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV78 ) @ SV135 )
             != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV180 ) @ SY784 ) )
            | ~ ( ( SV78 != SV180 )
                | ( SV135 != SY784 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1884]) ).

thf(1965,plain,
    ! [SV181: $i,SV137: $i,SV82: $i,SV4: $i] :
      ( ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ SV4 @ SV82 @ SV137 ) @ SV82 @ SV181 )
        = ( fun_up1149430426on_val @ SV4 @ SV82 @ SV181 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1886]) ).

thf(1966,plain,
    ! [SV182: $i,SV138: $i,SV83: $i,SV5: $i] :
      ( ( ( map_ad325961431ar_val @ SV5 @ ( fun_up1149430426on_val @ SV83 @ SV138 @ ( hAPP_val_option_val @ some_val @ SV182 ) ) )
        = ( fun_up1149430426on_val @ ( map_ad325961431ar_val @ SV5 @ SV83 ) @ SV138 @ ( hAPP_val_option_val @ some_val @ SV182 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1887]) ).

thf(1967,plain,
    ! [SV9: $i] :
      ( ( SV9
       != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK1_SY323 @ SV9 ) ) @ ( sK10_SY700 @ SV9 ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[1889]) ).

thf(1968,plain,
    ! [SV10: $i,SV140: $i,SV86: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV86 ) @ SV140 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV10 ) @ SV86 ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV10 ) @ SV140 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1890]) ).

thf(1969,plain,
    ! [SV11: $i] :
      ( ( ! [SY785: $i] :
            ( SV11
           != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK2_SY327 @ SV11 ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( sK11_SY701 @ SV11 ) ) @ SY785 ) ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[1891]) ).

thf(1970,plain,
    ! [SV87: $i,SV12: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV12 ) @ SV87 ) )
            | ( hBOOL @ ( hAPP_P282169671l_bool @ SV87 @ SV12 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1892]) ).

thf(1971,plain,
    ! [SV12: $i,SV87: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV87 @ SV12 ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV12 ) @ SV87 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1892]) ).

thf(1972,plain,
    ! [SV13: $i] :
      ( ( ~ ! [SY331: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ SY331 ) )
        | ! [SY332: $i,SY333: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY332 ) @ SY333 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1893]) ).

thf(1973,plain,
    ! [SV13: $i] :
      ( ( ~ ! [SY334: $i,SY335: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY334 ) @ SY335 ) ) )
        | ! [SY336: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ SY336 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1894]) ).

thf(1974,plain,
    ! [SV183: $i,SV141: $i,SV88: $i,SV14: $i] :
      ( ( ! [SY786: $i,SY787: $i,SY788: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV14 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV88 ) @ SV141 ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV183 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY786 ) @ SY787 ) ) ) ) @ ( red @ SY788 ) ) )
            | ( hBOOL @ ( hext @ SV88 @ SY786 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1895]) ).

thf(1975,plain,
    ! [SV15: $i,SV89: $i] :
      ( ( ( ! [SY576: $i,SY577: $i,SY578: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV89 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY576 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY577 ) @ SY578 ) ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P1708370145l_bool @ SV89 @ SV15 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1896]) ).

thf(1976,plain,
    ! [SV16: $i,SV184: $i,SV142: $i,SV90: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV90 ) @ SV142 ) ) @ SV184 ) )
        | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV142 ) @ SV16 ) ) @ ( transi2024712006on_val @ SV184 ) ) )
        | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV90 ) @ SV16 ) ) @ ( transi2024712006on_val @ SV184 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1897]) ).

thf(1977,plain,
    ! [SV17: $i,SV185: $i,SV143: $i,SV91: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV91 ) @ SV143 ) ) @ ( transi2024712006on_val @ SV185 ) ) )
        | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV143 ) @ SV17 ) ) @ SV185 ) )
        | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV91 ) @ SV17 ) ) @ ( transi2024712006on_val @ SV185 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1898]) ).

thf(1978,plain,
    ! [SV18: $i,SV186: $i,SV144: $i,SV92: $i] :
      ( ( ! [SY789: $i,SY790: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV92 ) @ SV144 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV186 ) @ SY789 ) ) ) @ ( red @ SY790 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ SV18 @ SV92 ) ) @ SV144 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ SV18 @ SV186 ) ) @ SY789 ) ) ) @ ( red @ SY790 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1899]) ).

thf(1979,plain,
    ! [SV19: $i,SV145: $i,SV93: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV93 ) @ SV145 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV19 ) @ SV93 ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV19 ) @ SV145 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1900]) ).

thf(1980,plain,
    ! [SV187: $i,SV146: $i,SV94: $i,SV20: $i] :
      ( ( ! [SY791: $i] :
            ( ( ( fun_up204312361on_val @ SV20 @ SV94 @ ( hAPP_val_option_val @ some_val @ SV146 ) )
             != ( fun_up204312361on_val @ SV187 @ SV94 @ ( hAPP_val_option_val @ some_val @ SY791 ) ) )
            | ( SV146 = SY791 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1901]) ).

thf(1981,plain,
    ! [SV95: $i,SV21: $i,SV147: $i,SV188: $i] :
      ( ( ~ ( ~ ( ( SV188 != SV147 )
                | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV21 @ SV147 @ SV95 ) @ SV188 )
                  = SV95 ) )
            | ~ ( ~ ( ( SV188 != SV147 ) )
                | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV21 @ SV147 @ SV95 ) @ SV188 )
                  = ( hAPP_l207779698on_val @ SV21 @ SV188 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1902]) ).

thf(1982,plain,
    ! [SV22: $i] :
      ( ( ~ ~ ! [SY367: $i] :
                ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ SY367 ) )
        | ~ ! [SY368: $i] :
              ~ ~ ! [SY369: $i] :
                    ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY368 ) @ SY369 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1903]) ).

thf(1983,plain,
    ! [SV22: $i] :
      ( ( ~ ~ ! [SY370: $i] :
                ~ ~ ! [SY371: $i] :
                      ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY370 ) @ SY371 ) ) )
        | ~ ! [SY372: $i] :
              ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ SY372 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1904]) ).

thf(1984,plain,
    ! [SV23: $i,SV96: $i] :
      ( ( ~ ( ~ ! [SY593: $i,SY594: $i] :
                  ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY593 ) @ SY594 ) ) @ SV96 ) )
                        | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY593 ) @ SY594 ) ) @ SV23 ) ) )
                    | ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY593 ) @ SY594 ) ) @ SV23 ) )
                        | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY593 ) @ SY594 ) ) @ SV96 ) ) ) )
            | ( SV96 = SV23 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1905]) ).

thf(1985,plain,
    ! [SV23: $i,SV96: $i] :
      ( ( ~ ( ( SV96 != SV23 )
            | ! [SY595: $i,SY596: $i] :
                ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY595 ) @ SY596 ) ) @ SV96 ) )
                      | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY595 ) @ SY596 ) ) @ SV23 ) ) )
                  | ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY595 ) @ SY596 ) ) @ SV23 ) )
                      | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY595 ) @ SY596 ) ) @ SV96 ) ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1905]) ).

thf(1986,plain,
    ! [SV97: $i,SV24: $i,SV189: $i,SV148: $i] :
      ( ( ! [SY792: $i,SY793: $i,SY794: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV148 ) @ SV189 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY792 ) @ SY793 ) ) ) @ ( red @ SY794 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ SV148 @ SV24 @ SV97 ) ) @ SV189 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ SY792 @ SV24 @ SV97 ) ) @ SY793 ) ) ) @ ( red @ SY794 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1906]) ).

thf(1987,plain,
    ! [SV190: $i,SV149: $i,SV98: $i,SV25: $i] :
      ( ( ! [SY795: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) ) @ ( transi2024712006on_val @ SY795 ) ) )
            | ~ ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 )
                 != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) )
            | ~ ! [SY796: $i,SY797: $i] :
                  ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY796 ) @ SY797 ) ) ) @ SY795 ) )
                  | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY796 ) @ SY797 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) ) @ ( transi2024712006on_val @ SY795 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1907]) ).

thf(1988,plain,
    ! [SV99: $i,SV26: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV26 ) @ SV99 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV26 ) @ ( transi2024712006on_val @ SV99 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1908]) ).

thf(1989,plain,
    ! [SV150: $i,SV100: $i,SV27: $i] :
      ( ( ( ( hAPP_l207779698on_val @ SV27 @ SV100 )
         != ( hAPP_val_option_val @ some_val @ SV150 ) )
        = $true )
      | ( ( ( fun_up1149430426on_val @ SV27 @ SV100 @ ( hAPP_val_option_val @ some_val @ SV150 ) )
          = SV27 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1909]) ).

thf(1990,plain,
    ! [SV28: $i] :
      ( ( ( SV28 = none_val )
        = $true )
      | ( ( ~ ! [SY393: $i] :
                ( SV28
               != ( hAPP_val_option_val @ some_val @ SY393 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1910]) ).

thf(1991,plain,
    ! [SV191: $i,SV151: $i,SV101: $i,SV29: $i] :
      ( ( ~ ( ~ ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV29 ) @ SV101 )
                 != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV151 ) @ SV191 ) )
                | ~ ( ( SV29 != SV151 )
                    | ( SV101 != SV191 ) ) )
            | ~ ( ~ ~ ( ( SV29 != SV151 )
                      | ( SV101 != SV191 ) )
                | ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV29 ) @ SV101 )
                  = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV151 ) @ SV191 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1911]) ).

thf(1992,plain,
    ! [SV102: $i,SV30: $i] :
      ( ( ~ ( ( ( hAPP_val_option_val @ some_val @ SV30 )
             != ( hAPP_val_option_val @ some_val @ SV102 ) )
            | ( SV30 = SV102 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1912]) ).

thf(1993,plain,
    ! [SV102: $i,SV30: $i] :
      ( ( ~ ( ( SV30 != SV102 )
            | ( ( hAPP_val_option_val @ some_val @ SV30 )
              = ( hAPP_val_option_val @ some_val @ SV102 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1912]) ).

thf(1994,plain,
    ! [SV31: $i] :
      ( ( ~ ! [SY398: $i] :
              ( SV31
             != ( hAPP_val_option_val @ some_val @ SY398 ) )
        | ( SV31 = none_val ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1913]) ).

thf(1995,plain,
    ! [SV31: $i] :
      ( ( ( SV31 != none_val )
        | ! [SY399: $i] :
            ( SV31
           != ( hAPP_val_option_val @ some_val @ SY399 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1914]) ).

thf(1996,plain,
    ! [SV192: $i,SV152: $i,SV103: $i,SV32: $i] :
      ( ( ! [SY798: $i] :
            ( ( ( fun_up1149430426on_val @ SV32 @ SV103 @ ( hAPP_val_option_val @ some_val @ SV152 ) )
             != ( fun_up1149430426on_val @ SV192 @ SV103 @ ( hAPP_val_option_val @ some_val @ SY798 ) ) )
            | ( SV152 = SY798 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1915]) ).

thf(1997,plain,
    ! [SV33: $i,SV104: $i] :
      ( ( ( ! [SY613: $i,SY614: $i,SY615: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV104 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY613 ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY614 ) @ SY615 ) ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV104 @ SV33 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1916]) ).

thf(1998,plain,
    ! [SV34: $i] :
      ( ( ~ ( ( SV34 != none_val ) )
        | ~ ! [SY408: $i] :
              ( SV34
             != ( hAPP_val_option_val @ some_val @ SY408 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1917]) ).

thf(1999,plain,
    ! [SV34: $i] :
      ( ( ~ ~ ! [SY409: $i] :
                ( SV34
               != ( hAPP_val_option_val @ some_val @ SY409 ) )
        | ( SV34 != none_val ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1918]) ).

thf(2000,plain,
    ! [SV35: $i,SV193: $i,SV153: $i,SV105: $i] :
      ( ( ! [SY799: $i,SY800: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV105 ) @ SV153 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV193 ) @ SY799 ) ) ) @ ( red @ SY800 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ SV105 @ SV35 ) ) @ SV153 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ SV193 @ SV35 ) ) @ SY799 ) ) ) @ ( red @ SY800 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1919]) ).

thf(2001,plain,
    ! [SV154: $i,SV106: $i,SV36: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV36 ) @ SV106 ) ) @ ( transi2024712006on_val @ SV154 ) ) ) )
        = $true )
      | ( ( ~ ( ( SV36 != SV106 ) )
          | ~ ! [SY729: $i] :
                ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV36 ) @ SY729 ) ) @ ( transi2024712006on_val @ SV154 ) ) )
                | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY729 ) @ SV106 ) ) @ SV154 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1920]) ).

thf(2002,plain,
    ! [SV155: $i,SV107: $i,SV37: $i,SV194: $i] :
      ( ( ! [SY801: $i,SY802: $i,SY803: $i,SY804: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV194 ) @ SY801 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY802 ) @ SY803 ) ) ) @ ( red @ SY804 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ SV194 @ SV37 @ SV107 @ SV155 ) ) @ SY801 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ SY802 @ SV37 @ SV107 @ SV155 ) ) @ SY803 ) ) ) @ ( red @ SY804 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1921]) ).

thf(2003,plain,
    ! [SV195: $i,SV156: $i,SV108: $i,SV38: $i] :
      ( ( ! [SY805: $i] :
            ~ ( ~ ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
                   != ( hAPP_val_option_val @ some_val @ SY805 ) )
                  | ~ ( ( SV195 != SV108 )
                      | ( SV156 != SY805 ) )
                  | ~ ( ~ ( ( SV195 != SV108 ) )
                      | ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
                       != ( hAPP_val_option_val @ some_val @ SY805 ) ) ) )
              | ~ ( ~ ( ~ ( ( SV195 != SV108 )
                          | ( SV156 != SY805 ) )
                      | ~ ( ~ ( ( SV195 != SV108 ) )
                          | ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
                           != ( hAPP_val_option_val @ some_val @ SY805 ) ) ) )
                  | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
                    = ( hAPP_val_option_val @ some_val @ SY805 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1922]) ).

thf(2004,plain,
    ! [SV39: $i] :
      ( ( SV39
       != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( sK3_SY429 @ SV39 ) ) @ ( sK12_SY737 @ SV39 ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[1923]) ).

thf(2005,plain,
    ! [SV40: $i,SV196: $i,SV157: $i,SV109: $i] :
      ( ( ! [SY806: $i,SY807: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV109 ) @ SV157 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV196 ) @ SY806 ) ) ) @ ( red @ SY807 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ SV40 @ SV109 ) ) @ SV157 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ SV40 @ SV196 ) ) @ SY806 ) ) ) @ ( red @ SY807 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1924]) ).

thf(2006,plain,
    ! [SV158: $i,SV110: $i,SV41: $i] :
      ( ( ( ( hAPP_l207779698on_val @ SV41 @ SV110 )
         != SV158 )
        = $true )
      | ( ( ( fun_up1149430426on_val @ SV41 @ SV110 @ SV158 )
          = SV41 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1925]) ).

thf(2007,plain,
    ! [SV42: $i,SV111: $i] :
      ( ( ( ! [SY636: $i,SY637: $i,SY638: $i,SY639: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV111 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY636 ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY637 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY638 ) @ SY639 ) ) ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV111 @ SV42 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1926]) ).

thf(2008,plain,
    ! [SV43: $i,SV197: $i,SV159: $i,SV112: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV112 ) @ SV159 ) ) @ ( transi2024712006on_val @ SV197 ) ) )
        | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV159 ) @ SV43 ) ) @ ( transi2024712006on_val @ SV197 ) ) )
        | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV112 ) @ SV43 ) ) @ ( transi2024712006on_val @ SV197 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1927]) ).

thf(2009,plain,
    ! [SV198: $i,SV160: $i,SV113: $i,SV44: $i] :
      ( ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV44 ) @ SV113 )
         != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV160 ) @ SV198 ) )
        | ~ ( ( SV44 != SV160 )
            | ( SV113 != SV198 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1928]) ).

thf(2010,plain,
    ! [SV199: $i,SV161: $i,SV114: $i,SV45: $i] :
      ( ( ~ ( ~ ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV45 ) @ SV114 )
                 != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV161 ) @ SV199 ) )
                | ~ ( ( SV45 != SV161 )
                    | ( SV114 != SV199 ) ) )
            | ~ ( ~ ~ ( ( SV45 != SV161 )
                      | ( SV114 != SV199 ) )
                | ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV45 ) @ SV114 )
                  = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV161 ) @ SV199 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1929]) ).

thf(2011,plain,
    ! [SV115: $i,SV46: $i,SV200: $i,SV162: $i] :
      ( ( ~ ( ~ ( ( SV162 != SV200 )
                | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV46 @ SV200 @ SV115 ) @ SV162 )
                  = SV115 ) )
            | ~ ( ~ ( ( SV162 != SV200 ) )
                | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV46 @ SV200 @ SV115 ) @ SV162 )
                  = ( hAPP_l207779698on_val @ SV46 @ SV162 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1930]) ).

thf(2012,plain,
    ! [SV47: $i,SV163: $i,SV116: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV116 ) @ SV163 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV163 ) @ SV47 ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV116 ) @ SV47 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1931]) ).

thf(2013,plain,
    ! [SV117: $i,SV48: $i] :
      ( ( ~ ( ( ( bool @ SV48 )
             != ( bool @ SV117 ) )
            | ~ ( ~ ( ~ ( hBOOL @ SV48 )
                    | ( hBOOL @ SV117 ) )
                | ~ ( ~ ( hBOOL @ SV117 )
                    | ( hBOOL @ SV48 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1932]) ).

thf(2014,plain,
    ! [SV117: $i,SV48: $i] :
      ( ( ~ ( ~ ~ ( ~ ( ~ ( hBOOL @ SV48 )
                      | ( hBOOL @ SV117 ) )
                  | ~ ( ~ ( hBOOL @ SV117 )
                      | ( hBOOL @ SV48 ) ) )
            | ( ( bool @ SV48 )
              = ( bool @ SV117 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1932]) ).

thf(2015,plain,
    ! [SV49: $i] :
      ( ( ~ ~ ! [SY458: $i] :
                ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ SY458 ) )
        | ~ ! [SY459: $i] :
              ~ ~ ! [SY460: $i] :
                    ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY459 ) @ SY460 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1933]) ).

thf(2016,plain,
    ! [SV49: $i] :
      ( ( ~ ~ ! [SY461: $i] :
                ~ ~ ! [SY462: $i] :
                      ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY461 ) @ SY462 ) ) )
        | ~ ! [SY463: $i] :
              ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ SY463 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1934]) ).

thf(2017,plain,
    ! [SV118: $i,SV50: $i,SV201: $i,SV164: $i] :
      ( ( ! [SY808: $i,SY809: $i,SY810: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV164 ) @ SV201 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY808 ) @ SY809 ) ) ) @ ( red @ SY810 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ SV164 @ SV50 @ SV118 ) ) @ SV201 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ SY808 @ SV50 @ SV118 ) ) @ SY809 ) ) ) @ ( red @ SY810 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1935]) ).

thf(2018,plain,
    ! [SV202: $i,SV165: $i,SV119: $i,SV51: $i] :
      ( ( ~ ( ~ ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV51 ) @ SV119 )
                 != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV165 ) @ SV202 ) )
                | ~ ( ( SV51 != SV165 )
                    | ( SV119 != SV202 ) ) )
            | ~ ( ~ ~ ( ( SV51 != SV165 )
                      | ( SV119 != SV202 ) )
                | ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV51 ) @ SV119 )
                  = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV165 ) @ SV202 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1936]) ).

thf(2019,plain,
    ! [SV120: $i,SV52: $i,SV203: $i,SV166: $i] :
      ( ( ~ ( ( SV166 != SV203 ) )
        | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV52 @ SV203 @ SV120 ) @ SV166 )
          = ( hAPP_l207779698on_val @ SV52 @ SV166 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1937]) ).

thf(2020,plain,
    ! [SV167: $i,SV121: $i,SV53: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV53 ) @ ( semila751111325l_bool @ SV121 @ SV167 ) ) ) )
        = $true )
      | ( ( ~ ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV53 ) @ SV121 ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV53 ) @ SV167 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1938]) ).

thf(2021,plain,
    ! [SV122: $i,SV54: $i,SV204: $i,SV168: $i] :
      ( ( ! [SY811: $i,SY812: $i,SY813: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV168 ) @ SV204 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY811 ) @ SY812 ) ) ) @ ( red @ SY813 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ SV168 @ SV54 @ SV122 ) ) @ SV204 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ SY811 @ SV54 @ SV122 ) ) @ SY812 ) ) ) @ ( red @ SY813 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1939]) ).

thf(2022,plain,
    ! [SV55: $i] :
      ( ( ! [SY814: $i,SY815: $i] :
            ( SV55
           != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK4_SY484 @ SV55 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK13_SY755 @ SV55 ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY814 ) @ SY815 ) ) ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[1940]) ).

thf(2023,plain,
    ! [SV56: $i] :
      ( ( SV56
       != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( sK5_SY488 @ SV56 ) ) @ ( sK14_SY758 @ SV56 ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[1941]) ).

thf(2024,plain,
    ! [SV57: $i,SV123: $i] :
      ( ( ( ! [SY664: $i] :
              ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SY664 ) @ SV123 ) )
              | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SY664 ) @ SV57 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV123 ) @ SV57 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1942]) ).

thf(2025,plain,
    ! [SV124: $i,SV58: $i,SV205: $i,SV169: $i] :
      ( ( ! [SY816: $i,SY817: $i,SY818: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV169 ) @ SV205 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY816 ) @ SY817 ) ) ) @ ( red @ SY818 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ SV169 @ SV58 @ SV124 ) ) @ SV205 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ SY816 @ SV58 @ SV124 ) ) @ SY817 ) ) ) @ ( red @ SY818 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1943]) ).

thf(2026,plain,
    ! [SV59: $i] :
      ( ( ~ ~ ! [SY498: $i] :
                ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ SY498 ) )
        | ~ ! [SY499: $i] :
              ~ ~ ! [SY500: $i] :
                    ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY499 ) @ SY500 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1944]) ).

thf(2027,plain,
    ! [SV59: $i] :
      ( ( ~ ~ ! [SY501: $i] :
                ~ ~ ! [SY502: $i] :
                      ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY501 ) @ SY502 ) ) )
        | ~ ! [SY503: $i] :
              ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ SY503 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1945]) ).

thf(2028,plain,
    ! [SV60: $i,SV170: $i,SV125: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV125 ) @ SV170 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV60 ) @ SV125 ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV60 ) @ SV170 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1946]) ).

thf(2029,plain,
    ! [SV171: $i,SV126: $i,SV61: $i] :
      ( ( ~ ( ( ( fun_up1149430426on_val @ SV61 @ SV126 @ SV171 )
             != SV61 )
            | ( ( hAPP_l207779698on_val @ SV61 @ SV126 )
              = SV171 ) )
        | ~ ( ( ( hAPP_l207779698on_val @ SV61 @ SV126 )
             != SV171 )
            | ( ( fun_up1149430426on_val @ SV61 @ SV126 @ SV171 )
              = SV61 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1947]) ).

thf(2030,plain,
    ! [SV62: $i] :
      ( ( SV62
       != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK6_SY508 @ SV62 ) ) @ ( sK15_SY763 @ SV62 ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[1948]) ).

thf(2031,plain,
    ! [SV172: $i,SV127: $i,SV63: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV63 ) @ SV127 ) ) @ ( transi2024712006on_val @ SV172 ) ) ) )
        = $true )
      | ( ( ~ ( ( SV63 != SV127 ) )
          | ~ ! [SY764: $i] :
                ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV63 ) @ SY764 ) ) @ SV172 ) )
                | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY764 ) @ SV127 ) ) @ ( transi2024712006on_val @ SV172 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1949]) ).

thf(2032,plain,
    ! [SV173: $i,SV128: $i,SV65: $i,SV206: $i] :
      ( ( ! [SY819: $i] :
            ( ~ ( ( SV206 != SY819 ) )
            | ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ SV65 @ SV206 @ SV128 ) @ SY819 @ SV173 )
              = ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ SV65 @ SY819 @ SV173 ) @ SV206 @ SV128 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1950]) ).

thf(2033,plain,
    ! [SV66: $i,SV207: $i,SV174: $i,SV129: $i] :
      ( ( ! [SY820: $i,SY821: $i,SY822: $i,SY823: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV129 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV174 ) @ SV207 ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY820 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY821 ) @ SY822 ) ) ) ) @ ( red @ SY823 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV129 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV174 ) @ ( map_ad325961431ar_val @ SV66 @ SV207 ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY820 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY821 ) @ ( map_ad325961431ar_val @ SV66 @ SY822 ) ) ) ) ) @ ( red @ SY823 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1951]) ).

thf(2034,plain,
    ! [SV67: $i] :
      ( ( ! [SY824: $i] :
            ( SV67
           != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK7_SY524 @ SV67 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK16_SY772 @ SV67 ) ) @ SY824 ) ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[1952]) ).

thf(2035,plain,
    ! [SV69: $i] :
      ( ( ~ ! [SY527: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ SY527 ) )
        | ! [SY528: $i,SY529: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY528 ) @ SY529 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1953]) ).

thf(2036,plain,
    ! [SV69: $i] :
      ( ( ~ ! [SY530: $i,SY531: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY530 ) @ SY531 ) ) )
        | ! [SY532: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ SY532 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1954]) ).

thf(2037,plain,
    ! [SV70: $i,SV175: $i,SV130: $i] :
      ( ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV130 ) @ SV175 ) )
              | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV130 ) @ SV70 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV130 ) @ ( semila751111325l_bool @ SV70 @ SV175 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1955]) ).

thf(2038,plain,
    ! [SV71: $i] :
      ( ( ~ ! [SY535: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ SY535 ) )
        | ! [SY536: $i,SY537: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY536 ) @ SY537 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1956]) ).

thf(2039,plain,
    ! [SV71: $i] :
      ( ( ~ ! [SY538: $i,SY539: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY538 ) @ SY539 ) ) )
        | ! [SY540: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ SY540 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1957]) ).

thf(2040,plain,
    ! [SV72: $i] :
      ( ( SV72
       != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK8_SY541 @ SV72 ) ) @ ( sK17_SY774 @ SV72 ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[1958]) ).

thf(2041,plain,
    ! [SV208: $i,SV176: $i,SV131: $i,SV73: $i] :
      ( ( ! [SY825: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV73 ) @ SV131 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV176 ) @ SV208 ) ) ) @ ( red @ SY825 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ SV73 ) ) @ SV131 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ SV176 ) ) @ SV208 ) ) ) @ ( red @ SY825 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1959]) ).

thf(2042,plain,
    ! [SV177: $i,SV132: $i,SV74: $i,SV209: $i] :
      ( ( ! [SY826: $i,SY827: $i,SY828: $i,SY829: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV209 ) @ SY826 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY827 ) @ SY828 ) ) ) @ ( red @ SY829 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ SV209 @ SV74 @ SV132 @ SV177 ) ) @ SY826 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ SY827 @ SV74 @ SV132 @ SV177 ) ) @ SY828 ) ) ) @ ( red @ SY829 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1960]) ).

thf(2043,plain,
    ! [SV75: $i,SV178: $i,SV133: $i] :
      ( ( ( ~ ( hBOOL @ ( hext @ SV133 @ SV178 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hext @ SV178 @ SV75 ) )
          | ( hBOOL @ ( hext @ SV133 @ SV75 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1961]) ).

thf(2044,plain,
    ! [SV76: $i] :
      ( ( SV76
       != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK9_SY556 @ SV76 ) ) @ ( sK18_SY782 @ SV76 ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[1962]) ).

thf(2045,plain,
    ! [SV210: $i,SV179: $i,SV134: $i,SV77: $i] :
      ( ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV77 ) @ SV134 )
         != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV179 ) @ SV210 ) )
        | ~ ( ( SV77 != SV179 )
            | ( SV134 != SV210 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1963]) ).

thf(2046,plain,
    ! [SV211: $i,SV180: $i,SV135: $i,SV78: $i] :
      ( ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV78 ) @ SV135 )
         != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV180 ) @ SV211 ) )
        | ~ ( ( SV78 != SV180 )
            | ( SV135 != SV211 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1964]) ).

thf(2047,plain,
    ! [SV9: $i] :
      ( ( SV9
        = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK1_SY323 @ SV9 ) ) @ ( sK10_SY700 @ SV9 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1967]) ).

thf(2048,plain,
    ! [SV10: $i,SV140: $i,SV86: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV86 ) @ SV140 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV10 ) @ SV86 ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV10 ) @ SV140 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1968]) ).

thf(2049,plain,
    ! [SV11: $i] :
      ( ( SV11
       != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK2_SY327 @ SV11 ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( sK11_SY701 @ SV11 ) ) @ ( sK19_SY785 @ SV11 ) ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[1969]) ).

thf(2050,plain,
    ! [SV87: $i,SV12: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV12 ) @ SV87 ) )
        | ( hBOOL @ ( hAPP_P282169671l_bool @ SV87 @ SV12 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1970]) ).

thf(2051,plain,
    ! [SV12: $i,SV87: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV87 @ SV12 ) )
        | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV12 ) @ SV87 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1971]) ).

thf(2052,plain,
    ! [SV13: $i] :
      ( ( ( ~ ! [SY331: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ SY331 ) ) )
        = $true )
      | ( ( ! [SY332: $i,SY333: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY332 ) @ SY333 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1972]) ).

thf(2053,plain,
    ! [SV13: $i] :
      ( ( ( ~ ! [SY334: $i,SY335: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY334 ) @ SY335 ) ) ) )
        = $true )
      | ( ( ! [SY336: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ SY336 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1973]) ).

thf(2054,plain,
    ! [SV212: $i,SV183: $i,SV141: $i,SV88: $i,SV14: $i] :
      ( ( ! [SY830: $i,SY831: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV14 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV88 ) @ SV141 ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV183 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV212 ) @ SY830 ) ) ) ) @ ( red @ SY831 ) ) )
            | ( hBOOL @ ( hext @ SV88 @ SV212 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1974]) ).

thf(2055,plain,
    ! [SV15: $i,SV89: $i] :
      ( ( ( ! [SY832: $i,SY833: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV89 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK20_SY576 @ SV15 @ SV89 ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY832 ) @ SY833 ) ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P1708370145l_bool @ SV89 @ SV15 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[1975]) ).

thf(2056,plain,
    ! [SV16: $i,SV184: $i,SV142: $i,SV90: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV90 ) @ SV142 ) ) @ SV184 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV142 ) @ SV16 ) ) @ ( transi2024712006on_val @ SV184 ) ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV90 ) @ SV16 ) ) @ ( transi2024712006on_val @ SV184 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1976]) ).

thf(2057,plain,
    ! [SV17: $i,SV185: $i,SV143: $i,SV91: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV91 ) @ SV143 ) ) @ ( transi2024712006on_val @ SV185 ) ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV143 ) @ SV17 ) ) @ SV185 ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV91 ) @ SV17 ) ) @ ( transi2024712006on_val @ SV185 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1977]) ).

thf(2058,plain,
    ! [SV18: $i,SV213: $i,SV186: $i,SV144: $i,SV92: $i] :
      ( ( ! [SY834: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV92 ) @ SV144 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV186 ) @ SV213 ) ) ) @ ( red @ SY834 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ SV18 @ SV92 ) ) @ SV144 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ SV18 @ SV186 ) ) @ SV213 ) ) ) @ ( red @ SY834 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1978]) ).

thf(2059,plain,
    ! [SV19: $i,SV145: $i,SV93: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV93 ) @ SV145 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV19 ) @ SV93 ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV19 ) @ SV145 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1979]) ).

thf(2060,plain,
    ! [SV214: $i,SV187: $i,SV146: $i,SV94: $i,SV20: $i] :
      ( ( ( ( fun_up204312361on_val @ SV20 @ SV94 @ ( hAPP_val_option_val @ some_val @ SV146 ) )
         != ( fun_up204312361on_val @ SV187 @ SV94 @ ( hAPP_val_option_val @ some_val @ SV214 ) ) )
        | ( SV146 = SV214 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1980]) ).

thf(2061,plain,
    ! [SV95: $i,SV21: $i,SV147: $i,SV188: $i] :
      ( ( ~ ( ( SV188 != SV147 )
            | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV21 @ SV147 @ SV95 ) @ SV188 )
              = SV95 ) )
        | ~ ( ~ ( ( SV188 != SV147 ) )
            | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV21 @ SV147 @ SV95 ) @ SV188 )
              = ( hAPP_l207779698on_val @ SV21 @ SV188 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1981]) ).

thf(2062,plain,
    ! [SV22: $i] :
      ( ( ( ~ ~ ! [SY367: $i] :
                  ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ SY367 ) ) )
        = $true )
      | ( ( ~ ! [SY368: $i] :
                ~ ~ ! [SY369: $i] :
                      ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY368 ) @ SY369 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1982]) ).

thf(2063,plain,
    ! [SV22: $i] :
      ( ( ( ~ ~ ! [SY370: $i] :
                  ~ ~ ! [SY371: $i] :
                        ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY370 ) @ SY371 ) ) ) )
        = $true )
      | ( ( ~ ! [SY372: $i] :
                ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ SY372 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1983]) ).

thf(2064,plain,
    ! [SV23: $i,SV96: $i] :
      ( ( ~ ! [SY593: $i,SY594: $i] :
              ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY593 ) @ SY594 ) ) @ SV96 ) )
                    | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY593 ) @ SY594 ) ) @ SV23 ) ) )
                | ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY593 ) @ SY594 ) ) @ SV23 ) )
                    | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY593 ) @ SY594 ) ) @ SV96 ) ) ) )
        | ( SV96 = SV23 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1984]) ).

thf(2065,plain,
    ! [SV23: $i,SV96: $i] :
      ( ( ( SV96 != SV23 )
        | ! [SY595: $i,SY596: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY595 ) @ SY596 ) ) @ SV96 ) )
                  | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY595 ) @ SY596 ) ) @ SV23 ) ) )
              | ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY595 ) @ SY596 ) ) @ SV23 ) )
                  | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY595 ) @ SY596 ) ) @ SV96 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1985]) ).

thf(2066,plain,
    ! [SV97: $i,SV24: $i,SV215: $i,SV189: $i,SV148: $i] :
      ( ( ! [SY835: $i,SY836: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV148 ) @ SV189 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV215 ) @ SY835 ) ) ) @ ( red @ SY836 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ SV148 @ SV24 @ SV97 ) ) @ SV189 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ SV215 @ SV24 @ SV97 ) ) @ SY835 ) ) ) @ ( red @ SY836 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1986]) ).

thf(2067,plain,
    ! [SV216: $i,SV190: $i,SV149: $i,SV98: $i,SV25: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) ) @ ( transi2024712006on_val @ SV216 ) ) )
        | ~ ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 )
             != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) )
        | ~ ! [SY837: $i,SY838: $i] :
              ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY837 ) @ SY838 ) ) ) @ SV216 ) )
              | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY837 ) @ SY838 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) ) @ ( transi2024712006on_val @ SV216 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1987]) ).

thf(2068,plain,
    ! [SV150: $i,SV100: $i,SV27: $i] :
      ( ( ( ( hAPP_l207779698on_val @ SV27 @ SV100 )
          = ( hAPP_val_option_val @ some_val @ SV150 ) )
        = $false )
      | ( ( ( fun_up1149430426on_val @ SV27 @ SV100 @ ( hAPP_val_option_val @ some_val @ SV150 ) )
          = SV27 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1989]) ).

thf(2069,plain,
    ! [SV28: $i] :
      ( ( ( ! [SY393: $i] :
              ( SV28
             != ( hAPP_val_option_val @ some_val @ SY393 ) ) )
        = $false )
      | ( ( SV28 = none_val )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1990]) ).

thf(2070,plain,
    ! [SV191: $i,SV151: $i,SV101: $i,SV29: $i] :
      ( ( ~ ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV29 ) @ SV101 )
             != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV151 ) @ SV191 ) )
            | ~ ( ( SV29 != SV151 )
                | ( SV101 != SV191 ) ) )
        | ~ ( ~ ~ ( ( SV29 != SV151 )
                  | ( SV101 != SV191 ) )
            | ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV29 ) @ SV101 )
              = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV151 ) @ SV191 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1991]) ).

thf(2071,plain,
    ! [SV102: $i,SV30: $i] :
      ( ( ( ( hAPP_val_option_val @ some_val @ SV30 )
         != ( hAPP_val_option_val @ some_val @ SV102 ) )
        | ( SV30 = SV102 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1992]) ).

thf(2072,plain,
    ! [SV102: $i,SV30: $i] :
      ( ( ( SV30 != SV102 )
        | ( ( hAPP_val_option_val @ some_val @ SV30 )
          = ( hAPP_val_option_val @ some_val @ SV102 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1993]) ).

thf(2073,plain,
    ! [SV31: $i] :
      ( ( ( ~ ! [SY398: $i] :
                ( SV31
               != ( hAPP_val_option_val @ some_val @ SY398 ) ) )
        = $true )
      | ( ( SV31 = none_val )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1994]) ).

thf(2074,plain,
    ! [SV31: $i] :
      ( ( ( SV31 != none_val )
        = $true )
      | ( ( ! [SY399: $i] :
              ( SV31
             != ( hAPP_val_option_val @ some_val @ SY399 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1995]) ).

thf(2075,plain,
    ! [SV217: $i,SV192: $i,SV152: $i,SV103: $i,SV32: $i] :
      ( ( ( ( fun_up1149430426on_val @ SV32 @ SV103 @ ( hAPP_val_option_val @ some_val @ SV152 ) )
         != ( fun_up1149430426on_val @ SV192 @ SV103 @ ( hAPP_val_option_val @ some_val @ SV217 ) ) )
        | ( SV152 = SV217 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1996]) ).

thf(2076,plain,
    ! [SV33: $i,SV104: $i] :
      ( ( ( ! [SY839: $i,SY840: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV104 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK21_SY613 @ SV33 @ SV104 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY839 ) @ SY840 ) ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV104 @ SV33 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[1997]) ).

thf(2077,plain,
    ! [SV34: $i] :
      ( ( ( ~ ( ( SV34 != none_val ) ) )
        = $true )
      | ( ( ~ ! [SY408: $i] :
                ( SV34
               != ( hAPP_val_option_val @ some_val @ SY408 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1998]) ).

thf(2078,plain,
    ! [SV34: $i] :
      ( ( ( ~ ~ ! [SY409: $i] :
                  ( SV34
                 != ( hAPP_val_option_val @ some_val @ SY409 ) ) )
        = $true )
      | ( ( SV34 != none_val )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1999]) ).

thf(2079,plain,
    ! [SV35: $i,SV218: $i,SV193: $i,SV153: $i,SV105: $i] :
      ( ( ! [SY841: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV105 ) @ SV153 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV193 ) @ SV218 ) ) ) @ ( red @ SY841 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ SV105 @ SV35 ) ) @ SV153 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ SV193 @ SV35 ) ) @ SV218 ) ) ) @ ( red @ SY841 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2000]) ).

thf(2080,plain,
    ! [SV154: $i,SV106: $i,SV36: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV36 ) @ SV106 ) ) @ ( transi2024712006on_val @ SV154 ) ) )
        = $false )
      | ( ( ~ ( ( SV36 != SV106 ) )
          | ~ ! [SY729: $i] :
                ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV36 ) @ SY729 ) ) @ ( transi2024712006on_val @ SV154 ) ) )
                | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY729 ) @ SV106 ) ) @ SV154 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2001]) ).

thf(2081,plain,
    ! [SV155: $i,SV107: $i,SV37: $i,SV219: $i,SV194: $i] :
      ( ( ! [SY842: $i,SY843: $i,SY844: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV194 ) @ SV219 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY842 ) @ SY843 ) ) ) @ ( red @ SY844 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ SV194 @ SV37 @ SV107 @ SV155 ) ) @ SV219 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ SY842 @ SV37 @ SV107 @ SV155 ) ) @ SY843 ) ) ) @ ( red @ SY844 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2002]) ).

thf(2082,plain,
    ! [SV220: $i,SV195: $i,SV156: $i,SV108: $i,SV38: $i] :
      ( ( ~ ( ~ ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
                 != ( hAPP_val_option_val @ some_val @ SV220 ) )
                | ~ ( ( SV195 != SV108 )
                    | ( SV156 != SV220 ) )
                | ~ ( ~ ( ( SV195 != SV108 ) )
                    | ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
                     != ( hAPP_val_option_val @ some_val @ SV220 ) ) ) )
            | ~ ( ~ ( ~ ( ( SV195 != SV108 )
                        | ( SV156 != SV220 ) )
                    | ~ ( ~ ( ( SV195 != SV108 ) )
                        | ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
                         != ( hAPP_val_option_val @ some_val @ SV220 ) ) ) )
                | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
                  = ( hAPP_val_option_val @ some_val @ SV220 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2003]) ).

thf(2083,plain,
    ! [SV39: $i] :
      ( ( SV39
        = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( sK3_SY429 @ SV39 ) ) @ ( sK12_SY737 @ SV39 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2004]) ).

thf(2084,plain,
    ! [SV40: $i,SV221: $i,SV196: $i,SV157: $i,SV109: $i] :
      ( ( ! [SY845: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV109 ) @ SV157 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV196 ) @ SV221 ) ) ) @ ( red @ SY845 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ SV40 @ SV109 ) ) @ SV157 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ SV40 @ SV196 ) ) @ SV221 ) ) ) @ ( red @ SY845 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2005]) ).

thf(2085,plain,
    ! [SV158: $i,SV110: $i,SV41: $i] :
      ( ( ( ( hAPP_l207779698on_val @ SV41 @ SV110 )
          = SV158 )
        = $false )
      | ( ( ( fun_up1149430426on_val @ SV41 @ SV110 @ SV158 )
          = SV41 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2006]) ).

thf(2086,plain,
    ! [SV42: $i,SV111: $i] :
      ( ( ( ! [SY846: $i,SY847: $i,SY848: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV111 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK22_SY636 @ SV42 @ SV111 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY846 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY847 ) @ SY848 ) ) ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV111 @ SV42 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2007]) ).

thf(2087,plain,
    ! [SV43: $i,SV197: $i,SV159: $i,SV112: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV112 ) @ SV159 ) ) @ ( transi2024712006on_val @ SV197 ) ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV159 ) @ SV43 ) ) @ ( transi2024712006on_val @ SV197 ) ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV112 ) @ SV43 ) ) @ ( transi2024712006on_val @ SV197 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2008]) ).

thf(2088,plain,
    ! [SV198: $i,SV160: $i,SV113: $i,SV44: $i] :
      ( ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV44 ) @ SV113 )
         != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV160 ) @ SV198 ) )
        = $true )
      | ( ( ~ ( ( SV44 != SV160 )
              | ( SV113 != SV198 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2009]) ).

thf(2089,plain,
    ! [SV199: $i,SV161: $i,SV114: $i,SV45: $i] :
      ( ( ~ ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV45 ) @ SV114 )
             != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV161 ) @ SV199 ) )
            | ~ ( ( SV45 != SV161 )
                | ( SV114 != SV199 ) ) )
        | ~ ( ~ ~ ( ( SV45 != SV161 )
                  | ( SV114 != SV199 ) )
            | ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV45 ) @ SV114 )
              = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV161 ) @ SV199 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[2010]) ).

thf(2090,plain,
    ! [SV115: $i,SV46: $i,SV200: $i,SV162: $i] :
      ( ( ~ ( ( SV162 != SV200 )
            | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV46 @ SV200 @ SV115 ) @ SV162 )
              = SV115 ) )
        | ~ ( ~ ( ( SV162 != SV200 ) )
            | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV46 @ SV200 @ SV115 ) @ SV162 )
              = ( hAPP_l207779698on_val @ SV46 @ SV162 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[2011]) ).

thf(2091,plain,
    ! [SV47: $i,SV163: $i,SV116: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV116 ) @ SV163 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV163 ) @ SV47 ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV116 ) @ SV47 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2012]) ).

thf(2092,plain,
    ! [SV117: $i,SV48: $i] :
      ( ( ( ( bool @ SV48 )
         != ( bool @ SV117 ) )
        | ~ ( ~ ( ~ ( hBOOL @ SV48 )
                | ( hBOOL @ SV117 ) )
            | ~ ( ~ ( hBOOL @ SV117 )
                | ( hBOOL @ SV48 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2013]) ).

thf(2093,plain,
    ! [SV117: $i,SV48: $i] :
      ( ( ~ ~ ( ~ ( ~ ( hBOOL @ SV48 )
                  | ( hBOOL @ SV117 ) )
              | ~ ( ~ ( hBOOL @ SV117 )
                  | ( hBOOL @ SV48 ) ) )
        | ( ( bool @ SV48 )
          = ( bool @ SV117 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2014]) ).

thf(2094,plain,
    ! [SV49: $i] :
      ( ( ( ~ ~ ! [SY458: $i] :
                  ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ SY458 ) ) )
        = $true )
      | ( ( ~ ! [SY459: $i] :
                ~ ~ ! [SY460: $i] :
                      ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY459 ) @ SY460 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2015]) ).

thf(2095,plain,
    ! [SV49: $i] :
      ( ( ( ~ ~ ! [SY461: $i] :
                  ~ ~ ! [SY462: $i] :
                        ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY461 ) @ SY462 ) ) ) )
        = $true )
      | ( ( ~ ! [SY463: $i] :
                ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ SY463 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2016]) ).

thf(2096,plain,
    ! [SV118: $i,SV50: $i,SV222: $i,SV201: $i,SV164: $i] :
      ( ( ! [SY849: $i,SY850: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV164 ) @ SV201 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV222 ) @ SY849 ) ) ) @ ( red @ SY850 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ SV164 @ SV50 @ SV118 ) ) @ SV201 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ SV222 @ SV50 @ SV118 ) ) @ SY849 ) ) ) @ ( red @ SY850 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2017]) ).

thf(2097,plain,
    ! [SV202: $i,SV165: $i,SV119: $i,SV51: $i] :
      ( ( ~ ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV51 ) @ SV119 )
             != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV165 ) @ SV202 ) )
            | ~ ( ( SV51 != SV165 )
                | ( SV119 != SV202 ) ) )
        | ~ ( ~ ~ ( ( SV51 != SV165 )
                  | ( SV119 != SV202 ) )
            | ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV51 ) @ SV119 )
              = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV165 ) @ SV202 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[2018]) ).

thf(2098,plain,
    ! [SV120: $i,SV52: $i,SV203: $i,SV166: $i] :
      ( ( ( ~ ( ( SV166 != SV203 ) ) )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV52 @ SV203 @ SV120 ) @ SV166 )
          = ( hAPP_l207779698on_val @ SV52 @ SV166 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2019]) ).

thf(2099,plain,
    ! [SV167: $i,SV121: $i,SV53: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV53 ) @ ( semila751111325l_bool @ SV121 @ SV167 ) ) )
        = $false )
      | ( ( ~ ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV53 ) @ SV121 ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV53 ) @ SV167 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2020]) ).

thf(2100,plain,
    ! [SV122: $i,SV54: $i,SV223: $i,SV204: $i,SV168: $i] :
      ( ( ! [SY851: $i,SY852: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV168 ) @ SV204 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV223 ) @ SY851 ) ) ) @ ( red @ SY852 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ SV168 @ SV54 @ SV122 ) ) @ SV204 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ SV223 @ SV54 @ SV122 ) ) @ SY851 ) ) ) @ ( red @ SY852 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2021]) ).

thf(2101,plain,
    ! [SV55: $i] :
      ( ( ! [SY853: $i] :
            ( SV55
           != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK4_SY484 @ SV55 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK13_SY755 @ SV55 ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( sK23_SY814 @ SV55 ) ) @ SY853 ) ) ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[2022]) ).

thf(2102,plain,
    ! [SV56: $i] :
      ( ( SV56
        = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( sK5_SY488 @ SV56 ) ) @ ( sK14_SY758 @ SV56 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2023]) ).

thf(2103,plain,
    ! [SV123: $i,SV57: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( sK24_SY664 @ SV57 @ SV123 ) ) @ SV123 ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( sK24_SY664 @ SV57 @ SV123 ) ) @ SV57 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV123 ) @ SV57 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2024]) ).

thf(2104,plain,
    ! [SV124: $i,SV58: $i,SV224: $i,SV205: $i,SV169: $i] :
      ( ( ! [SY854: $i,SY855: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV169 ) @ SV205 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV224 ) @ SY854 ) ) ) @ ( red @ SY855 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ SV169 @ SV58 @ SV124 ) ) @ SV205 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ SV224 @ SV58 @ SV124 ) ) @ SY854 ) ) ) @ ( red @ SY855 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2025]) ).

thf(2105,plain,
    ! [SV59: $i] :
      ( ( ( ~ ~ ! [SY498: $i] :
                  ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ SY498 ) ) )
        = $true )
      | ( ( ~ ! [SY499: $i] :
                ~ ~ ! [SY500: $i] :
                      ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY499 ) @ SY500 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2026]) ).

thf(2106,plain,
    ! [SV59: $i] :
      ( ( ( ~ ~ ! [SY501: $i] :
                  ~ ~ ! [SY502: $i] :
                        ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY501 ) @ SY502 ) ) ) )
        = $true )
      | ( ( ~ ! [SY503: $i] :
                ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ SY503 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2027]) ).

thf(2107,plain,
    ! [SV60: $i,SV170: $i,SV125: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV125 ) @ SV170 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV60 ) @ SV125 ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV60 ) @ SV170 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2028]) ).

thf(2108,plain,
    ! [SV171: $i,SV126: $i,SV61: $i] :
      ( ( ~ ( ( ( fun_up1149430426on_val @ SV61 @ SV126 @ SV171 )
             != SV61 )
            | ( ( hAPP_l207779698on_val @ SV61 @ SV126 )
              = SV171 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2029]) ).

thf(2109,plain,
    ! [SV171: $i,SV126: $i,SV61: $i] :
      ( ( ~ ( ( ( hAPP_l207779698on_val @ SV61 @ SV126 )
             != SV171 )
            | ( ( fun_up1149430426on_val @ SV61 @ SV126 @ SV171 )
              = SV61 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2029]) ).

thf(2110,plain,
    ! [SV62: $i] :
      ( ( SV62
        = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK6_SY508 @ SV62 ) ) @ ( sK15_SY763 @ SV62 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2030]) ).

thf(2111,plain,
    ! [SV172: $i,SV127: $i,SV63: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV63 ) @ SV127 ) ) @ ( transi2024712006on_val @ SV172 ) ) )
        = $false )
      | ( ( ~ ( ( SV63 != SV127 ) )
          | ~ ! [SY764: $i] :
                ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV63 ) @ SY764 ) ) @ SV172 ) )
                | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY764 ) @ SV127 ) ) @ ( transi2024712006on_val @ SV172 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2031]) ).

thf(2112,plain,
    ! [SV173: $i,SV128: $i,SV65: $i,SV225: $i,SV206: $i] :
      ( ( ~ ( ( SV206 != SV225 ) )
        | ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ SV65 @ SV206 @ SV128 ) @ SV225 @ SV173 )
          = ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ SV65 @ SV225 @ SV173 ) @ SV206 @ SV128 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2032]) ).

thf(2113,plain,
    ! [SV66: $i,SV226: $i,SV207: $i,SV174: $i,SV129: $i] :
      ( ( ! [SY856: $i,SY857: $i,SY858: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV129 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV174 ) @ SV207 ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV226 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY856 ) @ SY857 ) ) ) ) @ ( red @ SY858 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV129 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV174 ) @ ( map_ad325961431ar_val @ SV66 @ SV207 ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV226 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY856 ) @ ( map_ad325961431ar_val @ SV66 @ SY857 ) ) ) ) ) @ ( red @ SY858 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2033]) ).

thf(2114,plain,
    ! [SV67: $i] :
      ( ( SV67
       != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK7_SY524 @ SV67 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK16_SY772 @ SV67 ) ) @ ( sK25_SY824 @ SV67 ) ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[2034]) ).

thf(2115,plain,
    ! [SV69: $i] :
      ( ( ( ~ ! [SY527: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ SY527 ) ) )
        = $true )
      | ( ( ! [SY528: $i,SY529: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY528 ) @ SY529 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2035]) ).

thf(2116,plain,
    ! [SV69: $i] :
      ( ( ( ~ ! [SY530: $i,SY531: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY530 ) @ SY531 ) ) ) )
        = $true )
      | ( ( ! [SY532: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ SY532 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2036]) ).

thf(2117,plain,
    ! [SV70: $i,SV175: $i,SV130: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV130 ) @ SV175 ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV130 ) @ SV70 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV130 ) @ ( semila751111325l_bool @ SV70 @ SV175 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2037]) ).

thf(2118,plain,
    ! [SV71: $i] :
      ( ( ( ~ ! [SY535: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ SY535 ) ) )
        = $true )
      | ( ( ! [SY536: $i,SY537: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY536 ) @ SY537 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2038]) ).

thf(2119,plain,
    ! [SV71: $i] :
      ( ( ( ~ ! [SY538: $i,SY539: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY538 ) @ SY539 ) ) ) )
        = $true )
      | ( ( ! [SY540: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ SY540 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2039]) ).

thf(2120,plain,
    ! [SV72: $i] :
      ( ( SV72
        = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK8_SY541 @ SV72 ) ) @ ( sK17_SY774 @ SV72 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2040]) ).

thf(2121,plain,
    ! [SV227: $i,SV208: $i,SV176: $i,SV131: $i,SV73: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV73 ) @ SV131 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV176 ) @ SV208 ) ) ) @ ( red @ SV227 ) ) )
        | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ SV73 ) ) @ SV131 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ SV176 ) ) @ SV208 ) ) ) @ ( red @ SV227 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2041]) ).

thf(2122,plain,
    ! [SV177: $i,SV132: $i,SV74: $i,SV228: $i,SV209: $i] :
      ( ( ! [SY859: $i,SY860: $i,SY861: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV209 ) @ SV228 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY859 ) @ SY860 ) ) ) @ ( red @ SY861 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ SV209 @ SV74 @ SV132 @ SV177 ) ) @ SV228 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ SY859 @ SV74 @ SV132 @ SV177 ) ) @ SY860 ) ) ) @ ( red @ SY861 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2042]) ).

thf(2123,plain,
    ! [SV75: $i,SV178: $i,SV133: $i] :
      ( ( ( hBOOL @ ( hext @ SV133 @ SV178 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hext @ SV178 @ SV75 ) )
          | ( hBOOL @ ( hext @ SV133 @ SV75 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2043]) ).

thf(2124,plain,
    ! [SV76: $i] :
      ( ( SV76
        = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK9_SY556 @ SV76 ) ) @ ( sK18_SY782 @ SV76 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2044]) ).

thf(2125,plain,
    ! [SV210: $i,SV179: $i,SV134: $i,SV77: $i] :
      ( ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV77 ) @ SV134 )
         != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV179 ) @ SV210 ) )
        = $true )
      | ( ( ~ ( ( SV77 != SV179 )
              | ( SV134 != SV210 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2045]) ).

thf(2126,plain,
    ! [SV211: $i,SV180: $i,SV135: $i,SV78: $i] :
      ( ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV78 ) @ SV135 )
         != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV180 ) @ SV211 ) )
        = $true )
      | ( ( ~ ( ( SV78 != SV180 )
              | ( SV135 != SV211 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2046]) ).

thf(2127,plain,
    ! [SV140: $i,SV86: $i,SV10: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV10 ) @ SV86 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV10 ) @ SV140 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV86 ) @ SV140 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2048]) ).

thf(2128,plain,
    ! [SV11: $i] :
      ( ( SV11
        = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK2_SY327 @ SV11 ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( sK11_SY701 @ SV11 ) ) @ ( sK19_SY785 @ SV11 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2049]) ).

thf(2129,plain,
    ! [SV87: $i,SV12: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV12 ) @ SV87 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV87 @ SV12 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2050]) ).

thf(2130,plain,
    ! [SV12: $i,SV87: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV87 @ SV12 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV12 ) @ SV87 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2051]) ).

thf(2131,plain,
    ! [SV13: $i] :
      ( ( ( ! [SY331: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ SY331 ) ) )
        = $false )
      | ( ( ! [SY332: $i,SY333: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY332 ) @ SY333 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2052]) ).

thf(2132,plain,
    ! [SV13: $i] :
      ( ( ( ! [SY334: $i,SY335: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY334 ) @ SY335 ) ) ) )
        = $false )
      | ( ( ! [SY336: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ SY336 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2053]) ).

thf(2133,plain,
    ! [SV229: $i,SV212: $i,SV183: $i,SV141: $i,SV88: $i,SV14: $i] :
      ( ( ! [SY862: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV14 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV88 ) @ SV141 ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV183 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV212 ) @ SV229 ) ) ) ) @ ( red @ SY862 ) ) )
            | ( hBOOL @ ( hext @ SV88 @ SV212 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2054]) ).

thf(2134,plain,
    ! [SV15: $i,SV89: $i] :
      ( ( ( ! [SY863: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV89 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK20_SY576 @ SV15 @ SV89 ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( sK26_SY832 @ SV15 @ SV89 ) ) @ SY863 ) ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P1708370145l_bool @ SV89 @ SV15 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2055]) ).

thf(2135,plain,
    ! [SV16: $i,SV184: $i,SV142: $i,SV90: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV90 ) @ SV142 ) ) @ SV184 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV142 ) @ SV16 ) ) @ ( transi2024712006on_val @ SV184 ) ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV90 ) @ SV16 ) ) @ ( transi2024712006on_val @ SV184 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2056]) ).

thf(2136,plain,
    ! [SV17: $i,SV185: $i,SV143: $i,SV91: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV91 ) @ SV143 ) ) @ ( transi2024712006on_val @ SV185 ) ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV143 ) @ SV17 ) ) @ SV185 ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV91 ) @ SV17 ) ) @ ( transi2024712006on_val @ SV185 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2057]) ).

thf(2137,plain,
    ! [SV18: $i,SV230: $i,SV213: $i,SV186: $i,SV144: $i,SV92: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV92 ) @ SV144 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV186 ) @ SV213 ) ) ) @ ( red @ SV230 ) ) )
        | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ SV18 @ SV92 ) ) @ SV144 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ SV18 @ SV186 ) ) @ SV213 ) ) ) @ ( red @ SV230 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2058]) ).

thf(2138,plain,
    ! [SV145: $i,SV93: $i,SV19: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV19 ) @ SV93 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV19 ) @ SV145 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV93 ) @ SV145 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2059]) ).

thf(2139,plain,
    ! [SV214: $i,SV187: $i,SV146: $i,SV94: $i,SV20: $i] :
      ( ( ( ( fun_up204312361on_val @ SV20 @ SV94 @ ( hAPP_val_option_val @ some_val @ SV146 ) )
         != ( fun_up204312361on_val @ SV187 @ SV94 @ ( hAPP_val_option_val @ some_val @ SV214 ) ) )
        = $true )
      | ( ( SV146 = SV214 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2060]) ).

thf(2140,plain,
    ! [SV95: $i,SV21: $i,SV147: $i,SV188: $i] :
      ( ( ~ ( ( SV188 != SV147 )
            | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV21 @ SV147 @ SV95 ) @ SV188 )
              = SV95 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2061]) ).

thf(2141,plain,
    ! [SV95: $i,SV21: $i,SV147: $i,SV188: $i] :
      ( ( ~ ( ~ ( ( SV188 != SV147 ) )
            | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV21 @ SV147 @ SV95 ) @ SV188 )
              = ( hAPP_l207779698on_val @ SV21 @ SV188 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2061]) ).

thf(2142,plain,
    ! [SV22: $i] :
      ( ( ( ~ ! [SY367: $i] :
                ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ SY367 ) ) )
        = $false )
      | ( ( ~ ! [SY368: $i] :
                ~ ~ ! [SY369: $i] :
                      ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY368 ) @ SY369 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2062]) ).

thf(2143,plain,
    ! [SV22: $i] :
      ( ( ( ~ ! [SY370: $i] :
                ~ ~ ! [SY371: $i] :
                      ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY370 ) @ SY371 ) ) ) )
        = $false )
      | ( ( ~ ! [SY372: $i] :
                ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ SY372 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2063]) ).

thf(2144,plain,
    ! [SV23: $i,SV96: $i] :
      ( ( ( ~ ! [SY593: $i,SY594: $i] :
                ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY593 ) @ SY594 ) ) @ SV96 ) )
                      | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY593 ) @ SY594 ) ) @ SV23 ) ) )
                  | ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY593 ) @ SY594 ) ) @ SV23 ) )
                      | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY593 ) @ SY594 ) ) @ SV96 ) ) ) ) )
        = $true )
      | ( ( SV96 = SV23 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2064]) ).

thf(2145,plain,
    ! [SV23: $i,SV96: $i] :
      ( ( ( SV96 != SV23 )
        = $true )
      | ( ( ! [SY595: $i,SY596: $i] :
              ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY595 ) @ SY596 ) ) @ SV96 ) )
                    | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY595 ) @ SY596 ) ) @ SV23 ) ) )
                | ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY595 ) @ SY596 ) ) @ SV23 ) )
                    | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY595 ) @ SY596 ) ) @ SV96 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2065]) ).

thf(2146,plain,
    ! [SV97: $i,SV24: $i,SV231: $i,SV215: $i,SV189: $i,SV148: $i] :
      ( ( ! [SY864: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV148 ) @ SV189 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV215 ) @ SV231 ) ) ) @ ( red @ SY864 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ SV148 @ SV24 @ SV97 ) ) @ SV189 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ SV215 @ SV24 @ SV97 ) ) @ SV231 ) ) ) @ ( red @ SY864 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2066]) ).

thf(2147,plain,
    ! [SV216: $i,SV190: $i,SV149: $i,SV98: $i,SV25: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) ) @ ( transi2024712006on_val @ SV216 ) ) ) )
        = $true )
      | ( ( ~ ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 )
               != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) )
          | ~ ! [SY837: $i,SY838: $i] :
                ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY837 ) @ SY838 ) ) ) @ SV216 ) )
                | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY837 ) @ SY838 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) ) @ ( transi2024712006on_val @ SV216 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2067]) ).

thf(2148,plain,
    ! [SV28: $i] :
      ( ( ( SV28
         != ( hAPP_val_option_val @ some_val @ ( sK27_SY393 @ SV28 ) ) )
        = $false )
      | ( ( SV28 = none_val )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2069]) ).

thf(2149,plain,
    ! [SV191: $i,SV151: $i,SV101: $i,SV29: $i] :
      ( ( ~ ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV29 ) @ SV101 )
             != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV151 ) @ SV191 ) )
            | ~ ( ( SV29 != SV151 )
                | ( SV101 != SV191 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2070]) ).

thf(2150,plain,
    ! [SV191: $i,SV101: $i,SV151: $i,SV29: $i] :
      ( ( ~ ( ~ ~ ( ( SV29 != SV151 )
                  | ( SV101 != SV191 ) )
            | ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV29 ) @ SV101 )
              = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV151 ) @ SV191 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2070]) ).

thf(2151,plain,
    ! [SV102: $i,SV30: $i] :
      ( ( ( ( hAPP_val_option_val @ some_val @ SV30 )
         != ( hAPP_val_option_val @ some_val @ SV102 ) )
        = $true )
      | ( ( SV30 = SV102 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2071]) ).

thf(2152,plain,
    ! [SV102: $i,SV30: $i] :
      ( ( ( SV30 != SV102 )
        = $true )
      | ( ( ( hAPP_val_option_val @ some_val @ SV30 )
          = ( hAPP_val_option_val @ some_val @ SV102 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2072]) ).

thf(2153,plain,
    ! [SV31: $i] :
      ( ( ( ! [SY398: $i] :
              ( SV31
             != ( hAPP_val_option_val @ some_val @ SY398 ) ) )
        = $false )
      | ( ( SV31 = none_val )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2073]) ).

thf(2154,plain,
    ! [SV31: $i] :
      ( ( ( SV31 = none_val )
        = $false )
      | ( ( ! [SY399: $i] :
              ( SV31
             != ( hAPP_val_option_val @ some_val @ SY399 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2074]) ).

thf(2155,plain,
    ! [SV217: $i,SV192: $i,SV152: $i,SV103: $i,SV32: $i] :
      ( ( ( ( fun_up1149430426on_val @ SV32 @ SV103 @ ( hAPP_val_option_val @ some_val @ SV152 ) )
         != ( fun_up1149430426on_val @ SV192 @ SV103 @ ( hAPP_val_option_val @ some_val @ SV217 ) ) )
        = $true )
      | ( ( SV152 = SV217 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2075]) ).

thf(2156,plain,
    ! [SV33: $i,SV104: $i] :
      ( ( ( ! [SY865: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV104 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK21_SY613 @ SV33 @ SV104 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK28_SY839 @ SV33 @ SV104 ) ) @ SY865 ) ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV104 @ SV33 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2076]) ).

thf(2157,plain,
    ! [SV34: $i] :
      ( ( ( SV34 != none_val )
        = $false )
      | ( ( ~ ! [SY408: $i] :
                ( SV34
               != ( hAPP_val_option_val @ some_val @ SY408 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2077]) ).

thf(2158,plain,
    ! [SV34: $i] :
      ( ( ( ~ ! [SY409: $i] :
                ( SV34
               != ( hAPP_val_option_val @ some_val @ SY409 ) ) )
        = $false )
      | ( ( SV34 != none_val )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2078]) ).

thf(2159,plain,
    ! [SV35: $i,SV232: $i,SV218: $i,SV193: $i,SV153: $i,SV105: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV105 ) @ SV153 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV193 ) @ SV218 ) ) ) @ ( red @ SV232 ) ) )
        | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ SV105 @ SV35 ) ) @ SV153 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ SV193 @ SV35 ) ) @ SV218 ) ) ) @ ( red @ SV232 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2079]) ).

thf(2160,plain,
    ! [SV154: $i,SV106: $i,SV36: $i] :
      ( ( ( ~ ( ( SV36 != SV106 ) ) )
        = $true )
      | ( ( ~ ! [SY729: $i] :
                ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV36 ) @ SY729 ) ) @ ( transi2024712006on_val @ SV154 ) ) )
                | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY729 ) @ SV106 ) ) @ SV154 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV36 ) @ SV106 ) ) @ ( transi2024712006on_val @ SV154 ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2080]) ).

thf(2161,plain,
    ! [SV155: $i,SV107: $i,SV37: $i,SV233: $i,SV219: $i,SV194: $i] :
      ( ( ! [SY866: $i,SY867: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV194 ) @ SV219 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV233 ) @ SY866 ) ) ) @ ( red @ SY867 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ SV194 @ SV37 @ SV107 @ SV155 ) ) @ SV219 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ SV233 @ SV37 @ SV107 @ SV155 ) ) @ SY866 ) ) ) @ ( red @ SY867 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2081]) ).

thf(2162,plain,
    ! [SV220: $i,SV195: $i,SV156: $i,SV108: $i,SV38: $i] :
      ( ( ~ ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
             != ( hAPP_val_option_val @ some_val @ SV220 ) )
            | ~ ( ( SV195 != SV108 )
                | ( SV156 != SV220 ) )
            | ~ ( ~ ( ( SV195 != SV108 ) )
                | ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
                 != ( hAPP_val_option_val @ some_val @ SV220 ) ) ) )
        | ~ ( ~ ( ~ ( ( SV195 != SV108 )
                    | ( SV156 != SV220 ) )
                | ~ ( ~ ( ( SV195 != SV108 ) )
                    | ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
                     != ( hAPP_val_option_val @ some_val @ SV220 ) ) ) )
            | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
              = ( hAPP_val_option_val @ some_val @ SV220 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[2082]) ).

thf(2163,plain,
    ! [SV40: $i,SV234: $i,SV221: $i,SV196: $i,SV157: $i,SV109: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV109 ) @ SV157 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV196 ) @ SV221 ) ) ) @ ( red @ SV234 ) ) )
        | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ SV40 @ SV109 ) ) @ SV157 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ SV40 @ SV196 ) ) @ SV221 ) ) ) @ ( red @ SV234 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2084]) ).

thf(2164,plain,
    ! [SV42: $i,SV111: $i] :
      ( ( ( ! [SY868: $i,SY869: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV111 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK22_SY636 @ SV42 @ SV111 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK29_SY846 @ SV42 @ SV111 ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY868 ) @ SY869 ) ) ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV111 @ SV42 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2086]) ).

thf(2165,plain,
    ! [SV43: $i,SV197: $i,SV159: $i,SV112: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV112 ) @ SV159 ) ) @ ( transi2024712006on_val @ SV197 ) ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV159 ) @ SV43 ) ) @ ( transi2024712006on_val @ SV197 ) ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV112 ) @ SV43 ) ) @ ( transi2024712006on_val @ SV197 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2087]) ).

thf(2166,plain,
    ! [SV198: $i,SV160: $i,SV113: $i,SV44: $i] :
      ( ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV44 ) @ SV113 )
          = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV160 ) @ SV198 ) )
        = $false )
      | ( ( ~ ( ( SV44 != SV160 )
              | ( SV113 != SV198 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2088]) ).

thf(2167,plain,
    ! [SV199: $i,SV161: $i,SV114: $i,SV45: $i] :
      ( ( ~ ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV45 ) @ SV114 )
             != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV161 ) @ SV199 ) )
            | ~ ( ( SV45 != SV161 )
                | ( SV114 != SV199 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2089]) ).

thf(2168,plain,
    ! [SV199: $i,SV114: $i,SV161: $i,SV45: $i] :
      ( ( ~ ( ~ ~ ( ( SV45 != SV161 )
                  | ( SV114 != SV199 ) )
            | ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV45 ) @ SV114 )
              = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV161 ) @ SV199 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2089]) ).

thf(2169,plain,
    ! [SV115: $i,SV46: $i,SV200: $i,SV162: $i] :
      ( ( ~ ( ( SV162 != SV200 )
            | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV46 @ SV200 @ SV115 ) @ SV162 )
              = SV115 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2090]) ).

thf(2170,plain,
    ! [SV115: $i,SV46: $i,SV200: $i,SV162: $i] :
      ( ( ~ ( ~ ( ( SV162 != SV200 ) )
            | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV46 @ SV200 @ SV115 ) @ SV162 )
              = ( hAPP_l207779698on_val @ SV46 @ SV162 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2090]) ).

thf(2171,plain,
    ! [SV116: $i,SV47: $i,SV163: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV163 ) @ SV47 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV116 ) @ SV47 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV116 ) @ SV163 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2091]) ).

thf(2172,plain,
    ! [SV117: $i,SV48: $i] :
      ( ( ( ( bool @ SV48 )
         != ( bool @ SV117 ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ SV48 )
                  | ( hBOOL @ SV117 ) )
              | ~ ( ~ ( hBOOL @ SV117 )
                  | ( hBOOL @ SV48 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2092]) ).

thf(2173,plain,
    ! [SV117: $i,SV48: $i] :
      ( ( ( ~ ~ ( ~ ( ~ ( hBOOL @ SV48 )
                    | ( hBOOL @ SV117 ) )
                | ~ ( ~ ( hBOOL @ SV117 )
                    | ( hBOOL @ SV48 ) ) ) )
        = $true )
      | ( ( ( bool @ SV48 )
          = ( bool @ SV117 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2093]) ).

thf(2174,plain,
    ! [SV49: $i] :
      ( ( ( ~ ! [SY458: $i] :
                ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ SY458 ) ) )
        = $false )
      | ( ( ~ ! [SY459: $i] :
                ~ ~ ! [SY460: $i] :
                      ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY459 ) @ SY460 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2094]) ).

thf(2175,plain,
    ! [SV49: $i] :
      ( ( ( ~ ! [SY461: $i] :
                ~ ~ ! [SY462: $i] :
                      ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY461 ) @ SY462 ) ) ) )
        = $false )
      | ( ( ~ ! [SY463: $i] :
                ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ SY463 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2095]) ).

thf(2176,plain,
    ! [SV118: $i,SV50: $i,SV235: $i,SV222: $i,SV201: $i,SV164: $i] :
      ( ( ! [SY870: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV164 ) @ SV201 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV222 ) @ SV235 ) ) ) @ ( red @ SY870 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ SV164 @ SV50 @ SV118 ) ) @ SV201 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ SV222 @ SV50 @ SV118 ) ) @ SV235 ) ) ) @ ( red @ SY870 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2096]) ).

thf(2177,plain,
    ! [SV202: $i,SV165: $i,SV119: $i,SV51: $i] :
      ( ( ~ ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV51 ) @ SV119 )
             != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV165 ) @ SV202 ) )
            | ~ ( ( SV51 != SV165 )
                | ( SV119 != SV202 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2097]) ).

thf(2178,plain,
    ! [SV202: $i,SV119: $i,SV165: $i,SV51: $i] :
      ( ( ~ ( ~ ~ ( ( SV51 != SV165 )
                  | ( SV119 != SV202 ) )
            | ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV51 ) @ SV119 )
              = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV165 ) @ SV202 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2097]) ).

thf(2179,plain,
    ! [SV120: $i,SV52: $i,SV203: $i,SV166: $i] :
      ( ( ( SV166 != SV203 )
        = $false )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV52 @ SV203 @ SV120 ) @ SV166 )
          = ( hAPP_l207779698on_val @ SV52 @ SV166 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2098]) ).

thf(2180,plain,
    ! [SV167: $i,SV121: $i,SV53: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV53 ) @ SV121 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV53 ) @ SV167 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV53 ) @ ( semila751111325l_bool @ SV121 @ SV167 ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2099]) ).

thf(2181,plain,
    ! [SV122: $i,SV54: $i,SV236: $i,SV223: $i,SV204: $i,SV168: $i] :
      ( ( ! [SY871: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV168 ) @ SV204 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV223 ) @ SV236 ) ) ) @ ( red @ SY871 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ SV168 @ SV54 @ SV122 ) ) @ SV204 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ SV223 @ SV54 @ SV122 ) ) @ SV236 ) ) ) @ ( red @ SY871 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2100]) ).

thf(2182,plain,
    ! [SV55: $i] :
      ( ( SV55
       != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK4_SY484 @ SV55 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK13_SY755 @ SV55 ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( sK23_SY814 @ SV55 ) ) @ ( sK30_SY853 @ SV55 ) ) ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[2101]) ).

thf(2183,plain,
    ! [SV123: $i,SV57: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( sK24_SY664 @ SV57 @ SV123 ) ) @ SV123 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV123 ) @ SV57 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2103]) ).

thf(2184,plain,
    ! [SV123: $i,SV57: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( sK24_SY664 @ SV57 @ SV123 ) ) @ SV57 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV123 ) @ SV57 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2103]) ).

thf(2185,plain,
    ! [SV124: $i,SV58: $i,SV237: $i,SV224: $i,SV205: $i,SV169: $i] :
      ( ( ! [SY872: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV169 ) @ SV205 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV224 ) @ SV237 ) ) ) @ ( red @ SY872 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ SV169 @ SV58 @ SV124 ) ) @ SV205 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ SV224 @ SV58 @ SV124 ) ) @ SV237 ) ) ) @ ( red @ SY872 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2104]) ).

thf(2186,plain,
    ! [SV59: $i] :
      ( ( ( ~ ! [SY498: $i] :
                ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ SY498 ) ) )
        = $false )
      | ( ( ~ ! [SY499: $i] :
                ~ ~ ! [SY500: $i] :
                      ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY499 ) @ SY500 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2105]) ).

thf(2187,plain,
    ! [SV59: $i] :
      ( ( ( ~ ! [SY501: $i] :
                ~ ~ ! [SY502: $i] :
                      ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY501 ) @ SY502 ) ) ) )
        = $false )
      | ( ( ~ ! [SY503: $i] :
                ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ SY503 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2106]) ).

thf(2188,plain,
    ! [SV170: $i,SV125: $i,SV60: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV60 ) @ SV125 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV60 ) @ SV170 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV125 ) @ SV170 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2107]) ).

thf(2189,plain,
    ! [SV171: $i,SV126: $i,SV61: $i] :
      ( ( ( ( fun_up1149430426on_val @ SV61 @ SV126 @ SV171 )
         != SV61 )
        | ( ( hAPP_l207779698on_val @ SV61 @ SV126 )
          = SV171 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2108]) ).

thf(2190,plain,
    ! [SV171: $i,SV126: $i,SV61: $i] :
      ( ( ( ( hAPP_l207779698on_val @ SV61 @ SV126 )
         != SV171 )
        | ( ( fun_up1149430426on_val @ SV61 @ SV126 @ SV171 )
          = SV61 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2109]) ).

thf(2191,plain,
    ! [SV172: $i,SV127: $i,SV63: $i] :
      ( ( ( ~ ( ( SV63 != SV127 ) ) )
        = $true )
      | ( ( ~ ! [SY764: $i] :
                ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV63 ) @ SY764 ) ) @ SV172 ) )
                | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY764 ) @ SV127 ) ) @ ( transi2024712006on_val @ SV172 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV63 ) @ SV127 ) ) @ ( transi2024712006on_val @ SV172 ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2111]) ).

thf(2192,plain,
    ! [SV173: $i,SV128: $i,SV65: $i,SV225: $i,SV206: $i] :
      ( ( ( ~ ( ( SV206 != SV225 ) ) )
        = $true )
      | ( ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ SV65 @ SV206 @ SV128 ) @ SV225 @ SV173 )
          = ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ SV65 @ SV225 @ SV173 ) @ SV206 @ SV128 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2112]) ).

thf(2193,plain,
    ! [SV66: $i,SV238: $i,SV226: $i,SV207: $i,SV174: $i,SV129: $i] :
      ( ( ! [SY873: $i,SY874: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV129 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV174 ) @ SV207 ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV226 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV238 ) @ SY873 ) ) ) ) @ ( red @ SY874 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV129 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV174 ) @ ( map_ad325961431ar_val @ SV66 @ SV207 ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV226 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV238 ) @ ( map_ad325961431ar_val @ SV66 @ SY873 ) ) ) ) ) @ ( red @ SY874 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2113]) ).

thf(2194,plain,
    ! [SV67: $i] :
      ( ( SV67
        = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK7_SY524 @ SV67 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK16_SY772 @ SV67 ) ) @ ( sK25_SY824 @ SV67 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2114]) ).

thf(2195,plain,
    ! [SV69: $i] :
      ( ( ( ! [SY527: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ SY527 ) ) )
        = $false )
      | ( ( ! [SY528: $i,SY529: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY528 ) @ SY529 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2115]) ).

thf(2196,plain,
    ! [SV69: $i] :
      ( ( ( ! [SY530: $i,SY531: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY530 ) @ SY531 ) ) ) )
        = $false )
      | ( ( ! [SY532: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ SY532 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2116]) ).

thf(2197,plain,
    ! [SV70: $i,SV175: $i,SV130: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV130 ) @ SV175 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV130 ) @ ( semila751111325l_bool @ SV70 @ SV175 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2117]) ).

thf(2198,plain,
    ! [SV175: $i,SV70: $i,SV130: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV130 ) @ SV70 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV130 ) @ ( semila751111325l_bool @ SV70 @ SV175 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2117]) ).

thf(2199,plain,
    ! [SV71: $i] :
      ( ( ( ! [SY535: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ SY535 ) ) )
        = $false )
      | ( ( ! [SY536: $i,SY537: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY536 ) @ SY537 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2118]) ).

thf(2200,plain,
    ! [SV71: $i] :
      ( ( ( ! [SY538: $i,SY539: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY538 ) @ SY539 ) ) ) )
        = $false )
      | ( ( ! [SY540: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ SY540 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2119]) ).

thf(2201,plain,
    ! [SV227: $i,SV208: $i,SV176: $i,SV131: $i,SV73: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV73 ) @ SV131 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV176 ) @ SV208 ) ) ) @ ( red @ SV227 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ SV73 ) ) @ SV131 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ SV176 ) ) @ SV208 ) ) ) @ ( red @ SV227 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2121]) ).

thf(2202,plain,
    ! [SV177: $i,SV132: $i,SV74: $i,SV239: $i,SV228: $i,SV209: $i] :
      ( ( ! [SY875: $i,SY876: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV209 ) @ SV228 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV239 ) @ SY875 ) ) ) @ ( red @ SY876 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ SV209 @ SV74 @ SV132 @ SV177 ) ) @ SV228 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ SV239 @ SV74 @ SV132 @ SV177 ) ) @ SY875 ) ) ) @ ( red @ SY876 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2122]) ).

thf(2203,plain,
    ! [SV133: $i,SV75: $i,SV178: $i] :
      ( ( ( ~ ( hBOOL @ ( hext @ SV178 @ SV75 ) ) )
        = $true )
      | ( ( hBOOL @ ( hext @ SV133 @ SV75 ) )
        = $true )
      | ( ( hBOOL @ ( hext @ SV133 @ SV178 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2123]) ).

thf(2204,plain,
    ! [SV210: $i,SV179: $i,SV134: $i,SV77: $i] :
      ( ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV77 ) @ SV134 )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV179 ) @ SV210 ) )
        = $false )
      | ( ( ~ ( ( SV77 != SV179 )
              | ( SV134 != SV210 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2125]) ).

thf(2205,plain,
    ! [SV211: $i,SV180: $i,SV135: $i,SV78: $i] :
      ( ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV78 ) @ SV135 )
          = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV180 ) @ SV211 ) )
        = $false )
      | ( ( ~ ( ( SV78 != SV180 )
              | ( SV135 != SV211 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2126]) ).

thf(2206,plain,
    ! [SV140: $i,SV86: $i,SV10: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV10 ) @ SV86 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV10 ) @ SV140 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV86 ) @ SV140 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2127]) ).

thf(2207,plain,
    ! [SV87: $i,SV12: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV12 ) @ SV87 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV87 @ SV12 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2129]) ).

thf(2208,plain,
    ! [SV12: $i,SV87: $i] :
      ( ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV87 @ SV12 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV12 ) @ SV87 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2130]) ).

thf(2209,plain,
    ! [SV13: $i] :
      ( ( ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ ( sK31_SY331 @ SV13 ) ) )
        = $false )
      | ( ( ! [SY332: $i,SY333: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY332 ) @ SY333 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2131]) ).

thf(2210,plain,
    ! [SV13: $i] :
      ( ( ( ! [SY877: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK32_SY334 @ SV13 ) ) @ SY877 ) ) ) )
        = $false )
      | ( ( ! [SY336: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ SY336 ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2132]) ).

thf(2211,plain,
    ! [SV240: $i,SV229: $i,SV212: $i,SV183: $i,SV141: $i,SV88: $i,SV14: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV14 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV88 ) @ SV141 ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV183 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV212 ) @ SV229 ) ) ) ) @ ( red @ SV240 ) ) )
        | ( hBOOL @ ( hext @ SV88 @ SV212 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2133]) ).

thf(2212,plain,
    ! [SV15: $i,SV89: $i] :
      ( ( ( hBOOL @ ( hAPP_P1708370145l_bool @ SV89 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK20_SY576 @ SV15 @ SV89 ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( sK26_SY832 @ SV15 @ SV89 ) ) @ ( sK33_SY863 @ SV15 @ SV89 ) ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P1708370145l_bool @ SV89 @ SV15 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2134]) ).

thf(2213,plain,
    ! [SV90: $i,SV184: $i,SV16: $i,SV142: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV142 ) @ SV16 ) ) @ ( transi2024712006on_val @ SV184 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV90 ) @ SV16 ) ) @ ( transi2024712006on_val @ SV184 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV90 ) @ SV142 ) ) @ SV184 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2135]) ).

thf(2214,plain,
    ! [SV91: $i,SV185: $i,SV17: $i,SV143: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV143 ) @ SV17 ) ) @ SV185 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV91 ) @ SV17 ) ) @ ( transi2024712006on_val @ SV185 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV91 ) @ SV143 ) ) @ ( transi2024712006on_val @ SV185 ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2136]) ).

thf(2215,plain,
    ! [SV18: $i,SV230: $i,SV213: $i,SV186: $i,SV144: $i,SV92: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV92 ) @ SV144 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV186 ) @ SV213 ) ) ) @ ( red @ SV230 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ SV18 @ SV92 ) ) @ SV144 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ SV18 @ SV186 ) ) @ SV213 ) ) ) @ ( red @ SV230 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2137]) ).

thf(2216,plain,
    ! [SV145: $i,SV93: $i,SV19: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV19 ) @ SV93 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV19 ) @ SV145 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV93 ) @ SV145 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2138]) ).

thf(2217,plain,
    ! [SV214: $i,SV187: $i,SV146: $i,SV94: $i,SV20: $i] :
      ( ( ( ( fun_up204312361on_val @ SV20 @ SV94 @ ( hAPP_val_option_val @ some_val @ SV146 ) )
          = ( fun_up204312361on_val @ SV187 @ SV94 @ ( hAPP_val_option_val @ some_val @ SV214 ) ) )
        = $false )
      | ( ( SV146 = SV214 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2139]) ).

thf(2218,plain,
    ! [SV95: $i,SV21: $i,SV147: $i,SV188: $i] :
      ( ( ( SV188 != SV147 )
        | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV21 @ SV147 @ SV95 ) @ SV188 )
          = SV95 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2140]) ).

thf(2219,plain,
    ! [SV95: $i,SV21: $i,SV147: $i,SV188: $i] :
      ( ( ~ ( ( SV188 != SV147 ) )
        | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV21 @ SV147 @ SV95 ) @ SV188 )
          = ( hAPP_l207779698on_val @ SV21 @ SV188 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2141]) ).

thf(2220,plain,
    ! [SV22: $i] :
      ( ( ( ! [SY367: $i] :
              ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ SY367 ) ) )
        = $true )
      | ( ( ~ ! [SY368: $i] :
                ~ ~ ! [SY369: $i] :
                      ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY368 ) @ SY369 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2142]) ).

thf(2221,plain,
    ! [SV22: $i] :
      ( ( ( ! [SY370: $i] :
              ~ ~ ! [SY371: $i] :
                    ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY370 ) @ SY371 ) ) ) )
        = $true )
      | ( ( ~ ! [SY372: $i] :
                ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ SY372 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2143]) ).

thf(2222,plain,
    ! [SV23: $i,SV96: $i] :
      ( ( ( ! [SY593: $i,SY594: $i] :
              ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY593 ) @ SY594 ) ) @ SV96 ) )
                    | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY593 ) @ SY594 ) ) @ SV23 ) ) )
                | ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY593 ) @ SY594 ) ) @ SV23 ) )
                    | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY593 ) @ SY594 ) ) @ SV96 ) ) ) ) )
        = $false )
      | ( ( SV96 = SV23 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2144]) ).

thf(2223,plain,
    ! [SV23: $i,SV96: $i] :
      ( ( ( SV96 = SV23 )
        = $false )
      | ( ( ! [SY595: $i,SY596: $i] :
              ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY595 ) @ SY596 ) ) @ SV96 ) )
                    | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY595 ) @ SY596 ) ) @ SV23 ) ) )
                | ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY595 ) @ SY596 ) ) @ SV23 ) )
                    | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY595 ) @ SY596 ) ) @ SV96 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2145]) ).

thf(2224,plain,
    ! [SV97: $i,SV24: $i,SV241: $i,SV231: $i,SV215: $i,SV189: $i,SV148: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV148 ) @ SV189 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV215 ) @ SV231 ) ) ) @ ( red @ SV241 ) ) )
        | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ SV148 @ SV24 @ SV97 ) ) @ SV189 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ SV215 @ SV24 @ SV97 ) ) @ SV231 ) ) ) @ ( red @ SV241 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2146]) ).

thf(2225,plain,
    ! [SV216: $i,SV190: $i,SV149: $i,SV98: $i,SV25: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) ) @ ( transi2024712006on_val @ SV216 ) ) )
        = $false )
      | ( ( ~ ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 )
               != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) )
          | ~ ! [SY837: $i,SY838: $i] :
                ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY837 ) @ SY838 ) ) ) @ SV216 ) )
                | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY837 ) @ SY838 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) ) @ ( transi2024712006on_val @ SV216 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2147]) ).

thf(2226,plain,
    ! [SV28: $i] :
      ( ( ( SV28
          = ( hAPP_val_option_val @ some_val @ ( sK27_SY393 @ SV28 ) ) )
        = $true )
      | ( ( SV28 = none_val )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2148]) ).

thf(2227,plain,
    ! [SV191: $i,SV151: $i,SV101: $i,SV29: $i] :
      ( ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV29 ) @ SV101 )
         != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV151 ) @ SV191 ) )
        | ~ ( ( SV29 != SV151 )
            | ( SV101 != SV191 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2149]) ).

thf(2228,plain,
    ! [SV191: $i,SV101: $i,SV151: $i,SV29: $i] :
      ( ( ~ ~ ( ( SV29 != SV151 )
              | ( SV101 != SV191 ) )
        | ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV29 ) @ SV101 )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV151 ) @ SV191 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2150]) ).

thf(2229,plain,
    ! [SV102: $i,SV30: $i] :
      ( ( ( ( hAPP_val_option_val @ some_val @ SV30 )
          = ( hAPP_val_option_val @ some_val @ SV102 ) )
        = $false )
      | ( ( SV30 = SV102 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2151]) ).

thf(2230,plain,
    ! [SV102: $i,SV30: $i] :
      ( ( ( SV30 = SV102 )
        = $false )
      | ( ( ( hAPP_val_option_val @ some_val @ SV30 )
          = ( hAPP_val_option_val @ some_val @ SV102 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2152]) ).

thf(2231,plain,
    ! [SV31: $i] :
      ( ( ( SV31
         != ( hAPP_val_option_val @ some_val @ ( sK34_SY398 @ SV31 ) ) )
        = $false )
      | ( ( SV31 = none_val )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2153]) ).

thf(2232,plain,
    ! [SV242: $i,SV31: $i] :
      ( ( ( SV31
         != ( hAPP_val_option_val @ some_val @ SV242 ) )
        = $true )
      | ( ( SV31 = none_val )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2154]) ).

thf(2233,plain,
    ! [SV217: $i,SV192: $i,SV152: $i,SV103: $i,SV32: $i] :
      ( ( ( ( fun_up1149430426on_val @ SV32 @ SV103 @ ( hAPP_val_option_val @ some_val @ SV152 ) )
          = ( fun_up1149430426on_val @ SV192 @ SV103 @ ( hAPP_val_option_val @ some_val @ SV217 ) ) )
        = $false )
      | ( ( SV152 = SV217 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2155]) ).

thf(2234,plain,
    ! [SV33: $i,SV104: $i] :
      ( ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV104 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK21_SY613 @ SV33 @ SV104 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK28_SY839 @ SV33 @ SV104 ) ) @ ( sK35_SY865 @ SV33 @ SV104 ) ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV104 @ SV33 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2156]) ).

thf(2235,plain,
    ! [SV34: $i] :
      ( ( ( SV34 = none_val )
        = $true )
      | ( ( ~ ! [SY408: $i] :
                ( SV34
               != ( hAPP_val_option_val @ some_val @ SY408 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2157]) ).

thf(2236,plain,
    ! [SV34: $i] :
      ( ( ( ! [SY409: $i] :
              ( SV34
             != ( hAPP_val_option_val @ some_val @ SY409 ) ) )
        = $true )
      | ( ( SV34 != none_val )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2158]) ).

thf(2237,plain,
    ! [SV35: $i,SV232: $i,SV218: $i,SV193: $i,SV153: $i,SV105: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV105 ) @ SV153 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV193 ) @ SV218 ) ) ) @ ( red @ SV232 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ SV105 @ SV35 ) ) @ SV153 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ SV193 @ SV35 ) ) @ SV218 ) ) ) @ ( red @ SV232 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2159]) ).

thf(2238,plain,
    ! [SV154: $i,SV106: $i,SV36: $i] :
      ( ( ( SV36 != SV106 )
        = $false )
      | ( ( ~ ! [SY729: $i] :
                ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV36 ) @ SY729 ) ) @ ( transi2024712006on_val @ SV154 ) ) )
                | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY729 ) @ SV106 ) ) @ SV154 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV36 ) @ SV106 ) ) @ ( transi2024712006on_val @ SV154 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2160]) ).

thf(2239,plain,
    ! [SV155: $i,SV107: $i,SV37: $i,SV243: $i,SV233: $i,SV219: $i,SV194: $i] :
      ( ( ! [SY878: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV194 ) @ SV219 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV233 ) @ SV243 ) ) ) @ ( red @ SY878 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ SV194 @ SV37 @ SV107 @ SV155 ) ) @ SV219 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ SV233 @ SV37 @ SV107 @ SV155 ) ) @ SV243 ) ) ) @ ( red @ SY878 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2161]) ).

thf(2240,plain,
    ! [SV220: $i,SV195: $i,SV156: $i,SV108: $i,SV38: $i] :
      ( ( ~ ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
             != ( hAPP_val_option_val @ some_val @ SV220 ) )
            | ~ ( ( SV195 != SV108 )
                | ( SV156 != SV220 ) )
            | ~ ( ~ ( ( SV195 != SV108 ) )
                | ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
                 != ( hAPP_val_option_val @ some_val @ SV220 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2162]) ).

thf(2241,plain,
    ! [SV38: $i,SV220: $i,SV156: $i,SV108: $i,SV195: $i] :
      ( ( ~ ( ~ ( ~ ( ( SV195 != SV108 )
                    | ( SV156 != SV220 ) )
                | ~ ( ~ ( ( SV195 != SV108 ) )
                    | ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
                     != ( hAPP_val_option_val @ some_val @ SV220 ) ) ) )
            | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
              = ( hAPP_val_option_val @ some_val @ SV220 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2162]) ).

thf(2242,plain,
    ! [SV40: $i,SV234: $i,SV221: $i,SV196: $i,SV157: $i,SV109: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV109 ) @ SV157 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV196 ) @ SV221 ) ) ) @ ( red @ SV234 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ SV40 @ SV109 ) ) @ SV157 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ SV40 @ SV196 ) ) @ SV221 ) ) ) @ ( red @ SV234 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2163]) ).

thf(2243,plain,
    ! [SV42: $i,SV111: $i] :
      ( ( ( ! [SY879: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV111 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK22_SY636 @ SV42 @ SV111 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK29_SY846 @ SV42 @ SV111 ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( sK36_SY868 @ SV42 @ SV111 ) ) @ SY879 ) ) ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV111 @ SV42 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2164]) ).

thf(2244,plain,
    ! [SV112: $i,SV197: $i,SV43: $i,SV159: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV159 ) @ SV43 ) ) @ ( transi2024712006on_val @ SV197 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV112 ) @ SV43 ) ) @ ( transi2024712006on_val @ SV197 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV112 ) @ SV159 ) ) @ ( transi2024712006on_val @ SV197 ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2165]) ).

thf(2245,plain,
    ! [SV198: $i,SV113: $i,SV160: $i,SV44: $i] :
      ( ( ( ( SV44 != SV160 )
          | ( SV113 != SV198 ) )
        = $false )
      | ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV44 ) @ SV113 )
          = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV160 ) @ SV198 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2166]) ).

thf(2246,plain,
    ! [SV199: $i,SV161: $i,SV114: $i,SV45: $i] :
      ( ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV45 ) @ SV114 )
         != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV161 ) @ SV199 ) )
        | ~ ( ( SV45 != SV161 )
            | ( SV114 != SV199 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2167]) ).

thf(2247,plain,
    ! [SV199: $i,SV114: $i,SV161: $i,SV45: $i] :
      ( ( ~ ~ ( ( SV45 != SV161 )
              | ( SV114 != SV199 ) )
        | ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV45 ) @ SV114 )
          = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV161 ) @ SV199 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2168]) ).

thf(2248,plain,
    ! [SV115: $i,SV46: $i,SV200: $i,SV162: $i] :
      ( ( ( SV162 != SV200 )
        | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV46 @ SV200 @ SV115 ) @ SV162 )
          = SV115 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2169]) ).

thf(2249,plain,
    ! [SV115: $i,SV46: $i,SV200: $i,SV162: $i] :
      ( ( ~ ( ( SV162 != SV200 ) )
        | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV46 @ SV200 @ SV115 ) @ SV162 )
          = ( hAPP_l207779698on_val @ SV46 @ SV162 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2170]) ).

thf(2250,plain,
    ! [SV116: $i,SV47: $i,SV163: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV163 ) @ SV47 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV116 ) @ SV47 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV116 ) @ SV163 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2171]) ).

thf(2251,plain,
    ! [SV117: $i,SV48: $i] :
      ( ( ( ( bool @ SV48 )
          = ( bool @ SV117 ) )
        = $false )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ SV48 )
                  | ( hBOOL @ SV117 ) )
              | ~ ( ~ ( hBOOL @ SV117 )
                  | ( hBOOL @ SV48 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2172]) ).

thf(2252,plain,
    ! [SV117: $i,SV48: $i] :
      ( ( ( ~ ( ~ ( ~ ( hBOOL @ SV48 )
                  | ( hBOOL @ SV117 ) )
              | ~ ( ~ ( hBOOL @ SV117 )
                  | ( hBOOL @ SV48 ) ) ) )
        = $false )
      | ( ( ( bool @ SV48 )
          = ( bool @ SV117 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2173]) ).

thf(2253,plain,
    ! [SV49: $i] :
      ( ( ( ! [SY458: $i] :
              ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ SY458 ) ) )
        = $true )
      | ( ( ~ ! [SY459: $i] :
                ~ ~ ! [SY460: $i] :
                      ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY459 ) @ SY460 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2174]) ).

thf(2254,plain,
    ! [SV49: $i] :
      ( ( ( ! [SY461: $i] :
              ~ ~ ! [SY462: $i] :
                    ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY461 ) @ SY462 ) ) ) )
        = $true )
      | ( ( ~ ! [SY463: $i] :
                ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ SY463 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2175]) ).

thf(2255,plain,
    ! [SV118: $i,SV50: $i,SV244: $i,SV235: $i,SV222: $i,SV201: $i,SV164: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV164 ) @ SV201 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV222 ) @ SV235 ) ) ) @ ( red @ SV244 ) ) )
        | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ SV164 @ SV50 @ SV118 ) ) @ SV201 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ SV222 @ SV50 @ SV118 ) ) @ SV235 ) ) ) @ ( red @ SV244 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2176]) ).

thf(2256,plain,
    ! [SV202: $i,SV165: $i,SV119: $i,SV51: $i] :
      ( ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV51 ) @ SV119 )
         != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV165 ) @ SV202 ) )
        | ~ ( ( SV51 != SV165 )
            | ( SV119 != SV202 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2177]) ).

thf(2257,plain,
    ! [SV202: $i,SV119: $i,SV165: $i,SV51: $i] :
      ( ( ~ ~ ( ( SV51 != SV165 )
              | ( SV119 != SV202 ) )
        | ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV51 ) @ SV119 )
          = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV165 ) @ SV202 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2178]) ).

thf(2258,plain,
    ! [SV120: $i,SV52: $i,SV203: $i,SV166: $i] :
      ( ( ( SV166 = SV203 )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV52 @ SV203 @ SV120 ) @ SV166 )
          = ( hAPP_l207779698on_val @ SV52 @ SV166 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2179]) ).

thf(2259,plain,
    ! [SV167: $i,SV121: $i,SV53: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV53 ) @ SV121 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV53 ) @ SV167 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV53 ) @ ( semila751111325l_bool @ SV121 @ SV167 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2180]) ).

thf(2260,plain,
    ! [SV122: $i,SV54: $i,SV245: $i,SV236: $i,SV223: $i,SV204: $i,SV168: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV168 ) @ SV204 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV223 ) @ SV236 ) ) ) @ ( red @ SV245 ) ) )
        | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ SV168 @ SV54 @ SV122 ) ) @ SV204 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ SV223 @ SV54 @ SV122 ) ) @ SV236 ) ) ) @ ( red @ SV245 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2181]) ).

thf(2261,plain,
    ! [SV55: $i] :
      ( ( SV55
        = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK4_SY484 @ SV55 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK13_SY755 @ SV55 ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( sK23_SY814 @ SV55 ) ) @ ( sK30_SY853 @ SV55 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2182]) ).

thf(2262,plain,
    ! [SV123: $i,SV57: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( sK24_SY664 @ SV57 @ SV123 ) ) @ SV123 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV123 ) @ SV57 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2183]) ).

thf(2263,plain,
    ! [SV124: $i,SV58: $i,SV246: $i,SV237: $i,SV224: $i,SV205: $i,SV169: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV169 ) @ SV205 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV224 ) @ SV237 ) ) ) @ ( red @ SV246 ) ) )
        | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ SV169 @ SV58 @ SV124 ) ) @ SV205 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ SV224 @ SV58 @ SV124 ) ) @ SV237 ) ) ) @ ( red @ SV246 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2185]) ).

thf(2264,plain,
    ! [SV59: $i] :
      ( ( ( ! [SY498: $i] :
              ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ SY498 ) ) )
        = $true )
      | ( ( ~ ! [SY499: $i] :
                ~ ~ ! [SY500: $i] :
                      ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY499 ) @ SY500 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2186]) ).

thf(2265,plain,
    ! [SV59: $i] :
      ( ( ( ! [SY501: $i] :
              ~ ~ ! [SY502: $i] :
                    ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY501 ) @ SY502 ) ) ) )
        = $true )
      | ( ( ~ ! [SY503: $i] :
                ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ SY503 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2187]) ).

thf(2266,plain,
    ! [SV170: $i,SV125: $i,SV60: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV60 ) @ SV125 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV60 ) @ SV170 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ SV125 ) @ SV170 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2188]) ).

thf(2267,plain,
    ! [SV171: $i,SV126: $i,SV61: $i] :
      ( ( ( ( fun_up1149430426on_val @ SV61 @ SV126 @ SV171 )
         != SV61 )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ SV61 @ SV126 )
          = SV171 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2189]) ).

thf(2268,plain,
    ! [SV171: $i,SV126: $i,SV61: $i] :
      ( ( ( ( hAPP_l207779698on_val @ SV61 @ SV126 )
         != SV171 )
        = $true )
      | ( ( ( fun_up1149430426on_val @ SV61 @ SV126 @ SV171 )
          = SV61 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2190]) ).

thf(2269,plain,
    ! [SV172: $i,SV127: $i,SV63: $i] :
      ( ( ( SV63 != SV127 )
        = $false )
      | ( ( ~ ! [SY764: $i] :
                ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV63 ) @ SY764 ) ) @ SV172 ) )
                | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY764 ) @ SV127 ) ) @ ( transi2024712006on_val @ SV172 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV63 ) @ SV127 ) ) @ ( transi2024712006on_val @ SV172 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2191]) ).

thf(2270,plain,
    ! [SV173: $i,SV128: $i,SV65: $i,SV225: $i,SV206: $i] :
      ( ( ( SV206 != SV225 )
        = $false )
      | ( ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ SV65 @ SV206 @ SV128 ) @ SV225 @ SV173 )
          = ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ SV65 @ SV225 @ SV173 ) @ SV206 @ SV128 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2192]) ).

thf(2271,plain,
    ! [SV66: $i,SV247: $i,SV238: $i,SV226: $i,SV207: $i,SV174: $i,SV129: $i] :
      ( ( ! [SY880: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV129 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV174 ) @ SV207 ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV226 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV238 ) @ SV247 ) ) ) ) @ ( red @ SY880 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV129 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV174 ) @ ( map_ad325961431ar_val @ SV66 @ SV207 ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV226 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV238 ) @ ( map_ad325961431ar_val @ SV66 @ SV247 ) ) ) ) ) @ ( red @ SY880 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2193]) ).

thf(2272,plain,
    ! [SV69: $i] :
      ( ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ ( sK37_SY527 @ SV69 ) ) )
        = $false )
      | ( ( ! [SY528: $i,SY529: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY528 ) @ SY529 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2195]) ).

thf(2273,plain,
    ! [SV69: $i] :
      ( ( ( ! [SY881: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK38_SY530 @ SV69 ) ) @ SY881 ) ) ) )
        = $false )
      | ( ( ! [SY532: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ SY532 ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2196]) ).

thf(2274,plain,
    ! [SV70: $i,SV175: $i,SV130: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV130 ) @ SV175 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV130 ) @ ( semila751111325l_bool @ SV70 @ SV175 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2197]) ).

thf(2275,plain,
    ! [SV71: $i] :
      ( ( ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ ( sK39_SY535 @ SV71 ) ) )
        = $false )
      | ( ( ! [SY536: $i,SY537: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY536 ) @ SY537 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2199]) ).

thf(2276,plain,
    ! [SV71: $i] :
      ( ( ( ! [SY882: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( sK40_SY538 @ SV71 ) ) @ SY882 ) ) ) )
        = $false )
      | ( ( ! [SY540: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ SY540 ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2200]) ).

thf(2277,plain,
    ! [SV227: $i,SV208: $i,SV176: $i,SV131: $i,SV73: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV73 ) @ SV131 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV176 ) @ SV208 ) ) ) @ ( red @ SV227 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ SV73 ) ) @ SV131 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ SV176 ) ) @ SV208 ) ) ) @ ( red @ SV227 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2201]) ).

thf(2278,plain,
    ! [SV177: $i,SV132: $i,SV74: $i,SV248: $i,SV239: $i,SV228: $i,SV209: $i] :
      ( ( ! [SY883: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV209 ) @ SV228 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV239 ) @ SV248 ) ) ) @ ( red @ SY883 ) ) )
            | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ SV209 @ SV74 @ SV132 @ SV177 ) ) @ SV228 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ SV239 @ SV74 @ SV132 @ SV177 ) ) @ SV248 ) ) ) @ ( red @ SY883 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2202]) ).

thf(2279,plain,
    ! [SV133: $i,SV75: $i,SV178: $i] :
      ( ( ( hBOOL @ ( hext @ SV178 @ SV75 ) )
        = $false )
      | ( ( hBOOL @ ( hext @ SV133 @ SV75 ) )
        = $true )
      | ( ( hBOOL @ ( hext @ SV133 @ SV178 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2203]) ).

thf(2280,plain,
    ! [SV210: $i,SV134: $i,SV179: $i,SV77: $i] :
      ( ( ( ( SV77 != SV179 )
          | ( SV134 != SV210 ) )
        = $false )
      | ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV77 ) @ SV134 )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV179 ) @ SV210 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2204]) ).

thf(2281,plain,
    ! [SV211: $i,SV135: $i,SV180: $i,SV78: $i] :
      ( ( ( ( SV78 != SV180 )
          | ( SV135 != SV211 ) )
        = $false )
      | ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV78 ) @ SV135 )
          = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV180 ) @ SV211 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2205]) ).

thf(2282,plain,
    ! [SV249: $i,SV13: $i] :
      ( ( ( ! [SY884: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV249 ) @ SY884 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ ( sK31_SY331 @ SV13 ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2209]) ).

thf(2283,plain,
    ! [SV13: $i] :
      ( ( ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK32_SY334 @ SV13 ) ) @ ( sK41_SY877 @ SV13 ) ) ) )
        = $false )
      | ( ( ! [SY336: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ SY336 ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2210]) ).

thf(2284,plain,
    ! [SV240: $i,SV229: $i,SV212: $i,SV183: $i,SV141: $i,SV88: $i,SV14: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV14 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV88 ) @ SV141 ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV183 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV212 ) @ SV229 ) ) ) ) @ ( red @ SV240 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hext @ SV88 @ SV212 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2211]) ).

thf(2285,plain,
    ! [SV90: $i,SV184: $i,SV16: $i,SV142: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV142 ) @ SV16 ) ) @ ( transi2024712006on_val @ SV184 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV90 ) @ SV16 ) ) @ ( transi2024712006on_val @ SV184 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV90 ) @ SV142 ) ) @ SV184 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2213]) ).

thf(2286,plain,
    ! [SV91: $i,SV185: $i,SV17: $i,SV143: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV143 ) @ SV17 ) ) @ SV185 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV91 ) @ SV17 ) ) @ ( transi2024712006on_val @ SV185 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV91 ) @ SV143 ) ) @ ( transi2024712006on_val @ SV185 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2214]) ).

thf(2287,plain,
    ! [SV18: $i,SV230: $i,SV213: $i,SV186: $i,SV144: $i,SV92: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV92 ) @ SV144 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV186 ) @ SV213 ) ) ) @ ( red @ SV230 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ SV18 @ SV92 ) ) @ SV144 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ SV18 @ SV186 ) ) @ SV213 ) ) ) @ ( red @ SV230 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2215]) ).

thf(2288,plain,
    ! [SV95: $i,SV21: $i,SV147: $i,SV188: $i] :
      ( ( ( SV188 != SV147 )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV21 @ SV147 @ SV95 ) @ SV188 )
          = SV95 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2218]) ).

thf(2289,plain,
    ! [SV95: $i,SV21: $i,SV147: $i,SV188: $i] :
      ( ( ( ~ ( ( SV188 != SV147 ) ) )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV21 @ SV147 @ SV95 ) @ SV188 )
          = ( hAPP_l207779698on_val @ SV21 @ SV188 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2219]) ).

thf(2290,plain,
    ! [SV250: $i,SV22: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ SV250 ) ) )
        = $true )
      | ( ( ~ ! [SY368: $i] :
                ~ ~ ! [SY369: $i] :
                      ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY368 ) @ SY369 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2220]) ).

thf(2291,plain,
    ! [SV251: $i,SV22: $i] :
      ( ( ( ~ ~ ! [SY885: $i] :
                  ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV251 ) @ SY885 ) ) ) )
        = $true )
      | ( ( ~ ! [SY372: $i] :
                ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ SY372 ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2221]) ).

thf(2292,plain,
    ! [SV96: $i,SV23: $i] :
      ( ( ( ! [SY886: $i] :
              ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ SY886 ) ) @ SV96 ) )
                    | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ SY886 ) ) @ SV23 ) ) )
                | ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ SY886 ) ) @ SV23 ) )
                    | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ SY886 ) ) @ SV96 ) ) ) ) )
        = $false )
      | ( ( SV96 = SV23 )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2222]) ).

thf(2293,plain,
    ! [SV23: $i,SV96: $i,SV252: $i] :
      ( ( ( ! [SY887: $i] :
              ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV252 ) @ SY887 ) ) @ SV96 ) )
                    | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV252 ) @ SY887 ) ) @ SV23 ) ) )
                | ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV252 ) @ SY887 ) ) @ SV23 ) )
                    | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV252 ) @ SY887 ) ) @ SV96 ) ) ) ) )
        = $true )
      | ( ( SV96 = SV23 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2223]) ).

thf(2294,plain,
    ! [SV97: $i,SV24: $i,SV241: $i,SV231: $i,SV215: $i,SV189: $i,SV148: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV148 ) @ SV189 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV215 ) @ SV231 ) ) ) @ ( red @ SV241 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ SV148 @ SV24 @ SV97 ) ) @ SV189 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ SV215 @ SV24 @ SV97 ) ) @ SV231 ) ) ) @ ( red @ SV241 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2224]) ).

thf(2295,plain,
    ! [SV216: $i,SV190: $i,SV149: $i,SV98: $i,SV25: $i] :
      ( ( ( ~ ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 )
               != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) ) )
        = $true )
      | ( ( ~ ! [SY837: $i,SY838: $i] :
                ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY837 ) @ SY838 ) ) ) @ SV216 ) )
                | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY837 ) @ SY838 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) ) @ ( transi2024712006on_val @ SV216 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) ) @ ( transi2024712006on_val @ SV216 ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2225]) ).

thf(2296,plain,
    ! [SV191: $i,SV151: $i,SV101: $i,SV29: $i] :
      ( ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV29 ) @ SV101 )
         != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV151 ) @ SV191 ) )
        = $true )
      | ( ( ~ ( ( SV29 != SV151 )
              | ( SV101 != SV191 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2227]) ).

thf(2297,plain,
    ! [SV191: $i,SV101: $i,SV151: $i,SV29: $i] :
      ( ( ( ~ ~ ( ( SV29 != SV151 )
                | ( SV101 != SV191 ) ) )
        = $true )
      | ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV29 ) @ SV101 )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV151 ) @ SV191 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2228]) ).

thf(2298,plain,
    ! [SV31: $i] :
      ( ( ( SV31
          = ( hAPP_val_option_val @ some_val @ ( sK34_SY398 @ SV31 ) ) )
        = $true )
      | ( ( SV31 = none_val )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2231]) ).

thf(2299,plain,
    ! [SV242: $i,SV31: $i] :
      ( ( ( SV31
          = ( hAPP_val_option_val @ some_val @ SV242 ) )
        = $false )
      | ( ( SV31 = none_val )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2232]) ).

thf(2300,plain,
    ! [SV34: $i] :
      ( ( ( ! [SY408: $i] :
              ( SV34
             != ( hAPP_val_option_val @ some_val @ SY408 ) ) )
        = $false )
      | ( ( SV34 = none_val )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2235]) ).

thf(2301,plain,
    ! [SV253: $i,SV34: $i] :
      ( ( ( SV34
         != ( hAPP_val_option_val @ some_val @ SV253 ) )
        = $true )
      | ( ( SV34 != none_val )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2236]) ).

thf(2302,plain,
    ! [SV35: $i,SV232: $i,SV218: $i,SV193: $i,SV153: $i,SV105: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV105 ) @ SV153 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV193 ) @ SV218 ) ) ) @ ( red @ SV232 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ SV105 @ SV35 ) ) @ SV153 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ SV193 @ SV35 ) ) @ SV218 ) ) ) @ ( red @ SV232 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2237]) ).

thf(2303,plain,
    ! [SV154: $i,SV106: $i,SV36: $i] :
      ( ( ( SV36 = SV106 )
        = $true )
      | ( ( ~ ! [SY729: $i] :
                ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV36 ) @ SY729 ) ) @ ( transi2024712006on_val @ SV154 ) ) )
                | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY729 ) @ SV106 ) ) @ SV154 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV36 ) @ SV106 ) ) @ ( transi2024712006on_val @ SV154 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2238]) ).

thf(2304,plain,
    ! [SV155: $i,SV107: $i,SV37: $i,SV254: $i,SV243: $i,SV233: $i,SV219: $i,SV194: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV194 ) @ SV219 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV233 ) @ SV243 ) ) ) @ ( red @ SV254 ) ) )
        | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ SV194 @ SV37 @ SV107 @ SV155 ) ) @ SV219 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ SV233 @ SV37 @ SV107 @ SV155 ) ) @ SV243 ) ) ) @ ( red @ SV254 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2239]) ).

thf(2305,plain,
    ! [SV220: $i,SV195: $i,SV156: $i,SV108: $i,SV38: $i] :
      ( ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
         != ( hAPP_val_option_val @ some_val @ SV220 ) )
        | ~ ( ( SV195 != SV108 )
            | ( SV156 != SV220 ) )
        | ~ ( ~ ( ( SV195 != SV108 ) )
            | ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
             != ( hAPP_val_option_val @ some_val @ SV220 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2240]) ).

thf(2306,plain,
    ! [SV38: $i,SV220: $i,SV156: $i,SV108: $i,SV195: $i] :
      ( ( ~ ( ~ ( ( SV195 != SV108 )
                | ( SV156 != SV220 ) )
            | ~ ( ~ ( ( SV195 != SV108 ) )
                | ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
                 != ( hAPP_val_option_val @ some_val @ SV220 ) ) ) )
        | ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2241]) ).

thf(2307,plain,
    ! [SV40: $i,SV234: $i,SV221: $i,SV196: $i,SV157: $i,SV109: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV109 ) @ SV157 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV196 ) @ SV221 ) ) ) @ ( red @ SV234 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ SV40 @ SV109 ) ) @ SV157 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ SV40 @ SV196 ) ) @ SV221 ) ) ) @ ( red @ SV234 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2242]) ).

thf(2308,plain,
    ! [SV42: $i,SV111: $i] :
      ( ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV111 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK22_SY636 @ SV42 @ SV111 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK29_SY846 @ SV42 @ SV111 ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( sK36_SY868 @ SV42 @ SV111 ) ) @ ( sK43_SY879 @ SV42 @ SV111 ) ) ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV111 @ SV42 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2243]) ).

thf(2309,plain,
    ! [SV112: $i,SV197: $i,SV43: $i,SV159: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV159 ) @ SV43 ) ) @ ( transi2024712006on_val @ SV197 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV112 ) @ SV43 ) ) @ ( transi2024712006on_val @ SV197 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV112 ) @ SV159 ) ) @ ( transi2024712006on_val @ SV197 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2244]) ).

thf(2310,plain,
    ! [SV198: $i,SV113: $i,SV160: $i,SV44: $i] :
      ( ( ( SV44 != SV160 )
        = $false )
      | ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV44 ) @ SV113 )
          = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV160 ) @ SV198 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2245]) ).

thf(2311,plain,
    ! [SV160: $i,SV44: $i,SV198: $i,SV113: $i] :
      ( ( ( SV113 != SV198 )
        = $false )
      | ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV44 ) @ SV113 )
          = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV160 ) @ SV198 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2245]) ).

thf(2312,plain,
    ! [SV199: $i,SV161: $i,SV114: $i,SV45: $i] :
      ( ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV45 ) @ SV114 )
         != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV161 ) @ SV199 ) )
        = $true )
      | ( ( ~ ( ( SV45 != SV161 )
              | ( SV114 != SV199 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2246]) ).

thf(2313,plain,
    ! [SV199: $i,SV114: $i,SV161: $i,SV45: $i] :
      ( ( ( ~ ~ ( ( SV45 != SV161 )
                | ( SV114 != SV199 ) ) )
        = $true )
      | ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV45 ) @ SV114 )
          = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV161 ) @ SV199 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2247]) ).

thf(2314,plain,
    ! [SV115: $i,SV46: $i,SV200: $i,SV162: $i] :
      ( ( ( SV162 != SV200 )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV46 @ SV200 @ SV115 ) @ SV162 )
          = SV115 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2248]) ).

thf(2315,plain,
    ! [SV115: $i,SV46: $i,SV200: $i,SV162: $i] :
      ( ( ( ~ ( ( SV162 != SV200 ) ) )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV46 @ SV200 @ SV115 ) @ SV162 )
          = ( hAPP_l207779698on_val @ SV46 @ SV162 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2249]) ).

thf(2316,plain,
    ! [SV117: $i,SV48: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV48 )
              | ( hBOOL @ SV117 ) )
          | ~ ( ~ ( hBOOL @ SV117 )
              | ( hBOOL @ SV48 ) ) )
        = $false )
      | ( ( ( bool @ SV48 )
          = ( bool @ SV117 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2251]) ).

thf(2317,plain,
    ! [SV117: $i,SV48: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV48 )
              | ( hBOOL @ SV117 ) )
          | ~ ( ~ ( hBOOL @ SV117 )
              | ( hBOOL @ SV48 ) ) )
        = $true )
      | ( ( ( bool @ SV48 )
          = ( bool @ SV117 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2252]) ).

thf(2318,plain,
    ! [SV255: $i,SV49: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ SV255 ) ) )
        = $true )
      | ( ( ~ ! [SY459: $i] :
                ~ ~ ! [SY460: $i] :
                      ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY459 ) @ SY460 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2253]) ).

thf(2319,plain,
    ! [SV256: $i,SV49: $i] :
      ( ( ( ~ ~ ! [SY888: $i] :
                  ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV256 ) @ SY888 ) ) ) )
        = $true )
      | ( ( ~ ! [SY463: $i] :
                ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ SY463 ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2254]) ).

thf(2320,plain,
    ! [SV118: $i,SV50: $i,SV244: $i,SV235: $i,SV222: $i,SV201: $i,SV164: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV164 ) @ SV201 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV222 ) @ SV235 ) ) ) @ ( red @ SV244 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ SV164 @ SV50 @ SV118 ) ) @ SV201 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ SV222 @ SV50 @ SV118 ) ) @ SV235 ) ) ) @ ( red @ SV244 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2255]) ).

thf(2321,plain,
    ! [SV202: $i,SV165: $i,SV119: $i,SV51: $i] :
      ( ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV51 ) @ SV119 )
         != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV165 ) @ SV202 ) )
        = $true )
      | ( ( ~ ( ( SV51 != SV165 )
              | ( SV119 != SV202 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2256]) ).

thf(2322,plain,
    ! [SV202: $i,SV119: $i,SV165: $i,SV51: $i] :
      ( ( ( ~ ~ ( ( SV51 != SV165 )
                | ( SV119 != SV202 ) ) )
        = $true )
      | ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV51 ) @ SV119 )
          = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV165 ) @ SV202 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2257]) ).

thf(2323,plain,
    ! [SV167: $i,SV121: $i,SV53: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV53 ) @ SV121 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV53 ) @ SV167 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV53 ) @ ( semila751111325l_bool @ SV121 @ SV167 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2259]) ).

thf(2324,plain,
    ! [SV122: $i,SV54: $i,SV245: $i,SV236: $i,SV223: $i,SV204: $i,SV168: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV168 ) @ SV204 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV223 ) @ SV236 ) ) ) @ ( red @ SV245 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ SV168 @ SV54 @ SV122 ) ) @ SV204 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ SV223 @ SV54 @ SV122 ) ) @ SV236 ) ) ) @ ( red @ SV245 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2260]) ).

thf(2325,plain,
    ! [SV124: $i,SV58: $i,SV246: $i,SV237: $i,SV224: $i,SV205: $i,SV169: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV169 ) @ SV205 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV224 ) @ SV237 ) ) ) @ ( red @ SV246 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ SV169 @ SV58 @ SV124 ) ) @ SV205 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ SV224 @ SV58 @ SV124 ) ) @ SV237 ) ) ) @ ( red @ SV246 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2263]) ).

thf(2326,plain,
    ! [SV257: $i,SV59: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ SV257 ) ) )
        = $true )
      | ( ( ~ ! [SY499: $i] :
                ~ ~ ! [SY500: $i] :
                      ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY499 ) @ SY500 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2264]) ).

thf(2327,plain,
    ! [SV258: $i,SV59: $i] :
      ( ( ( ~ ~ ! [SY889: $i] :
                  ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV258 ) @ SY889 ) ) ) )
        = $true )
      | ( ( ~ ! [SY503: $i] :
                ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ SY503 ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2265]) ).

thf(2328,plain,
    ! [SV171: $i,SV126: $i,SV61: $i] :
      ( ( ( ( fun_up1149430426on_val @ SV61 @ SV126 @ SV171 )
          = SV61 )
        = $false )
      | ( ( ( hAPP_l207779698on_val @ SV61 @ SV126 )
          = SV171 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2267]) ).

thf(2329,plain,
    ! [SV171: $i,SV126: $i,SV61: $i] :
      ( ( ( ( hAPP_l207779698on_val @ SV61 @ SV126 )
          = SV171 )
        = $false )
      | ( ( ( fun_up1149430426on_val @ SV61 @ SV126 @ SV171 )
          = SV61 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2268]) ).

thf(2330,plain,
    ! [SV172: $i,SV127: $i,SV63: $i] :
      ( ( ( SV63 = SV127 )
        = $true )
      | ( ( ~ ! [SY764: $i] :
                ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV63 ) @ SY764 ) ) @ SV172 ) )
                | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY764 ) @ SV127 ) ) @ ( transi2024712006on_val @ SV172 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV63 ) @ SV127 ) ) @ ( transi2024712006on_val @ SV172 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2269]) ).

thf(2331,plain,
    ! [SV173: $i,SV128: $i,SV65: $i,SV225: $i,SV206: $i] :
      ( ( ( SV206 = SV225 )
        = $true )
      | ( ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ SV65 @ SV206 @ SV128 ) @ SV225 @ SV173 )
          = ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ SV65 @ SV225 @ SV173 ) @ SV206 @ SV128 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2270]) ).

thf(2332,plain,
    ! [SV66: $i,SV259: $i,SV247: $i,SV238: $i,SV226: $i,SV207: $i,SV174: $i,SV129: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV129 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV174 ) @ SV207 ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV226 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV238 ) @ SV247 ) ) ) ) @ ( red @ SV259 ) ) )
        | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV129 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV174 ) @ ( map_ad325961431ar_val @ SV66 @ SV207 ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV226 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV238 ) @ ( map_ad325961431ar_val @ SV66 @ SV247 ) ) ) ) ) @ ( red @ SV259 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2271]) ).

thf(2333,plain,
    ! [SV260: $i,SV69: $i] :
      ( ( ( ! [SY890: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV260 ) @ SY890 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ ( sK37_SY527 @ SV69 ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2272]) ).

thf(2334,plain,
    ! [SV69: $i] :
      ( ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK38_SY530 @ SV69 ) ) @ ( sK44_SY881 @ SV69 ) ) ) )
        = $false )
      | ( ( ! [SY532: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ SY532 ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2273]) ).

thf(2335,plain,
    ! [SV70: $i,SV175: $i,SV130: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV130 ) @ SV175 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ SV130 ) @ ( semila751111325l_bool @ SV70 @ SV175 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2274]) ).

thf(2336,plain,
    ! [SV261: $i,SV71: $i] :
      ( ( ( ! [SY891: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV261 ) @ SY891 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ ( sK39_SY535 @ SV71 ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2275]) ).

thf(2337,plain,
    ! [SV71: $i] :
      ( ( ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( sK40_SY538 @ SV71 ) ) @ ( sK45_SY882 @ SV71 ) ) ) )
        = $false )
      | ( ( ! [SY540: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ SY540 ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2276]) ).

thf(2338,plain,
    ! [SV177: $i,SV132: $i,SV74: $i,SV262: $i,SV248: $i,SV239: $i,SV228: $i,SV209: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV209 ) @ SV228 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV239 ) @ SV248 ) ) ) @ ( red @ SV262 ) ) )
        | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ SV209 @ SV74 @ SV132 @ SV177 ) ) @ SV228 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ SV239 @ SV74 @ SV132 @ SV177 ) ) @ SV248 ) ) ) @ ( red @ SV262 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2278]) ).

thf(2339,plain,
    ! [SV210: $i,SV134: $i,SV179: $i,SV77: $i] :
      ( ( ( SV77 != SV179 )
        = $false )
      | ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV77 ) @ SV134 )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV179 ) @ SV210 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2280]) ).

thf(2340,plain,
    ! [SV179: $i,SV77: $i,SV210: $i,SV134: $i] :
      ( ( ( SV134 != SV210 )
        = $false )
      | ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV77 ) @ SV134 )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV179 ) @ SV210 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2280]) ).

thf(2341,plain,
    ! [SV211: $i,SV135: $i,SV180: $i,SV78: $i] :
      ( ( ( SV78 != SV180 )
        = $false )
      | ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV78 ) @ SV135 )
          = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV180 ) @ SV211 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2281]) ).

thf(2342,plain,
    ! [SV180: $i,SV78: $i,SV211: $i,SV135: $i] :
      ( ( ( SV135 != SV211 )
        = $false )
      | ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV78 ) @ SV135 )
          = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV180 ) @ SV211 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2281]) ).

thf(2343,plain,
    ! [SV263: $i,SV249: $i,SV13: $i] :
      ( ( ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV249 ) @ SV263 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ ( sK31_SY331 @ SV13 ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2282]) ).

thf(2344,plain,
    ! [SV264: $i,SV13: $i] :
      ( ( ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ SV264 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_P1708370145l_bool @ SV13 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK32_SY334 @ SV13 ) ) @ ( sK41_SY877 @ SV13 ) ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2283]) ).

thf(2345,plain,
    ! [SV240: $i,SV229: $i,SV212: $i,SV183: $i,SV141: $i,SV88: $i,SV14: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV14 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV88 ) @ SV141 ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV183 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV212 ) @ SV229 ) ) ) ) @ ( red @ SV240 ) ) )
        = $false )
      | ( ( hBOOL @ ( hext @ SV88 @ SV212 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2284]) ).

thf(2346,plain,
    ! [SV95: $i,SV21: $i,SV147: $i,SV188: $i] :
      ( ( ( SV188 = SV147 )
        = $false )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV21 @ SV147 @ SV95 ) @ SV188 )
          = SV95 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2288]) ).

thf(2347,plain,
    ! [SV95: $i,SV21: $i,SV147: $i,SV188: $i] :
      ( ( ( SV188 != SV147 )
        = $false )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV21 @ SV147 @ SV95 ) @ SV188 )
          = ( hAPP_l207779698on_val @ SV21 @ SV188 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2289]) ).

thf(2348,plain,
    ! [SV250: $i,SV22: $i] :
      ( ( ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ SV250 ) )
        = $false )
      | ( ( ~ ! [SY368: $i] :
                ~ ~ ! [SY369: $i] :
                      ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY368 ) @ SY369 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2290]) ).

thf(2349,plain,
    ! [SV251: $i,SV22: $i] :
      ( ( ( ~ ! [SY885: $i] :
                ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV251 ) @ SY885 ) ) ) )
        = $false )
      | ( ( ~ ! [SY372: $i] :
                ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ SY372 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2291]) ).

thf(2350,plain,
    ! [SV96: $i,SV23: $i] :
      ( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV96 ) )
                  | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV23 ) ) )
              | ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV23 ) )
                  | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV96 ) ) ) ) )
        = $false )
      | ( ( SV96 = SV23 )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2292]) ).

thf(2351,plain,
    ! [SV23: $i,SV96: $i,SV265: $i,SV252: $i] :
      ( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV252 ) @ SV265 ) ) @ SV96 ) )
                  | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV252 ) @ SV265 ) ) @ SV23 ) ) )
              | ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV252 ) @ SV265 ) ) @ SV23 ) )
                  | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV252 ) @ SV265 ) ) @ SV96 ) ) ) ) )
        = $true )
      | ( ( SV96 = SV23 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2293]) ).

thf(2352,plain,
    ! [SV97: $i,SV24: $i,SV241: $i,SV231: $i,SV215: $i,SV189: $i,SV148: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV148 ) @ SV189 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV215 ) @ SV231 ) ) ) @ ( red @ SV241 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ SV148 @ SV24 @ SV97 ) ) @ SV189 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ SV215 @ SV24 @ SV97 ) ) @ SV231 ) ) ) @ ( red @ SV241 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2294]) ).

thf(2353,plain,
    ! [SV216: $i,SV190: $i,SV149: $i,SV98: $i,SV25: $i] :
      ( ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 )
         != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) )
        = $false )
      | ( ( ~ ! [SY837: $i,SY838: $i] :
                ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY837 ) @ SY838 ) ) ) @ SV216 ) )
                | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY837 ) @ SY838 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) ) @ ( transi2024712006on_val @ SV216 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) ) @ ( transi2024712006on_val @ SV216 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2295]) ).

thf(2354,plain,
    ! [SV191: $i,SV151: $i,SV101: $i,SV29: $i] :
      ( ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV29 ) @ SV101 )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV151 ) @ SV191 ) )
        = $false )
      | ( ( ~ ( ( SV29 != SV151 )
              | ( SV101 != SV191 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2296]) ).

thf(2355,plain,
    ! [SV191: $i,SV101: $i,SV151: $i,SV29: $i] :
      ( ( ( ~ ( ( SV29 != SV151 )
              | ( SV101 != SV191 ) ) )
        = $false )
      | ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV29 ) @ SV101 )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV151 ) @ SV191 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2297]) ).

thf(2356,plain,
    ! [SV34: $i] :
      ( ( ( SV34
         != ( hAPP_val_option_val @ some_val @ ( sK47_SY408 @ SV34 ) ) )
        = $false )
      | ( ( SV34 = none_val )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2300]) ).

thf(2357,plain,
    ! [SV253: $i,SV34: $i] :
      ( ( ( SV34
          = ( hAPP_val_option_val @ some_val @ SV253 ) )
        = $false )
      | ( ( SV34 != none_val )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2301]) ).

thf(2358,plain,
    ! [SV106: $i,SV154: $i,SV36: $i] :
      ( ( ( ! [SY729: $i] :
              ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV36 ) @ SY729 ) ) @ ( transi2024712006on_val @ SV154 ) ) )
              | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY729 ) @ SV106 ) ) @ SV154 ) ) ) )
        = $false )
      | ( ( SV36 = SV106 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV36 ) @ SV106 ) ) @ ( transi2024712006on_val @ SV154 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2303]) ).

thf(2359,plain,
    ! [SV155: $i,SV107: $i,SV37: $i,SV254: $i,SV243: $i,SV233: $i,SV219: $i,SV194: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV194 ) @ SV219 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV233 ) @ SV243 ) ) ) @ ( red @ SV254 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ SV194 @ SV37 @ SV107 @ SV155 ) ) @ SV219 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ SV233 @ SV37 @ SV107 @ SV155 ) ) @ SV243 ) ) ) @ ( red @ SV254 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2304]) ).

thf(2360,plain,
    ! [SV220: $i,SV195: $i,SV156: $i,SV108: $i,SV38: $i] :
      ( ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
         != ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $true )
      | ( ( ~ ( ( SV195 != SV108 )
              | ( SV156 != SV220 ) )
          | ~ ( ~ ( ( SV195 != SV108 ) )
              | ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
               != ( hAPP_val_option_val @ some_val @ SV220 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2305]) ).

thf(2361,plain,
    ! [SV38: $i,SV220: $i,SV156: $i,SV108: $i,SV195: $i] :
      ( ( ( ~ ( ~ ( ( SV195 != SV108 )
                  | ( SV156 != SV220 ) )
              | ~ ( ~ ( ( SV195 != SV108 ) )
                  | ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
                   != ( hAPP_val_option_val @ some_val @ SV220 ) ) ) ) )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2306]) ).

thf(2362,plain,
    ! [SV198: $i,SV113: $i,SV160: $i,SV44: $i] :
      ( ( ( SV44 = SV160 )
        = $true )
      | ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV44 ) @ SV113 )
          = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV160 ) @ SV198 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2310]) ).

thf(2363,plain,
    ! [SV160: $i,SV44: $i,SV198: $i,SV113: $i] :
      ( ( ( SV113 = SV198 )
        = $true )
      | ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV44 ) @ SV113 )
          = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV160 ) @ SV198 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2311]) ).

thf(2364,plain,
    ! [SV199: $i,SV161: $i,SV114: $i,SV45: $i] :
      ( ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV45 ) @ SV114 )
          = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV161 ) @ SV199 ) )
        = $false )
      | ( ( ~ ( ( SV45 != SV161 )
              | ( SV114 != SV199 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2312]) ).

thf(2365,plain,
    ! [SV199: $i,SV114: $i,SV161: $i,SV45: $i] :
      ( ( ( ~ ( ( SV45 != SV161 )
              | ( SV114 != SV199 ) ) )
        = $false )
      | ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV45 ) @ SV114 )
          = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV161 ) @ SV199 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2313]) ).

thf(2366,plain,
    ! [SV115: $i,SV46: $i,SV200: $i,SV162: $i] :
      ( ( ( SV162 = SV200 )
        = $false )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV46 @ SV200 @ SV115 ) @ SV162 )
          = SV115 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2314]) ).

thf(2367,plain,
    ! [SV115: $i,SV46: $i,SV200: $i,SV162: $i] :
      ( ( ( SV162 != SV200 )
        = $false )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV46 @ SV200 @ SV115 ) @ SV162 )
          = ( hAPP_l207779698on_val @ SV46 @ SV162 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2315]) ).

thf(2368,plain,
    ! [SV117: $i,SV48: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV48 )
              | ( hBOOL @ SV117 ) ) )
        = $false )
      | ( ( ( bool @ SV48 )
          = ( bool @ SV117 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2316]) ).

thf(2369,plain,
    ! [SV48: $i,SV117: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV117 )
              | ( hBOOL @ SV48 ) ) )
        = $false )
      | ( ( ( bool @ SV48 )
          = ( bool @ SV117 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2316]) ).

thf(2370,plain,
    ! [SV117: $i,SV48: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV48 )
              | ( hBOOL @ SV117 ) ) )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ SV117 )
              | ( hBOOL @ SV48 ) ) )
        = $true )
      | ( ( ( bool @ SV48 )
          = ( bool @ SV117 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2317]) ).

thf(2371,plain,
    ! [SV255: $i,SV49: $i] :
      ( ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ SV255 ) )
        = $false )
      | ( ( ~ ! [SY459: $i] :
                ~ ~ ! [SY460: $i] :
                      ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY459 ) @ SY460 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2318]) ).

thf(2372,plain,
    ! [SV256: $i,SV49: $i] :
      ( ( ( ~ ! [SY888: $i] :
                ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV256 ) @ SY888 ) ) ) )
        = $false )
      | ( ( ~ ! [SY463: $i] :
                ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ SY463 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2319]) ).

thf(2373,plain,
    ! [SV118: $i,SV50: $i,SV244: $i,SV235: $i,SV222: $i,SV201: $i,SV164: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV164 ) @ SV201 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV222 ) @ SV235 ) ) ) @ ( red @ SV244 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ SV164 @ SV50 @ SV118 ) ) @ SV201 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ SV222 @ SV50 @ SV118 ) ) @ SV235 ) ) ) @ ( red @ SV244 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2320]) ).

thf(2374,plain,
    ! [SV202: $i,SV165: $i,SV119: $i,SV51: $i] :
      ( ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV51 ) @ SV119 )
          = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV165 ) @ SV202 ) )
        = $false )
      | ( ( ~ ( ( SV51 != SV165 )
              | ( SV119 != SV202 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2321]) ).

thf(2375,plain,
    ! [SV202: $i,SV119: $i,SV165: $i,SV51: $i] :
      ( ( ( ~ ( ( SV51 != SV165 )
              | ( SV119 != SV202 ) ) )
        = $false )
      | ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV51 ) @ SV119 )
          = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV165 ) @ SV202 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2322]) ).

thf(2376,plain,
    ! [SV122: $i,SV54: $i,SV245: $i,SV236: $i,SV223: $i,SV204: $i,SV168: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV168 ) @ SV204 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV223 ) @ SV236 ) ) ) @ ( red @ SV245 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ SV168 @ SV54 @ SV122 ) ) @ SV204 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ SV223 @ SV54 @ SV122 ) ) @ SV236 ) ) ) @ ( red @ SV245 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2324]) ).

thf(2377,plain,
    ! [SV124: $i,SV58: $i,SV246: $i,SV237: $i,SV224: $i,SV205: $i,SV169: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV169 ) @ SV205 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV224 ) @ SV237 ) ) ) @ ( red @ SV246 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ SV169 @ SV58 @ SV124 ) ) @ SV205 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ SV224 @ SV58 @ SV124 ) ) @ SV237 ) ) ) @ ( red @ SV246 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2325]) ).

thf(2378,plain,
    ! [SV257: $i,SV59: $i] :
      ( ( ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ SV257 ) )
        = $false )
      | ( ( ~ ! [SY499: $i] :
                ~ ~ ! [SY500: $i] :
                      ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY499 ) @ SY500 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2326]) ).

thf(2379,plain,
    ! [SV258: $i,SV59: $i] :
      ( ( ( ~ ! [SY889: $i] :
                ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV258 ) @ SY889 ) ) ) )
        = $false )
      | ( ( ~ ! [SY503: $i] :
                ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ SY503 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2327]) ).

thf(2380,plain,
    ! [SV127: $i,SV172: $i,SV63: $i] :
      ( ( ( ! [SY764: $i] :
              ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV63 ) @ SY764 ) ) @ SV172 ) )
              | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY764 ) @ SV127 ) ) @ ( transi2024712006on_val @ SV172 ) ) ) ) )
        = $false )
      | ( ( SV63 = SV127 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV63 ) @ SV127 ) ) @ ( transi2024712006on_val @ SV172 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2330]) ).

thf(2381,plain,
    ! [SV66: $i,SV259: $i,SV247: $i,SV238: $i,SV226: $i,SV207: $i,SV174: $i,SV129: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV129 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV174 ) @ SV207 ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV226 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV238 ) @ SV247 ) ) ) ) @ ( red @ SV259 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV129 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV174 ) @ ( map_ad325961431ar_val @ SV66 @ SV207 ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV226 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV238 ) @ ( map_ad325961431ar_val @ SV66 @ SV247 ) ) ) ) ) @ ( red @ SV259 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2332]) ).

thf(2382,plain,
    ! [SV266: $i,SV260: $i,SV69: $i] :
      ( ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV260 ) @ SV266 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ ( sK37_SY527 @ SV69 ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2333]) ).

thf(2383,plain,
    ! [SV267: $i,SV69: $i] :
      ( ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ SV267 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV69 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK38_SY530 @ SV69 ) ) @ ( sK44_SY881 @ SV69 ) ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2334]) ).

thf(2384,plain,
    ! [SV268: $i,SV261: $i,SV71: $i] :
      ( ( ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV261 ) @ SV268 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ ( sK39_SY535 @ SV71 ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2336]) ).

thf(2385,plain,
    ! [SV269: $i,SV71: $i] :
      ( ( ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ SV269 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_P159683425l_bool @ SV71 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( sK40_SY538 @ SV71 ) ) @ ( sK45_SY882 @ SV71 ) ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2337]) ).

thf(2386,plain,
    ! [SV177: $i,SV132: $i,SV74: $i,SV262: $i,SV248: $i,SV239: $i,SV228: $i,SV209: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV209 ) @ SV228 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV239 ) @ SV248 ) ) ) @ ( red @ SV262 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ SV209 @ SV74 @ SV132 @ SV177 ) ) @ SV228 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ SV239 @ SV74 @ SV132 @ SV177 ) ) @ SV248 ) ) ) @ ( red @ SV262 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2338]) ).

thf(2387,plain,
    ! [SV210: $i,SV134: $i,SV179: $i,SV77: $i] :
      ( ( ( SV77 = SV179 )
        = $true )
      | ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV77 ) @ SV134 )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV179 ) @ SV210 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2339]) ).

thf(2388,plain,
    ! [SV179: $i,SV77: $i,SV210: $i,SV134: $i] :
      ( ( ( SV134 = SV210 )
        = $true )
      | ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV77 ) @ SV134 )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV179 ) @ SV210 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2340]) ).

thf(2389,plain,
    ! [SV211: $i,SV135: $i,SV180: $i,SV78: $i] :
      ( ( ( SV78 = SV180 )
        = $true )
      | ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV78 ) @ SV135 )
          = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV180 ) @ SV211 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2341]) ).

thf(2390,plain,
    ! [SV180: $i,SV78: $i,SV211: $i,SV135: $i] :
      ( ( ( SV135 = SV211 )
        = $true )
      | ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV78 ) @ SV135 )
          = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV180 ) @ SV211 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2342]) ).

thf(2391,plain,
    ! [SV95: $i,SV21: $i,SV147: $i,SV188: $i] :
      ( ( ( SV188 = SV147 )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV21 @ SV147 @ SV95 ) @ SV188 )
          = ( hAPP_l207779698on_val @ SV21 @ SV188 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2347]) ).

thf(2392,plain,
    ! [SV250: $i,SV22: $i] :
      ( ( ( ! [SY368: $i] :
              ~ ~ ! [SY369: $i] :
                    ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SY368 ) @ SY369 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ SV250 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2348]) ).

thf(2393,plain,
    ! [SV251: $i,SV22: $i] :
      ( ( ( ! [SY885: $i] :
              ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV251 ) @ SY885 ) ) ) )
        = $true )
      | ( ( ~ ! [SY372: $i] :
                ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ SY372 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2349]) ).

thf(2394,plain,
    ! [SV96: $i,SV23: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV96 ) )
              | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV23 ) ) )
          | ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV23 ) )
              | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV96 ) ) ) )
        = $true )
      | ( ( SV96 = SV23 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2350]) ).

thf(2395,plain,
    ! [SV23: $i,SV96: $i,SV265: $i,SV252: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV252 ) @ SV265 ) ) @ SV96 ) )
              | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV252 ) @ SV265 ) ) @ SV23 ) ) )
          | ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV252 ) @ SV265 ) ) @ SV23 ) )
              | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV252 ) @ SV265 ) ) @ SV96 ) ) ) )
        = $false )
      | ( ( SV96 = SV23 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2351]) ).

thf(2396,plain,
    ! [SV216: $i,SV190: $i,SV149: $i,SV98: $i,SV25: $i] :
      ( ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) )
        = $true )
      | ( ( ~ ! [SY837: $i,SY838: $i] :
                ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY837 ) @ SY838 ) ) ) @ SV216 ) )
                | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY837 ) @ SY838 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) ) @ ( transi2024712006on_val @ SV216 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) ) @ ( transi2024712006on_val @ SV216 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2353]) ).

thf(2397,plain,
    ! [SV191: $i,SV101: $i,SV151: $i,SV29: $i] :
      ( ( ( ( SV29 != SV151 )
          | ( SV101 != SV191 ) )
        = $false )
      | ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV29 ) @ SV101 )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV151 ) @ SV191 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2354]) ).

thf(2398,plain,
    ! [SV191: $i,SV101: $i,SV151: $i,SV29: $i] :
      ( ( ( ( SV29 != SV151 )
          | ( SV101 != SV191 ) )
        = $true )
      | ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV29 ) @ SV101 )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV151 ) @ SV191 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2355]) ).

thf(2399,plain,
    ! [SV34: $i] :
      ( ( ( SV34
          = ( hAPP_val_option_val @ some_val @ ( sK47_SY408 @ SV34 ) ) )
        = $true )
      | ( ( SV34 = none_val )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2356]) ).

thf(2400,plain,
    ! [SV253: $i,SV34: $i] :
      ( ( ( SV34 = none_val )
        = $false )
      | ( ( SV34
          = ( hAPP_val_option_val @ some_val @ SV253 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2357]) ).

thf(2401,plain,
    ! [SV154: $i,SV106: $i,SV36: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV36 ) @ ( sK48_SY729 @ SV106 @ SV154 @ SV36 ) ) ) @ ( transi2024712006on_val @ SV154 ) ) )
          | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK48_SY729 @ SV106 @ SV154 @ SV36 ) ) @ SV106 ) ) @ SV154 ) ) )
        = $false )
      | ( ( SV36 = SV106 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV36 ) @ SV106 ) ) @ ( transi2024712006on_val @ SV154 ) ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2358]) ).

thf(2402,plain,
    ! [SV155: $i,SV107: $i,SV37: $i,SV254: $i,SV243: $i,SV233: $i,SV219: $i,SV194: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV194 ) @ SV219 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV233 ) @ SV243 ) ) ) @ ( red @ SV254 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ SV194 @ SV37 @ SV107 @ SV155 ) ) @ SV219 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ SV233 @ SV37 @ SV107 @ SV155 ) ) @ SV243 ) ) ) @ ( red @ SV254 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2359]) ).

thf(2403,plain,
    ! [SV220: $i,SV195: $i,SV156: $i,SV108: $i,SV38: $i] :
      ( ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $false )
      | ( ( ~ ( ( SV195 != SV108 )
              | ( SV156 != SV220 ) )
          | ~ ( ~ ( ( SV195 != SV108 ) )
              | ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
               != ( hAPP_val_option_val @ some_val @ SV220 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2360]) ).

thf(2404,plain,
    ! [SV38: $i,SV220: $i,SV156: $i,SV108: $i,SV195: $i] :
      ( ( ( ~ ( ( SV195 != SV108 )
              | ( SV156 != SV220 ) )
          | ~ ( ~ ( ( SV195 != SV108 ) )
              | ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
               != ( hAPP_val_option_val @ some_val @ SV220 ) ) ) )
        = $false )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2361]) ).

thf(2405,plain,
    ! [SV199: $i,SV114: $i,SV161: $i,SV45: $i] :
      ( ( ( ( SV45 != SV161 )
          | ( SV114 != SV199 ) )
        = $false )
      | ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV45 ) @ SV114 )
          = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV161 ) @ SV199 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2364]) ).

thf(2406,plain,
    ! [SV199: $i,SV114: $i,SV161: $i,SV45: $i] :
      ( ( ( ( SV45 != SV161 )
          | ( SV114 != SV199 ) )
        = $true )
      | ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV45 ) @ SV114 )
          = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV161 ) @ SV199 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2365]) ).

thf(2407,plain,
    ! [SV115: $i,SV46: $i,SV200: $i,SV162: $i] :
      ( ( ( SV162 = SV200 )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV46 @ SV200 @ SV115 ) @ SV162 )
          = ( hAPP_l207779698on_val @ SV46 @ SV162 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2367]) ).

thf(2408,plain,
    ! [SV117: $i,SV48: $i] :
      ( ( ( ~ ( hBOOL @ SV48 )
          | ( hBOOL @ SV117 ) )
        = $true )
      | ( ( ( bool @ SV48 )
          = ( bool @ SV117 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2368]) ).

thf(2409,plain,
    ! [SV48: $i,SV117: $i] :
      ( ( ( ~ ( hBOOL @ SV117 )
          | ( hBOOL @ SV48 ) )
        = $true )
      | ( ( ( bool @ SV48 )
          = ( bool @ SV117 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2369]) ).

thf(2410,plain,
    ! [SV117: $i,SV48: $i] :
      ( ( ( ~ ( hBOOL @ SV48 )
          | ( hBOOL @ SV117 ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ SV117 )
              | ( hBOOL @ SV48 ) ) )
        = $true )
      | ( ( ( bool @ SV48 )
          = ( bool @ SV117 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2370]) ).

thf(2411,plain,
    ! [SV255: $i,SV49: $i] :
      ( ( ( ! [SY459: $i] :
              ~ ~ ! [SY460: $i] :
                    ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SY459 ) @ SY460 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ SV255 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2371]) ).

thf(2412,plain,
    ! [SV256: $i,SV49: $i] :
      ( ( ( ! [SY888: $i] :
              ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV256 ) @ SY888 ) ) ) )
        = $true )
      | ( ( ~ ! [SY463: $i] :
                ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ SY463 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2372]) ).

thf(2413,plain,
    ! [SV202: $i,SV119: $i,SV165: $i,SV51: $i] :
      ( ( ( ( SV51 != SV165 )
          | ( SV119 != SV202 ) )
        = $false )
      | ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV51 ) @ SV119 )
          = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV165 ) @ SV202 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2374]) ).

thf(2414,plain,
    ! [SV202: $i,SV119: $i,SV165: $i,SV51: $i] :
      ( ( ( ( SV51 != SV165 )
          | ( SV119 != SV202 ) )
        = $true )
      | ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV51 ) @ SV119 )
          = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV165 ) @ SV202 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2375]) ).

thf(2415,plain,
    ! [SV257: $i,SV59: $i] :
      ( ( ( ! [SY499: $i] :
              ~ ~ ! [SY500: $i] :
                    ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY499 ) @ SY500 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ SV257 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2378]) ).

thf(2416,plain,
    ! [SV258: $i,SV59: $i] :
      ( ( ( ! [SY889: $i] :
              ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV258 ) @ SY889 ) ) ) )
        = $true )
      | ( ( ~ ! [SY503: $i] :
                ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ SY503 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2379]) ).

thf(2417,plain,
    ! [SV172: $i,SV127: $i,SV63: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV63 ) @ ( sK49_SY764 @ SV127 @ SV172 @ SV63 ) ) ) @ SV172 ) )
          | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK49_SY764 @ SV127 @ SV172 @ SV63 ) ) @ SV127 ) ) @ ( transi2024712006on_val @ SV172 ) ) ) )
        = $false )
      | ( ( SV63 = SV127 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV63 ) @ SV127 ) ) @ ( transi2024712006on_val @ SV172 ) ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2380]) ).

thf(2418,plain,
    ! [SV66: $i,SV259: $i,SV247: $i,SV238: $i,SV226: $i,SV207: $i,SV174: $i,SV129: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV129 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV174 ) @ SV207 ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV226 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV238 ) @ SV247 ) ) ) ) @ ( red @ SV259 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV129 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV174 ) @ ( map_ad325961431ar_val @ SV66 @ SV207 ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV226 ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV238 ) @ ( map_ad325961431ar_val @ SV66 @ SV247 ) ) ) ) ) @ ( red @ SV259 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2381]) ).

thf(2419,plain,
    ! [SV177: $i,SV132: $i,SV74: $i,SV262: $i,SV248: $i,SV239: $i,SV228: $i,SV209: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV209 ) @ SV228 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV239 ) @ SV248 ) ) ) @ ( red @ SV262 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ SV209 @ SV74 @ SV132 @ SV177 ) ) @ SV228 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ SV239 @ SV74 @ SV132 @ SV177 ) ) @ SV248 ) ) ) @ ( red @ SV262 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2386]) ).

thf(2420,plain,
    ! [SV250: $i,SV22: $i] :
      ( ( ( ~ ~ ! [SY892: $i] :
                  ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( sK50_SY368 @ SV250 @ SV22 ) ) @ SY892 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ SV250 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2392]) ).

thf(2421,plain,
    ! [SV270: $i,SV251: $i,SV22: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV251 ) @ SV270 ) ) ) )
        = $true )
      | ( ( ~ ! [SY372: $i] :
                ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ SY372 ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2393]) ).

thf(2422,plain,
    ! [SV96: $i,SV23: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV96 ) )
              | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV23 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV23 ) )
              | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV96 ) ) ) )
        = $true )
      | ( ( SV96 = SV23 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2394]) ).

thf(2423,plain,
    ! [SV23: $i,SV96: $i,SV265: $i,SV252: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV252 ) @ SV265 ) ) @ SV96 ) )
              | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV252 ) @ SV265 ) ) @ SV23 ) ) ) )
        = $false )
      | ( ( SV96 = SV23 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2395]) ).

thf(2424,plain,
    ! [SV96: $i,SV23: $i,SV265: $i,SV252: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV252 ) @ SV265 ) ) @ SV23 ) )
              | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV252 ) @ SV265 ) ) @ SV96 ) ) ) )
        = $false )
      | ( ( SV96 = SV23 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2395]) ).

thf(2425,plain,
    ! [SV190: $i,SV149: $i,SV216: $i,SV98: $i,SV25: $i] :
      ( ( ( ! [SY837: $i,SY838: $i] :
              ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY837 ) @ SY838 ) ) ) @ SV216 ) )
              | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SY837 ) @ SY838 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) ) @ ( transi2024712006on_val @ SV216 ) ) ) ) )
        = $false )
      | ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) ) @ ( transi2024712006on_val @ SV216 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2396]) ).

thf(2426,plain,
    ! [SV191: $i,SV101: $i,SV151: $i,SV29: $i] :
      ( ( ( SV29 != SV151 )
        = $false )
      | ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV29 ) @ SV101 )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV151 ) @ SV191 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2397]) ).

thf(2427,plain,
    ! [SV151: $i,SV29: $i,SV191: $i,SV101: $i] :
      ( ( ( SV101 != SV191 )
        = $false )
      | ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV29 ) @ SV101 )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV151 ) @ SV191 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2397]) ).

thf(2428,plain,
    ! [SV191: $i,SV101: $i,SV151: $i,SV29: $i] :
      ( ( ( SV29 != SV151 )
        = $true )
      | ( ( SV101 != SV191 )
        = $true )
      | ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV29 ) @ SV101 )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV151 ) @ SV191 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2398]) ).

thf(2429,plain,
    ! [SV154: $i,SV106: $i,SV36: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV36 ) @ ( sK48_SY729 @ SV106 @ SV154 @ SV36 ) ) ) @ ( transi2024712006on_val @ SV154 ) ) ) )
        = $false )
      | ( ( SV36 = SV106 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV36 ) @ SV106 ) ) @ ( transi2024712006on_val @ SV154 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2401]) ).

thf(2430,plain,
    ! [SV36: $i,SV154: $i,SV106: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK48_SY729 @ SV106 @ SV154 @ SV36 ) ) @ SV106 ) ) @ SV154 ) ) )
        = $false )
      | ( ( SV36 = SV106 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV36 ) @ SV106 ) ) @ ( transi2024712006on_val @ SV154 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2401]) ).

thf(2431,plain,
    ! [SV38: $i,SV220: $i,SV156: $i,SV108: $i,SV195: $i] :
      ( ( ( ~ ( ( SV195 != SV108 )
              | ( SV156 != SV220 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ( SV195 != SV108 ) )
              | ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
               != ( hAPP_val_option_val @ some_val @ SV220 ) ) ) )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2403]) ).

thf(2432,plain,
    ! [SV38: $i,SV220: $i,SV156: $i,SV108: $i,SV195: $i] :
      ( ( ( ~ ( ( SV195 != SV108 )
              | ( SV156 != SV220 ) ) )
        = $false )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2404]) ).

thf(2433,plain,
    ! [SV156: $i,SV220: $i,SV38: $i,SV108: $i,SV195: $i] :
      ( ( ( ~ ( ~ ( ( SV195 != SV108 ) )
              | ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
               != ( hAPP_val_option_val @ some_val @ SV220 ) ) ) )
        = $false )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2404]) ).

thf(2434,plain,
    ! [SV199: $i,SV114: $i,SV161: $i,SV45: $i] :
      ( ( ( SV45 != SV161 )
        = $false )
      | ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV45 ) @ SV114 )
          = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV161 ) @ SV199 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2405]) ).

thf(2435,plain,
    ! [SV161: $i,SV45: $i,SV199: $i,SV114: $i] :
      ( ( ( SV114 != SV199 )
        = $false )
      | ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV45 ) @ SV114 )
          = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV161 ) @ SV199 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2405]) ).

thf(2436,plain,
    ! [SV199: $i,SV114: $i,SV161: $i,SV45: $i] :
      ( ( ( SV45 != SV161 )
        = $true )
      | ( ( SV114 != SV199 )
        = $true )
      | ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV45 ) @ SV114 )
          = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV161 ) @ SV199 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2406]) ).

thf(2437,plain,
    ! [SV117: $i,SV48: $i] :
      ( ( ( ~ ( hBOOL @ SV48 ) )
        = $true )
      | ( ( hBOOL @ SV117 )
        = $true )
      | ( ( ( bool @ SV48 )
          = ( bool @ SV117 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2408]) ).

thf(2438,plain,
    ! [SV48: $i,SV117: $i] :
      ( ( ( ~ ( hBOOL @ SV117 ) )
        = $true )
      | ( ( hBOOL @ SV48 )
        = $true )
      | ( ( ( bool @ SV48 )
          = ( bool @ SV117 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2409]) ).

thf(2439,plain,
    ! [SV117: $i,SV48: $i] :
      ( ( ( ~ ( hBOOL @ SV48 ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ SV117 )
              | ( hBOOL @ SV48 ) ) )
        = $true )
      | ( ( ( bool @ SV48 )
          = ( bool @ SV117 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2410]) ).

thf(2440,plain,
    ! [SV48: $i,SV117: $i] :
      ( ( ( hBOOL @ SV117 )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ SV117 )
              | ( hBOOL @ SV48 ) ) )
        = $true )
      | ( ( ( bool @ SV48 )
          = ( bool @ SV117 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2410]) ).

thf(2441,plain,
    ! [SV255: $i,SV49: $i] :
      ( ( ( ~ ~ ! [SY893: $i] :
                  ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK51_SY459 @ SV255 @ SV49 ) ) @ SY893 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ SV255 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2411]) ).

thf(2442,plain,
    ! [SV271: $i,SV256: $i,SV49: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV256 ) @ SV271 ) ) ) )
        = $true )
      | ( ( ~ ! [SY463: $i] :
                ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ SY463 ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2412]) ).

thf(2443,plain,
    ! [SV202: $i,SV119: $i,SV165: $i,SV51: $i] :
      ( ( ( SV51 != SV165 )
        = $false )
      | ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV51 ) @ SV119 )
          = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV165 ) @ SV202 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2413]) ).

thf(2444,plain,
    ! [SV165: $i,SV51: $i,SV202: $i,SV119: $i] :
      ( ( ( SV119 != SV202 )
        = $false )
      | ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV51 ) @ SV119 )
          = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV165 ) @ SV202 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2413]) ).

thf(2445,plain,
    ! [SV202: $i,SV119: $i,SV165: $i,SV51: $i] :
      ( ( ( SV51 != SV165 )
        = $true )
      | ( ( SV119 != SV202 )
        = $true )
      | ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV51 ) @ SV119 )
          = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV165 ) @ SV202 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2414]) ).

thf(2446,plain,
    ! [SV257: $i,SV59: $i] :
      ( ( ( ~ ~ ! [SY894: $i] :
                  ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK52_SY499 @ SV257 @ SV59 ) ) @ SY894 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ SV257 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2415]) ).

thf(2447,plain,
    ! [SV272: $i,SV258: $i,SV59: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV258 ) @ SV272 ) ) ) )
        = $true )
      | ( ( ~ ! [SY503: $i] :
                ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ SY503 ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2416]) ).

thf(2448,plain,
    ! [SV172: $i,SV127: $i,SV63: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV63 ) @ ( sK49_SY764 @ SV127 @ SV172 @ SV63 ) ) ) @ SV172 ) ) )
        = $false )
      | ( ( SV63 = SV127 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV63 ) @ SV127 ) ) @ ( transi2024712006on_val @ SV172 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2417]) ).

thf(2449,plain,
    ! [SV63: $i,SV172: $i,SV127: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK49_SY764 @ SV127 @ SV172 @ SV63 ) ) @ SV127 ) ) @ ( transi2024712006on_val @ SV172 ) ) ) )
        = $false )
      | ( ( SV63 = SV127 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV63 ) @ SV127 ) ) @ ( transi2024712006on_val @ SV172 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2417]) ).

thf(2450,plain,
    ! [SV250: $i,SV22: $i] :
      ( ( ( ~ ! [SY892: $i] :
                ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( sK50_SY368 @ SV250 @ SV22 ) ) @ SY892 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ SV250 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2420]) ).

thf(2451,plain,
    ! [SV270: $i,SV251: $i,SV22: $i] :
      ( ( ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV251 ) @ SV270 ) ) )
        = $false )
      | ( ( ~ ! [SY372: $i] :
                ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ SY372 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2421]) ).

thf(2452,plain,
    ! [SV96: $i,SV23: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV96 ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV23 ) ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV23 ) )
              | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV96 ) ) ) )
        = $true )
      | ( ( SV96 = SV23 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2422]) ).

thf(2453,plain,
    ! [SV23: $i,SV96: $i,SV265: $i,SV252: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV252 ) @ SV265 ) ) @ SV96 ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV252 ) @ SV265 ) ) @ SV23 ) ) )
        = $true )
      | ( ( SV96 = SV23 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2423]) ).

thf(2454,plain,
    ! [SV96: $i,SV23: $i,SV265: $i,SV252: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV252 ) @ SV265 ) ) @ SV23 ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV252 ) @ SV265 ) ) @ SV96 ) ) )
        = $true )
      | ( ( SV96 = SV23 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2424]) ).

thf(2455,plain,
    ! [SV216: $i,SV149: $i,SV190: $i,SV98: $i,SV25: $i] :
      ( ( ( ! [SY895: $i] :
              ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK53_SY837 @ SV190 @ SV149 @ SV216 @ SV98 @ SV25 ) ) @ SY895 ) ) ) @ SV216 ) )
              | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK53_SY837 @ SV190 @ SV149 @ SV216 @ SV98 @ SV25 ) ) @ SY895 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) ) @ ( transi2024712006on_val @ SV216 ) ) ) ) )
        = $false )
      | ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) ) @ ( transi2024712006on_val @ SV216 ) ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2425]) ).

thf(2456,plain,
    ! [SV191: $i,SV101: $i,SV151: $i,SV29: $i] :
      ( ( ( SV29 = SV151 )
        = $true )
      | ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV29 ) @ SV101 )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV151 ) @ SV191 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2426]) ).

thf(2457,plain,
    ! [SV151: $i,SV29: $i,SV191: $i,SV101: $i] :
      ( ( ( SV101 = SV191 )
        = $true )
      | ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV29 ) @ SV101 )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV151 ) @ SV191 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2427]) ).

thf(2458,plain,
    ! [SV191: $i,SV101: $i,SV151: $i,SV29: $i] :
      ( ( ( SV29 = SV151 )
        = $false )
      | ( ( SV101 != SV191 )
        = $true )
      | ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV29 ) @ SV101 )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV151 ) @ SV191 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2428]) ).

thf(2459,plain,
    ! [SV154: $i,SV106: $i,SV36: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV36 ) @ ( sK48_SY729 @ SV106 @ SV154 @ SV36 ) ) ) @ ( transi2024712006on_val @ SV154 ) ) )
        = $true )
      | ( ( SV36 = SV106 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV36 ) @ SV106 ) ) @ ( transi2024712006on_val @ SV154 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2429]) ).

thf(2460,plain,
    ! [SV36: $i,SV154: $i,SV106: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK48_SY729 @ SV106 @ SV154 @ SV36 ) ) @ SV106 ) ) @ SV154 ) )
        = $true )
      | ( ( SV36 = SV106 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV36 ) @ SV106 ) ) @ ( transi2024712006on_val @ SV154 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2430]) ).

thf(2461,plain,
    ! [SV38: $i,SV220: $i,SV156: $i,SV108: $i,SV195: $i] :
      ( ( ( ( SV195 != SV108 )
          | ( SV156 != SV220 ) )
        = $false )
      | ( ( ~ ( ~ ( ( SV195 != SV108 ) )
              | ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
               != ( hAPP_val_option_val @ some_val @ SV220 ) ) ) )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2431]) ).

thf(2462,plain,
    ! [SV38: $i,SV220: $i,SV156: $i,SV108: $i,SV195: $i] :
      ( ( ( ( SV195 != SV108 )
          | ( SV156 != SV220 ) )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2432]) ).

thf(2463,plain,
    ! [SV156: $i,SV220: $i,SV38: $i,SV108: $i,SV195: $i] :
      ( ( ( ~ ( ( SV195 != SV108 ) )
          | ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
           != ( hAPP_val_option_val @ some_val @ SV220 ) ) )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2433]) ).

thf(2464,plain,
    ! [SV199: $i,SV114: $i,SV161: $i,SV45: $i] :
      ( ( ( SV45 = SV161 )
        = $true )
      | ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV45 ) @ SV114 )
          = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV161 ) @ SV199 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2434]) ).

thf(2465,plain,
    ! [SV161: $i,SV45: $i,SV199: $i,SV114: $i] :
      ( ( ( SV114 = SV199 )
        = $true )
      | ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV45 ) @ SV114 )
          = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV161 ) @ SV199 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2435]) ).

thf(2466,plain,
    ! [SV199: $i,SV114: $i,SV161: $i,SV45: $i] :
      ( ( ( SV45 = SV161 )
        = $false )
      | ( ( SV114 != SV199 )
        = $true )
      | ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV45 ) @ SV114 )
          = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV161 ) @ SV199 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2436]) ).

thf(2467,plain,
    ! [SV117: $i,SV48: $i] :
      ( ( ( hBOOL @ SV48 )
        = $false )
      | ( ( hBOOL @ SV117 )
        = $true )
      | ( ( ( bool @ SV48 )
          = ( bool @ SV117 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2437]) ).

thf(2468,plain,
    ! [SV48: $i,SV117: $i] :
      ( ( ( hBOOL @ SV117 )
        = $false )
      | ( ( hBOOL @ SV48 )
        = $true )
      | ( ( ( bool @ SV48 )
          = ( bool @ SV117 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2438]) ).

thf(2469,plain,
    ! [SV117: $i,SV48: $i] :
      ( ( ( hBOOL @ SV48 )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ SV117 )
              | ( hBOOL @ SV48 ) ) )
        = $true )
      | ( ( ( bool @ SV48 )
          = ( bool @ SV117 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2439]) ).

thf(2470,plain,
    ! [SV48: $i,SV117: $i] :
      ( ( ( ~ ( hBOOL @ SV117 )
          | ( hBOOL @ SV48 ) )
        = $false )
      | ( ( hBOOL @ SV117 )
        = $false )
      | ( ( ( bool @ SV48 )
          = ( bool @ SV117 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2440]) ).

thf(2471,plain,
    ! [SV255: $i,SV49: $i] :
      ( ( ( ~ ! [SY893: $i] :
                ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK51_SY459 @ SV255 @ SV49 ) ) @ SY893 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ SV255 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2441]) ).

thf(2472,plain,
    ! [SV271: $i,SV256: $i,SV49: $i] :
      ( ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV256 ) @ SV271 ) ) )
        = $false )
      | ( ( ~ ! [SY463: $i] :
                ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ SY463 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2442]) ).

thf(2473,plain,
    ! [SV202: $i,SV119: $i,SV165: $i,SV51: $i] :
      ( ( ( SV51 = SV165 )
        = $true )
      | ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV51 ) @ SV119 )
          = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV165 ) @ SV202 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2443]) ).

thf(2474,plain,
    ! [SV165: $i,SV51: $i,SV202: $i,SV119: $i] :
      ( ( ( SV119 = SV202 )
        = $true )
      | ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV51 ) @ SV119 )
          = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV165 ) @ SV202 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2444]) ).

thf(2475,plain,
    ! [SV202: $i,SV119: $i,SV165: $i,SV51: $i] :
      ( ( ( SV51 = SV165 )
        = $false )
      | ( ( SV119 != SV202 )
        = $true )
      | ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV51 ) @ SV119 )
          = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV165 ) @ SV202 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2445]) ).

thf(2476,plain,
    ! [SV257: $i,SV59: $i] :
      ( ( ( ~ ! [SY894: $i] :
                ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK52_SY499 @ SV257 @ SV59 ) ) @ SY894 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ SV257 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2446]) ).

thf(2477,plain,
    ! [SV272: $i,SV258: $i,SV59: $i] :
      ( ( ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV258 ) @ SV272 ) ) )
        = $false )
      | ( ( ~ ! [SY503: $i] :
                ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ SY503 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2447]) ).

thf(2478,plain,
    ! [SV172: $i,SV127: $i,SV63: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV63 ) @ ( sK49_SY764 @ SV127 @ SV172 @ SV63 ) ) ) @ SV172 ) )
        = $true )
      | ( ( SV63 = SV127 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV63 ) @ SV127 ) ) @ ( transi2024712006on_val @ SV172 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2448]) ).

thf(2479,plain,
    ! [SV63: $i,SV172: $i,SV127: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK49_SY764 @ SV127 @ SV172 @ SV63 ) ) @ SV127 ) ) @ ( transi2024712006on_val @ SV172 ) ) )
        = $true )
      | ( ( SV63 = SV127 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV63 ) @ SV127 ) ) @ ( transi2024712006on_val @ SV172 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2449]) ).

thf(2480,plain,
    ! [SV250: $i,SV22: $i] :
      ( ( ( ! [SY892: $i] :
              ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( sK50_SY368 @ SV250 @ SV22 ) ) @ SY892 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ SV250 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2450]) ).

thf(2481,plain,
    ! [SV270: $i,SV251: $i,SV22: $i] :
      ( ( ( ! [SY372: $i] :
              ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ SY372 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV251 ) @ SV270 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2451]) ).

thf(2482,plain,
    ! [SV96: $i,SV23: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV96 ) ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV23 ) )
              | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV96 ) ) ) )
        = $true )
      | ( ( SV96 = SV23 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2452]) ).

thf(2483,plain,
    ! [SV96: $i,SV23: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV23 ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV23 ) )
              | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV96 ) ) ) )
        = $true )
      | ( ( SV96 = SV23 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2452]) ).

thf(2484,plain,
    ! [SV23: $i,SV96: $i,SV265: $i,SV252: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV252 ) @ SV265 ) ) @ SV96 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV252 ) @ SV265 ) ) @ SV23 ) )
        = $true )
      | ( ( SV96 = SV23 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2453]) ).

thf(2485,plain,
    ! [SV96: $i,SV23: $i,SV265: $i,SV252: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV252 ) @ SV265 ) ) @ SV23 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV252 ) @ SV265 ) ) @ SV96 ) )
        = $true )
      | ( ( SV96 = SV23 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2454]) ).

thf(2486,plain,
    ! [SV216: $i,SV149: $i,SV190: $i,SV98: $i,SV25: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK53_SY837 @ SV190 @ SV149 @ SV216 @ SV98 @ SV25 ) ) @ ( sK54_SY895 @ SV216 @ SV149 @ SV190 @ SV98 @ SV25 ) ) ) ) @ SV216 ) )
          | ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK53_SY837 @ SV190 @ SV149 @ SV216 @ SV98 @ SV25 ) ) @ ( sK54_SY895 @ SV216 @ SV149 @ SV190 @ SV98 @ SV25 ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) ) @ ( transi2024712006on_val @ SV216 ) ) ) )
        = $false )
      | ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) ) @ ( transi2024712006on_val @ SV216 ) ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2455]) ).

thf(2487,plain,
    ! [SV151: $i,SV29: $i,SV191: $i,SV101: $i] :
      ( ( ( SV101 = SV191 )
        = $false )
      | ( ( SV29 = SV151 )
        = $false )
      | ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV29 ) @ SV101 )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV151 ) @ SV191 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2458]) ).

thf(2488,plain,
    ! [SV156: $i,SV220: $i,SV38: $i,SV108: $i,SV195: $i] :
      ( ( ( SV195 != SV108 )
        = $false )
      | ( ( ~ ( ~ ( ( SV195 != SV108 ) )
              | ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
               != ( hAPP_val_option_val @ some_val @ SV220 ) ) ) )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2461]) ).

thf(2489,plain,
    ! [SV38: $i,SV108: $i,SV195: $i,SV220: $i,SV156: $i] :
      ( ( ( SV156 != SV220 )
        = $false )
      | ( ( ~ ( ~ ( ( SV195 != SV108 ) )
              | ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
               != ( hAPP_val_option_val @ some_val @ SV220 ) ) ) )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2461]) ).

thf(2490,plain,
    ! [SV38: $i,SV220: $i,SV156: $i,SV108: $i,SV195: $i] :
      ( ( ( SV195 != SV108 )
        = $true )
      | ( ( SV156 != SV220 )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2462]) ).

thf(2491,plain,
    ! [SV156: $i,SV220: $i,SV38: $i,SV108: $i,SV195: $i] :
      ( ( ( ~ ( ( SV195 != SV108 ) ) )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
         != ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2463]) ).

thf(2492,plain,
    ! [SV161: $i,SV45: $i,SV199: $i,SV114: $i] :
      ( ( ( SV114 = SV199 )
        = $false )
      | ( ( SV45 = SV161 )
        = $false )
      | ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV45 ) @ SV114 )
          = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV161 ) @ SV199 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2466]) ).

thf(2493,plain,
    ! [SV48: $i,SV117: $i] :
      ( ( ( ~ ( hBOOL @ SV117 )
          | ( hBOOL @ SV48 ) )
        = $false )
      | ( ( hBOOL @ SV48 )
        = $true )
      | ( ( ( bool @ SV48 )
          = ( bool @ SV117 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2469]) ).

thf(2494,plain,
    ! [SV48: $i,SV117: $i] :
      ( ( ( ~ ( hBOOL @ SV117 ) )
        = $false )
      | ( ( hBOOL @ SV117 )
        = $false )
      | ( ( ( bool @ SV48 )
          = ( bool @ SV117 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2470]) ).

thf(2495,plain,
    ! [SV117: $i,SV48: $i] :
      ( ( ( hBOOL @ SV48 )
        = $false )
      | ( ( hBOOL @ SV117 )
        = $false )
      | ( ( ( bool @ SV48 )
          = ( bool @ SV117 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2470]) ).

thf(2496,plain,
    ! [SV255: $i,SV49: $i] :
      ( ( ( ! [SY893: $i] :
              ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK51_SY459 @ SV255 @ SV49 ) ) @ SY893 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ SV255 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2471]) ).

thf(2497,plain,
    ! [SV271: $i,SV256: $i,SV49: $i] :
      ( ( ( ! [SY463: $i] :
              ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ SY463 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV256 ) @ SV271 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2472]) ).

thf(2498,plain,
    ! [SV165: $i,SV51: $i,SV202: $i,SV119: $i] :
      ( ( ( SV119 = SV202 )
        = $false )
      | ( ( SV51 = SV165 )
        = $false )
      | ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV51 ) @ SV119 )
          = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV165 ) @ SV202 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2475]) ).

thf(2499,plain,
    ! [SV257: $i,SV59: $i] :
      ( ( ( ! [SY894: $i] :
              ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK52_SY499 @ SV257 @ SV59 ) ) @ SY894 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ SV257 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2476]) ).

thf(2500,plain,
    ! [SV272: $i,SV258: $i,SV59: $i] :
      ( ( ( ! [SY503: $i] :
              ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ SY503 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV258 ) @ SV272 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2477]) ).

thf(2501,plain,
    ! [SV250: $i,SV22: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( sK50_SY368 @ SV250 @ SV22 ) ) @ ( sK55_SY892 @ SV250 @ SV22 ) ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ SV250 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2480]) ).

thf(2502,plain,
    ! [SV251: $i,SV270: $i,SV22: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( sK56_SY372 @ SV270 @ SV251 @ SV22 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV251 ) @ SV270 ) ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2481]) ).

thf(2503,plain,
    ! [SV96: $i,SV23: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV96 ) )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV23 ) )
              | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV96 ) ) ) )
        = $true )
      | ( ( SV96 = SV23 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2482]) ).

thf(2504,plain,
    ! [SV96: $i,SV23: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV23 ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV96 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV23 ) )
        = $false )
      | ( ( SV96 = SV23 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2483]) ).

thf(2505,plain,
    ! [SV23: $i,SV96: $i,SV265: $i,SV252: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV252 ) @ SV265 ) ) @ SV96 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV252 ) @ SV265 ) ) @ SV23 ) )
        = $true )
      | ( ( SV96 = SV23 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2484]) ).

thf(2506,plain,
    ! [SV96: $i,SV23: $i,SV265: $i,SV252: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV252 ) @ SV265 ) ) @ SV23 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV252 ) @ SV265 ) ) @ SV96 ) )
        = $true )
      | ( ( SV96 = SV23 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2485]) ).

thf(2507,plain,
    ! [SV216: $i,SV149: $i,SV190: $i,SV98: $i,SV25: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK53_SY837 @ SV190 @ SV149 @ SV216 @ SV98 @ SV25 ) ) @ ( sK54_SY895 @ SV216 @ SV149 @ SV190 @ SV98 @ SV25 ) ) ) ) @ SV216 ) ) )
        = $false )
      | ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) ) @ ( transi2024712006on_val @ SV216 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2486]) ).

thf(2508,plain,
    ! [SV25: $i,SV98: $i,SV216: $i,SV149: $i,SV190: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK53_SY837 @ SV190 @ SV149 @ SV216 @ SV98 @ SV25 ) ) @ ( sK54_SY895 @ SV216 @ SV149 @ SV190 @ SV98 @ SV25 ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) ) @ ( transi2024712006on_val @ SV216 ) ) ) )
        = $false )
      | ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) ) @ ( transi2024712006on_val @ SV216 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2486]) ).

thf(2509,plain,
    ! [SV156: $i,SV220: $i,SV38: $i,SV108: $i,SV195: $i] :
      ( ( ( SV195 = SV108 )
        = $true )
      | ( ( ~ ( ~ ( ( SV195 != SV108 ) )
              | ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
               != ( hAPP_val_option_val @ some_val @ SV220 ) ) ) )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2488]) ).

thf(2510,plain,
    ! [SV38: $i,SV108: $i,SV195: $i,SV220: $i,SV156: $i] :
      ( ( ( SV156 = SV220 )
        = $true )
      | ( ( ~ ( ~ ( ( SV195 != SV108 ) )
              | ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
               != ( hAPP_val_option_val @ some_val @ SV220 ) ) ) )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2489]) ).

thf(2511,plain,
    ! [SV38: $i,SV220: $i,SV156: $i,SV108: $i,SV195: $i] :
      ( ( ( SV195 = SV108 )
        = $false )
      | ( ( SV156 != SV220 )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2490]) ).

thf(2512,plain,
    ! [SV156: $i,SV220: $i,SV38: $i,SV108: $i,SV195: $i] :
      ( ( ( SV195 != SV108 )
        = $false )
      | ( ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
         != ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2491]) ).

thf(2513,plain,
    ! [SV48: $i,SV117: $i] :
      ( ( ( ~ ( hBOOL @ SV117 ) )
        = $false )
      | ( ( hBOOL @ SV48 )
        = $true )
      | ( ( ( bool @ SV48 )
          = ( bool @ SV117 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2493]) ).

thf(2514,plain,
    ! [SV117: $i,SV48: $i] :
      ( ( ( hBOOL @ SV48 )
        = $false )
      | ( ( hBOOL @ SV48 )
        = $true )
      | ( ( ( bool @ SV48 )
          = ( bool @ SV117 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2493]) ).

thf(2515,plain,
    ! [SV48: $i,SV117: $i] :
      ( ( ( hBOOL @ SV117 )
        = $true )
      | ( ( hBOOL @ SV117 )
        = $false )
      | ( ( ( bool @ SV48 )
          = ( bool @ SV117 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2494]) ).

thf(2516,plain,
    ! [SV255: $i,SV49: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK51_SY459 @ SV255 @ SV49 ) ) @ ( sK57_SY893 @ SV255 @ SV49 ) ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ SV255 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2496]) ).

thf(2517,plain,
    ! [SV256: $i,SV271: $i,SV49: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( sK58_SY463 @ SV271 @ SV256 @ SV49 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV256 ) @ SV271 ) ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2497]) ).

thf(2518,plain,
    ! [SV257: $i,SV59: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK52_SY499 @ SV257 @ SV59 ) ) @ ( sK59_SY894 @ SV257 @ SV59 ) ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ SV257 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2499]) ).

thf(2519,plain,
    ! [SV258: $i,SV272: $i,SV59: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( sK60_SY503 @ SV272 @ SV258 @ SV59 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV258 ) @ SV272 ) ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2500]) ).

thf(2520,plain,
    ! [SV250: $i,SV22: $i] :
      ( ( ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( sK50_SY368 @ SV250 @ SV22 ) ) @ ( sK55_SY892 @ SV250 @ SV22 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ SV250 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2501]) ).

thf(2521,plain,
    ! [SV251: $i,SV270: $i,SV22: $i] :
      ( ( ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( sK56_SY372 @ SV270 @ SV251 @ SV22 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_P159683425l_bool @ SV22 @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ SV251 ) @ SV270 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2502]) ).

thf(2522,plain,
    ! [SV96: $i,SV23: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV23 ) )
          | ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV96 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV96 ) )
        = $true )
      | ( ( SV96 = SV23 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2503]) ).

thf(2523,plain,
    ! [SV96: $i,SV23: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV23 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV23 ) )
        = $false )
      | ( ( SV96 = SV23 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2504]) ).

thf(2524,plain,
    ! [SV96: $i,SV23: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV96 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV23 ) )
        = $false )
      | ( ( SV96 = SV23 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2504]) ).

thf(2525,plain,
    ! [SV216: $i,SV149: $i,SV190: $i,SV98: $i,SV25: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK53_SY837 @ SV190 @ SV149 @ SV216 @ SV98 @ SV25 ) ) @ ( sK54_SY895 @ SV216 @ SV149 @ SV190 @ SV98 @ SV25 ) ) ) ) @ SV216 ) )
        = $true )
      | ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) ) @ ( transi2024712006on_val @ SV216 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2507]) ).

thf(2526,plain,
    ! [SV25: $i,SV98: $i,SV216: $i,SV149: $i,SV190: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK53_SY837 @ SV190 @ SV149 @ SV216 @ SV98 @ SV25 ) ) @ ( sK54_SY895 @ SV216 @ SV149 @ SV190 @ SV98 @ SV25 ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) ) @ ( transi2024712006on_val @ SV216 ) ) )
        = $true )
      | ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV25 ) @ SV98 ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV149 ) @ SV190 ) ) ) @ ( transi2024712006on_val @ SV216 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2508]) ).

thf(2527,plain,
    ! [SV156: $i,SV220: $i,SV38: $i,SV108: $i,SV195: $i] :
      ( ( ( ~ ( ( SV195 != SV108 ) )
          | ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
           != ( hAPP_val_option_val @ some_val @ SV220 ) ) )
        = $false )
      | ( ( SV195 = SV108 )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2509]) ).

thf(2528,plain,
    ! [SV156: $i,SV220: $i,SV38: $i,SV108: $i,SV195: $i] :
      ( ( ( ~ ( ( SV195 != SV108 ) )
          | ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
           != ( hAPP_val_option_val @ some_val @ SV220 ) ) )
        = $false )
      | ( ( SV156 = SV220 )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2510]) ).

thf(2529,plain,
    ! [SV38: $i,SV108: $i,SV195: $i,SV220: $i,SV156: $i] :
      ( ( ( SV156 = SV220 )
        = $false )
      | ( ( SV195 = SV108 )
        = $false )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2511]) ).

thf(2530,plain,
    ! [SV156: $i,SV220: $i,SV38: $i,SV108: $i,SV195: $i] :
      ( ( ( SV195 = SV108 )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
         != ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2512]) ).

thf(2531,plain,
    ! [SV48: $i,SV117: $i] :
      ( ( ( hBOOL @ SV117 )
        = $true )
      | ( ( hBOOL @ SV48 )
        = $true )
      | ( ( ( bool @ SV48 )
          = ( bool @ SV117 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2513]) ).

thf(2532,plain,
    ! [SV255: $i,SV49: $i] :
      ( ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK51_SY459 @ SV255 @ SV49 ) ) @ ( sK57_SY893 @ SV255 @ SV49 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ SV255 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2516]) ).

thf(2533,plain,
    ! [SV256: $i,SV271: $i,SV49: $i] :
      ( ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( sK58_SY463 @ SV271 @ SV256 @ SV49 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_P282169671l_bool @ SV49 @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ SV256 ) @ SV271 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2517]) ).

thf(2534,plain,
    ! [SV257: $i,SV59: $i] :
      ( ( ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( sK52_SY499 @ SV257 @ SV59 ) ) @ ( sK59_SY894 @ SV257 @ SV59 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ SV257 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2518]) ).

thf(2535,plain,
    ! [SV258: $i,SV272: $i,SV59: $i] :
      ( ( ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( sK60_SY503 @ SV272 @ SV258 @ SV59 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_P1708370145l_bool @ SV59 @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ SV258 ) @ SV272 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2519]) ).

thf(2536,plain,
    ! [SV96: $i,SV23: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV23 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV96 ) )
        = $true )
      | ( ( SV96 = SV23 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2522]) ).

thf(2537,plain,
    ! [SV96: $i,SV23: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV96 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV96 ) )
        = $true )
      | ( ( SV96 = SV23 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2522]) ).

thf(2538,plain,
    ! [SV96: $i,SV23: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV23 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV23 ) )
        = $false )
      | ( ( SV96 = SV23 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2523]) ).

thf(2539,plain,
    ! [SV220: $i,SV156: $i,SV38: $i,SV108: $i,SV195: $i] :
      ( ( ( ~ ( ( SV195 != SV108 ) ) )
        = $false )
      | ( ( SV195 = SV108 )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2527]) ).

thf(2540,plain,
    ! [SV156: $i,SV108: $i,SV220: $i,SV195: $i,SV38: $i] :
      ( ( ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
         != ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $false )
      | ( ( SV195 = SV108 )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2527]) ).

thf(2541,plain,
    ! [SV38: $i,SV220: $i,SV156: $i,SV108: $i,SV195: $i] :
      ( ( ( ~ ( ( SV195 != SV108 ) ) )
        = $false )
      | ( ( SV156 = SV220 )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2528]) ).

thf(2542,plain,
    ! [SV108: $i,SV156: $i,SV220: $i,SV195: $i,SV38: $i] :
      ( ( ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
         != ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $false )
      | ( ( SV156 = SV220 )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2528]) ).

thf(2543,plain,
    ! [SV156: $i,SV108: $i,SV220: $i,SV195: $i,SV38: $i] :
      ( ( ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $false )
      | ( ( SV195 = SV108 )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2530]) ).

thf(2544,plain,
    ! [SV96: $i,SV23: $i] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV23 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( sK42_SY593 @ SV23 @ SV96 ) ) @ ( sK46_SY886 @ SV96 @ SV23 ) ) ) @ SV96 ) )
        = $true )
      | ( ( SV96 = SV23 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2536]) ).

thf(2545,plain,
    ! [SV220: $i,SV156: $i,SV38: $i,SV108: $i,SV195: $i] :
      ( ( ( SV195 != SV108 )
        = $true )
      | ( ( SV195 = SV108 )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2539]) ).

thf(2546,plain,
    ! [SV156: $i,SV108: $i,SV220: $i,SV195: $i,SV38: $i] :
      ( ( ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $true )
      | ( ( SV195 = SV108 )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2540]) ).

thf(2547,plain,
    ! [SV38: $i,SV220: $i,SV156: $i,SV108: $i,SV195: $i] :
      ( ( ( SV195 != SV108 )
        = $true )
      | ( ( SV156 = SV220 )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2541]) ).

thf(2548,plain,
    ! [SV108: $i,SV156: $i,SV220: $i,SV195: $i,SV38: $i] :
      ( ( ( ( hAPP_l207779698on_val @ SV38 @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $true )
      | ( ( SV156 = SV220 )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2542]) ).

thf(2549,plain,
    ! [SV220: $i,SV156: $i,SV38: $i,SV108: $i,SV195: $i] :
      ( ( ( SV195 = SV108 )
        = $false )
      | ( ( SV195 = SV108 )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2545]) ).

thf(2550,plain,
    ! [SV38: $i,SV220: $i,SV156: $i,SV108: $i,SV195: $i] :
      ( ( ( SV195 = SV108 )
        = $false )
      | ( ( SV156 = SV220 )
        = $true )
      | ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ SV38 @ SV108 @ ( hAPP_val_option_val @ some_val @ SV156 ) ) @ SV195 )
          = ( hAPP_val_option_val @ some_val @ SV220 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2547]) ).

thf(2551,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[1577,2550,2549,2548,2546,2544,2543,2538,2537,2535,2534,2533,2532,2531,2529,2526,2525,2524,2521,2520,2515,2514,2506,2505,2498,2495,2492,2487,2479,2478,2474,2473,2468,2467,2465,2464,2460,2459,2457,2456,2419,2418,2407,2402,2400,2399,2391,2390,2389,2388,2387,2385,2384,2383,2382,2377,2376,2373,2366,2363,2362,2352,2346,2345,2344,2343,2335,2331,2329,2328,2323,2309,2308,2307,2302,2299,2298,2287,2286,2285,2279,2277,2266,2262,2261,2258,2250,2234,2233,2230,2229,2226,2217,2216,2212,2208,2207,2206,2198,2194,2184,2128,2124,2120,2110,2102,2085,2083,2068,2047,1988,1966,1965,1888,1885,1874,1870,1813,1809,1808,1737,1736,1733,1655]) ).

thf(2552,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[2551]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWW478+3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05  % Command  : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.19  % Computer : n026.cluster.edu
% 0.07/0.19  % Model    : x86_64 x86_64
% 0.07/0.19  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19  % Memory   : 8046.5625MB
% 0.07/0.19  % OS       : Linux 6.8.0-71-generic
% 0.07/0.19  % CPULimit : 300
% 0.07/0.19  % WCLimit  : 300
% 0.07/0.19  % DateTime : Tue Oct  6 17:02:32 UTC 2026
% 0.07/0.19  % CPUTime  : 
% 0.07/0.19  Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.62/4.19  ............
% 23.62/4.19  
% 23.62/4.19   No.of.Axioms: 81
% 23.62/4.19  
% 23.62/4.19   Length.of.Defs: 0
% 23.62/4.19  
% 23.62/4.19   Contains.Choice.Funs: false
% 23.62/4.19  ...........................................................................
% 23.62/4.19  
% 23.62/4.19  ********************************
% 23.62/4.19  *   All subproblems solved!    *
% 23.62/4.19  ********************************
% 23.62/4.19  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:81,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:298,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2551,loop_count:0,foatp_calls:1,translation:fof_full)
% 23.62/4.19  
% 23.62/4.19  %**** Beginning of derivation protocol ****
% 23.62/4.19  % SZS output start CNFRefutation
% See solution above
% 4.15/4.21  
% 4.15/4.21  %**** End of derivation protocol ****
% 4.15/4.21  %**** no. of clauses in derivation: 1143 ****
% 4.15/4.21  %**** clause counter: 2551 ****
% 4.15/4.21  
% 4.15/4.21  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:81,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:298,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2551,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------